Anal. Chem. 1994,66, 1560-1565
Reversible Voltammetric Response of Electrodes Coated with Permselective Redox Films Jody Redepennlng,' Benjamin R. Mlller,t and Sandra Burnham* Department of Chemistty, Universiw of Nebraska, Lincoln, Nebraska 68588-0304
Experimental and calculated cyclic voltammograms are compared for electrodes modified with thin films of permselective ion exchangers in which the exchange sites are covalently attached redox sites. The voltammograms are considered in the thin-layer limit in which mass transfer does not limit the current response. Additionally, it is assumed that neither the rate of heterogeneous electron transfer at the electrode-film interface nor the rate of homogeneous electron transfer in the bulk of the film limit the current. Under these circumstances, changes in the charge on the polymer backbone change the Donnan potential at the film-solution interface to produce broadened, asymmetrical voltammograms. Shifts in the a p parent formal potentials for permselective redox films are also predicted if the activity of the counterion in the bathing electrolyte solution changes. Good agreement between the permserective model and experiment is obtained for the shape of the voltammograms. Once changing liquid junction potentials and changing activity coefficients in solution taken into account, good agreement is also obtained for the shifts in the apparent formal potentials. It has been recognized since the early 1960s that the contribution of diffusional mass transport to a voltammetric current response can be neglected when the thickness of an electrochemical cell is much less than the thickness of the diffusion layer.'" A greatly simplifiedcurrent-potential curve results. It was recognized during the 1970s that cyclic voltammetry for reversible redox couples immobilized on electrodesurfacescan bemodeled by assuming that theactivities of the oxidized and reduced species are proportional to their surface Equations similar to those that describe cyclic voltammetry for redox couples in thin-layer cells result. In both models peak currents are proportional to the potential sweep rate, there is no separation between the anodic and cathodic peaks of the same redox couple, and the full width of the wave at half-maximum (Efwhm) is 90.6 mV for a oneelectron process. A large number of systems involving immobilized redox couples do not give current-potential curves + Present address: Scripps Institute of Oceanography, University of California, La Jolla, CA 92037. t Present address: Department of Chemistry, Standford University, Stanford, CA 94305. (1) Schmidt, E.; Gygax, H. R. Chimia 1962, 16, 156. (2) Sluyters, J. H. Recl. Trau. Chim. Pays-Bas 1963, 82, 100. (3) Christensen, C. R.; Anson, F. C. Anal. Chem. 1963, 35, 205. (4) Reilley, C. N. Pure Appl. Chem. 1968, 18, 137. (5) Hubbard. A. T.; Anson, F. C. ElectroanaL Chem. 1970.4, 129. (6) Hubbard, A. T. CRC Crif.Rev. Anal. Chem. 1973, 2, 201. (7) Lane, R. F.; Hubbard, A. T. J. Phys. Chem. 1973, 77, 1401. (8) (a) Laviron, E. J. Electroanal. Chem. 1974, 52, 355. (b) Laviron, E. J. Electroanal. Chem. 1974,52,395.(c) Laviron, E. J . Electroanal. Chem. 1979, 100, 263. (9) Angerstein-Kozlowska, H.; J. Klinger; Conway, B. E. J. Electroanal. Chem. 1977, 75, 45.
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that are consistent with that expected from the simple model. Consequently, more sophisticated models for describing the current-potential curves of redox species immobilized on electrode surfaces have appeared.*-1° These models attempt to account for site-site interactions that change as the overall oxidation state of the immobilized layer changes. Currentpotential curves exhibiting Efwhm greater than or less than 90.6 mV can result, depending on the nature of theinteractions. Similar behavior is expected for thin polymeric films on electrodes, and interaction parameters that depend on the concentration of redox sites can be used to achieve particularly good fits toexperimental data.' For moredetailed discussions of models developed prior to 1984 for surface waves, sections of a review article12 and sections of a textbook are recommended.'3 There is also work in recent literature that contributes to the present understanding of voltammetric surface waves. In 1985, Gerischer and Scherson described how the electric field at an electrode interface may interact with the permanent dipole of adsorbed redox species to produce distorted surface waves.14 In 1986, the influence of electrolyte concentration on the apparent formal potentials of redox couples in permselective ion exchangers was described.15 Buck et al. continued to produce work elucidating how mass and charge transport can be coupled in surface films on electrodes.16 In 1991, Rowe and Creager were able to show how ion pairing can influence the formal potentials of self-assembled monolayers of ferrocenylhexanethiol on gold electrodes,17 and in the same year, Acevedo and Abruna studied variations in the formal potential of surface-confined osmium complexes as the solvent and the surface coverage were systematically varied.18 Most recently, Smith and White have introduced a theory that describes how interfacial potentials may produce nonideal voltammetric behavior for electroactive adsorbates on e1e~trodes.l~ We assert that if the concentration of redox sites is high, and if one of the oxidation states has a net positive or negative ~
~~
~~
~
(10) Brown, A. P.; Anson, F. C. Anal. Chem. 1977, 49, 1589. (11) Ikeda, T.; Leidner, C. R.; Murray, R. W. J. Electroanal. Chem. 1982, 138, 343. (12) Murray, R. W. Electroanal. Chem. 1984, 13, 200-206. (1 3) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; J. Wiley: New York, 1980; pp 409-413, 521-531. (14) Gerischer, H.; Scherson, D. A. J . Electroanal. Chem. 1985, 188, 33. (15) (a) Naegeli, R.; Redepcnning, J.; Anson, F. C. J. Phys. Chem. 1986,90,6227. (b) Redepenning, J.; Anson, F. C. J. Phys. Chem. 1987, 91,4549. (16) (a) Buck, R. P.; Madaras, M. B.; Mackel, Rainer J. Electroanal. Chem. 1993, 362, 33. (b) Buck, R. P.; Vanysek, P. J . Electroanal. Chem. 1991, 297, 19. (c) Buck, R. P.; Vanysck, P. J. Electroanal. Chem. 1990,292,73.(d) Buck, R. P. J . Electroanal. Chem. 1989,271,l.( e )Buck, R. P. J . Phys. Chem. 1989, 93, 6212. (17) Rowe, G. K.; Creager, S. E. Lnngmuir 1991, 7, 2307. (18) Acevedo, D.; Abruna, H. D. J. Phys. Chem. 1991, 95, 9590. (19)Smith, C P.; White, H. S. Anal. Chem. 1992, 64, 2398.
0003-2700/94/0386-1560$04.50/0
0 1994 American Chemical Society
charge, then ion transport may play an important role in determining the voltammetric response of modified electrode surfaces. It is expected that one type of electrolyte ion may dominate the process of maintaining macroscopic electroneutrality for redox films that behave as ionexchangers. Hence, as the electrolyte concentration changes in solution, it is expected that the free energy of transporting counterions across the film-solution interface will change and that it should be possible to use the electrolyte concentration to shift the apparent formal potential of this type of redox couple. Additionally, if the oxidation state of an ion-exchanging redox film is changed, then the charge on the redox sites will change. Consequently, the free energy for transporting counterions across the film-solution interface will change as the oxidation state of the film is changed. This should produce surface waves that are broader than the “normal” 90.6 mV full width at half-maximum. Another way of thinking about these ionic effects is to consider how the Donnan potential at film-solution interface may influence the voltammetry of ion-exchanging redox films. It is well-known that changes in theconcentration of exchange sites and changes in the concentration of electrolyte ions in solution have a direct influence on the Donnan potential at the surface of ion exchangers.20 In the discussion below we describe how changes in the Donnan potential may influence the voltammetric response observed for thin ideally permselective redox films that undergo reversible electron transfer. We have opted to focus on the influence of the Donnan potential for a model system that is free of activity effects and electric field effects that have been included in other models.
EXPERIMENTAL DETAILS Materials. N,N’-Bis[(p-trimethoxysilyl)propyl]-4,4~-bipyridinium dibromide (1) was synthesized by refluxing 4,4/bipyridine (Aldrich) with 1-bromo-3-(trimethoxysiIy1)propane (Petrarch) in acetonitrile (Burdick & Jackson, distilled in glass) as described by Bookbinder and Wrighton.*l Prior to being derivatized with I, platinum electrode surfaces were pretreated according to the procedure of Lenhard and Murray.22 Electrodes were derivatized by exposing pretreated surfaces to -3 mM solutions of I in acetonitrile overnight. Tetrabutylammonium bromide (Aldrich, 99%) was used as purchased. Apparatus and Procedures. A PAR Model 273 potentiostat, an IBM XT computer, and a Graphtec Model WX1200 x-y recorder were used to acquire all electrochemical data. All of the voltammetry was performed in an inert atmosphere box under N2. Voltammetricdata were analyzed using a modified version of Headstart. All electrolyte activities are reported as molalities because activity coefficientsfor tetrabutylammonium bromide ((TBA)Br) in acetonitrile have been measured in units of molality.23 The reference electrode was a silver wire exposed to an acetonitrile solution containing 1.33 X 10-4 m AgNOs and 0.133 m (TBA)Br. This solution was separated from the working electrode compartment, which contained various concentrations of (TBA)Br in acetonitrile, by a porous vycor (20) Helfferich, F. Ion Exchange; McGraw-Hi]!: New York, 1962. (21) (a) Bookbinder, D. C.; Wrighton, M. S. J. Am. Chem. Soe. 1980,102,5123. (b) Bookbinder,D. C.; Wrighton, M. S. J . Electrochem. Soe. 1983,130,1080. (22) Lenhard, J. R.; Murray, R. W. J. Electroonul. Chem. 1977, 78, 195. (23) Barthel, J.; Kunz, W. J. J. Solution Chem. 1988, 17, 399.
frit (Corning). Because the liquid junction potential (E,) across the vycor frit changed as the concentration of (TBA)Br in the working electrode compartment changed, it was necessary to correct the cell potentials for these changing E,. This was done by using the limiting equivalent conductivities of TBA+ and B r in acetonitrile to calculate transport numbers at infinite dilution.24 These values were used to approximate transport numbers at the nonzero concentrations used in our experiments and to estimate liquid junction potentials using the Henderson equation.2s,26
RESULTS AND DISCUSSION Development of Model. The half-reaction for an electroactive permselective film on an electrode surface can be represented by eq 1, which is the case when the film is a cationic redox polymer with covalently incorporated redox sites. poly-Oxm++ mX;
+ ne- = poly-Red”-n)+ + ( m- n)Xp-
+ nX,-
(1)
In eq 1 Xp- and Xs- denote monovalent counterions in the polymer and in solution, respectively. The electrode potential for this half-reaction can be related to the formal potential by eq 2
where CO, and C R are ~ the concentrations of oxidized and reduced sites in the polymer and C X ( ~ )and CX(~) are the concentrations of counterions in the polymer and in solution. Instead of thinking of eq 2 as being simply the Nernstian behavior for the the half-reaction represented by eq 1, it is useful to conceptualize it as shown in eq 3 = EuNemtw + EDonnan
(3)
where E*Ne,.,,,t*
= Eo’
T In c, + Rn F ,C
(4)
and where (5)
Iff is defined as the fraction of polymeric redox sites in the oxidized state, (24) Springer, C. H.; Coetzee, R. L.; Kay, R. L. J. Phys. Chem. 1%9, 73, 471. (25) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; J. Wiley: New York, 1980, p 71. (26) Thelimiting equivalentconductivitieslistedin ref22 for tetraisoamylammonium and tetraisoamylboride are nearly identical. Consequently, we had hopcd that it might be possible to eliminate much of the liquid junction potential by preparing a salt bridge containing a saturated solution of tetraisoamylammonium tetraisoamylboride in acetonitrile. Our hopes were thwarted by the relatively low solubility of this salt (-0.1 m ) in acetonitrile. We point out that the solubility of this salt is quite high in tetrahydrofuran (>0.6 m ) , however.
Ana&tlcalChemlstry, Vol. 66, No. 9, May 1, 1994
1561
f = C,,/C,* then the concentration of oxidized sites, the concentration of reduced sites, and the concentration of counterions in the polymer are given by eqs 7-9, respectively,
c, c, Cx(,, = mC,
= fC,*
= (1- nc,*
+ (m- n)C,
(7) (8)
or Cx(,, = (m- n - nnCp (9)
where C,* is defined as the bulk concentration of redox sites. If eqs 7-9 aresubstituted into eq 2, then theelectrode potential can be represented as
E = Eo'
+ mnFl n f + QF l n 1-f
and if E is measured when f = 0.5, then the apparent formal potential, (Edapp, can be related to the formal potential by eq 11.
Without calculating the exact position and shape of the surface waves expected for electrodes modified with permselective films, some general observations can be made. Note in eqs 2, 10, and 11 that the electrode potential depends on the supporting electrolyte concentration in solution. In particular, note that if E is measured at f = 0.5 in solutions with different electrolyte concentrations, then according to eq 11, the apparent formal potential will shift by 59.2 mV toward more negative potentials for each factor of 10 by which CX(~) increases. This potential shift is associated with changes in the Donnan potential at the polymer-solution interface. As can be seen in eqs 3 and 5, for each factor of 10 by which C,*/CX(~) changes, the Donnan potential changes by 59.2 mV, and so too does the apparent formal potential measured for the film. Changes in the Donnan potential at the film-solution interface also manifest themselves in a more subtle manner. Refer again to eq 1 and consider the case when the charge on the oxidized redox site is equal to 1, If the concentration of redox sites is, for example, 1 M, then the concentration of counterions in the film is also 1 M when the film is fully oxidized. As the film approaches a fully reduced state, however, the concentration of ion exchange sites approaches zero because the reduced redox sites are neutral. Consequently, an infinitely large change should occur for ln{Cx(,)/ CX(~)) in eq 2. The change in E h n n a n with f suggests that surface waves for permselective films on electrodes should be significantly broader than the 90.6/n mV Efwhm expected for electroactive thin films which are not permselective. In order to obtain an expression for the current when a linear potential ramp is applied to an electrode modified with a film exhibiting the thermodynamic properties described 1662
Aneiytlcai Chemistry, Voi. 66,No. 9, M y 1, 1994
0L 4.3
P ' d.2
4.1
0.0
E - E"
- . -0.2
-0.1
-0.3
Figure 1. Comparisons of voltammetric surface waves for permselectbe redox films with that of a nonpermselective thin-layer cell. Permselectivewaves are for the case In wMch the Donnan potential is 59.2 mV when f = 0.5, Le., when ( m - I + t)Cp*ICX(I) = 10. The response for the thin-layer cell Is shtfted by 59.2 mV from P' for comparitbe purposes: (a) thin-layer cell; (b) permselective +3/+2 couple, Cp"/f& = 4; (c) permselective +2/+1 couple, Gel%,)= 2013; (d) permselectbe +1/0 couple, Cp*/i& = 20.
above, it will be assumed that the oxidized and reduced sites are at equilibrium with the electrode surface at all potentials and that the film is thin enough so that Cox and C R are ~ uniform across the film. Thus, knowledge of the diffusion coefficients in the film is not required. It is also implicit in these assumptions that transport of counterions in the film to maintain macroscopic electroneutrality is not rate limiting. Under these conditions the current is given by eq 12.
The time dependence offis obtained as follows. Rearranging eq 10 and making the definition shown in eq 13 gives eq 14.
By taking the derivative of eq 14 with respect to time, solving for df/dt, and substituting the result into eq 12, one can obtain the following expression for the current in terms off.
. n2iFaVCp*v RT
1=
+
(m- n nf) (m- n + nn + n2(1-n
) (15)
The sweep rate is given by Y = -(dE/dt) in eq 15. The currentpotential response can be calculated using this equation and eq 10, which gives the potential as a function off. A single current-potential equation can also be derived, but it is significantly more complex and provides no additional insight into the voltammetric behavior of these films. Voltammograms for polymers with different charges on the oxidized sites are compared in Figure 1. The alignment of these voltammograms requires further explanation. Comparisons of voltammograms for polymers with the same
Table 1. Mmmdonles8 Peak Currents and € -,,
dimensionless type of surface wave CPsaL nonpermselective thin-layer cell 0.250 permselective +1/0and 0/-1 0.172 permselective +2/+1 and -1/-2 0.214 permselective +3/+2 and -2/-3 0.227
Efnhm
(mv) 90.6 131 109 101
%ai
0 12.9 1.5 0.6
concentration of redox sites but different site charges reveal waves which are shifted with respect to each other because the Donnan potentials for these films are not equal for the same values off. To distinguish these relatively large shifts from more subtle effects, polymers with different concentrations of sites but the same Donnan potential whenf= 0.5 are compared in Figure 1. More specifically, in this figure the ratio of the concentration of counterions in the film to the concentration of counterions in the polymer was chosen to be 10 whenf= 0.5. The ratios of C,*/CX(~)necessary to achieve this condition for each case are indicated in the figure caption. The voltammograms in Figure 1 are displayed in comparison to the response expected for a conventional thin-layer cell. The shape of the conventional response is identical to that of the chemically nonexistent but mathematically predicted shape of a permselective film for the limit in which the charge on the oxidized redox sites approaches infinity. As this limit is approached, the change in Donnan potential upon reducing the polymer approaches zero and no broadening of the surface wave occurs. As is expected from eq 11, surface waves for polymers with different site charges are broadened to different degrees. Changes in the Donnan potential during a voltammogram are different for polymers with different charges on the exchange sites. Dimensionless peak currents and Efwhm are given in Table 1. It can also be seen in Figure 1 that the electrode potentials at the peak currents are not aligned for the different polymers. This is most pronounced for polymers with univalent oxidized sites, and it is due to the asymmetry in the wave shapes. Even after correcting for the Donnan potential it is found that the potential values at ipeakareshiftedfrom (Edapp. By setting the derivative of eq 15 with respect to E equal to zero, the value offat ipcak can be determined. For a polymer withunivalent oxidizedsites,f= 0.586 at ipcak. By substituting this value offinto eq 11, Epk can be determined and compared with the value of (Ed),,, found by substitutingf = 0.5 into the same eq. Thus, Epeak is found to be 12.9 mV positive of (Ed),,, for polymers with +1/0 valencies for the redox sites. In Table 1 the differences between Epcak and (Ed),,, are also included for polymers with +3/+2 and +2/+1 valencies. Practically speaking, these difference are small, and the differences are probably small enough to be within experimental error of each other in all but the +1/0 case. It is necessary to point out several general aspects of this model before proceeding to a comparison of the model with real systems. First, considering eqs 10 and 15, note that by changing the sign of the ramp rate the sign of the current changes. Also note that the potential for the peak oxidation current and the potentia' for the peak reduction current are the same. so, for cyclic voltammetry, the Current response is symmetrical about the current axis. Second, surface waves that are mirror images of those shown in Figure 1 are expected
for permselective redox polymers that are cation exchangers. For example, for 0/-1 couples, tailing of the surface waves is present a t potentials positive ofEpcakinsteadof at potentials negative of Emk as is the case for +1/0 couples. Also note that the sign of the Donnan potential is reversed for cation exchangers and that the apparent formal potential will shift to more positive values as the electrolyte concentration in solution increases. Consequently, the sign of the shift in apparent formal potential (with the change in electrolyte concentration) is a useful indicator of the type of ion transport dominant in the redox film. Comparisonof Model with Real Systems. A survey of the literature reveals a number of systems that qualitatively appear to exhibit the wave shapes predicted by the permselective model. We looked for systems with two reversible one-electron couples with different formal potentials because the model predicts that the twocouples should havedifferent wave shapes. Some of Chambers' polymeric TCNQ systems appear to exhibit voltammograms consistent with those expected from the permselective model, but Chambers has demonstrated that these materials tend to show complex behavior that is dependent on both the nature and the concentration of the supporting e l e ~ t r o l y t e . ~Consequently, ~ we have avoided comparisons between these polymeric TCNQ systems and the permselective model. Some of Mazur's polyimides also appear to give voltammograms consistent with the permselective model: a 0/-1 couple that is broadened and skewed in comparison to the-1 /-2 couple is observed.28 In our hands, however, these materials degraded relatively quickly upon cycling through the -1/-2 couple. Moutet et al. have constructed viologens with pendant pyrrole groups that can be electrochemically polymerized onto electrode^.^^ It was also true for these films that there was enough degradation of the peak currents over the course of several experiments to prevent us from making rigorous comparisons to the model. The films appeared to be highly permselective, and the wave shapes were in good agreement with that predicted by the model, but the results were only qualitatively useful. We have had the most success in comparing the permselective model for surface waves with voltammograms obtained for thin films of the viologen polymer first described by Bookbinder and Wrighton.21 These films are quite stable, and it has been possible to demonstrate that the films are highly permselective. In order to establish that the viologen films are permselective, it was necessary to establish that the apparent formal potentials exhibited the proper dependence on electrolyte activity. Although there is relatively little known about activity coefficients of electrolytes in nonaqueous media, recent vapor pressure measurements by BarthelZ3 have provided activity coefficients for several tetraalkylammonium halides in acetonitrile. Among these electrolytes is tetrabutylammonium bromide, the electrolyte used in this study. Figure 2 shows the electrolyte dependence of the apparent formal potentials of a viologen film on a platinum electrode in acetonitrile when (TBA)Br is the supporting electrolyte. (27) Inzelt, G.;Szabo, L.; Chambers, J. Q.;Day, R. W.J. Electroanal. Chem.
1988, 242,265. (28) Mazur, S.;Lugg, P. S.;Yarnitzky, C. J. Electrochem. Soc. 1987,134,346. (29) (a) Bidan, G.; Deronzier, A.; Moutet, J.-C. J. Chem. Soc., Chem. Commun. 1984,1185. (b) Coche, L.; Deronzier,A,; Moutet, J.-C. J. Electroanal. Chem. 1986,198, 187. (e) Coche, L.; Moutet, J . 4 . J. Electrwnal. Chem. 1988,245, 313.
Analytical Chemistry, Vol. 66,No. 9, M y 1, 1994
1563
I 3
i
-0.4 -2.5
-5+0.6
-1.5
-0.2 I
+0.2
-0.5
ha Flgurr 2. Influence of (TBA)Br activity on apparent formal potential for vlologen-modified electrodes in acetonitrile.
The raw data give slopes of -67.7 f 2.4 and -63.4 f 2.9 mV for the +2/+1 and +1/0 couples, respectively. After correcting for the changing liquid junction potentials at the interface between the filling solution in the reference compartment and the electrolyte solution to which the working electrode was exposed, these slopes become -53.4 f 2.4 mV and -49.1 f 2.9 mV for the +2/+1 and +1/0 couples, respectively (assuming no uncertainty in the liquid junction potentials). It is clear from these slopes that the films are highly permselective in the +2 and + 1 oxidation states. The fact that the slopes are not exactly -59.2 mV suggests that the films might not be ideally permselective, i.e., there might be some cation transport involved in charge compensation. Another alternative is that the films are actually ideally permselective but the activity of redox sites or the activity of electrolyte counterions in the redox polymer is changing as the electrolyte activity changes in solution. The change in activity could be due to changes in the activity coefficients in the polymer or to changes in the concentration of exchange sites due to changes in polymer swelling. The films should swell more in dilute electrolyte solutions than in concentrated electrolyte solutions because in the former case the osmotic pressure is greater. Although a detailed study of the influence of electrolyte activity on polymer swelling is beyond the scope of this work, we suspect that an electrochemical quartz crystal microbalance could be used successfully to examine this phenomenon. Having established that the viologen films are highly permselective under these conditions, we can compare the wave shapes expected from the permselective model with the voltammetric wave shapes obtained experimentally. Figure 3a shows a typical voltammogram for a viologen-modified electrode before the charging current has been removed. Background correction was accomplished by subtracting a current response that changed linearly with the applied potential. For the voltammogram shown in Figure 3a, a straight line was drawn from the current at +0.30 V to the current at -0.70 V for both the forward and reverse ramps. The result of subtracting these baselines from the raw data is shown in Figure 3b as the solid line. To keep the figure from becoming cluttered, only the data between +0.30 V and 4 - 7 0V aredisplayed. The dimensionlesscurrent was obtained 1564
AnalyticalChemistty, Vol. 66, No. 9, May 1, 1994
-0.6
-1
I
x TS ’& ’.&+ I
0.25 0.2
I‘
3
Flgurr 3. (a, top) Cyclic vottammogramof vlologen-modlfled electrode in acetonitrilewith (TBA)Br as the supporting electrolyte, u = 20 mV/s. (b, bottom) W!d line, same voltammogram as in (a) after subtraction of nonfaradaic current: dashed line, voltammogram calculated using permselective model.
by multiplying the current at each point by (RT/nZFuQr), where R, T, n, F, and u are defined as they were in eqs 1-15, and where Qf is the total charge obtained by integrating the current for the surface waves. Alignment of the calculated wave shapes with the experimental results requires an explanation. As was described above, for permselective films on electrodes there is a difference of several millivolts between the apparent formal potential and the peak potentials. The waves calculated from the permselective model were aligned with the experimental results by using the integrated current to determine the potential (for each experimental wave) at which the charge passed was half of the total charge observed for the wave. Because the peak separations are not exactly zero, the midpoint between Qr/2 for the forward ramp and Qf/2 for the reverse ramp was taken to be the potential at which half of the sites were oxidized and half were reduced for each couple. We then aligned this potential with the point at whichf= 0.5 in the waves calculated from the permselective model. The surface waves calculated from the permselective model are shown as the dashed lines in Figure 3b. Although good agreement is obtained between the calculated wave shapes and those obtained experimentally, there are some differences worth noting. First, the peak separation is not zero for either of the experimental waves. The peak separation is 24 mV for the +2/+ 1 couple and 8 mV for the + 1 /O couple. Much of this separation is probably due to a
above. It may be true that more sophisticated models that include activity coefficients in permselective polymers may be necessary to adequately describe the wave shape for these systems. We are led to the following conclusions. If eq 1 is a valid description of the reversible redox process undergone by a thin film on an electrode, if the swelling of that film does not change as the oxidation state changes, and if the activity coefficients do not change as the oxidation state changes, then it must be true that eqs 10 and 15 can be used to describe the voltammetric wave shapes of the film and the dependence of the apparent formal potentials on electrolyte concentration. Moreover, if eq 1 is a valid description of the reversible redox process undergone by a thin film on an electrode surface, and if the experimentally measured surface waves are inconsistent with that expected from eqs 10 and 15, then it must be true that either the concentration of redox sites is changing as the oxidation state changes, or the activity Coefficients in the film are changing in the polymer as the oxidation state changes, or both. We also emphasize that if eq 1 is a valid means of representing the half-reaction of interest, then descriptions of wave shapes based on interaction parameters found in refs 8-1 1 will lead to an inaccurate representation of the surface. Finally, because of the high concentration of exchange sites in redox films (relative to the concentration of electrolyte ions in solution), we assert that permselective descriptions may frequently be appropriate for describing voltammetric wave shapes and apparent formal potentials. As long as the concentration of redox sites is high compared to the amount of free electrolyte in solution and in the polymer, it seems likely that half-reactions such as eq 1will be useful in describing SUMMARY the response. One type of electrolyte ion will dominate the We have demonstrated that one particular system is in process of maintaining electroneutrality. Just as the voltgood agreement with the model presented above, and we have ammetric response of a thin-layer cell can be used to model mentioned other systems that qualitatively appear to give the the response of redox films on electrodes by assuming that the expected voltammetric shapes; however, there are other activity coefficients do not change throughout the course of systems that we suspect are highly permselective that do not the voltammogram, this constant-activity permselectivemodel exhibit the expected wave shape. We point out two noteworthy can be used to approximate the response of thin films in which examples. First, some of the analogs to the viologen examined charge transport is dominated by one type of ion. It is expected here give +2/+ 1 and 1/O waves that are nearly identical.33 that more sophisticated models capable of accounting for It would be interesting to know whether these films are actually changes in site-site and electrolyte-site interactions will permselective. Second, using an electrochemicalquartz crystal eventually evolve to provide more generally useful and more microbalance, Buttry has demonstrated that eq 1 is valid for accurate descriptions of the voltammetric response of permpoly(viny1ferrocene) films when perchlorate and hexafluselective redox films. orophosphate salts are used as the supporting e l e ~ t r o l y t e . ~ ~ Although it appears to be true that the poly(viny1ferricinium) ACKNOWLEDGMENT form of these films is highly permselective, the surface waves This research was supported by the donors of the Petroleum are too broad and are skewed in the wrong direction to be Research Fund and by N S F Cooperative Agreement OSRconsistent with the simple permselective model presented 9255225. Discussions with Fred Anson and R. P. Buck are also a pleasure to acknowledge. S.B. acknowledges the (30)Lennox. J. C.: Murrav. R. W. J . Am. Chem. Soc. 1978. 100. 3710. University of Nebraska for a summer undergraduate research i3li Smith, D. F.; Willma;, K.;Kuo, K.; Murray, R. W. J. Electround. Chem. fellowship. 1979, 95. 217.
small amount of uncompensated resistance. To avoid the threat of the potentiostat losing potential control and destroying the films, we opted not to use positive feedback to compensate for the resistance. As expected, the experimental results exhibit a wave for the 1/O couple that is significantly broader than that of the +2/+1 couple, but both waves are somewhat broader than predicted. As has been described by other workers, this could be due to a distribution of formal potentials in t h e p ~ l y m e r ? ~Alternatively, . ~ ~ ~ ~ the broader than expected waves could be due to activities of oxidized sites, reduced sites, or exchanged electrolyte that deviate from the values assumed in the simple model. The model described above assumes that the activity coefficients of redox sites and exchanged ions are constant throughout the voltammogram and that the concentration of redox sites does not change. This is a good approximation when considering the current response for a reversible redox couple dissolved at comparatively low concentrations in a thin-layer cell, but we suspect it can be a poor approximation for the high concentrations of electroactive sites present in redox films on electrodes. In particular, for redox films in which one of the oxidation states is neutral, significant changes in polymer swelling and wild swings in activity coefficients might accompany changes in the oxidation state of the polymer. Changes in film swelling and changes in activity coefficients are apparently quite small for the viologen films we have examined, however. The voltammetric wave shapes for these viologen-modified electrodes are in very good agreement with that expected from the simple permselective model.
+
+
~~
~
(32) Albcry, W. J.; Boutelle, M. G.; Colby, P.; Hillman, A. R. J . Electroonu/. Chem. 1982,133, 135. (33) (a) Dominey, R. N.; Lewis, T. J.; Wrighton, M.S. J . Phys. Chem. 1983.87, 5345. (b) Lewis, T. J.; White, H. S.; Wrighton, M.S. J. Am. Chem. Soc. 1984, 106,6941. (34) Varineau, P. T.; Buttry, D. A. J. Phys. Chem. 1987, 91, 1292.
Received for review November 11, 1999. Accepted February 28,
1994." a
Abstract published in Aduunce ACS Abstructs, April 1, 1994.
AnalyticalChemistty, Vol. 06, No. 9, May 1, 1994
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