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Electrochemical Corrosion Rate Measurement ndash A Comparison
Dr David LovedayGamry Instrumentswwwgamrycom
Overviewbull Corrosion Testing Theorybull Polarization Resistance (LPR)bull Electrochemical Frequency Modulation
(EFM)bull EISbull Comparison
Why Are Electrochemical Techniques Used for Corrosion Measurement
bull Corrosion is an electrochemical or ldquoredoxrdquo process involving electron transfer
Fe Fe2+ + 2endash
redox = reduction-oxidation
bull A broad range of electrochemical techniques have been developed specifically for corrosion measurement
bull Electrochemical techniques are fast
bull Electrochemical techniques are sensitive
bull Can be used in the lab or in the field
Electrochemical Techniques are Fast
bull Corrosion is an inherently slow process A typical corrosion rate is 10 milli-inches per year (mpy) or 0254 millimeters per year (mmpy) or 254 microns per year
bull The ldquobestrdquo corrosion tests are weight loss measurements after exposure However they are very slow (weeks months or years)
bull Electrochemical instruments polarize the sample to accelerate the corrosion process and make the measurement in minutes or hours
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
Oxygen O2 + 2H2O + 2endash 4OHndash (neutralalkaline)O2 + 4H+ + 4endash H2 + 2OHndash (acid)
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Overviewbull Corrosion Testing Theorybull Polarization Resistance (LPR)bull Electrochemical Frequency Modulation
(EFM)bull EISbull Comparison
Why Are Electrochemical Techniques Used for Corrosion Measurement
bull Corrosion is an electrochemical or ldquoredoxrdquo process involving electron transfer
Fe Fe2+ + 2endash
redox = reduction-oxidation
bull A broad range of electrochemical techniques have been developed specifically for corrosion measurement
bull Electrochemical techniques are fast
bull Electrochemical techniques are sensitive
bull Can be used in the lab or in the field
Electrochemical Techniques are Fast
bull Corrosion is an inherently slow process A typical corrosion rate is 10 milli-inches per year (mpy) or 0254 millimeters per year (mmpy) or 254 microns per year
bull The ldquobestrdquo corrosion tests are weight loss measurements after exposure However they are very slow (weeks months or years)
bull Electrochemical instruments polarize the sample to accelerate the corrosion process and make the measurement in minutes or hours
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
Oxygen O2 + 2H2O + 2endash 4OHndash (neutralalkaline)O2 + 4H+ + 4endash H2 + 2OHndash (acid)
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Why Are Electrochemical Techniques Used for Corrosion Measurement
bull Corrosion is an electrochemical or ldquoredoxrdquo process involving electron transfer
Fe Fe2+ + 2endash
redox = reduction-oxidation
bull A broad range of electrochemical techniques have been developed specifically for corrosion measurement
bull Electrochemical techniques are fast
bull Electrochemical techniques are sensitive
bull Can be used in the lab or in the field
Electrochemical Techniques are Fast
bull Corrosion is an inherently slow process A typical corrosion rate is 10 milli-inches per year (mpy) or 0254 millimeters per year (mmpy) or 254 microns per year
bull The ldquobestrdquo corrosion tests are weight loss measurements after exposure However they are very slow (weeks months or years)
bull Electrochemical instruments polarize the sample to accelerate the corrosion process and make the measurement in minutes or hours
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
Oxygen O2 + 2H2O + 2endash 4OHndash (neutralalkaline)O2 + 4H+ + 4endash H2 + 2OHndash (acid)
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Electrochemical Techniques are Fast
bull Corrosion is an inherently slow process A typical corrosion rate is 10 milli-inches per year (mpy) or 0254 millimeters per year (mmpy) or 254 microns per year
bull The ldquobestrdquo corrosion tests are weight loss measurements after exposure However they are very slow (weeks months or years)
bull Electrochemical instruments polarize the sample to accelerate the corrosion process and make the measurement in minutes or hours
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
Oxygen O2 + 2H2O + 2endash 4OHndash (neutralalkaline)O2 + 4H+ + 4endash H2 + 2OHndash (acid)
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
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ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
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Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
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Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
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Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Electrochemical Techniques Are Sensitive
bull Electrochemical techniques can measure very low corrosion rates
bull A sample with a low corrosion rate will exhibit a low current during the electrochemical experiment Corrosion scientists often use ldquoraterdquo and ldquocurrentrdquo interchangeably
bull Electrochemical instruments can be designed to measure low currents very accurately A 1 cm2 iron sample with a corrosion rate of 1 mpy (milli-inch per year) will exhibit a current in the range of 2-5 μA which can be measured very accurately by a modern potentiostat
bull 4 milli-inches corresponds roughly to the diameter of a human hair
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
Oxygen O2 + 2H2O + 2endash 4OHndash (neutralalkaline)O2 + 4H+ + 4endash H2 + 2OHndash (acid)
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
A Review of Electrochemistry
Electrochemistry ndash The study of chemical reactions accompanied by the exchange of electrons Electron-transfer is always a factor in electrochemistry Additional chemistry is sometimesa factor in electrochemistry
O = Oxidized Species Red = Reduced SpeciesOxidation Loss of electrons Fe Fe2+ + 2 e-
Reduction Gain of electrons 2H+ + 2e- H2(Remember that LEO (the lion) says GER)
General Echem Reaction Ox + ne- RedThe Oxidized species accepts an electron to form the Reduced species
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
Oxygen O2 + 2H2O + 2endash 4OHndash (neutralalkaline)O2 + 4H+ + 4endash H2 + 2OHndash (acid)
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Redox Reactions (Half-Reactions) in Corrosion
Oxidation The Metal Being TestedFe Fe2+ + 2endash
Reduction Usually Some Solution SpeciesHydrogen ion 2H+ + 2endash H2Water 2H2O + 2endash H2 + 2OHndash
Oxygen O2 + 2H2O + 2endash 4OHndash (neutralalkaline)O2 + 4H+ + 4endash H2 + 2OHndash (acid)
bull Oxidation is always accompanied by Reduction in both the Real World and the electrochemical experiment
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
What is PotentialPotential or Voltage (E sometimes V)
ndash Unit Volt (milliVolt microVolt)ndash The Potential is the driving force for the redox reaction ndash The potential is related to the thermodynamics of the
systemΔG = -n F ΔE (negative ΔG is spontaneous)
ndash Potential is always measured versus a Reference Electrodendash A more positive voltage is more oxidative and a more
negative voltage is more reductivendash 0 Volts is not nothing Redox reactions happen at 0 volts
that do not happen at +1 volt
Remember There is no correlation between the thermodynamics of the chemical system and the kinetics (rate) of the reaction
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
What is Current
Current (i or I) ndash Unit Ampere (mA microA nA pA fA)ndash Electron flow is the result of a redox reactionndash Current measures the rate of the reaction (electrons per
second)ndash Zero current is nothing ie if the current is zero no redox
reactions are occurring (thatrsquos not quite true in corrosion) ndash Anodic (oxidation) and cathodic (reduction) currents have
different polarity (signs)ndash Current may be expressed as current or current densityndash Donrsquot worry about which way the current flows
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
A Simple Description of Potential and Current as a Flowing Water Circuit
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Range of Potential and Current that is Encountered in Corrosion Experiments
bull 95 of electrochemical corrosion experiments take place within plusmn 2 volts vs SCE
bull Current can vary from hundreds of milliamps to femtoamps(10-15 amps) Thatrsquos 12-13 orders of magnitude Modern potentiostats are capable of auto-ranging the current over 7-11 decades of current which makes your life relatively easy
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Electrochemical Techniques
Electrochemistry is simple in principalhellipthere are only three variables potential (E) current (i) and time
ldquoActive Experimentsrdquo Apply an excitation measure a response Make something happen
bull Potentiostatic Apply amp Control E Measure i Plot E vs i or i vs tbull Galvanostatic Apply amp Control i Measure E Plot i vs E or E vs t
ldquoPassive Experimentsrdquo Observe the experiment electrochemicallybull Potentiometric Measure E at i=0 (pH Meter open circuit measurement) bull Zero Resistance Ammeter (ZRA) Measure i between two connected
electrodes (galvanic corrosion electrochemical noise)
bull Active experiments give faster results but risk changing the sample
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Controlled Potential (Potentiostatic) Experiments are Most Commonly Used in the Corrosion Lab
bull In most electrochemical corrosion experiments the potential is controlled Because of the relationship between the potential and the thermodynamics of the system controlled potential experiments are more informative than controlled current experiments
bull The (three-electrode) Potentiostat is the electronic instrument that controls the potential between the Working Electrode (your sample) and the
while it measures the current between the Working Electrode and the Counter Electrode
bull Why three electrodes A three-electrode Potentiostat allows potential control and current measurement at the Working Electrode with no ldquointerferencerdquo from other electrochemical events in the cell
bull To perform an electrochemical measurement we change the potential in some systematic way and measure the current response The applied potential may allow a redox reaction to occur and the current will be indicative of the rate (kinetics) of the reaction
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
The 3-Electrode Electrochemical Cell
bull Working Electrode Corrosion sample being studied
ndash Active area should be knownElectrode Saturated Calomel
(SCE) or Silver-Silver Chloride (AgAgCl)ndash Pseudo-reference may be acceptable
bull Counter Electrode Should be conductive and inert (Graphite or Platinum)
bull Solution may be stirred and deaerated to remove O2 or saturated with CO2 or H2S
bull Temperature control is encouraged Rates of chemical reactions are very temperature dependent
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
bull The Open Circuit Potential EOC is the potential difference between the metal Working Electrode and the Reference Electrode when immersed in the electrolyte
bull EOC is a ldquomixed potentialrdquo whose value is determined by the potentials of the two or more half-reactions of the electrochemical system not by the potentiostat
bull EOC is where corrosion occurs in service
bull EOC is the starting point for virtually all electrochemical corrosion experiments A stable EOC is taken to indicate that the corroding system has reach a ldquosteady staterdquo and the experiment may begin This may require minutes to days
The Open Circuit Potential
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
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ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
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PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
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Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
The Open Circuit Potential
bull No measurable current is flowing at Eoc If we apply a potential equal to Eocwith our potentiostat the current will be zero
bull An applied voltage that is positive of EOC will accelerate an oxidation (corrosion) reaction An applied voltage that is negative of EOC will accelerate a reduction reaction This makes life somewhat easy
bull The terms ldquoEOCrdquo and ldquoEcorrrdquo (corrosion potential) are often used interchangeably
bull The value of the EOC is not particularly useful as a predictive tool
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
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ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Quantitative Corrosion Rate Measurements
bull Polarization Resistance Electrochemical Frequency Modulation EIS and (Tafel Plots) are experiments designed to measure the rate of uniformcorrosion in units of penetration (mmpy or mpy)
bull Designed to measure the corrosion current ICORR from which we can calculate the corrosion rate
bull Unlike weight loss electrochemical techniques provide a ldquosnapshotrdquo of the corrosion rate
bull Should be performed when the system has reached ldquosteady staterdquo indicated by a stable EOC
bull Note ldquoLinear Polarization Resistance (LPR)rdquo is not a correct term but we use it anyway The correct term is ldquoPolarization Resistancerdquo (See CORROSION November 2005)
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
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Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Corrosion Current Icorr
bull At EOC imeas = 0 but we know that corrosion is occurringFe Fe2+ + 2 e-
2H+ + 2e- H2
Fe + 2H+ Fe2+ + H2
bull We need to somehow measure the current due to the anodic or cathodic half-reaction This current is called the Corrosion Current ICORR
bull The goal of the Polarization Resistance experiment is to determine the Corrosion Current
bull From the Corrosion Current we can calculate corrosion rate
bull Donrsquot forget the electrode area iCORR is usually current (A) and ICORR is usually current density (Acm2)
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Precision of Electrochemical Corrosion Rate Measurements
bull Corrosion is a messy business-Dr Jerry FrankelThe Ohio State University
bull Corrosion is a surface process involving a large number of variables that are difficult to understand andor control
bull A Relative Standard Deviation of 15 is Excellent
bull A minimum of 3 replicates is recommended for corrosion measurements (ldquoIncrease Your Confidence in Corrosion Test Datardquo Steve Tait MATERIALS PERFORMANCE March 2001)
Error as a Function of Sample Size
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Comments on the Precision of Electrochemical Corrosion Measurements
bull Electrochemical instrumentation is very accurate (lt05 error)
bull High purity Fe polished to a mirror finish gives great results
bull When corrosion occurs anodic and cathodic reactions are occurring simultaneously on the surface of the sample
bull The surface of a metal sample is nothomogeneous In fact it may be veryheterogeneous
bull The anodic and cathodic sites may ldquoturn onrdquo or ldquoturn offrdquo and move around as the local environment changes
bull Electrolyte impurities can also affect the results
bull The corrosion environment is verydynamic and the result ishellippoor precision
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Electrochemical Corrosion Measurements are based on good solid science developed over many years
So wersquoll touch very briefly on the theoretical aspects of electrochemical corrosion measurement
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Mixed Potential TheoryThe principal of charge conservation requires that there must be a least one
reduction and one oxidation in an electrochemical reaction
bull 2H+ + 2e- H2
bull Zn Zn2+ + 2e-
bull The anodic current equals the cathodic current at icorr
bull Both reactions must occur on the same surface so their potentials must shift to a common value which is Ecorr (same as EOC)
bull This is an example of a ldquomixed potential systemrdquo and Eoc is called a ldquomixed potentialrdquo
ldquoPrinciples and Prevention of Corrosionrdquo Jones
Note The log X axis may sometimes be labeled ldquoAPPLIED CURRENT DENSITYrdquo Donrsquot let this confuse you
22
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Butler-Volmer Equation
The Butler-Volmer Equation is a general electrochemical equation that describes the relationship between the potential and the current (kinetics) in a mixed potential system
I = Ia + Ic = ICORR(e(23(E-Eoc)βa) ndash e(-23(E-Eoc)βc))
Where I = cell current (A)ICORR = corrosion current (A) E = applied potential (V)Eoc = corrosion potential (V)βa = anodic Tafel constant (Vdecade)βc = cathodic Tafel constant (Vdecade)
Rate of anodic reaction Rate of cathodic reaction
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Graphical Representation of the Butler-Volmer Relationship between Potential and Current in a Mixed Potential System
J Scully amp R Kelly ASM Handbook Volume 13A 2003
M + 2H+ M2+ + H2
An experiment like this is called a ldquoTafel Plotrdquo and is relatively common in todayrsquos corrosion laboratory
Experimental data from the corrosion measurement system
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
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-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Butler-Volmer Equation
The Butler-Volmer Equation only holds if
bull The rate is charge-transfer controlled (aka activation-controlled electron-transfer controlled) Complicating factors arendash Passivityndash Diffusion-controlled (concentration polarization)ndash Adsorption
bull Only one reduction and one oxidation reaction are occurring (first order)ndash Alloys can be complicated
bull If the Butler-Volmer equation doesnrsquot hold then the electrochemical response will not be ldquoclassicrdquo and must be interpreted in terms of the chemistry of the system
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Stern-Geary Equation and Polarization Resistancebull The purpose of the Polarization Resistance experiment is to determine the
Polarization Resistance (Rp)
bull The Stern-Geary Equation describes the relationship between the Polarization Resistance (Rp) and the Corrosion Current (iCORR)
bull RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
bull IMPORTANT The Stern-Geary Equation is derived from the Butler-Volmer Equation via a series expansion in which ΔE βac is assumed to be less than 01
bull Therefore in the Polarization Resistance technique the applied potential should be within plusmn5-10 mV of Eoc
bull The plot of potential vs current is approximately linear in this region
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
The Polarization Resistance Experiment
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Experimental Procedure for Polarization Resistance
1 Measure EOC and allow to stabilize
2 Apply initial E that is 10 mV negative of EOC
3 Scan at a slow scan rate (~0125 mVs) to a final E that is 10 mV positive of EOC
4 Measure current plot E (Y-axis) versus I (X-axis)
5 Measure slope which has units of resistance (Ei = R)
6 Convert Rp to icorr using the Stern-Geary Equation
7 Convert icorr to Corrosion Rate
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Polarization ResistanceCarbon Steel
05M KCl (aq) solution
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
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ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Calculation of ICORR from RP
Stern-Geary Equation
RP = ∆E∆i = szligaszligc23 iCORR (szliga + szligc)
WhereRP = Slope at the origin of the Polarization Resistance Plot in ohms
or ohms-cm2
iCORR = Corrosion Current Amperes or Amperescm2
szliga szligc = Tafel Constants from a Tafel Curve voltsdecade of current
Note The area of the electrode must be taken into account somewhere
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
I Calculation of Corrosion Rate from ICORR
Faradayrsquos Law
Q = nFmA = it
Q = coulombs (A-seq) n = number of electrons F = the Faraday (96487 coulombsequivalent) m = mass (g) A = atomic weight i = current (A) t = time (s)
Since Equivalent Weight (EW) = Anm = it(EW)F
Corrosion Rate (gs) = mt = i(EW)F
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
II Calculation of Corrosion Rate from ICORR
From the engineering standpoint it is convenient to express Corrosion Rate in units of penetration mpy (milli-inches per year) mmpy (mm per year) or microns per year
Divide both sides of the equation Corrosion Rate (gs) = mt = i(EW)F
by electrode area and densityCorrosion Rate (cms) = i(EW)FdA
iA = current density (I) After conversion of cm to inches or mm and seconds to years
Corrosion Rate (mpy) = 013 Icorr (EW)dCorrosion Rate (mmpy) = 000327 Icorr(EW)d
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Polarization ResistanceCarbon Steel
Corrosion rate = 607 mpy
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Electrochemical Frequency ModulationEFM
What is it
bull Apply 2 sine waves simultaneously
bull Non-destructivebull Measure current vs
time response
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Theorybull Potential excitation
ndash 120578120578 = 119881119881[sin1205961205961119905119905 + sin1205961205962119905119905]bull Butler-Volmer Response
ndash Activation controlled (kinetics)ndash Non-linear
ndash 119894119894 = 119894119894119888119888119888119888119888119888119888119888[119890119890 120578120578 119861119861119860119860 minus 119890119890minus 120578120578 119861119861119862119862]
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
More Theorybull Waveform - 120578120578 = 119881119881[sin119860119860119905119905 + sin119861119861119905119905]bull Expand the exponentials using a Taylor
expansion
ndash 119890119890119909119909 = 1 + 1199091199091
+ 1199091199092
2+ 1199091199093
3+ ⋯ minusinfin lt 119909119909 lt infin
bull Trigonometryndash cos 2119909119909 = 2 sin2 119909119909 minus 1ndash sin 3119909119909 = 3 sin 119909119909 minus 4sin3 119909119909ndash sin 119909119909 + 119910119910 = sin 119909119909 cos119910119910 + cos 119909119909 sin119910119910ndash hellip
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
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ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
And then A Miracle Occursbull 119894119894 = 119886119886[
]119904119904119894119894119904119904 119860119860119905119905 + sin 119861119861119905119905 ] + 119887119887 [119888119888119888119888119904119904(
)119860119860 minus
119861119861 119905119905 minus cos(119860119860 + 119861119861)119905119905 + c[119904119904119894119894119904119904 2119860119860 minus 119861119861 119905119905 minus1199041199041198941198941199041199042119860119860 + 119861119861)119905119905+119904119904119894119894119904119904 2119860119860 + 119861119861 119905119905 minus 119904119904119894119894119904119904(2119861119861 +119860119860)119905119905] + d[minus119888119888119888119888119904119904 2119860119860119905119905 minus 119888119888119888119888119904119904 2119861119861119905119905 ] +e[minus sin 3119860119860 119905119905 minus sin 3119861119861 119905119905]ndash Where a b c d and e are the amplitudes at
each frequency
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
An Examplebull A = 2 Hz B = 5 Hzbull None of the frequencies can be duplicated
Freq AmpltudeA 2 2 aB 5 5 a
B-A 5-2 3 bA+B 2+5 7 bB-2A 5-2(2) 1 c2B-A 2(5)-2 8 cA+2B 2+2(5) 12 c2A+B 2(2)+5 9 c2(A) 2(2) 4 d2(B) 2(5) 10 d3(A) 3(2) 6 e3(B) 3(5) 15 e
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
The EFM ExperimentWhat we do
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Intermodulation Spectrum
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Theorybull With abcd and e you can calculate
ndash 119894119894119888119888119888119888119888119888119888119888ndash 120573120573119860119860ndash 120573120573119862119862
a icorr VβA + VβCb (14) icorr (VβA)2 - (VβC)2
c (124) icorr (VβA)3 + (VβC)3
d (12) icorr (VβA)2 - (VβC)2
e (18) icorr (VβA)3 + (VβC)3
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Theorybull In addition to Icorr an internal quality check
can made by ratioing the amplitudes of the different harmonic and intermodulation peaks
bull db yields a value of 2 and ec yields a value of 3
bull These are independent of any variables
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
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-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
EFM of Carbon Steel
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
EFM of Carbon Steel
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
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03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
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-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
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-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Electrochemical Impedance Spectroscopy EIS
bull Brief Overview of EISbull EIS Results for Carbon Steel
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Electrochemistry as a Circuit
bull Double Layer Capacitance
bull Electron Transfer Resistance
bull Uncompensated (electrolyte) Resistance
Randles Cell(Simplified)
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Bode Plot
220
240
260
280
300
320
340
360
-300 -200 -100 000 100 200 300 400 500 600
Log Freq (Hz)
Log
Mod
ulus
(O
hm)
-7000
-6000
-5000
-4000
-3000
-2000
-1000
000
1000
Pha
se (D
egre
e)
Phase Angle
Impedance
Ru
Ru + Rp
RU
RP
CDL
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
50000303995 | 50000303995 | 50000303995 | 50000303995 | ||||
49000042456 | 49000042456 | 49000042456 | 49000042456 | ||||
48000672121 | 48000672121 | 48000672121 | 48000672121 | ||||
4700043122 | 4700043122 | 4700043122 | 4700043122 | ||||
46000052684 | 46000052684 | 46000052684 | 46000052684 | ||||
45001554832 | 45001554832 | 45001554832 | 45001554832 | ||||
44000835989 | 44000835989 | 44000835989 | 44000835989 | ||||
43000386737 | 43000386737 | 43000386737 | 43000386737 | ||||
42001087201 | 42001087201 | 42001087201 | 42001087201 | ||||
40999291328 | 40999291328 | 40999291328 | 40999291328 | ||||
399992182 | 399992182 | 399992182 | 399992182 | ||||
38999626914 | 38999626914 | 38999626914 | 38999626914 | ||||
38001050617 | 38001050617 | 38001050617 | 38001050617 | ||||
36999400027 | 36999400027 | 36999400027 | 36999400027 | ||||
35999845411 | 35999845411 | 35999845411 | 35999845411 | ||||
3500053879 | 3500053879 | 3500053879 | 3500053879 | ||||
33998743849 | 33998743849 | 33998743849 | 33998743849 | ||||
33000234384 | 33000234384 | 33000234384 | 33000234384 | ||||
31998895026 | 31998895026 | 31998895026 | 31998895026 | ||||
3100039528 | 3100039528 | 3100039528 | 3100039528 | ||||
29999782847 | 29999782847 | 29999782847 | 29999782847 | ||||
28999096494 | 28999096494 | 28999096494 | 28999096494 | ||||
28000183469 | 28000183469 | 28000183469 | 28000183469 | ||||
27001003036 | 27001003036 | 27001003036 | 27001003036 | ||||
26001110714 | 26001110714 | 26001110714 | 26001110714 | ||||
24998423564 | 24998423564 | 24998423564 | 24998423564 | ||||
23999937011 | 23999937011 | 23999937011 | 23999937011 | ||||
22999320153 | 22999320153 | 22999320153 | 22999320153 | ||||
22001196781 | 22001196781 | 22001196781 | 22001196781 | ||||
21000636732 | 21000636732 | 21000636732 | 21000636732 | ||||
20000390847 | 20000390847 | 20000390847 | 20000390847 | ||||
18998658986 | 18998658986 | 18998658986 | 18998658986 | ||||
18000093991 | 18000093991 | 18000093991 | 18000093991 | ||||
16990420912 | 16990420912 | 16990420912 | 16990420912 | ||||
1602124045 | 1602124045 | 1602124045 | 1602124045 | ||||
1499402499 | 1499402499 | 1499402499 | 1499402499 | ||||
13977853723 | 13977853723 | 13977853723 | 13977853723 | ||||
13010538812 | 13010538812 | 13010538812 | 13010538812 | ||||
11984756349 | 11984756349 | 11984756349 | 11984756349 | ||||
10969169617 | 10969169617 | 10969169617 | 10969169617 | ||||
0999943538 | 0999943538 | 0999943538 | 0999943538 | ||||
08972910703 | 08972910703 | 08972910703 | 08972910703 | ||||
08004579361 | 08004579361 | 08004579361 | 08004579361 | ||||
06987510647 | 06987510647 | 06987510647 | 06987510647 | ||||
05991207513 | 05991207513 | 05991207513 | 05991207513 | ||||
0499299343 | 0499299343 | 0499299343 | 0499299343 | ||||
03998207684 | 03998207684 | 03998207684 | 03998207684 | ||||
02999189533 | 02999189533 | 02999189533 | 02999189533 | ||||
01995494967 | 01995494967 | 01995494967 | 01995494967 | ||||
00994354614 | 00994354614 | 00994354614 | 00994354614 | ||||
00000260569 | 00000260569 | 00000260569 | 00000260569 | ||||
-00998519858 | -00998519858 | -00998519858 | -00998519858 | ||||
-01999307233 | -01999307233 | -01999307233 | -01999307233 | ||||
-03000002024 | -03000002024 | -03000002024 | -03000002024 | ||||
-0399820225 | -0399820225 | -0399820225 | -0399820225 | ||||
-04999063003 | -04999063003 | -04999063003 | -04999063003 | ||||
-05999699918 | -05999699918 | -05999699918 | -05999699918 | ||||
-07001420079 | -07001420079 | -07001420079 | -07001420079 | ||||
-07998994986 | -07998994986 | -07998994986 | -07998994986 | ||||
-09000708672 | -09000708672 | -09000708672 | -09000708672 | ||||
-10000260585 | -10000260585 | -10000260585 | -10000260585 | ||||
-10999115648 | -10999115648 | -10999115648 | -10999115648 | ||||
-11999499933 | -11999499933 | -11999499933 | -11999499933 | ||||
-12998676433 | -12998676433 | -12998676433 | -12998676433 | ||||
-14000187317 | -14000187317 | -14000187317 | -14000187317 | ||||
-14999557334 | -14999557334 | -14999557334 | -14999557334 | ||||
-16000495256 | -16000495256 | -16000495256 | -16000495256 | ||||
-16999700321 | -16999700321 | -16999700321 | -16999700321 | ||||
-17998885404 | -17998885404 | -17998885404 | -17998885404 | ||||
-18998707966 | -18998707966 | -18998707966 | -18998707966 | ||||
-19999565727 | -19999565727 | -19999565727 | -19999565727 | ||||
-21000154375 | -21000154375 | -21000154375 | -21000154375 | ||||
-22000394726 | -22000394726 | -22000394726 | -22000394726 | ||||
-22999889377 | -22999889377 | -22999889377 | -22999889377 | ||||
-23998987443 | -23998987443 | -23998987443 | -23998987443 |
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
DataFileName | Copeland_EIS_DummyDTA | |||||||||||||||||||||||||||||||||||||||||||||||
PointCount | 75 | |||||||||||||||||||||||||||||||||||||||||||||||
Title | Potentiostatic EIS | |||||||||||||||||||||||||||||||||||||||||||||||
Date | 1291999 | |||||||||||||||||||||||||||||||||||||||||||||||
Time | 104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ChartTitle | Potentiostatic EIS Copeland_EIS_DummyDTA 1291999-104155 | |||||||||||||||||||||||||||||||||||||||||||||||
ModelName | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParamCount | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLabels | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelParams | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | 1000E+00 | ||||||||||||||||||||||||||||
ModelError | ||||||||||||||||||||||||||||||||||||||||||||||||
ModelLock | ||||||||||||||||||||||||||||||||||||||||||||||||
NumberOfIterations | 30 | |||||||||||||||||||||||||||||||||||||||||||||||
AnalCurveFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
PlotType | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
PlotImmittance | 1 | |||||||||||||||||||||||||||||||||||||||||||||||
YLog | ||||||||||||||||||||||||||||||||||||||||||||||||
AspectRatio | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1ChartName | Chart 9 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp1EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1AxisRange | -3 | 6 | 22 | 36 | -70 | 10 | ||||||||||||||||||||||||||||||||||||||||||
Disp1FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp1Labels | Log Freq (Hz) | Log Modulus (Ohm) | Phase (Degree) | |||||||||||||||||||||||||||||||||||||||||||||
Disp1MatchToList | Modulus | Phase | ||||||||||||||||||||||||||||||||||||||||||||||
Disp2ChartName | Chart 10 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp2EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2AxisRange | -3 | 6 | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||
Disp2FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp2Labels | Log Freq (Hz) | Real (Ohm) | -Imag (Ohm) | |||||||||||||||||||||||||||||||||||||||||||||
Disp2MatchToList | Real | Imaginary | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3ChartName | Chart 11 | |||||||||||||||||||||||||||||||||||||||||||||||
Disp3EnablePointsFlag | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3AxisRange | 0 | 3500 | -200 | 1600 | ||||||||||||||||||||||||||||||||||||||||||||
Disp3FitAxisRange | ||||||||||||||||||||||||||||||||||||||||||||||||
Disp3Labels | Real (Ohm) | -Imag (Ohm) | ||||||||||||||||||||||||||||||||||||||||||||||
Disp3MatchToList | Nyquist | |||||||||||||||||||||||||||||||||||||||||||||||
CurveFreq | CurveReal | CurveImag | CurveMod | CurvePhz | CurveSigma | FitCurveReal | FitCurveImag | FitCurveMod | FitCurvePhz | DispFreqData | DispRealData | DispImagData | DispModData | DispPhzData | DispSigmaData | AnalRealData | AnalImagData | AnalModData | AnalPhzData | Display1PointStatus | Display2PointStatus | Display3PointStatus | PtTog | |||||||||||||||||||||||||
DataTable | 100007 | 197837 | -818946 | 1980064287444 | -23704047221 | 1 | 500 | 198E+02 | 819E+00 | 230 | -237 | |||||||||||||||||||||||||||||||||||||
794336 | 198011 | -74073 | 1981494996569 | -21423517997 | 1 | 490 | 198E+02 | 741E+00 | 230 | -214 | ||||||||||||||||||||||||||||||||||||||
631055 | 198313 | -705642 | 1984385018897 | -20378522094 | 1 | 480 | 198E+02 | 706E+00 | 230 | -204 | ||||||||||||||||||||||||||||||||||||||
501237 | 19868 | -699586 | 1988031298977 | -20166484582 | 1 | 470 | 199E+02 | 700E+00 | 230 | -202 | ||||||||||||||||||||||||||||||||||||||
398112 | 198979 | -719506 | 1991090438162 | -20709071618 | 1 | 460 | 199E+02 | 720E+00 | 230 | -207 | ||||||||||||||||||||||||||||||||||||||
316341 | 199241 | -772258 | 1993906074088 | -22196729596 | 1 | 450 | 199E+02 | 772E+00 | 230 | -222 | ||||||||||||||||||||||||||||||||||||||
251237 | 199352 | -858266 | 1995366682008 | -24652208443 | 1 | 440 | 199E+02 | 858E+00 | 230 | -247 | ||||||||||||||||||||||||||||||||||||||
199544 | 199656 | -100152 | 1999070348113 | -28716798728 | 1 | 430 | 200E+02 | 100E+01 | 230 | -287 | ||||||||||||||||||||||||||||||||||||||
158529 | 1997 | -118848 | 200053339065 | -3405842011 | 1 | 420 | 200E+02 | 119E+01 | 230 | -341 | ||||||||||||||||||||||||||||||||||||||
125872 | 199786 | -143551 | 200301060137 | -4109775349 | 1 | 410 | 200E+02 | 144E+01 | 230 | -411 | ||||||||||||||||||||||||||||||||||||||
99982 | 199837 | -174189 | 2005947273639 | -49816264977 | 1 | 400 | 200E+02 | 174E+01 | 230 | -498 | ||||||||||||||||||||||||||||||||||||||
79426 | 199908 | -216789 | 2010800416979 | -61892190417 | 1 | 390 | 200E+02 | 217E+01 | 230 | -619 | ||||||||||||||||||||||||||||||||||||||
63111 | 200123 | -270474 | 2019425090855 | -76971064803 | 1 | 380 | 200E+02 | 270E+01 | 231 | -770 | ||||||||||||||||||||||||||||||||||||||
501118 | 200286 | -337721 | 203113358828 | -9571145688 | 1 | 370 | 200E+02 | 338E+01 | 231 | -957 | ||||||||||||||||||||||||||||||||||||||
398093 | 200471 | -421307 | 2048502324223 | -118684808519 | 1 | 360 | 200E+02 | 421E+01 | 231 | -1187 | ||||||||||||||||||||||||||||||||||||||
316267 | 200618 | -529281 | 207482446712 | -147793187339 | 1 | 350 | 201E+02 | 529E+01 | 232 | -1478 | ||||||||||||||||||||||||||||||||||||||
251116 | 201521 | -663971 | 2121774925137 | -182360078708 | 1 | 340 | 202E+02 | 664E+01 | 233 | -1824 | ||||||||||||||||||||||||||||||||||||||
199537 | 202518 | -832837 | 2189742336662 | -223544730168 | 1 | 330 | 203E+02 | 833E+01 | 234 | -2235 | ||||||||||||||||||||||||||||||||||||||
158449 | 203751 | -104814 | 2291297549359 | -272222871934 | 1 | 320 | 204E+02 | 105E+02 | 236 | -2722 | ||||||||||||||||||||||||||||||||||||||
125904 | 206128 | -131571 | 2445397317922 | -32549990886 | 1 | 310 | 206E+02 | 132E+02 | 239 | -3255 | ||||||||||||||||||||||||||||||||||||||
99995 | 209422 | -165316 | 2668088340741 | -382872712393 | 1 | 300 | 209E+02 | 165E+02 | 243 | -3829 | ||||||||||||||||||||||||||||||||||||||
794163 | 214955 | -207526 | 2987853622603 | -439926020742 | 1 | 290 | 215E+02 | 208E+02 | 248 | -4399 | ||||||||||||||||||||||||||||||||||||||
630984 | 223426 | -260272 | 3430170425212 | -493561293044 | 1 | 280 | 223E+02 | 260E+02 | 254 | -4936 | ||||||||||||||||||||||||||||||||||||||
501303 | 236723 | -326084 | 4029498154671 | -540219594231 | 1 | 270 | 237E+02 | 326E+02 | 261 | -5402 | ||||||||||||||||||||||||||||||||||||||
398209 | 257186 | -407639 | 48198982657 | -577515135083 | 1 | 260 | 257E+02 | 408E+02 | 268 | -5775 | ||||||||||||||||||||||||||||||||||||||
316113 | 289367 | -508128 | 5847455216357 | -603395000341 | 1 | 250 | 289E+02 | 508E+02 | 277 | -6034 | ||||||||||||||||||||||||||||||||||||||
251185 | 338627 | -628516 | 7139331953236 | -616854435848 | 1 | 240 | 339E+02 | 629E+02 | 285 | -6169 | ||||||||||||||||||||||||||||||||||||||
199495 | 413459 | -770704 | 8746044822072 | -617878098514 | 1 | 230 | 413E+02 | 771E+02 | 294 | -6179 | ||||||||||||||||||||||||||||||||||||||
158533 | 523702 | -931289 | 10684395099045 | -606491667235 | 1 | 220 | 524E+02 | 931E+02 | 303 | -6065 | ||||||||||||||||||||||||||||||||||||||
125911 | 681991 | -110344 | 12971860150653 | -58281489506 | 1 | 210 | 682E+02 | 110E+03 | 311 | -5828 | ||||||||||||||||||||||||||||||||||||||
100009 | 897989 | -127019 | 15555599892711 | -54740751829 | 1 | 200 | 898E+02 | 127E+03 | 319 | -5474 | ||||||||||||||||||||||||||||||||||||||
794083 | 11739 | -14089 | 18338594329992 | -501988292287 | 1 | 190 | 117E+03 | 141E+03 | 326 | -5020 | ||||||||||||||||||||||||||||||||||||||
630971 | 149621 | -149272 | 21134941122464 | -449330990757 | 1 | 180 | 150E+03 | 149E+03 | 333 | -4493 | ||||||||||||||||||||||||||||||||||||||
500083 | 18449 | -150193 | 23789598010265 | -391489775991 | 1 | 170 | 184E+03 | 150E+03 | 338 | -3915 | ||||||||||||||||||||||||||||||||||||||
400059 | 216695 | -143776 | 26005434278435 | -33564065985 | 1 | 160 | 217E+03 | 144E+03 | 342 | -3356 | ||||||||||||||||||||||||||||||||||||||
315793 | 246389 | -130759 | 27893629273008 | -279549571603 | 1 | 150 | 246E+03 | 131E+03 | 345 | -2795 | ||||||||||||||||||||||||||||||||||||||
249911 | 26973 | -114197 | 29290822403784 | -229465956169 | 1 | 140 | 270E+03 | 114E+03 | 347 | -2295 | ||||||||||||||||||||||||||||||||||||||
200011 | 286318 | -97426 | 30243978342804 | -187920019037 | 1 | 130 | 286E+03 | 974E+02 | 348 | -1879 | ||||||||||||||||||||||||||||||||||||||
157934 | 298647 | -805698 | 30932430114855 | -150979711484 | 1 | 120 | 299E+03 | 806E+02 | 349 | -1510 | ||||||||||||||||||||||||||||||||||||||
125002 | 306963 | -658326 | 31394301169442 | -121045388297 | 1 | 110 | 307E+03 | 658E+02 | 350 | -1210 | ||||||||||||||||||||||||||||||||||||||
99987 | 312319 | -536292 | 31688996332109 | -97434033292 | 1 | 100 | 312E+03 | 536E+02 | 350 | -974 | ||||||||||||||||||||||||||||||||||||||
789389 | 315996 | -428735 | 31889121815793 | -77265590178 | 1 | 090 | 316E+03 | 429E+02 | 350 | -773 | ||||||||||||||||||||||||||||||||||||||
631623 | 318248 | -34491 | 32011157208855 | -61854451326 | 1 | 080 | 318E+03 | 345E+02 | 351 | -619 | ||||||||||||||||||||||||||||||||||||||
499748 | 319812 | -274518 | 32098803196886 | -49060894261 | 1 | 070 | 320E+03 | 275E+02 | 351 | -491 | ||||||||||||||||||||||||||||||||||||||
397302 | 320637 | -219075 | 32138454276031 | -39086553209 | 1 | 060 | 321E+03 | 219E+02 | 351 | -391 | ||||||||||||||||||||||||||||||||||||||
315718 | 321204 | -175331 | 32168217111243 | -31244214759 | 1 | 050 | 321E+03 | 175E+02 | 351 | -312 | ||||||||||||||||||||||||||||||||||||||
251085 | 321593 | -138989 | 32189320755525 | -24747212738 | 1 | 040 | 322E+03 | 139E+02 | 351 | -247 | ||||||||||||||||||||||||||||||||||||||
199489 | 321803 | -112107 | 32199821521786 | -19952148875 | 1 | 030 | 322E+03 | 112E+02 | 351 | -200 | ||||||||||||||||||||||||||||||||||||||
158325 | 32205 | -886649 | 32217203035788 | -15770351196 | 1 | 020 | 322E+03 | 887E+01 | 351 | -158 | ||||||||||||||||||||||||||||||||||||||
125729 | 322105 | -710662 | 32218338733216 | -12639148203 | 1 | 010 | 322E+03 | 711E+01 | 351 | -126 | ||||||||||||||||||||||||||||||||||||||
100006 | 321746 | -560934 | 32179489307824 | -09987970382 | 1 | 000 | 322E+03 | 561E+01 | 351 | -100 | ||||||||||||||||||||||||||||||||||||||
0794599 | 321762 | -45268 | 32179384170963 | -08060287558 | 1 | -010 | 322E+03 | 453E+01 | 351 | -081 | ||||||||||||||||||||||||||||||||||||||
0631058 | 321834 | -353491 | 32185341251058 | -06292911249 | 1 | -020 | 322E+03 | 353E+01 | 351 | -063 | ||||||||||||||||||||||||||||||||||||||
0501187 | 321914 | -289151 | 32192698586183 | -05146308149 | 1 | -030 | 322E+03 | 289E+01 | 351 | -051 | ||||||||||||||||||||||||||||||||||||||
0398272 | 321814 | -228514 | 32182211306997 | -04068395941 | 1 | -040 | 322E+03 | 229E+01 | 351 | -041 | ||||||||||||||||||||||||||||||||||||||
0316296 | 321925 | -182947 | 32193019831243 | -03256031105 | 1 | -050 | 322E+03 | 183E+01 | 351 | -033 | ||||||||||||||||||||||||||||||||||||||
0251206 | 3218 | -134799 | 32180282328942 | -02400052396 | 1 | -060 | 322E+03 | 135E+01 | 351 | -024 | ||||||||||||||||||||||||||||||||||||||
0199461 | 321926 | -116363 | 32192810301491 | -02070997607 | 1 | -070 | 322E+03 | 116E+01 | 351 | -021 | ||||||||||||||||||||||||||||||||||||||
0158526 | 321797 | -939598 | 32179837173827 | -01672944336 | 1 | -080 | 322E+03 | 940E+00 | 351 | -017 | ||||||||||||||||||||||||||||||||||||||
0125872 | 321818 | -695417 | 32181875136294 | -01238103434 | 1 | -090 | 322E+03 | 695E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0099994 | 321738 | -649302 | 32173865518008 | -01156289084 | 1 | -100 | 322E+03 | 649E+00 | 351 | -012 | ||||||||||||||||||||||||||||||||||||||
0079449 | 321788 | -384654 | 32178822990081 | -00684893168 | 1 | -110 | 322E+03 | 385E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0063103 | 321783 | -395565 | 32178324313219 | -00704331603 | 1 | -120 | 322E+03 | 396E+00 | 351 | -007 | ||||||||||||||||||||||||||||||||||||||
0050134 | 321694 | -261325 | 3216941061424 | -00465436604 | 1 | -130 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0039809 | 321972 | -287376 | 32197212824865 | -00511393151 | 1 | -140 | 322E+03 | 287E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0031626 | 32181 | -260892 | 32181010575281 | -0046449791 | 1 | -150 | 322E+03 | 261E+00 | 351 | -005 | ||||||||||||||||||||||||||||||||||||||
0025116 | 321933 | -0828492 | 32193301066059 | -00147450227 | 1 | -160 | 322E+03 | 828E-01 | 351 | -001 | ||||||||||||||||||||||||||||||||||||||
0019954 | 321996 | -152985 | 3219960363427 | -00272220592 | 1 | -170 | 322E+03 | 153E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0015853 | 321891 | -098963 | 32189101521272 | -00176151618 | 1 | -180 | 322E+03 | 990E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0012593 | 321799 | -106047 | 32179901747359 | -00188814922 | 1 | -190 | 322E+03 | 106E+00 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0010001 | 321778 | -096916 | 32177801459502 | -00172568591 | 1 | -200 | 322E+03 | 969E-01 | 351 | -002 | ||||||||||||||||||||||||||||||||||||||
0007943 | 321845 | 0393767 | 32184500240881 | 00070099542 | 1 | -210 | 322E+03 | -394E-01 | 351 | 001 | ||||||||||||||||||||||||||||||||||||||
0006309 | 321606 | -162574 | 32160604109112 | -00289634001 | 1 | -220 | 322E+03 | 163E+00 | 351 | -003 | ||||||||||||||||||||||||||||||||||||||
0005012 | 321762 | -213078 | 3217620705525 | -00379425424 | 1 | -230 | 322E+03 | 213E+00 | 351 | -004 | ||||||||||||||||||||||||||||||||||||||
0003982 | 321657 | -0711705 | 32165700787367 | -00126773837 | 1 | -240 | 322E+03 | 712E-01 | 351 | -001 |
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Complex Plane (Nyquist) Plot
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
Ru Ru + Rp
High Freq Low FreqRU
RP
CDL
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Nyquist Plot with Fit
-200E+02
300E+02
800E+02
130E+03
180E+03
230E+03
000E+00 500E+02 100E+03 150E+03 200E+03 250E+03 300E+03 350E+03
Real (Ohm)
-Imag
(Ohm
)
ResultsRp = 3019E+03 plusmn
12E+01Ru = 1995E+02 plusmn
11E+00Cdl = 961E-07 plusmn 7E-09
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Criteria For Valid EISLinear ndash Stable - Causal
bull Linear The system obeys Ohmrsquos Law E = iZ The value of Z is independent of the magnitude of the perturbation If linear no harmonics are generated during the experiment
bull Stable The system does not change with time and returns to its original state after the perturbation is removed
bull Causal The response of the system is due only to the applied perturbation
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Electrochemistry A Linear SystemCircuit theory is simplified when the system is ldquolinearrdquo Z in a linear system is independent of excitation amplitude The response of a linear system is always at the excitation frequency (no harmonics
are generated)
Look at a small enough region of a current versus voltage curve and it becomes linear
If the excitation is too big harmonics are generated and EIS modeling does not work
The non-linear region can be utilized (EFM)
bullCurrent
bullVoltage
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
EIS of Carbon Steel
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Combined Results
Thatrsquos all folksbull Thank you for listeningbull Question
Thatrsquos all folksbull Thank you for listeningbull Question