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MAR a 5.1988 


Technical Report No. 68 




Purdue University 
Department of Chemistry 

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Purdue University 
Department of Chemistry 
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Element no 




The Influence of Uncompensated Solution Resistance on the Determination and Standard Electro- 
chemical Rate Constats Using Cyclic Voltammetry, and Some..Gonn 7 arrsond Trh-h-AC Vn^ra 1 Tl^<P^■ry 

Dr F. y - 


Milner and M.i J. Weaver 

13a type of report 

from 10/1/86 to 9/30/67 

14 DATE OF REPORT (Year. Month, Day) 

September 25. 1987 



17 1 







18 S(I)^CT TERMS (Continue on revene if necesury end identify by block number) 

‘lisital simulation analysis, uncompensated solution resis- 
tance, electrochemical rate constants, cyclic voltaiTtint.try^ 

solution resistance, K.'|, upon the evaluation of standard rate constants, using cyclic 

voltammetry. The results are expressed in terms of systematic deviations of "apparent 
measured" rate constants, k?^(app), evaluated in the conventional manner without regard for 
R , from the correspouding°actual values, kp^(true), as a function of Rj^ and other experi¬ 
mental parameters. Attention is focused on fine effects of altering the electrode area and 
the double-layer capacitance upon the extent of the deviations between k^(app) and k^^(true) 

and on comparisons with corresponding simulated results obtained from phase-selective ac 
impedance data. ..^The extent to which k*j^(app) < k ^(true) for small R^^ values was found to 

" efinir "" i - 

be similar for th^cyclic and ac voltammetric teefiniques. The latter“method is, however, 
regarded -as being preferable under most circumstances in view of the greater ease of mini¬ 
mizing, as well as ^aluating, R^^^ for ac Impedance measurements. The influence of solution 

resistance on 

k®, measurements using microelectrodes and without iR compensation is also 


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Contract N00014-86-K-0556 

Technical Report No. 68 

The Influence of Uncompensated Solution Resistance on the 
Determination and Standard Electrochemical Rate Constants 
Using Cyclic Voltammetry, and Some Comparisons with AC Voltammetry 

D. F. Milner and H. J. Weaver 

Prepared for Publication 

in the 

Anal. Chim. Acta 

198, 245-57 (1987) 

Purdue University 
Department of Chemistry 
Vest Lafayette, Indiana 47907 

September 25, 1987 



y.'': I 

Avt' ■!..1 'y v'■'( >»''i 

Dird i 


Reproduction in whole, or in part, is permitted for any purpose of the 
United States Govexmment. 

* This document has been approved for public release and sale; its 
distribution is unlimited. 

88 8 2 ? 091 

mn kti wm 

The Influence of Uncompensated Solution Resistance on 
the Determination of Standard Electrochemical Rate Constants 
Using Cyclic Voltammetry, and Some Comparisons with AC Voltammetry 

David F. Milner and Michael J. Weaver 
Department of Chemistry, Purdue University, 
West Lafayette, Indiana 47907, U.S.A. 

88 3 22 0 91 















^ I 


A digital simulation analysis Is presented of the deleterious effects 
of uncompensated solution resistance, upon the evaluation of standard 
rate constants, using cyclic voltammetry. The results are expressed 
In terms of systematic deviations of "apparent measured" rate constants, 

> evaluated in the conventional manner without regard for R^gi from 
the corresponding actual values, k®b(true), as a function of and other 
experimental parameters. Attention Is focused on the effects of altering 
the electrode area and the double-layer capacitance upon the extent of the 
deviations between k®b(app) and k®b(true), and on comparisons with 
corresponding simulated results obtained from phase-selective ac Impedance 
data. The extent to which k®b(spp) < small R^^ values was 
found to be similar for the cyclic and ac voltammetrlc techniques. The 
latter method is, however, regarded as being preferable under most 
circumstances in view of the greater of minimizing, as well as 
evaluating, R^^ for ac impedance measurements. The influence of solution 
resistance on k®b measurements using microelectrodes and without IR 
compensation is also considered. 

In recent years cyclic voltammetry (CV) has been utilized to determine 
standard electrochemical rate constants, k®, for a great number of redox 
couples under widely varying conditions. The rate constants have been most 

commonly derived from the cyclic voltammograms by using the Nicholson-Shain 

1 2 
type of analysis, although other methods have also been employed. 

Particularly given the common and sometimes indiscriminant use of CV for 

this purpose, it is Important to ascertain clearly the range of system 

properties and measurement conditions over which the observed rate 

parameters are indeed valid. This is of particular concern when relatively 

rapid rate constants are required to be evaluated, since the effect of even 

small positive amounts of uncompensated resistance, can easily be 

1 a 

misinterpreted as slow electrode kinetics under these conditions. In 

addition to the deleterious influence of solution resistance, measurement 

nonidealities associated with the effects of potentiostat bandwidth and 

double-layer charging current also need to be considered. 

Digital simulations of cyclic voltammograms of varying complexity have 

been performed for as long as cyclic voltammetry has been employed for 
s 13 

evaluating k for quaslreversible systems. ' These simulations have 
primarily been of the "idealized" form in which no instrumental or 
electrochemical artifacts, such as arising from R^g, the double-layer 
capacitance or finite amplifier bandwidths, are considered to affect 

the cell response. Although significant attention has been given to the 
development of algorithms which account for the influence of upon the 
cyclic voltammograms,^ surprisingly little effort has been directed towards 
providing analyses which enable the experimentalist to readily deduce the 
consequences for the reliable measurement of k®. A significant difficulty 

■ ■»* 

Is that the solution resistance distorts cyclic voltanunograms in a manner 

qualitatively similar to that of sluggish electrode kinetics.This can 

produce considerable uncertainty in evaluating the latter in the presence 

s 2-1 

of the former, especially for moderate or large k values (> 10 cm s ). 
While it is usual to employ positive-feedback compensation so to minimize 
Rusi is extremely difficult to reduce to zero without severely 

distorting the potential-time ramp applied to the cell.^ 

By means of digital simulations we have recently examined the combined 
influence of uncompensated solution resistance and other measurement 
nonidealities on the determination of k^ by means of ac impedance 
techniques.^ For this purpose it was found useful to distinguish between 
"apparent" observed rate constants, k®^(app), that are obtained for a given 
instrument and measurement conditions by means of the conventional analysis 
assuming such nonidealities to be absent, and the desired actual ("true") 
value of the rate constant, k®^(true). The extent of the systematic 
deviations between k®jj(app) and k®|j(true) was examined as a function of R^^ 
and the magnitude of k®|j(true) in order to provide means by which the 
reliability of the RqJjCspp) values could be diagnosed, and to enable the 
extent of the corrections to k®^(app) arising from the presence of 
measurement nonidealities to be determined.^ 

The present communication summarizes the results of a comparable 
digital simulation study aimed at assessing the reliability of k^^(app) 
values obtained by using cyclic voltammetry. Of particular interest is the 
extent to which the presence of uncompensated solution resistance provides 
an effective upper limit to the reliable evaluation of k®^(true) for a 
given set of measurement conditions, and how this limit for cyclic 


voltammetry compares to that for corresponding ac Impedance measurements. 
Simulation parameters are chosen so to correspond to a range of conditions 
appropriate to typical aqueous and nonaqueous media. The effect of varying 
the electrode area is considered, including conditions appropriate for 


The digital simulations of cyclic voltammograms performed in this 

study were of two types. For those instances where the effect of was 


not considered, the method of Nicholson was used, while those where this 
influence was included were finite difference simulations similar to those 


described by Feldberg. 

The values of the various system parameters employed in the 

simulations were selected to be representative of those commonly 

encountered for redox couples in nonaqueous solvents as well as aqueous 

media. The ranges of R,_ values chosen (< 50 ohm) are based on the minimum 

values that we have generally been able to obtain in studies utilizing 

common commercial potentiostats, such as the PAR 173/179 system (vide 

infra). The reactant (and product) diffusion coefficient was taken to be 1 
-5 2 *1 

X 10 cm s , the electrochemical transfer coefficient was assumed to 
equal 0.5, the number of electrons transferred, n, equals one, and the 
reactant concentration was taken to be lm{l unless otherwise noted. The 
voltammetric sweep rate was set at 20 V s'^ unless specified otherwise. 

The general procedure involved simulating cyclic voltammograms for a 
suitable range of system input parameters, including k®^j(true) and R^^ 
values, and extracting "apparent observed" rate constants, k®^(app), from 

the simulated voltammetrlc curves In the same fashion as is conventional 

for experimental data. For simplicity, this involved evaluating 
from the difference between the cathodic and anodic peak potentials, 
using AEp'f plots in the manner prescribed by Nicholson. Where 

necessary, simulations were performed under "ideal" conditions (i.e. for 
^us’ ^dl ~ generate more complete AE^-t data and thereby avoid any 

interpolation errors encountered by using Table I of ref. la. Strict 
adherence was also paid to the potential scan limits specified for the 
validity of the AEp-* relation in ref. la. 

All simulation programs were written in FORTRAN-77 and executed on a 
DEC LSI 11-73 microcomputer under the RSXll-M operating system. 


Origins of Distortion of Cyclic Voltammograms from Uncompensated Solution 

Before examining systematically the extent to which the presence of 
Ryg can lead to systematic differences between h®^(app) as determined by 
cyclic voltammograms and the required k®^(true) values, it is useful to 
clarify the origins of the underlying distortions in the current-potential 
profiles. Under most conditions, the solution resistance will be 
Incompletely compensated by the potentiostat positive-feedback circuitry so 
that R^^g will be positive. The presence of R^^ will yield a net ohmic 
potential drop, iR^g, through the solution in proportion to the current, i, 
flowing. Since the current peaks for the negative- and positive-going 
potential sweeps have opposite signs, the measured cathodic-anodic peak 
separation, AE_, will clearly be larger for positive R,,^ than the "ideal" 


case, where R^g * 0. 

An additional, less obvious, source of distortion arises from the fact 
that when R^g ^ 0 only the time derivative of the overall cell potential, 
dEceii/dt, will be held constant during the voltammetrlc scan, rather than 
the corresponding derivative of the double-layer potential, dE^^/dt, as is 
required for the exact applicability of the usual CV treatment. As a 
consequence, dE^j^/dt will vary with so to distort the measured AEp 

still further in the presence of R^g. This is illustrated in Fig. 1, which 
shows simulated i - and (dE^j^/dt) - traces for a negative-going 

potential sweep, with (dE^^gj^j^/dt) - i/ - 100 V s*^. The electrode area. A, 
is taken as 0.2 cm , R^g as 50 ohms, and as 20 /iF cm . The magnitude 
of dE^j^/dt is such that it is less negative when i is decreasing (Fig. lb). 
This "acceleration" of the effective sweep rate in the vicinity of the 
current peak contributes to larger AEp values than in the absence of 
uncompensated solution resistance. 

The nonfaradaic current, i^£, resulting from nonzero values will 
also contribute to this distortion. This is because 1^^ enhances the total 
current throughout the voltammogram, and therefore further enlarges AEp 
than when R^g - 0. This capacitive contribution to AEp, A(AEp), can be 
determined approximately from A(AEp) - 2 where v is the applied 

potential scan rate (‘^^cell^**^^ ’ However, the precise influence of 
upon AEp will be more complex, not only because is usually potential 

dependent, but also since the scan rate v in this relation should really be 
identified with (dE^j^/dt) rather than with (‘^^cell/*^^^ ■ 

It is well known that the presence of can lead to large systematic 
errors in the determination of k®^, since increasing or decreasing k®^ 
both lead to greater AE^ values under a given set of experimental 


conditions. A common procedure is to "fit" the experimental current- 

potential curves to corresponding simulated curves obtained for a set of 

s 2 c 7 

input parameters and trial k^^ values until the best match is obtained. ’ 

Although this procedure is in a sense preferable to the examination of AEp 

values alone, it is not always obvious that obtaining a "good fit" of the 

simulated to the experimental data is due to the correctness of the choice 

of k®^ rather than to an incorrect choice of other system variables, 


The crux of the problem is that the diagnosis of AEp values greater 
than the "reversible" limit (i.e. for k®^ *), (59/n)mV at 25*C, as 
arising purely from the presence of "finite" (i.e. measurable) k®^ values 
rather than at least partly from R^^ > 0 is far from straightforward. For 
example. Fig. 2 shows a pair of simulated cyclic voltammograms, the points 

S *" 1 

corresponding to k^^ - 0.04 cm s and R^^ - 0, and the solid trace 
referring to k®^^ - « and R^^ — 50 ohm. (The latter value is chosen here 
since it approximates the magnitude of R^^ that can be anticipated in many 


nonaqueous media. ) The close similarity in the two curves, in addition to 
the almost identical AEp values, clearly make the evaluation of k®^ values 
even as small as 0.04 cm s‘^ fraught with difficulty unless R^^ is known 
accurately, or preferably diminished substantially below 50 ohm. Although 
it is common to examine the dependence of AEp on the sweep rate, i/, in 


order to evaluate this procedure provides little or no diagnosis for 

the dominant presence of finite electrode kinetics rather than since 

both show a similar dependence 


This is illustrated in Fig. 3, 

which shows plots of dE^ against 1 / for the same conditions as in Fig. 2. 
Both the resistance-dominated (solid curve) and kinetics-dominated 


(squares)plots are almost indistinguishable. Clearly, then, substantial 
systematic errors in the evaluation of k®^, so that k®^j(app) < k®^(true), 
can occur for analyses of this type unless is known accurately. 

In principle, a distinction between resistive- and kinetically- 
dominated dEp behavior can be obtained by varying the bulk reactant 


concentration, C^, while holding all other parameters fixed. As shown in 
Fig. A, if the sweep-rate dependent dE is dominated by R , then dE 

r wa |ii 

should increase roughly linearily with whereas dEp will be independent 
of if the dEp response is dominated by sluggish kinetics, at least if 
these are first order so that k®^ is independent of This approach, 

however, is often not a practical one. In circumstances where either 
positive-feedback iR compensation and/or a Luggin probe is used to minimize 
Rus It is usually very difficult to maintain precisely the same R^^ values 
on successive measurements using solutions of varying reactant 

concentration. Moreover, the presence of nonfaradaic current leads to some 
influence of R^^ upon dEp even when -» 0 (Fig. 4). Consequently, it is 
difficult to use this strategy to diagnose the influence of R^^ upon the 
cyclic voltammograms except under relatively favorable circumstances. 

It is therefore apparent that an accurate knowledge of R^^ is a 

prerequisite for the reliable determination of k®^ by means of cyclic 

voltammetry. As noted above, we have previously utilized digital 


.*i' i.»i ~ 



til, i 

simulations to examine deviations between k®|j(true) and k®^(app) as a 
function of R for ac impedance measurements, where k^. (app) is determined 

from the conventional analysis that assumes that R 

0.” Such 

relationships enable estimates of k®j^(true) to be obtained from measured 

k®b(®PP) values if R^^ is known, as well as providing an upper limit to the 

k®b(®PP) values for which meaningful kinetic information can be extracted. 

Examples of such relationships obtained for cyclic voltammetry are 

shown in Figs. 5 and 6 in the form of plots (solid curves) of log k®^(app) 

versus R^^ for various k®jj(true) values. The k®^(app) values were obtained 

from the AEp values for simulated cyclic voltammograms by using the 

Nicholson analysis and ignoring the influence of The solid traces 

A, B, and C in Figs. 5 and 6 refer to k®^(true) values of ®, 1.0, and 0.1 
cm s , respectively. Complete coincidence between these k^^Ctrue) values 
and the corresponding k®|j(app) values in these plots is only observed when 
R^g - 0. A sweep rate of 20 V s'^ is used in these simulations, although 
similar results were obtained at least over the range 1 < »/ < 100 V s'^. 

The remaining conditions in Fig. 5 and 6 are also identical, with - 20 

■ 2 9 

ftF cm , except that the electrode area is taken to be 0.2 and 0.02 cm , 

respectively, in these two figures. Comparable results to those in Figs. 5 

and 6 were also obtained if smaller C^j^ values, in the range 2-20 fiF cm’^, 

were employed. Figure 7 shows such a set of results, obtained for the same 


conditions as in Fig. 6, but with C^jj^ - 2 /iF cm . 

From Fig. 5 we can see that for an electrode area of 0.2 cm a 
significant distinction between a completely reversible reaction [i.e. 
where k®^(true) - *] and that for which k®jj(true) - 1 cm s‘^ is only 
possible for very small R values (< 3 ohm). In other words, the knh(app) 


values are independent of k®jj(true) under these conditions, being virtually 
indistinguishable for larger (Fig. 5), so that no meaningful kinetic 

data can be extracted if k^jj^Ctrue) > 1 cm s . Also evident from Fig. 5 is 
that if is larger than about 10 ohms, no value for k®^(app) could be 

obtained that is larger than about 0.1 cm s"^, a frequently reported value 
(e.g. ref. 9). Furthermore, the avoidance of substantial discrepancies 
between k®^(app) and k®^(true) when the latter approaches 1 cm s'^ requires 
that only extremely small uncompensated resistances be present. For 

example, in order to evaluate a kQjj(true) value of 1 cm s to 50% accuracy 

S “1 

[i.e. to obtain kQjj(app) > 0.5 cm s under these conditions] it is 
required that R^^^ < 2 ohm. 

Comparing Fig. 5 and 6 shows that decreasing the electrode area 

Improves somewhat this unfavorable situation. Thus for an electrode area 

of 0.02 cm (Fig. 6) there is a clear experimental distinction between 
k®b(app) values corresponding to k||j(true) values of ® and 1 cm s’^ (curves 
A and B) even for moderate R^^ values (ca. 20 ohms), indicating that some 
kinetic information would be contained in experimental data gathered under 
these circumstances. Nevertheless, the k®^(app) values in curve B fall 


markedly below kQjj(true) under these conditions, so that the corrections 

necessary to extract the latter from the former are still substantial. The 

s -1 

errors involved in evaluating smaller k^jj(true) values, around 0.1 cm s , 

are relatively small since then k®^(app) - k®|j(true) even for R^g < 40 ohm 

(Fig. 6). This diminished influence of R^g with decreasing electrode area 

is, however, slightly misleading since the effective solution resistance 

will increase under these conditions, yielding probable increases in • 



luence ol 


ance on Rat 


Given that ac voltanunetry, particularly employing phase-selective 
impedance measurements, provides the most common means of evaluating 
other than by using cyclic voltammetry, it is of interest to compare 
quantitatively the extent to which the utility of these two techniques is 
impaired by the presence of uncompensated resistance. There is ample 
reason, however, to expect the nature and extent of the influences of 
upon these two techniques to be significantly different. In the ac 
voltammetric experiment using a stationary electrode, the principal effect 
of is to force the phase of the ac potential waveform across the double 
layer to differ from that applied by the potentiostat, yielding errors in 
the apparent phase angle of the current. While the presence of R^^ also 
forces the magnitude of the ac potential waveform across the double layer 
to differ from that controlled by the potentiostat, this is of little 
consequence since it is generally only the phase angle, rather than the 
magnitude, of the current which is of relevance to the evaluation of 
standard rate constants. 

The error introduced into the evaluation of by ac voltammetry 

therefore depends principally on the combined influence of R^^ and the 
double-layer capacitance, and is diminished with decreasing electrode area 
to the extent that the total capacitance is also decreased. The effects of 
Rus cyclic voltammetry have distinctly different origins, as discussed 
above. Although the extent of the error in evaluating k®^j with cyclic 
voltammetry also decreases with the electrode area, this arises primarily 
as a result of the decreased total current flowing through the cell. 



C ' 

As a consequence, we elected to compare simulated values of kob(aPP) : 

obtained from phase-selective ac impedance as well as cyclic voltammetry by | 


using conventional data analyses for the following three conditions: (a) J 

electrode area A - 0.2 cm^, - 20fiF cm*^; (b) A - 0,02 cm^, - 20nF j 

cm ; (c) A “ 0.02 cm , - 2pF cm The first two cases span the range ] 

of areas commonly encountered with these two techniques, while the second 
and third cases cover the typical range of capacitance values. The ' 

frequency range taken for the ac voltammetric data was between 100 and 500 I 


Hz, the analysis utilizing the frequency dependence of the quadrature to | 


in-phase current ratio, Iq/Ij (see ref. 6b for simulation details). The I 

resulting plots of log versus obtained with ac voltammetry for j 

cases a, b, and c are shown as the dashed curves in Figs. 5, 6, and 7, 

respectively, to be compared with the solid curves in each of these figures 

which (as already noted) show corresponding results obtained with cyclic 

voltammetry. (As noted above, the three log curves in each of 

these figures labeled A, B, and C, refer to log k®^j(true) values of <*>, 1.0 

and 0.1 cm s*^, respectively). 


For the large (0.2 cm ) electrode (Fig. 5), the degree to which 
s s 

kob(®PP) falls below k^^j(true) for a given R^^ value is more marked for ac 

voltammetry than for cyclic voltammetry. In other words, under the 

specific conditions prescribed by these simulations the degree of error 

induced in k®jj(app) by ignoring solution resistance effects, and therefore 

the extent of the corrections required to extract k®j^(true) from k®jj(app), 

is smaller for cyclic voltammetry than for ac voltammetry. However, for 

the smaller (0.02 cm ) electrode having the same double-layer capacitance 

-2 s 

per unit area (20^F cm ), the log kQ^(app) - R^^ curves obtained for the 

two techniques are more comparable (Fig. 6). Moreover, the substitution of 
a smaller double-layer capacitance (Fig. 7) yields slightly superior log 
kob(app) • Ryg curves for ac as compared with cyclic voltammetry (Fig. 7). 

These examples therefore suggest that roughly comparable errors are 
introduced into cyclic and ac voltammetrlc measurements of under 

"typical" conditions in the presence of at least small amounts of 
uncompensated resistance. However, consideration of other factors lead to 
the latter technique being clearly favored for this purpose. Most 
Importantly, it is crucial to minimize the value of the uncompensated 
resistance. This can be achieved relatively readily in the ac experiment 
since a small amplitude waveform having relatively low frequencies (> 2000 
Hz) is employed. In contrast, in the cyclic voltammetric experiment the 
abrupt change in the time derivative of the potential which occurs when the 
scan direction changes is equivalent to the sudden injection of high- 
frequency "noise", which will result in a dampened oscillation ("ringing") 
of the current. The avoidance of severe distortion in the i-E profile for 
the return scan therefore normally requires the presence of significant 
uncompensated resistance (> few ohms). 

In addition, the accurate estimation of for a given level of 

electronic resistance compensation in the ac impedance experiment is 

relatively straightforward, either by evaluating the quadrature and in- 

phase currents at potentials well separated from the ac voltammetric wave 

or by ac measurements in conjunction with a dummy-cell arrangement.^®’^ 

(The same procedures could, of course, be employed to estimate R for a 


given set of experimental conditions, including the resistance compensation 
setting, used in a cyclic voltammetric experiment.) An alternative 

approach to evaluate is to select a redox couple which under the 

measurement conditions employed is known to exhibit k®|j(true) -► «, so that 

the measured response is necessarily dominated by Although this 

method has obvious merits, the selection of such a redox couple requires 

11 12 

careful consideration. ’ In our experience, using a variety of 

potentiostats of commercial and in-house design, it is difficult to either 
measure or minimize even for ac impedance measurements to much less 

than 5 ohms or so in typical nonaqueous media. The corresponding minimum 
Ryg values attainable in cyclic voltammetric experiments are often 
substantially larger. 

Another advantage of the phase-selective impedance approach is that a 
distinction between apparent electrochemical irreversibility brought about 
by the presence of uncompensated resistance rather than by finite electrode 
kinetics can be made by examining the dependence of the (Ip/Ij) ratio upon 
the ac frequency, If the former factor is predominant, then the slope 

of the (Iq/Ij)-w plot will increase with increasing w, rather than be 
independent of w as will be the case when electrode kinetics controls this 
response.This diagnostic situation can be contrasted with the 
inability, noted above, of achieving a ready distinction between the 
dominant presence of R^^ and finite electrode kinetics by varying the sweep 
rate in cyclic voltammetry. 

Some Con siderations for Microelectrodes 

The virtues of employing electrodes of especially small dimensions, 
having radii down to (or below) 1 micron (so-called "microelectrodes" or 
"ultramicroelectrodes") for electrochemical measurements have recently been 
explored extensively, including preliminary applications to electrode 


kinetics.^® The advantage of such a marked diminution in electrode area 

can readily be seen by recalling that while the faradaic current decreases 

with the square of the electrode radius the effective solution resistance 


only increases in inverse proportion to the radius. Clearly, then, in 

the absence of IR compensation the deleterious influence of solution 
resistance will be dramatically reduced by employing micro- rather than 
conventional electrodes. This advantage is, however, offset somewhat by 
the IR compensation that is much more readily applied with larger 

Figure 8 shows illustrative plots of log k®^(app) versus log k®j^(true) 
obtained from simulated cyclic voltammograms for several conditions that 

are typically encountered with microelectrodes. All curves refer to a 

-1 -2 
sweep rate of 1000 V s and a double-layer capacitance of 20 /iF cm . 

(This sweep rate was chosen since comparable values are typically employed 

with microelectrodes and it is sufficiently rapid so to avoid influences 

from spherical diffusion even at the small electrodes considered here.) 

The solid traces A-C refer to an electrode diameter of 1 #ira, having R^^ 

values of 1 X 10^, 7 x 10^, and A x 10^ ohm, respectively. These R^^ 

values correspond to solution specific resistances, p, of 20, 140, and 800 

ohm cm, respectively, obtained from the relation R^ - p/4r where r is the 

radius of a disk electrode, since in the absence of iR compensation R^^ 

will equal the solution resistance R^. These values were chosen since they 

are appropriate for concentrated aqueous electrolytes,^^ and O.liJ 


electrolytes in acetonitrile and dichloroethane, respectively. While 
there is reasonable agreement between k®^(app) and k®^(true) for curves A 
and B at least up to k^^ - 10 cm s , indicating the virtual absence of R^^ 


effects up to this point, for curve C substantial deviations are observed 
even for markedly smaller rate constants. This illustrates the need to 
consider resistive effects when evaluating rapid values even with 
extremely small microelectrodes when relatively high resistance media are 

The solid curves E-F in Fig. 8 are the corresponding plots obtained 
for the same electrolyte (i.e. same p values) and other conditions as in 
curves A-C, but for an electrode diameter of 5 pm. This size is more 
typically employed at the present time in microelectrode experiments 
utilizing cyclic voltammetry.^^ While reasonable concordance between 
k®b(app) and k®^(true) is seen for k®^^ < 10 cm s*^ in the least resistive 
media (curve D), the results obtained for conditions corresponding to 
typical nonaqueous media (curves E and F) are substantially inferior. 
Indeed, the 5 pm electrode in dichloroethane shows that k®jj(app) « 
k®b(true) at least for k®^(true) > 1 cm s*^; i.e. the AEp values are 
determined almost entirely by solution resistance effects under these 

Figure 8 also contains a comparative log k®^(app) - log k®^(true) 
trace obtained for the conditions of curve E, but utilizing ac rather than 
cyclic voltammetry in the fashion prescribed above (dashed trace). As for 
the behavior noted above for the larger size electrodes, the influence of 
solution resistance upon the ac and cyclic voltammetric response is seen to 
be similar. Comparable behavior was also obtained for the other conditions 
considered in Fig. 8. 

The foregoing considerations demonstrate that the deleterious 
influence of uncompensated solution resistance imposes a severe and 

















sometimes unexpected limitation on the magnitude of standard rate constants 
that can be evaluated by means of cyclic voltammetry. In order to extract 
meaningful values using this technique, it is clearly imperative to 

obtain reliable estimates of for the measurement conditions employed, 
and to demonstrate that is sufficiently small so that 

approximates k®^(true). The observation of k®^(app) values that approach 
the limiting value dictated by the known uncompensated resistance; i.e. 
those corresponding to k®^(true) -► *, provides a clear signal that the 
desired electrode kinetics are not measurable under the conditions 
employed. Given a reliable knowledge of R^g, desired k^^^Ctrue) values can 
still be evaluated in the intermediate case of partial kinetic-resistive 
control from the k^^^Capp) values by using the appropriate k®^(app)- 

kQ^(true) relation extracted from digital simulations. 

Although the extent of the systematic errors in k^^^Capp) values 

obtained by cyclic and ac voltammetry are surprisingly comparable for 
typical R^g values, the latter technique would seem to exhibit clear 
advantages for the evaluation of fast electrode kinetics under most 
conditions. This stems both from the ability to better minimize and 

evaluate R^^ with ac impedance measurements, and from the diagnosis of 

dominant resistive effects from the observation of nonlinear (Ip/Ij) - 


As has already been well documented,^® the use of cyclic voltammetry 
with microelectrodes offers real advantages for evaluating standard rate 
constants. However, even under these conditions the influence of cell 
resistance can provide a serious Impediment to the evaluation of k®^ values 
greatly in excess of 1 cm s*^, especially for high resistance media and in 

the absence of IR compensation. It therefore would appear that values 

evaluated by any of these approaches, especially for moderately fast 
s *1 

reactions > 0.1 cm s ) should be regarded with some skepticism in the 

absence of due consideration of solution resistance effects by the 


This work is supported by the Office of Naval Research. 



1. (a) R. S. Nicholson, Anal. Chem. , 12 (1965), 1351; (b) R. S. 

Nicholson and I. Shain, Anal. Chem., 2^ (1964), 706. 

2. (a) J. M. Saveant and D. Tessier, J. Electroanal. Chem., S5 (1975), 

57; (b) J. M. Saveant and D. Tessier, J. Electroanal. Chem., 21 

(1977), 225; (c) K. B. Oldham, J. Electroanal. Chem., 21 (1976), 371; 

(d) P. E. Whitson, H. W. VandenBoren, and D. H. Evans, Anal. Chem., 4^ 
(1973), 1298; (e) B. Aalstad and V. D. Parker, J. Electroanal. Chem., 
122 (1981), 183; (f) B. Speiser, Anal. Chem., 57 (1985), 1390. 

3. S. W. Feldberg, in "Electroanalytical Chemistry - A Series of 

Advances", A. J. Bard, ed., M. Dekker, New York, Vol. 3, 1969, p. 199. 

4. (a) R. S. Nicholson, Anal. Chem., 21 (1965), 667; (b) W. T. DeVries 

and E. VanDalen, J. Electroanal. Chem., (1965), 183. 

5. (a) D. Garreau and J.-M. Saveant, J. Electroanal. Chem., Si (1978), 

63; (b) D. F. Milner, Ph.D. thesis, Purdue University, 1987. 

6. (a) D. F. Milner and M. J. Weaver, J. Electroanal. Chem., in press; 
(b) D. F. Milner and M. J. Weaver, J. Electroanal. Chem., 191 (1985), 

7. D. A. Corrigan and D. H. Evans, J. Electroanal. Chem., 106 (1980), 


8. V. D. Parker, "Electroanalytical Chemistry - A Series of Advances", A. 
J. Bard, ed., Vol. 14, M. Dekker, New York, 1986, p. 1. 

9. K. M. Radish, J. Q. Ding and T. Mallnskl, Anal. Chem., SS (1984), 


10. (a) J. 0. Howell and R. M. Wightman, Anal. Chem., SS (1984), 524; (b) 
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Chem., 20. (1986), 2911. 


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14. J. F. Chambers, J. Phys. Chem., 6Z (1958), 1136. 













Fife. 1 

Comparison between a simulated current-potential curve for a linear- 

sweep voltammogram (A) and the corresponding time derivative of the 

potential across the double layer, dE^^/dt (B). Simulation conditions are: 


reactant concentration - ImM; electrode area A - 0.2 cm , diffusion 

coefficient D — 1 x 10'^ cm s*^; sweep rate i/ - 100 V s*^, uncompensated 


resistance - 50 0, double-layer capacitance, — 20 /iF cm , true 

standard rate constant, k®^(true) - ®. 


Illustrative comparison of the simulated effects of uncompensated 
solution resistance and finite electrode kinetics on cyclic voltammograms. 
Solid trace is for - ImH, j/ - 20 V s*^, - 0, D - 1 x 10'^ cm s‘^, 

2 s .1 

A - 0.2 cm , - 0, and k^^Ctrue) - 0.04 cm s Squares are obtained 

for the same conditions, but for R^^^ - 50 fl and k®jj(true) - ®. 

F-U. ? 

Illustrative comparison of the simulated effects of uncompensated 
solution resistance (squares) and finite electrode kinetics (solid trace) 
on cyclic voltammetric potential peak separations, dEp, as a function of 
sweep rate, u. Simulation conditions as in Fig. 2. 


ru. ^ 

Dependence of cyclic voltammetric potential peak separation, AEpi upon 
reactant concentration in the presence of uncompensated solution 

resistance, values are A, 50 fl; B, 20 0; C, 5 n. Other 

s 19 

simulation conditions are: (true) - «o, i/ - 20 V s , - 20 /iF cm , 

D - 1 X 10"^ cm^ s'^, A - 0.2 cm^. 

I1&, ? 

Plots of log k®^(app), where k®^(app) is the "apparent" rate constant 
extracted from simulated cyclic voltammograms (solid traces) or ac 
voltammograms (dashed traces) assuming R^^ — 0, against R^^ for various 
values of the actual ("true") rate constant, k®^(true). Curves A, B, and C 
are for kQ^j(true) - «, 1, and 0.1 cm s* , respectively. Other simulation 
conditions are - ImJI, - 20 ptF cm*^, A - 0.2 cm^, D - 1 x 10’^ cm^ 
s The cyclic voltammetric sweep rate is 20 V s'^, and the ac impedance 
data are for frequencies between 100 and 500 Hz (see text for further 

Fts. ^ 

As for Fig. 5, but for an electrode area, A, of 0.02 cm^. 

E1&, 7 

As for Fig. 6, but for a double-layer capacitance, of 2 /iF cm*^. 

Fig. 8 





















5 i 



Illustrative relationships between k®^(app) and k®^(true) for some 
typical conditions encountered with cyclic voltammetry using 
microelectrodes. Curves A-C and D-F are for 1.0 and 5 fim diameter 
electrodes, respectively. Key to solution resistance conditions: A, 
Rys - 10^ n (p - 20 n cm); B, - 7 x 10^ 0 (p - 140 0 cm) ; C, - 
4 X 10^ O (p - 800 n cm): D, R,^ - 2 x 10^ 0 (p - 20 0 cm); E, R.^ - 10^ n 
(p - 140 n cm); F, R^^ - 7 x 10^ 0 (p - 800 n cm). Other simulation 
conditions are - ImM, u - 1000 V s*^, - 20 pF cm'^, D - 1 x 10'^ cm^ 
s The dashed curve is from a simulation corresponding to curve E, but 
obtained for ac impedance data taken between ac frequencies of 100-500 Hz. 




l^jL m