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1
Corrosion Rate, R
Corrosion rate can have different units.
Units
R = x/t, thickness loss per unit time mils per year (mpy)
mm per year (mm/y)
R = m/At, weight loss per unit area per unit time mg/dm2/day (mdd)
i = I/A = Q/At, current density Amperes/cm2 (A/cm2)
= nFm/MAt
Note:
• Values can be converted back and forth with appropriate constants.
• Weight loss and current have to be normalized by exposed area.
• Electrochemical measurement of corrosion rate (current) can be converted to other
units (next slide)
• These approaches assume uniform corrosion - valid for localized corrosion?
2
Faraday's Law
Needed to convert electrochemical measurement to other units.
’
equivalent = mole of charge
n (eq/mol) =
= charge on ion
mol charge mol matter
3
Thermodynamics vs. Kinetics
Corrosion resistance depends on both thermodynamics and kinetics.
From a corrosion standpoint, thermodynamics is the study of
materials’ tendency to corrode, while kinetics is the study of the
rate of corrosion.
Thermodynamics answers the question “can a metal corrode?” and
kinetics answers the question “how fast will it corrode?”
Remember that we have seen how Faraday’s constant relates current
to flux or rate:
J = i/nF
4
Kinetics at Equilibrium • Consider the electrochemical half-cell reaction at
equilibrium:
M Mz+ + ze-
• At equilibrium no net current flows to or from the
surface of the electrode. This, however, does not
mean that nothing is happening on the surface of the
electrode. A “dynamic equilibrium” condition exists
at the surface of the electrode where the rate in the
forward direction, rf, is equal to the rate in the reverse
direction, rr.
• When the reaction is at equilibrium, the electrode potential is equal to the
reversible potential, Erev.
E
Erev
log i io
rf
rr
inet = iox - ired = 0
M M+z
This is another form
of Faraday’s Law rf = rr = ioM/nF (g/cm2s)
where io is the exchange current density, which is
equivalent to the reversible rate at equilibrium, and M is
molecular weight.
5
Electrochemical Polarization
Erev
• At Erev, the electrochemical half-cell
reaction is at equilibrium and the rate in
both directions is io:
M Mz+ + ze-
What happens as you move away from
equilibrium?
• At potentials different from Erev, the
reaction will proceed predominantly in
one direction. At higher potentials it
will go in the oxidizing (anodic)
direction:
M Mz+ + ze-
• At lower potentials it will go in the
reducing (cathodic) direction:
Mz+ + ze- M
log i
E
io
(Ecorr)
(icorr)
O2 + 4H+ + 4e- → 2H2O
6
Electrochemical Polarization
Polarization, h = E - Erev, is a change in
potential from the reversible
(equilibrium) half-cell potential. h is also
called the overpotential or overvoltage.
Electrochemical kinetics describe the
relationship of current and overpotential.
As shown in the figure, there tends to be
an exponential dependence of current on
potential.
log i
E
io
Erev
h > 0
In electrochemistry, potential and current
are inter-dependent. You can control
either one and measure the other.
7
Substituting:
RT
nF)1(expi
RT
nFexpii 00net
hh
For an applied cathodic overpotential (potential less noble than
the reversible potential):
Development of Butler-Volmer Equation
Some references don’t have n in the Butler-Volmer equation. It is
really only valid for a simple one electron reaction anyway.
RT
nF)1(expi
RT
nFexpiiii c
0c
0acnet
hh
8
Tafel Equation
For a sufficiently large value of anodic polarization from the reversible
potential (overpotential h > 50 mV), the Butler-Volmer equation
simplifies to:
rearranging, one gets the Tafel equation:
where ba = 2.3RT/nF is the anodic Tafel slope. For = 0.5 and n = 1,
ba = 0.12 V (or V/decade). This calculation is only for a single
electron reaction. Most reactions are very complicated and b 0.12 V,
but b 0.12 V (often 0.04 – 0.15 V).
A similar equation is found for cathodic polarization:
RT
nFexpii a
0
h
ha = ba log (i/io) or i = i0 10h/b
hc = bc log (i/io)
9
Plots
ba
ha
hc
bc
ErevM/M+
log i
E
ioM/M+
The Tafel Equations describe the
polarization kinetics under
activation control and are straight
lines in a plot of E-log i. Such a
plot is called an Evans Diagram:
The Butler-Volmer Equation is
sometimes plotted in linear coordinates.
The symmetry of the curve will depend
on the symmetry factor, b. When b =
0.5, the curve is symmetrical:
Bockris and Reddy, Modern Electrochemistry
10
Measurement of Polarization Curves
In order to obtain the potential-current relationship, the potential can be stepped
incrementally or scanned at a fixed rate (potentiodynamic polarization). Alternatively, i
can be controlled at different values and E measured.
Potentiodynamic polarization - Typically start at a potential of about E = Eoc - 250 mV
and scan potential in the positive direction at 0.1 to 1 mV/s to a value about E = Eoc +
250 mV. (May want to go higher to look for other behavior such as passivation or
pitting.) Net current is measured at various intervals as a function of potential and
plotted as E vs. log |i|. Remember that the current density below the corrosion potential
is negative. Since log 0 = -, on log scale the curve points to left at Ecorr.
Jones
11
Determination of Corrosion Rate from
Measured Polarization Curves Corrosion rate can be determined from mass loss, which is time consuming and
has limited sensitivity.
Corrosion rate can be determined electrochemically from measured polarization
curves using our understanding of polarization behavior by:
1. Tafel extrapolation
2. Non linear least squares fit to ideal equation, which is similar in form to
the Butler-Volmer equation
3. Linear polarization resistance (discussed later)
Other electrochemical techniques will also be discussed later.
12
Determination of Corrosion Rate from
Polarization Curves 1. Tafel Extrapolation
Extrapolate Tafel behavior (straight line in semi-log plot) to Ecorr (zero-
current potential) to get icorr. Also get Tafel slopes from this analysis.
If anodic and cathodic extrapolations do not intersect at the zero-current
potential, typically consider cathodic extrapolation to be less in error.
Jones
13
Polarization Curves
The anodic portion of the polarization curve often does not exhibit Tafel
kinetics for a variety of reasons (surface roughens, films form, concentration
in solution changes).
Knowing that the net current near Ecorr is a sum of the anodic and cathodic
currents, one can determine the anodic Tafel slope from the net current and
the cathodic kinetics.
c
corr
a
corrcorrnet
b
)E2.3(Eexp
b
)E2.3(Eexpii
Jones
14
Determination of Corrosion Rate from
Polarization Curves Can get corrosion rate very accurately in minutes!
From Faraday’s Law: r = CMicorr/rnF
where:
C - constant to alter units of thickness and time icorr - corrosion current density (A/cm2)
M - molecular weight of metal (g/mol) r - density of metal (g/cm3)
Limitations:
• Lab environment may not be identical to
service environment.
• icorr could change with time, measurement is
representative of point in time.
• Polarization far from Ecorr will change electrode
surface – destructive test.
• Extrapolations are sometimes difficult because
of limited or no linear region, need 1 order of
magnitude current for Tafel slope.
• Anodic and cathodic lines might not
extrapolate to the same current density,
probably best to use extrapolation of
cathodic current.