factor afecting shape ie curves jce 60 (1983) 285

7/27/2019 Factor Afecting Shape IE Curves JCE 60 (1983) 285

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Voltammetry

Factors Affecting the Shape of Current-Potential CurvesJ. T. MaloySeton Hall University, South Orange, NJ 07079

Voltammetry, the fundamental electrochemical experi-ment, is the measurement of th e current which flows at anelectrode as a function of the potential applied to the elec-trode. The current-potential curve is the electrochemicalequivalent of a spectrum obtained in spectrophotometry.These curves may be used by the analytical chemist forqualitative and quantitatiue determinations and by the

whatever information is availahle from a given experiment,however, one must understand the factors which influence theshape of the voltammetric wave. I t is the in tent of this authorto provide this understanding.The voltammetric ex~ eri men ts illustrated in Fieure 1.Inthis experiment, the potential of the working electrode (versusa known reference) is determined bvthe variable power supplvvoltage applied across the working and auxiliary e~ectrddei.This wower su~wlv av be controlled bv a "wriceless" studentor a knew hai -lt & costly instrumental device called a po-tentiostat. The current flowing through the cell is then plottedas a function of working electrode potential. T he kind of vol-tammetry t hat is observed depends upon the way that t hepower supply voltage is varied and the physical and electro-chemical properties of the cell. In this paper, we want toconsider six different kinds of voltammetric waves: the re-versible and irreversible (or quasi-reversible) forms ofsteady-state, linear sweep, and sampled-current voltammetry.Thr ee of these six are illustrated in Figure 1.One of the voltammetric waves shown in Figure 1 curve c)indicates th at double layer charging can contribute a back-ground curren t to the observed current. These capacitive

The VoltammetrlcExperiment

Work lno

E l e c t r o d eFigure 1. The Voltammetr ic Experiment. Current passing through the workingelectrode is measwedas a function of the applied potential. Curvea: reversiblesteady state voltammetry. Curveb: irreversible sampled-currentvoltammetry.Curvec: reversible linear sweep voltammetry (showing the effect of double layercharging background current).

currents (which are due to the physical rearrangements of ionsin the double layer) can influence the shape of all non-steadystate voltammetric waves. Much attent ion has been directedto the minimization of these capacitive currents in electro-analysis. Because double layer charging phenomena are beingtreated elsewhere in this Symposium, we will only indicatethat these do influence voltammetric waveshape but theseeffects will not he considered in this paper. Ra ther , only fa r-adacc contributions to the total current will be considered;these currents (which ar chem~c aln nature) po to produce achange in oxidation sta te of some material inth e c&.Th e voltage waveforms used to produce the three kinds ofvoltammetry to be discussed in this paper are shown in Figure

2. Curve a shows a potential step to the limiting current po-tential used in a constant potential experiment called chro-noamperometry; we shall subsequently see tha t this potentialis sufficient to reduce the electrode surface concentration ofth e electroactive material to zero. In the three kinds of vol-tammetric experiments discussed herein, we either approachthis limiting current potential by a fast ramp (linear sweep),a slow ramp (steady-state) or a modified staircase (sampled-current) as shown in curves b, c, and d, respectively. In sam-pled-current voltammetry, the current is sampled at the samepoint on each step of the staircase as shown. In each of thethree voltammetric experiments, the potential varies with

I . / v - s w e e p r a t e 7/.sample tirn

0 TimeFigure2. Applied Potential Waveforms. Curve a: a potential step from the restDdential El to the limitino current ootential E, used in chronoamoerometrv. Curveb: high swkep rate capped-ram; used in lnear sweep voltahmetry. curve c:low Sweep rate ramp used in steady state voltammetry. Curved: multiple pa-tential step program used in sampled-current voitammetry.

Volume 60 Number 4 Aprii 1983 285


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time and so does the current. Each voltammetric wave is a plotof i (t ) versus E(t ).The faradaic current that flows at any time is a directmeasure of the rate of the electrochemical reaction taking

to the electrode (this is called mass transport); 2) the rate atwhich electrons transfer from electrode to solution species andvice versa (thi s is called charge transfer ). I t is sometimesuseful t o think of the current as heing controlled indepen-dently by either mass transport or charge transfer. Actuallythese two rate-limiting processes are inexorably intertwined,and i t is important to remember this.Mass transport takes place by the following three modes:(1)diffusion-the spontaneous movement of any materialfrom where it is to where it is not; (2) migration-the move-men t of charged particles in an electric field; and (3)conuec-tion-movement of material contained within a volume ele-men t of hydrodynamic (stirred) solution. These three modesof mass transport are illustrated in Figure 3. In mathematicalterms, the (mass transport) flux to the electrode is descrihed(in one dimension) by the Nernst-Planck equation:

+ a x , t ) u , ( x, t ) (1)where J is the flux (mol cm-2 s-1); D is the diffusion coeffi-cient (cm2 s-'1, C is the concentration (mol cm-31, 9 s theelectrostatic potential, and v, is the hydrodynamic velocity.In simple terms, this partial differential equation states thatthe flux of material toward the electrode is proportional eitherto the slope of the C or 9 profiles or the u, profile shown in thepanels a t the right of Figure 3. Note that this flux may heevaluated at different times and differentpositions. For ex-ample, a t the time represented by the concentration profilein the upper right panel, the diffusional flux a t position a isgreater than that at position b which is greater than tha t a tc; this is due to the slope of th e concentration profile heinggreatest at position a, etc. This slope a gives a good indicationof the diffusional flux a t the electrode surface. In fact, if thecurrent is either controlled by mass transport or a steady stateprocess, i t may he determined from the flux associated withthis slope:

i ( t )= nFAD--'c t , I x m o (2 )where n is "number of electrons" (faradays mol-I), A is theelectrode area, an d F = 96,500C faraday.-I We will use eqn.(2) extensiuely in this development of uoltammetry.

Figure 3. The Three Modes of Mass Transport. Differentdistance scales havebeen used to construct both th e illustrationsan d th e profiles at the right.

In order for eqn. (2) to he valid as claimed above, only dif-fusion may contribute to the flux at the electrode surface. Wecan usually see that this is so. For example, if we wish toeliminate conuective transport, we need only keep the solutionquiescent (don't stir it!); even if we do sti r the solution, how-ever, ean. (2 ) is valid. The fluid velocitv alwavs eoes to zero..at the e e c r r d ~1Irtm.,, where 11it I I C W I I I ~:jI1111i(1nieeti 111,~ m p t ~ ~ ~ t n i h l clrc rrd e 1+e IYe . :


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terms have nothing to do with the chemical reversihility ofth e redox reaction (e.g., participation in side reactions).Electrode surface conditions for an electrode obeying theNernst equation are illustrated in Figure 4. This figure showsthe concentration of solution species0 and R in th e vicinityof the electrode a t some unsoecified times durin r th e elec-- ~ - - ~~ ~ ~trolysis of a solution initially Eontaining only0.A


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a nerns tian wave.3) Since the slope of the c oncentration profile is one-half the lim -iting slope at E = EO',he half wave potential Elin (which isachieved when the curr ent is one-half the lim itine eurrent) isused for quolitotiue analysis

Thes e results would he obtained using a stirred solut


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Such hehavior is called kon-ne rnstian or, dependingupon theext ent of the deviation from reversihle hehavior, irreuerslbleor quasi-reversible heh avior. This kinetically controlled he-havior is illustrated for steady state voltammetry in Figure9. As in Figure 6, since the hulk concentrat ion is maintainedat dis tance 6 by convection, the steady-state slope of theconcentration profile is determined entirely by the steady-state concentrat ion a t the electrode surface. This is de ter-mined by the ra te of charge transfer at th at potential . Evenwithout doine anv rieorous mathematical analvsis, one factgiven potential, th e surface concentration of 0 will heg rea tertha n it would have been if the charge transfer ra te were fastenough to maintain th e laws of thermodynamics. Thu s, thekinetically-controlled curre nt a t a given potential is less t h anthe reversihle current a t he sam e potential . This af fects thevoltamme try in the following ways:

I j Even though limiting currents suitable for qunnti tatiue analy,qisare achieved at negative potentials, they are not achieved aseasily as in the case of the reversible wave. In th e wave shownin Figure 9, for example, limiting cur ren t hehavior is notachieved even after the potential is 300 mV beyond the onsetof electrolysis.

2) The rising portion of the voltammetric wave is not as steep asthat of the reversihle wave. reauirine in this examole 240 mV~,to go from 10 % of the limiting current to 90% of the limitingcurrent. This fails to meet th e diagnost ic criterion of revers-ihility cited above.3) T h e half-wave potentialE l,2 no longer corresponds t o E w since

Ell2 s now determined by charge transfer kinetics instead ofthermodynamics. The measurement of this potential provideskinetic informalion instead of thermodvnamic information. Itcannot beused for qualitative analysis because it depends uponthe experimental conditions.It is now clear why this waveshape an alysis is imp orta nt.

Only when the difference between reversihle a nd irreversiblevoltammetric waves is understood are we able to in te r ~ re th eresults of a given experime nt. On one hand, we get thermo-dynamic information from the reversihle wave; on the oth erhand, we can get kinetic information from the irreversihlewave. Depending upon the a pplica tion, each of these piecesof information can be valuahle. Similarly, we can always doquantitative analysis using any voltammetric wave that ex-hibits limiting curren t hehavior. However, qualitative analysisis possible only using reversihle waves. Thi s distinction is qu itei m ~ o r t a n tn kn uw in ~ here to look for a eiven voltammetricwave in routine e lectroa nalysis , i.e., th e "wavelength" of th eelectrochemical "transition." Because the rate of charee

. .position of th e quasi-reversible voltammetric wave is depen -den t upon these factors also.It has been left for the reader t o formulate verifiable13conclusions about the irreversihle voltammetric waves oh-tained in l inear sweep voltammetry and sampled-currentvoltamme try. Th e conclusions which may be reached are quitesimilar to those obtained for irreversihle steady state vol-tamm etry. Likewise, the principles developed herein may heused to c ultivate one's u ndersta nding of reversihle an d irre-versible cyclic voltammetry a nd thin-layer voltammetry. T heabilitv to visualize the relationshio between the con centrationgradiknt and the current (and the boundary conditions tha tdetermine that concentration eradient) is aui te im ~ or ta n tnunderstanding those factors which a ffe ct t he shape of cur-rent-potential curves

' Bard, A. J , and Faulkner. L. R , "Electrochemical Methods." Wiley,New York, 1980.Adams, R. N . , "Electrochemistry at Solid Electrodes," MarcelDekker, New York, 1967.Delahay, P. , "New Instrumental Methods in Electrochemistry.''Inte rscience, New York, 1954 .

Volume 60 Number 4 April 1983 289

factor afecting shape ie curves jce 60 (1983) 285

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