Anal. Chem. 1992, 64,1127-1131 Elliott, D. J. Integrated Ckcult Fabrfcetfon Technology; McGraw-HIII: New York, 1982. Elliot, D. J. MMkkgraphy; McGraw-Hill: New York, 1986. Sharlfi, F. Ph.D.Thesis, University of Illinois at Urbana-Champaign,
1989. W n , Q. J. ~ p p i mys. . Len. isrr, 31, 337. Frltsch-Faules, I.Ph.D. Thesis, University of Illinois at UrbanaChampaign. WQO. Anderson, L. 0.; Reiliy, C. N. J. Electrmnal. Chem. Interfachi Elecfrochem. 1065, 10, 295. Feldberg, S.W.; Rublnsteln, I. J . Electraenal. Chem. InferfaclalElecbochem. 1988. 240, 1.
1127
(34) Zhang, X.; Leddy, J.; Bard, A. J. J . Am. Chem. Soc. 1985, 107, 3719. (35) Shigehara, K.; Oyama, N.; Anson, F. C. J . Am. Chem. Soc. 1981, 103, 2552. (38) Kulesza, P. J.; Faszynska, M. €/ectrochim. Acta 1989, 34, 1749. (37) Penner, R. M.; Van Dyke, L. S.; Martin, C. R. J . phvs. Chem. 1988, 92, 5274.
for review
24, lgg2* Accepted
7, 1992.
Relationships between Measured Potential and Concentrations of Redox Centers in Polymer Networks Ingrid Fritscb-Faules and Larry R. Faulkner*
Department of Chemistry, University of Illinois, 1209 West California Street, Urbana, Illinois 61801
We have shown that a nernrtlan relationship exlsts between
the comentratkrw, C,of fed- (0) and ferrocyanide (R) and the applied potentlal in thin films of methylquatemizedpdy(4-vinylpyrklh) (OPVP) on d.Ctrode8 In aqueorw KNO, and potassium p-toiuenewlfonate (KOTs) electrolytes. Plots of E Eo' versus in (CdC,) cioseiy foikw expected nenwtlan behavior (ideally, dope = 25.5 mV and intercept = 0 mV at 22 "C). For the KNO, system,the observed slope was 26.4 f 0.3 mV and the Intercept was 3.6 f 0.14 mV. For the KOTs system,the cdope was 29.3 f 0.3 mV and the intercept was 7.8 f 0.11 mV. The nearfy nernstlan behavlor k somewhat wrprlrlng, considering the complex dynamics and thmnodyrwnics of QpVP/Fe(cN),~'c/c,where (a) both f m of the rodox coupb parlttion to Merent extents between f i h and rdutlon, (b) the mass transport In the film Is oxidationstate dopendent, and (c) the full-wknhs at haif maxlmum of peaks in cyclk voitammetry are greater than the nernstian responm of 89.7 mV. Callbration curves in the form of CdCo,- or CdCo,- versus E - Eo' allow us to convert the potontld p r d h In our companion pcrper to concentration profhs. Here CO,nurIs the maximum (equiilbrium) concentration of 0 at € - Eo' = +300 mV. Llkewb, CR,- Is the eqMbdum concentration of R at a strongly reducing potential ( € - Eo' = -300 mV). Concentratlons of 0 and R were determined by preconditioning the flhn for 1 h at a glven potential, folkwed with kng-pukswldth (20 000-32 000 ms) chn"ary (LPCC) featuring a step to either -300 mV or +300 mV M P O ' , wpectively. Experiments were carried out at 50-pm X 2" electrodes with the experimental arrangement described in the companion paper. The ratlo of ConuJCR- Is 0.44 tor KNO, Md 0.37 fOr KOTS electrolytes, suggesting that tho partitioning Is almost independent of the ldontfty of the electrolyte.
-
INTRODUCTION In the preceding companion paper,l we have shown that potential measurements a t a microelectrode array can probe the spatial distribution of electrochemically-generatedredox species within a polymer film. The experimental system
* To whom correspondence should be addressed. 0003-2700/92/0384-1127$03.00/0
involved electrostatically-bound ferri- and ferrocyanide (Fe(CN)63-/4-)in cross-linked methyl-quaternized poly(6vinylpyridine) (QPVP). In this paper, we report conversion of the potential measurements into redox center concentrationsusing calibration curves that were obtained experimentally with long-pulse-width chronocoulometry (LPCC). For a homogeneous, reversible redox system
uoO + ne- a uRR
(1)
the relationship between the potential and the concentrations of oxidized and reduced species is the Nernst equation2
where Eo is the standard potential of the couple, (0) and (R) are the activities, Co and C R are the concentrations, vo and U R are the stoichiometric coefficients, and yo and Y R are the activity coefficients for the oxidized and reduced species, respectively. Since the formal potential Eo' = Eo + (RT/nFj In (yoYo/yR~), eq 2 becomes
(3) If the relationship between E and Co or CRis nernstian, and if variations in activity coefficients are negligible, one can plot E - Eo' vs In (Co/Cd (YO = vR = 1 in our case) and obtain a straight line with an intercept of zero and a slope of RT/(nF) (= 25.5/n mV a t 22 "C). Polymer-modified electrode systems are not prone to ideal behavior. Although the electron exchange a t the electrode/solution interface may be very fast: there is usually a decrease in heterogeneous rate for a redox couple when incorporated in a confining polymer film; thus, a nernstian equilibrium may be difficult to establish. Possible causes include partial blocking of the electrode4 or an increase in electron-transfer activation energy. Interactions between electroactive species can also cause variations in activity coefficients as concentrations change in the film.6 QPVP/Fe(CN)63-/4-systems, in particular, demonstrate variable dynamic behavior,- some aspects of which can be explained by the partitioning of the oxidized and reduced species between the f ilm and electrolyte solution. Partitioning directly affects film concentrations and fluidity and is influenced by the concentration of redox centers in the electrolyte 0 1992 American Chemical Society
1128
ANALYTICAL CHEMISTRY, VOL. 64, NO. 10, MAY 15, 1992
Table I. Cyclic Voltammetry in 0.1 M KN03" experiment CV (100 mV/s) CV (5 mV/s)
i,/pA
E,,/mV
E,,/mV
AEfmV
Eo'/mV
iw/pA
130 f 3 142 f 1
181 f 3 175 f 3
52 f 2 32 f 2
156 f 2 159 f 2
2.82 f 0.06 0.18 f 0.01
2.82 f 0.07 0.14 f 0.01
FWHMJmV
FWHMJmV
126 f 1 112 f 4
106 f 1.4 108 f 5
Experiments were performed on the 50-pm electrode of an electrode array. The averages and standard deviations were determined from measurements made three times over 4.5 h at both flanking electrodes. Subscripts a and c refer to anodic and cathodic responses, respectively. Measurements are not normalized to the area of the electrode. Table 11. Chronocoulometry in 0.1 M KN03n experiment CC (250 ms) CC (32000 ms)
slope,/(pCfms1/2) 0.213 f 0.007 0.014 f 0.001
slope,/(pC/ms1/2)
intercept,/&
intercept,/&
0.380 f 0.019 0.014 f 0.001
-0.399 f 0.031 3.76 i 0.124
-1.399 f 0.098 3.11 f 0.206
Note a of Table I also applies in this instance. Slopes and intercepts were obtained from Anson plots. and the relative ratios of the two forms of the redox couple. For this system, it is essential to evaluate experimentally the relationship between concentration and potential and to compare it to the ideal nernstian relationship. The calibration curves were obtained at QPVP/Fe(CN)63-/4--coated,individually addressable, 50-pm X 2-mm electrodes. These electrodes are elements of the microelectrode arrays that were used to determine potential profiles in the preceding companion paper.' They were chosen for two reasons: (1)they exhibit simple thin-layer electrochemical behavior and (2) the electrochemical setup and conditions are the same as those in the potential profile experiments. Stepping to either -300 mV or +300 mV using LPCC after preconditioning a t a given potential allowed independent determination of the equilibrium concentrations of both 0 and R in the f i . LPCC was not performed on the inner 4-pm array electrodes because lateral diffusion of charge to their edges complicates the accurate determination of redox center concentrations.1° This paper focuses on the following points. First, the aging, transport, and partitioning characteristics of the redox/ polymer film are shown to be consistent with other work on this system in the literature. Second, we reveal the importance of preconditioning the redox/polymer at a given potential for times as great at 1h, so that we could reproducibly quantify ferri- and ferrocyanide in the film. Third, we demonstrate that the behavior in both KN03 and KOTs electrolytes is strongly affected by the differences in partitioning of the two redox forms between film and solution. Finally, we construct calibration curves linking potential to Co and CR from the LPCC data, and we show that they follow nernstian behavior.
EXPERIMENTAL SECTION Materials and Electrodes. Methyl-quaternized poly(4vinylpyridine)(QPVP)and potassium p-toluenesulfonate (KOTs) were prepared as described previously.' Reagent-grade K3Fe(CN), (J. T. Baker), KNO, (J. T. Baker), and a,a'-dibromo-m-xylene (97 % purity, Aldrich) were used without further purification. All aqueous solutions were prepared from water treated with a Milli-Q Water Purification System (Millipore). The electrochemical results presented in this paper were obtained with the 50-pm X 2-mm band electrodes flanking the microelectrode arrays whose fabrication was described in the companion paper.' Preparation of Fe(CN),*-loaded QPVP films and dry film thickness measurements were also described in the companion paper. Electrochemical Experiments. The support electrolyte, 0.1 M KNOBor 0.1 M KOTs in Milli-Q water, was purged with Nz for at least 15 min prior to use, and then an atmosphere of Nz was maintained over the electrochemical cell throughout the experiments. Reference electrodeswere Ag/AgCl, saturated KCl. The counter electrode was a Pt wire, sheathed with a glass tube that was fitted with a Vycor frit. Electrical contact to the working
electrodes was made with edge connectors. The electrochemistry was performed with a BioanalyticalSystems BAS-100A cybernetic potentiostat. Measures were not taken to control the temperature of the electrolyte, so the temperature was assumed to be that of the laboratory, -22 "C. Typical electrochemical behavior is discussed in ref 1. In this work, cyclic voltammetry (CV) was used to characterize film behavior and to determine formal potentials. Shortpulse-width (250 ms) chronocoulometry (CC) was then used to determine diffusion coefficientsfor ferricyanide (DO) in fully oxidized films. Before each of these film-characterizingexperiments,the modified electrodeswere preconditioned at +300 mV vs E"' with quiet times as long as 5 min. LPCC (20000-32000-mspulse width) was used to determine concentrations of 0 and R in the film at different potentials, and calibration curves were derived from these data. It was neceasary to preconditionthe films at each potential for 1h. As shown later, electrochemical preconditioning of QPVP/Fe(CN)6s/4- has a significant influence on subsequent electrochemicalexperiments. The duration of the preconditioning with active control of potential is called the quiet time. In order to quantify 0 and R in the film over the electrodes, the potential was stepped to either -300 mV vs E"', where 0 is completely reduced, or +300 mV vs E"' where R is completely oxidized. The current was integrated to obtain the charge Qo or QR. A 20 000-ms to 32 000-ms pulse width was sufficient time for the diffusion layer to reach the film boundary, at which time the electrochemical current to 0 or R falls off. Anson plots (Q vs t'I2) of the data give intercepts that yield QOor QP Double layer charging was negligible with respect to Qo and QR. (Compare intercepts from short-pulse-width CC and LPCC in Tables I and 11.) &or bars reported in this paper represent single standard deviations.
RESULTS AND DISCUSSION QPVP/Fe(CN),"/4- in KNOSElectrolyte. Equilibration and Film Characterization. Bruns' has demonstrated "aging" of QPVP/Fe(CN)6s films when they are initially placed in fresh electrolyte. He attributes the phenomenon, which manifests itself as a slow increase in the diffusivity of the redox species, to the equilibrium of redox species between the film and the solution and to long-term changes in solvation and structure of the film. Tables I and I1 list the averages and standard deviations of measurements from CV and CC experiments at the 50-pm electrodes of an array coated with &PVP/Fe(CN)63-/4-. The first set of measurements, taken immediately after setting up the cell, was similar to the last set. The small standard deviations in the tables indicate little variation in film characteristics over this period, hence we conclude that the electrochemicalassembly equilibrates during the initial setup time (45 min). The measurements in Tables I and I1 are representative of the QPVP/Fe(CN)63-/4-system and are consistent with reports in the literat~re."~Several aspecta of the system have already been described in the companion paper.' These include the formal potential ( ~ 1 5 mV) 8 and peak splitting from
ANALYTICAL CHEMISTRY, VOL. 64, NO. 10, MAY 15, 1992
CV experiments, as well as diffusion coefficients, Drb, and concentrations, Co and CR, of redox species in the film, as obtained from slopes and intercepts of Anson plots of CC and LPCC data. Of more relevance here are the full widths at half maximum (FWHM) of the CV peaks because they can be an indicator of kinetic and thermodynamic behavior. The full width at half maximum (FWHM) was 126 mV for the cathodic peak and 106 mV for the anodic peak a t 100 mV/s, or =110 mV for either peak at 5 mV/s scan rate. The peaks were clearly broader than for a nernstian system (89.7 mV). Such broadening might be attributed to a repulsive interaction of redox a distribution of Eo' valuesll of redox species in different microenvironments, or a variation in activity coefficientswith oxidation state.% The scan rate dependence of FWHM may be attributable to potential-dependent partitioning of 0 and R between film and solution or to slow kinetics of charge transport and reequilibration. Partitioning of Fe(CN),S-and Fe(CN)t-. The reduced and oxidized forms of the redox couple partition into the QPVP to different extents. Doblhofer and co-worker@ have observed Co/CR ratios as high as lo4. This unequal partitioning affects the response to slow potential sweeps (e.g. at 5 mV/s in Table I) so that one obtains a ratio of anodic and cathodic peak heights of less than one. Doblhofer and coworkers suggest that the slower scan rates allow the film time to become solvated at negative potentials, when a large amount of the reduced form leaves the film. The reverse scan recollects charge only from the reduced species that remain in the f i . At fast scan rates, the magnitudes of the forward and reverse peaks are similar. Since there is not enough time for complete reequilibration, the reverse scan recollects charge from most of the redox species.sd It has been proposed that the reduced species exhibits a smaller portion coefficient because it is more strongly solvated than the oxidized species, and because it forms an ion pair with K+. We found that the concentration of Fe(CN)z- in the film would increase when the electrode was left a t open circuit for a few minutes and especially when it was held a t oxidizing potentials. Thus, upon equilibration, a "maintenance" concentration had developed, whose source of redox centers is the film. Since the electrochemistry at the 50-pm electrode perturbs only a very small fraction of the entire film, there is a large supply of Fe(CN),3- from the surrounding polymer. Variations in Quiet Time. Figure 1shows the values of Qo and QR obtained from LPCC on a single QPVP/Fe(CN)63-I4-system in 0.1 M KNOB. In sequential experiments, the preconditioning potentials were alternated between +300 mV and -300 mV vs Eo' with increasing quiet times a t oxidizing (Figure la) and reducing (Figure l b ) potentials. The figure shows the dependence of Q on quiet time. Figure l a demonstrates a "reloading" phenomenon that occurs at oxidizing potentials. A significant decrease in the concentration of redox sites occurs whenever the electrode is held at negative potentials, as shown in Figure lb. When an oxidizing potential is applied subsequently, the portion of the film above the electrode regains redox centers from the solution or surrounding portions of the film. A 1-h quiet time was sufficient to restore equilibrium; hence, this quiet time preceded all LPCC experiments that were used to establish calibration curves. Concentration vs Potential. It was evident from the effects of the quiet times that the oxidized and reduced forms of the couple partition to different extents and at different rates into the QPVP polymer film. Since it takes longer for the film to reach an equilibrium concentration of Fe(CN)zthan of Fe(CN)e6 (see Figure l), the following procedure was developed to maximize the time for which the electrode was held in the oxidized state. To obtain Qo at different potentials,
2
4
6
8
10
12
14
16
1129
18
Experiment Number 3.2 -1
U 0 0.81
-
I
2
4
-
I
6
'
8
I
10
'
I
12
'
14
I
~
16
I
~
I
~
18
Experiment Number Figure 1. Effects of variation in quiet time on an LPCC determination of Qo and QRin a QPVP/Fe(CN)es'C film in 0.1 M KNO,; (0)collection of the 0 species, while stepping from E - Eo' = +300 to -300 mV; (a)collection of the R species while stepping from E - Eo' = -300 to +300 mV. (a) Quiet times are varied for the electrode heM at oxidizing potentials. (b) Quiet times are varied for the electrode held at reducing potentials.
a sequence of LPCC was performed, in the following order, where the potentials during quiet time were held at +300, +25, +0, -25, -50, -75, -100, -200 mV +200, +100, +75, +a, relative to Eo' and stepped to -300 mV vs E O ' . To determine Q R at different potentials, a sequence of LPCC experiments was performed, in the following order, where the potentials during quiet time were held a t +200, +loo, +75, +50, +25, +0, -25, -50, -75, -100, -200, -300 mV vs Eo' and stepped to +300 mV vs E O ' . The resulting data are represented in calibration curves that are displayed in two ways in Figure 2. The calibration curve of Figure 2b, where E -Eo' is plotted vs In (Co/CR), demonstrates behavior that is very close to nernstian. A linear fit to the data (correlation coefficient = 0.9994) using the relationship in eq 3 gave a slope of 26.4 f 0.3 mV. This is slightly higher than the ideal slope, RT/(nF) = 25.5 mV, where T = 22 "C and n = 1. The intercept, which should be 0 for the ideal case, is actually 3.6 f 0.14 mV. Another representation of the calibration curves is shown in Figure 2a. These curves allow a straightforward conversion of measured potentials into concentrations of redox species. It was desirable to generalize the calibration curves, so that they were less dependent on variations in loading of redox centers and in film thickness from sample to sample. The ratio of the maximum concentration of 0 in the f i , Cow, defied a t +300 mV vs E O ' , to that of R, CR,", defined a t -300 mV vs E O ' , was fairly reproducible despite variations in the extent of loading. Thus, concentrations of 0 and R, Co and CR,were normalized to C0,- to give C0/CoFm and CR/CO,". These ratios are equal to the ratios of the measured variables, QO/QO,max and QR/QO,max,and are independent of film thickness. Figure 2a is based on this convention and shows the ratios as a function of E - E"'. Based on dry f i i thickneas (ca. 5000 A), CO,marand CR," are typically 0.82 and 0.36 M when KNOBis used as the external electrolyte. For KOTs electrolyte, the corresponding values are 0.78 and 0.29 M. In the actual conversions of potential profiles into concentration profiles in the companion paper, we used calibration curves for which R was normalized to CR,", not CO,". The
~
1130
ANALYTICAL CHEMISTRY, VOL. 64, NO. 10, MAY 15, 1992
Table 111. Cyclic Voltammetry in 0.1 M KOTs" experiment CV (100mV/s) CV (5 mV/s)
E,/mV
E,,/mV
AE/mV
Eo'/mV
&/PA
i,/pA
95.9 f 5 126 f 1.5
169 f 1.5 152 f 2
72 f 5 25 f 1
133 f 4 139 f 2
2.58 f 0.37 0.15 f 0.03
FWHMJmV
FWHM,/ mV
129 f 0.8 104 f 1.2
124 f 2.8 105 f 4
2.34 f 0.29 0.11 f 0.02
Experiments were performed on the 50-pm electrodes of an electrode array. The averages and standard deviations were determined from three different sets of measurements made on the same film at both flanking electrodes over 2 days. Subscripts a and c refer to anodic and cathodic responses, respectively. Measurements are not normalized to the area of the electrode. Table IV. Chronocoulometry in 0.1 M KOTs" experiment
slope,/(pC/ms1/2)
slope,/(pC/ms1/2)
intercept,/pC
intercept,/pC
CC (250ms) CC (20000ms)
0.129 f 0.009 0.007 f 0.001
0.140f 0.019 0.010f 0.001
-0.356 f 0.033 3.63 f 0.26
-0.422 f 0.028 2.77 f 0.15
Note a of Table I11 also applies in this instance. Slopes and intercepts were obtained from Anson plots.
advantage of this approach is that it is independent of the from sample to samsmall variance of the ratio cO-/cRple. The representation used in Figure 2a, however, better illustrates the differential partitioning of 0 and R for our purposes here. Rearrangement of eq 3 generates equations that allow one to fit curves to the data in Figure 2a. Let cR/cO,m, = b bC,-,/CO,mal, where b is a fitting parameter that equals C-/Cow if the system is nernstian. Also, let a be another fitting parameter that equals nF/(RT) when the system is in eq 3 nernstian. Substituting CR = Co,-(b - bCo/C,,) and solving for Co/Co,maxyields b exp(a(E - E O ' ) ) (4) c ~ / c ~ w1 = b exp(a(E - E O ' ) )
J--
d
.
0
0.2
0
0 0.0 -300
-100
-io0
E
+
0
100
200
- E"' / mV
300
A similar equation is obtained for CR/CO,max:
To better understand how this relation works, let b = 0.44, which is a typical experimental value for the KNOBsystem. Then, when the electrode is held at a very reducing potential (E - Eo' is large in the negative direction), COlCo- = 0, CR - CR,", and CR/CO,m, = 0.44. When the electrode is held at a very oxidizing potential, CR/CO-, = 0, CO = CO,-, and CO/CO,max = 1. The curves that were fit to the data are the solid lines in Figure 2a. The a and b parameters are given in the f i i e for both the oxidized and reduced species. The purpose in fitting the curves is mainly to create an equation from which concentration profiles can be generated easily from potentials. However, it is of value to recognize that the a parameters for both curves in Figure 2a are close to, but less than, the nernstian value (0.0392 mV-'). The b parameters for both curves are similar to each other and correlate well with the typical value 0.44. QPVP/Fe(CN)63-/4- in KOTs Electrolyte. Film Characteristics. Since anions have a strong effect on the internal structure of QPVP, as shown by Oh and Faulkner? we investigated the concentration-potential relationship in KOTs supporting electrolyte, which dehydrates and compacts the film relative to the case in KNOBsolution. The usual CV and CC characterization experiments were performed on the QPVP/Fe(CN),*/' system in 0.1 M KOTs, and Table 111 and IV list typical results. The values remained constant, even after extensive electrochemical experimentation. Several differences between the KNOBand KOTs systems were observed, especially in Eo' (e136 mV), AEp, and D o s , . These characteristics are futher described in the companion paper.' The FWHMs in the KOTs system, especially for the
-4
-3
-2
-1
0
1
2
3
4
In (COICR) Figure 2. Two representations of a calibration curve determined by LPCC with quiet times of 1 h at a 5 0 - ~ melectrode coated with QPVP/F@CN)B""- in 0.1 M KNOS.
reduction of Fe(CN)6* (126 mv), were consistently larger than nernstian at both 100 and 5 mV/s. Concentration vs Potential. The calibration curves obtained for the QPVP/Fe(CN)6S-/4-film in 0.1 M KOTs are shown in Figure 3. The conditioning period prior to quantifying species in the film was the same as that used for the KNOBsystem. Differential partitioning of the redox forms is involved in the KOTs system, just as in KN03. Figure 3b demonstrates a nearly nernstian relationship between the potential and concentrationfor the KOTs system. The intercept is 7.8 0.11 mV and the slope is 29.3 f 0.26 mV, with a correlation coefficient of 0.9976. The data indicate the KOTs system is slightly less ideal than the KNOBsystem. This small contrast with the KNOBsystem is reflected in the a and b curve fitting parameters in Figure 3a, as well, where a is similar to the ideal value of 0.0392 mV-' (at 22 OC) and b correlates well with the experimental ratios of C-/Coof 0.37. In contrast, b = 0.44 in the KN03 system. The partitioning behavior, reflected by the b parameter, appears
*
ANALYTICAL CHEMISTRY, VOL. 64, NO. 10, MAY 15, 1992
-
a 0.034,b = 0.27
a
0 0.6
b
-3bo
-io0
-100
E
0
100
200
- Eo'I mV
300
1191
temd3 and describe their behavior in terms of capacity factors (for example, as the ratio of amounta of species in the solid and liquid phases). We have incorporated such ideas into digital simulations that illustrate the impact of capacity factors on the linearity of concentration profiles in systems such as QPVP/Fe(CN)63-/4-.14 ACKNOWLEDGMENT We are grateful to the National Science Foundation, the Division of Analytical Chemistry of the American Chemical Society, and the Procter and Gamble Co. for graduate fellowships to I.F.F. The support of the National Science Foundation for research costa under Grant CHE-86-07984is also acknowledged. Registry No. QPVP, 103747-18-8; KOTe, 16106-44-8;KN03, 7757-79-1; ferricyanide, 13408-62-3;ferrocyanide, 13408-63-4. REFERENCES
-
h
0
* w -4 -80 -120 -4
-3
-2
iA (cO0 I cR)1
2
3
4
Flgwe 9. Two representations of a calibration curve determined by LPCC wlth quiet times of 1 h at a 50-pm electrode coated wlth QPVPIFe(CN)B""- in 0.1 M KOTs.
to be the greatest difference in equilibrium behavior between the two systems. Overall, however, there is a strong resemblance between calibration curves, indicating that the electrolyte-induced structural changes do not greatly affect the relationship between applied potential and concentrations of 0 and R. CONCLUSIONS Our data support a nernstian model for equilibrium behavior in the QPVP/Fe(CN)63-/4-system, in spite of ita potential-dependent partitioning, oxidation-state-dependent diffusioncoefficients, and non-nemstian dynamics as reflected in full widths at half maximum. LPCC provides facile experimental determination of potential-concentration dependences. The calibration curves of CO/COSmsl and CR/CO,as functions of E - Eo' were obtained with remarkable reproducibility, and these curves are readily used to convert potential profiles to concentrations.' Separation science has placed much effort toward understanding partitioning of species among different p h s . 1 2 One may apply such theory to these electrostatically-bound sys-
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RECEIVED for review January 24,1992. Accepted February 7, 1992.
