introductiontoelectrochemistry2byt-140625150515-phpapp02

7/25/2019 introductiontoelectrochemistry2byt-140625150515-phpapp02

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uElectrochemistry 2

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2. Electrochemistry, as a province of academic.

2.1. Overview

2.2. Thermodynamics

2.3. Interface

2.4. Kinetics

2.. E!perimental "ethods

Recommended Text

Electrochemistry Principles, Methods, and Applications

C. M. A. Brett & A. M. O. Brett

OXOR! "#$%ER$T' PRE


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2.1. Overview

)1* Electrochemistry is a st+dy o redox reaction-- Red+ction a reactant /ains electron)s*0

- Oxidation a reactant loses electron)s*0

)(* Red+ction reactions tae place hetero/eneo+slyat $nteraces 2et3een electrodes and electrolyte)s*-

- Anode at 3hich oxidation reaction)s* tae)s* place.

- Cathode at 3hich red+ction reaction)s* tae)s* place.

)4* Chemical reactions incl+din/ redox reactionsare thermodynamically and ineticallycontrolled5a6ected-

- Thermodynamics 7 Potential di6erence

- 8inetics 7 Char/e and5or mass transer


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2.1. Overview

)1* Electrochemistry is a st+dy o redoxreaction-

- Red+ction a reactant /ains electron)s*0

-Oxidation a reactant loses electron)s*0

Red+ction-

C+(9)a:* 9 (e;

2.1. Overview

)(* Red+ction reactions tae placehetero/eneo+sly at $nteraces 2et3eenelectrodes and electrolyte)s*-

-Anode at 3hich oxidation reaction)s* tae)s*place.

- Cathode at 3hich red+ction reaction)s* tae)s*place.

=n(9)a:*

e;

=n)s*

e;

C+)s*

C+(9)a:*


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2.1. Overview

)4;a* Chemical reactions incl+din/ redoxreactions are thermodynamically andinetically controlled5a6ected-

-Thermodynamics 7 Potential di6erence

C+(9)a:* 9 (e;< [email protected]>

=n(9)a:* 9 (e;@

2.4. Kinetics@o 'ar, the kinetics o'

(0) electro&e processes

an&

(") mass transport to an electro&e

have een &iscusse&.

From now on, these two parts o' the electro&e process are

comine& an& we see how the relative rates o' the kinetics an&

transport cause the ehavior o' electrochemical systems to vary.

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2.4. Kinetics

Bass transport to the electro&e sur'ace assumes that this occurssolely an& always y &i''usion (except un&er 'orce& convection).

The mass trans'er coe''icient k&&escries the rate o' &i''usion

within the &i''usion layer, an& kcan& kaare the rate constants

o' the electro&e

reaction 'or re&uction

an& oxi&ation,

respectively.

Thus 'or the simpleelectro&e reaction

#ne-E,

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2.4. Kinetics

k&, an& k&,E are the mass trans'er coe''icients o' the species Y(oxi&i9ing agent) an& E (re&ucing agent). ?n general these

coe''icients &i''er ecause the &i''usion coe''icients &i''er. 8e

alrea&y have the Kutler-olmer expressions 'or the kinetic rate

constantsDkc=kc,oexpQ-7cnF(-*)2ETR

ka=ka,*expQ7anF(-*)2ETR.

Ossume that (c2t)=*, i.e. stea&y state, in other wor&s the

rate o' transport o' electroactive species is e$ual to the rate o'their reaction on the electro&e sur'ace (5ote that the rate o'

mass transport is usually lower than that o' reactions on the

electro&e sur'ace.). The stea&y state also means that the applie&

potential has a 'ixe& value.

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2.4. Kinetics

The 'lux o' electroactive species, 1, is

= k&,(QRP-QR

= k&,E(QER-QERP)

8hen all Y or E that reaches the electro&e is re&uce& oroxi&i9e&, we otain the &i''usion-limite& catho&ic or ano&ic

current &ensities 1l,%an& 1l,aD

,

@ince k&=A2Z, we can write

k&,o2k&,E=p=(A2AE)02",

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2.4. Kinetics

8e can point out extreme cases 'or this expressionD

[et us consi&er only Y present in solutionD 1l,a=* an& ka=*. Thus

that is

This result shows that the total 'lux is &ue to a transport an& a

reaction term. 8hen kcSSk&,othen

reaction transport

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2.4. Kinetics

an& the 'lux is &etermine& y the transport. n the other han&,when kc\\k&,o

an& the kinetics &etermines the 'lux.

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2.4. Kinetics

8e now consi&er the 'actors that a''ect the variation o' kc, ka,an& k&. The kinetic rate constants &epen& on the applie&

potential an& on the value o' the stan&ar& rate constant, k*.

8hen QRP=QERP, then kc=ka=k*.

Ot the moment we note that there are two extremes o'comparison etween k*an& k&D

k*SS k&] reversile system

k*\\ k&] irreversile system

The wor& reversile signi'ies that the system is at e$uilirium

at the electro&e sur'ace an& it is possile to apply the 5ernst

e$uation at any potential.

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2.4. Kinetics

k*SS k&] reversile system

k*\\ k&] irreversile system

These are

the variation o' currentwith applie& potential,

voltammograms.

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2.4. Kinetics

Eeversile reactions are those where koSSk& an&, at anypotential, there is always e$uilirium at the electro&e sur'ace.

The current is &etermine& only y the electronic energy

&i''erences etween the electro&e an& the &onor or acceptor

species in solution an& their rate o' supply. Opplying the 5ernste$uation

an& given that ^2nF=k&,*(Q*RP-QR) we have

that is

.

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2.4. Kinetics

@imilarly,.

@ustituting aove two e$uations in the 5ernst e$uation,

assuming the electro&e is uni'ormly accessile (?=O1), we get

the stea&y-state expression

where

=

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2.4. Kinetics02" is calle& the hal'-wave potential an& correspon&s to thepotential when the current is e$ual to (?l,a#?l,c)2".

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2.4. Kinetics

For irreversile reactions, ko\\k&, kinetics has an importantrole, especially 'or potentials close to e$. ?t is necessary to

apply a higher potential than 'or a reversile reaction in or&er

to overcome the activation arrier an& allow reaction to occur.

This extra potential is calle& the overpotential, I. Kecause o' theoverpotential only re&uction or only oxi&ation occurs an& the

voltammogram, or voltammetric curve, is &ivi&e& into two

parts. Ot the same time it shoul& e stresse& that the retar&ing

e''ect o' the kinetics causes a lower slope in the voltammograms

than 'or the reversile case.

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2.4. Kinetics

reversile system irreversile system

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2.4. Kinetics

The hal'-wave potential 'or re&uction or oxi&ation varies withk&, since there is not e$uilirium on the electro&e sur'ace. For

catho&ic an& ano&ic processes respectively we may write

where 7 is the charge trans'er coe''icient.

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2.4. Kinetics

The electrolyte &oule layer a''ectsthe kinetics o' electro&e reactions.

For charge trans'er to occur,

electroactive species have to reach at

least to the outer Melmholt9 plane.

Mence, the potential &i''erenceavailale to cause reaction is (LU-L)

an& not (LU-L@). nly when L_L@we

can say that the &oule layer &oes

not a''ect the electro&e kinetics.

O&&itionally, the concentration o'electroactive species will e, in

general, less at &istance xM'rom the

electro&e than outsi&e the &oule

layer in ulk solution.

L

LB

L

L

x

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2.. E!perimental "ethodsThe electrochemical response to an O% perturation is very

important in impe&ance techni$ues. This response cannot e

un&erstoo& without a knowle&ge o' the 'un&amental principles

o' O% circuits. 8e consi&er the application o' a sinusoi&al

voltage

where o is the maximum amplitu&e an& ` the 're$uency (unit

is ra&2s) to an electrical circuit that contains cominations o'

resistances an& capacitances which will a&e$uately representthe electrochemical cell. The response is a current, given y

where is the phase angle etween perturation an& response.

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2.. E!perimental "ethods?mpe&ances consist o' resistances, reactances (&erive& 'romcapacitive elements) an& in&uctances. ?n&uctances will not e

consi&ere& here, as 'or electrochemical cells, they only arise at

very high 're$uencies (S0 BM9).

?n the case o' a pure resistance, E, hmCs law =?E lea&s to

an& =*. There is no phase &i''erence etween potential an&

current.

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2.. E!perimental "ethodsFor a pure capacitor

=

8e see that L=H2", that is the current lags ehin& the potential

y H2". bV=(`%)-lis known as the reactance (measure& in ohms).

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2.. E!perimental "ethodsGiven the &i''erent phase angles o' resistances an& reactances&escrie& aove, representation in two &imensions is use'ul.

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2.. E!perimental "ethodsn the x-axis the phase angle is 9ero on rotating anticlockwiseaout the origin the phase angle increases pure reactances are

represente& on the -axis. The &istance 'rom the origin

correspon&s to the amplitu&e. This is precisely what is &one

with complex numers as represente& vectorially in the complexplaneD here the real axis is 'or resistances an& the imaginary

axis 'or reactances. The current is always on the real axis. Thus

it ecomes necessary to multiply reactances y -i.

-id

E

L

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2.. E!perimental "ethods8e exempli'y the use o' vectors in the complex plane with aresistance an& capacitance in series. The total potential

&i''erence is the sum o' the potential &i''erences across the two

elements. From >irchho''Cs law the currents have to e e$ual,

that is ?=?E=?%.

The &i''erences in potential are proportional to E an& dcrespectively. Their representation as vectors in the complex

plane is ]

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2.. E!perimental "ethodsThe vectorial sum o' - idc an& o' E gives the impe&ance . Os avector, the impe&ance is =E-idc. The magnitu&e o' the

impe&ance is !!=(E"#dc")02", an& the phase angle is

'ten the in-phase component

o' the impe&ance is re'erre& to

as : an& the out-o'-phase

component, i.e. at H2", is calle& ,

that is =C#i. Thus 'or this

case C=E, =-dc. This is a vertical

line in the complex plane impe&ance

plot, since C is constant ut varies with 're$uency.

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2.. E!perimental "ethodsFor %E parallel circuit, the total current is the sum o' the twoparts, the potential &i''erence across the two components eing

e$ualD

8e nee& to calculate the vectorial sum o' the currents. Thus02"-02".

The magnitu&e o' the impe&ance is -02"

an& the phase angle is , which is e$ual to the %E series

comination.

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@o, 02=02E#i`%, =E2(0#i`%E). This is easily separate& into

real an& imaginary parts via multiplication y (0-i`%E). Thus

, , .

This is a semicircle in the complex plane o' ra&ius E2" an&

maximum value o' !! &e'ine& y `%E=0.

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2..1. Impedance methodsThese metho&s involve the application o' a small perturation,

whereas in the metho&s ase& on linear sweep or potential

step the system is perture& 'ar 'rom e$uilirium. This small

impose& perturation can e o' applie& potential, or o' applie&

current rate. The small perturation rings a&vantagesD it is

possile to use limiting 'orms o' e$uations, which are normally

linear (e.g. the 'irst term in the expansion o' exponentials).

ul h i


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2..1. Impedance methodsThe response to the applie& perturation, which is generally

sinusoi&al, can &i''er in phase an& amplitu&e 'rom the applie&

signal. Beasurement o' the phase &i''erence an& the amplitu&e

(i.e. the impe&ance) permits analysis o' the electro&e process inrelation to contriutions 'rom &i''usion, kinetics, &oule layer,

couple& homogeneous reactions, etc. There are important

applications in stu&ies o' corrosion, memranes, ionic soli&s,

soli& electrolytes, con&ucting polymers, an& li$ui&2li$ui&inter'aces.


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2..1. Impedance methodsThe impe&ance is the proportionality 'actor etween potential

an& current i' these have &i''erent phases then we can &ivi&e

the impe&ance into a resistive part, E where the voltage an&

current are in phase, an& a reactive part, dc=l2`%, where thephase &i''erence etween current an& voltage is 3*


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2..1. Impedance methodsOny electrochemical cell can e represente& in terms o' an

e$uivalent electrical circuit that comprises a comination o'

resistances an& capacitances (in&uctances only 'or very high

're$uencies). This circuit shoul& contain at the very leastcomponents to representD

f the &oule layerD a pure capacitor o' capacity %&

f the impe&ance o' the 'ara&aic process '

f the un-compensate& resistance, Eg, which is, usually, the

solution resistance etween working an& re'erence electro&es.

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2..1. Impedance methodsf the &oule layerD a pure capacitor o' capacity, %&

f the impe&ance o' the 'ara&aic process, '

f the un-compensate& resistance, Eg, which is, usually, the

solution resistance etween working an& re'erence electro&es.

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2..1. Impedance methods

?mpe&ance o' the 'ara&aic process, 'Eesitance to charge trans'er, Ectan&,

?mpe&ance that measures the &i''iculty o' mass transport o'

the electroactive species, 8arurg impe&ance, w.

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2..1. Impedance methods

For kinetically 'avore& reactions Ect

* an& w pre&ominates.For &i''icult reactions Ectan& Ectpre&ominates.

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2..1. Impedance methods\lot o' the impe&ance in the complex planeS

The low-'re$uency limit

is a straight line, whichextrapolate& to the real

axis gives an intercept.

The line correspon&s to a

reaction controlle& solely

y &i''usion, an& theimpe&ance is the

8arurg impe&ance, the

phase angle eing H2.

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2..1. Impedance methods\lot o' the impe&ance in the complex planeS

Ot the high-'re$uency

limit the control is purely

kinetic, an& E%TSSw.

The electrical analogy is

an %E parallel

comination..

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2..1. %yclic voltammetry and linearsweep techni&ue

Cathodic c+rrent

Anodic c+rrent

Cyclic oltammo/ram

Qinear s3eep

Per,ectly

reMersi2le

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Electrochemistry 2



These techni$ues are potential sweep metho&s. They consist in

the application o' a continuously time-varying potential to the

working electro&e. This results in the occurrence o' oxi&ation or

re&uction reactions o' electroactive species in solution ('ara&aic

reactions) an& a capacitive current &ue to &oule layer

charging. The total current is ?tot=?F#?%=?F#%&(&2&t). Thus ?F

an& ?D this means that the capacitive current must e sutracte&in or&er to otain accurate values o' rate constants (usually ?%

&ecays to 9ero within \*.0 ms only when an appropriate

measuring system with a small %E time constant is use&).

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These techni$ues are potential sweep metho&s. They consist in

the application o' a continuously time-varying potential to the

working electro&e. This results in the occurrence o' oxi&ation orre&uction reactions o' electroactive species in solution ('ara&aic

reactions) an& a capacitive current &ue to &oule layer charging.

The total current is ?tot=?F#?%=?F#%&(&2&t). Thus ?Fan& ?D this

means that the capacitive current must e sutracte& in or&er tootain accurate values o' rate constants. sually ?%&ecays to 9ero

within \*.0 ms (ut only when an appropriate measuring system

with a small %E time constant is use&). 5ote that where E is the

solution resistance, E, an& % is the &oule layer capacitance, %&.

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Electrochemistry 22.. E!perimental "ethods


The oserve& current is &i''erent 'rom that in the stea&y state

(&c2&t=*). ?ts principal use has een to &iagnose mechanisms o'

electrochemical reactions, 'or the i&enti'ication o' species

present in solution an& 'or the semi$uantitative analysis o'

reaction rates. Olthough some improvements can e shown

recently, it is asically &i''icult to &etermine kinetic parameters

accurately 'rom these experimental results.

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