Non-Steady-State Rotating Disk Voltammetry of Redox Couples

or in steady-state experiments. The utility of non-steady- state cyclic voltammetry with Nafion-coated rotating disk electrodes to separate the contri...
1 downloads 0 Views 182KB Size
Download PDF
Anal. Chem. 1997, 69, 2661-2668

Non-Steady-State Rotating Disk Voltammetry of Redox Couples Incorporated in Perfluorsulfonated Ionomer Coatings on Electrodes Minglian Shi and Fred C. Anson*

Arthur Amos Noyes Laboratories, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125

The differences in the affinity of Nafion coatings for Ru(NH3)63+/2+ and Os(bpy)33+/2+ counterions and the difference in the mobilities of the two types of cations within Nafion are used to explain the differences in the voltammetric signatures that they exhibit. A new method is proposed with which to determine whether apparent diffusion coefficients of electroactive counterions in electrode coatings differ when they are evaluated in transient or in steady-state experiments. The utility of non-steadystate cyclic voltammetry with Nafion-coated rotating disk electrodes to separate the contribution to the observed current from dissolved and Nafion-confined reactants is demonstrated. In the preceding paper,1 the large difference in the mobilities of hydrophobic Ru(bpy)33+/2+ and hydrophilic Ru(NH3)63+/2+ redox couples incorporated at, or near, saturation levels in Nafion coatings on electrodes were correlated with the voltammetric responses exhibited by the two types of counterions and with their concentration profiles within the polyelectrolyte coatings. In this paper, some additional features that differentiate the behavior of the two classes of counterions are exposed and interpreted. Of particular interest may be a method that was devised to evaluate effective diffusion coefficients for the counterions within polyelectrolyte coatings when steady-state instead of transient currents are flowing through the coatings. The experimental behavior to be reported involves subjects such as the kinetics of ion exchange, migration of counterions in electric fields present in electrode coatings, and spatial variations in the diffusion coefficients of counterions in Nafion coatings that are not explicitly considered in this study. However, these topics have been analyzed in a number of relevant reports by previous investigators.2-11 A good review that addresses these and related topics is also available.12 The phenomena examined in this study (1) Shi, M.; Anson, F. C. Anal. Chem. 1997, 69, 2653 (preceding paper in this issue). (2) Helfferich, F. Ion Exchange; McGraw Hill: New York, 1962; Chapter 6. (3) Buck, R. P. In Fundamentals and Applications of Ion Exchange; Liberti, L., Millar, J. R., Eds.; Martinus Nijhoff Publ.: Dordrecht, The Netherlands, 1985; p 370. (4) Yap, W. T.; Durst, R. D.; Blubaugh, E. A.; Blubaugh, D. D. J. Electroanal. Chem. 1983, 144, 69. (5) Elliott, C. M.; Redepenning, J. G. J. Electroanal. Chem. 1984, 181, 137. (6) Niwa, K.; Doblhofer, K. Electrochim. Acta 1986, 31, 549. (7) Doblhofer, K.; Braun, H.; Lange, R. J. Electroanal. Chem. 1986, 206, 93. (8) Lange, R.; Doblhofer, K. J. Electroanal. Chem., 1987, 216 241. (9) Maksymiuk, K.; Doblhofer, K. Electrochim. Acta 1994, 39, 217. (10) Saveant, J.-M. J. Electroanal. Chem. 1986, 201, 211 and references therein. (11) Buck, R. P. J. Phys. Chem. 1988, 92, 6445 and references therein. S0003-2700(97)00138-8 CCC: $14.00

© 1997 American Chemical Society

became most prominent in cases where there were significant differences in the affinities of electrode coatings for the oxidized and reduced halves of electroactive counterions. The possible origins of such differences in affinity have been considered in several previous reports.7,13-15 EXPERIMENTAL SECTION The reagents, apparatus, and procedures employed were similar to those in the preceding paper except that the Os(bpy)33+/2+ couple was utilized in place of the Ru(bpy)33+/2+ couple because of the greater separation between its voltammetric response and that from the background supporting electrolyte. [Os(bpy)3]Cl2, obtained by the conventional procedure,16 was used to prepare stock solutions of Os(bpy)33+ by controlled potential oxidation of Os(bpy)32+ at 0.9 V. The solutions were prepared just before they were used. Nafion coatings were applied to glassy carbon electrodes by means of the spin-coating procedure previously described.17 The coatings were converted to their fully hydrated state17-19 by soaking in pure water for at least 1 h before each series of experiments. The behavior described in this report applies only to fully hydrated coatings. Less extensively hydrated coatings often exhibit higher resistances and lower mobilities of incorporated counterions than do fully hydrated coatings.18,19 RESULTS AND DISCUSSION Contrasts in the Voltammetric Behavior of Ru(NH3)63+ and Os(bpy)33+ Incorporated in Nafion Coatings on Rotating Disk Electrodes. We sought to compare the behavior in Nafion of the hydrophilic Ru(NH3)63+ and hydrophobic Os(bpy)33+ counterions when both were initially in their oxidized state. Stock solutions of Os(bpy)32+ were therefore electrooxidized to the metastable Os(bpy)33+ cation just before the latter ion was incorporated into Nafion coatings. The difference between the behavior of the two counterions was particularly striking when cyclic voltammograms were recorded at moderate scan rates with Nafion-coated rotating disk electrodes. Recording non-steady-state currents at rotating disk electrodes is unconventional, but when the rotating electrode is coated with a material, like Nafion, that spontaneously incorporates electroactive counterions from the solution, the (12) Majda, M. In Molecular Design of Electrode Surfaces; Murray, R. W., Ed.; John Wiley: New York, 1992; Chapter IV. (13) Szentirmay, M. N.; Martin, C. R. Anal. Chem. 1984, 56, 1898. (14) Tsou, Y.-M.; Anson, F. C. J. Electrochem. Soc. 1984, 131, 595. (15) Redepenning, J.; Tunison, H. M.; Moy, J. J. Phys. Chem. 1994, 98, 2426. (16) Creutz, C.; Chan, M.; Netzel, T. L.; Okumura, M.; Sutin, N. J. Am. Chem. Soc. 1980, 102, 1309. (17) Shi, M.; Anson, F. C. J. Electrochem. Soc. 1995, 142, 4205. (18) Shi, M.; Anson, F. C. J. Electroanal. Chem. 1996, 415, 41. (19) Shi, M.; Anson, F. C. J. Electroanal. Chem., in press.

Analytical Chemistry, Vol. 69, No. 14, July 15, 1997 2661

Figure 1. Cyclic voltammetry with Nafion-coated, glassy carbon rotating disk electrodes in solutions of Os(bpy)33+ or Ru(NH3)63+. (A) 0.2 mM Os(bpy)33+, initial potential, 1.0 V. Rotating rates as shown. Scan rate, solid curves 11.6 mV s-1; dashed curve, 0.18 mV s-1. (B) Curve 1: cyclic voltammogram recorded after the rotating (3600 rpm) Nafion-coated electrode was scanned to 0.2 V in the 0.2 mM Os(bpy)33+ solution and transferred to pure supporting electrolyte. Scan rate, 11.6 mV s-1; rotation rate, 0 rpm. Curve 2 is the same as the uppermost curve in A (ω ) 3600 rpm). Dotted curve, numerical summation of curve 1 and the dashed curve in (A). (C) As in (A) but with Ru(NH3)63+ instead of Os(bpy)33+. (D) As in (B) with Ru(NH3)63+ instead of Os(bpy)33+. Supporting electrolyte in all cases was 0.l M CH3COOLi/0.1 M CH3COOH.

deconvolution of voltammetric responses into contributions from the coating-confined and the dissolved reactants can be facilitated by combining non-steady-state cyclic voltammetry with rotating disk voltammetric measurements. Shown in Figure 1 are the current-potential responses obtained from a Nafion-coated disk electrode at three different rotation rates in a solution containing 0.2 mM Os(bpy)33+. The electrode potential was scanned at 11.6 mV s-1 from an initial potential of 1.0 V where the incorporated complex was present as Os(bpy)33+. The cathodic current peaks that appear at potentials more positive than those where the flat, steady-state current plateaus are reached result from the reduction of the Os(bpy)33+ incorporated in the Nafion coating. The peaks increase with the electrode rotation rate because they are superimposed on the steady-state plateau currents that increase with rotation rate. The peaks are not present when the currents are recorded under more nearly steady-state conditions. For example, the peakless, dashed curve in Figure 1A was obtained at a rotation rate of 3600 rpm but with a scan rate of only 0.18 mV s-1. 2662 Analytical Chemistry, Vol. 69, No. 14, July 15, 1997

The anodic peaks that appear in Figure 1A during the scan of the electrode to more positive potentials arise from the oxidation of the Os(bpy)32+ generated in the Nafion coating during the first half of the cyclic potential scan. All of the Os(bpy)32+ generated in the solution at the coating/solution interface is swept away by the rotation of the electrode so it does not contribute to the anodic current peaks. These peak currents decrease slightly as the electrode rotation rate increases because they represent the difference between the steady-state cathodic plateau currents (that increase with rotation rate) and the transient anodic peak currents that depend upon the potential scan rate but not upon the electrode rotation rate. As expected, the anodic peak is not present when the rate of the potential scan is very low (dashed curve in Figure 1A). To confirm the interpretation given for the shapes of the curves in Figure 1A, the individual responses from the dissolved reactant and that incorporated in the coating were recorded separately and then added together numerically. Curve 1 in Figure 1B was obtained when the rotated, Nafion-coated electrode was scanned to 0.2 V in the 0.2 mM Os(bpy)33+ solution and then transferred to a pure supporting electrolyte solution to record the cyclic voltammogram from 0.2 V. Addition of this voltammogram to the dashed curve in Figure 1A, which contains contributions only from the dissolved Os(bpy)33+, produced the dotted curve in Figure 1B. Curve 2 in Figure 1B is the experimental curve obtained when the Nafion-coated electrode was rotated in the 0.2 mM Os(bpy)33+ solution. The close agreement between curve 2 and the dotted curve is evident. The responses obtained when the experiments of Figure 1A were repeated with Ru(NH3)63+ as the reactant are shown in Figure 1C . The prominent cathodic current peak produced by the reduction of the Ru(NH3)63+ incorporated in the Nafion coating is followed by a cathodic plateau current. This pattern is similar to that in Figure 1A except for the larger cathodic plateau current that reflects the larger diffusion coefficient in solution of Ru(NH3)63+ (6.2 × 10-6 cm2 s-1 20 ) compared to Os(bpy)33+ (3.7 × 10-6 cm2 s-1 21 ). However, when the direction of the potential scan was reversed, the behavior of the Ru(NH3)63+ solution differed substantially from that obtained with the Os(bpy)33+ solution in Figure 1A. The anodic peak currents in Figure 1C are smaller and much more dependent on the electrode rotation rate than are those in Figure 1A. Ru(NH3)62+ cations are displaced from Nafion coatings by supporting electrolyte counterions (Li+) at a higher rate than Os(bpy)32+ counterions. However, this difference in the rate of cation exchange is not responsible for the difference in anodic peak currents in (A) and (C) because rapid transfer of an electrode held at -0.5 V in the Ru(NH3)63+ solution to a pure supporting electrolyte solution produced cyclic voltammograms for the Ru(NH3)63+/2+ couple in the coating that did not differ substantially from those obtained when the electrode was held at 0.1 V before the transfer. The source of the difference in the prominence of the anodic peak currents for the Ru(NH3)63+/2+ and Os(bpy)33+/2+ couple in Figure 1A and C can be traced to the difference between the relative positions of the steady-state current-potential curves for the reduction of the two reactants in solution and the corresponding, transient current-potential curves for the reduction of the (20) Kovach, P. M.; Caudill, W. L.; Peters, D. G.; Wightman, R. M. J. Electroanal. Chem. 1985, 185, 285. (21) Evaluated as part of this study from rotating disk voltammetry at a bare electrode.

two reactants when they are incorporated within Nafion coatings. The dashed curve in Figure 1C is the current-potential response obtained with the rotated, coated electrode in a 0.2 mM solution of Ru(NH3)63+. The curve was recorded at a scan rate of only 0.18 mV s-1 to minimize current contributions from the Ru(NH3)63+/2+ cations within the Nafion coating. Comparison of the dashed and solid curves in Figure 1C shows that the reduction of Ru(NH3)63+ in the solution proceeds at close to the diffusionconvection-controlled rate at potentials where the Ru(NH3)62+ confined within the Nafion is oxidized during the scan of the coated electrode to more positive potentials. The transient contribution of anodic current from the Ru(NH3)62+ in the Nafion does not depend on the electrode rotation rate but the contribution from the steady-state cathodic current increases with the rotation rate (ω1/2). The observed current is the difference between the two opposing contributions and the net result is that the anodic contributions become less and less distinct as the rotation rate is increased (Figure 1C). The contrasting behavior obtained with Os(bpy)33+, in which distinct anodic current peaks are present at all electrode rotation rates (Figure 1A), results because the contribution to the current from the reduction of the dissolved Os(bpy)33+ is small at potentials where the oxidation of the Os(bpy)32+ within the Nafion coating occurs (compare the dashed and solid curves in Figure 1A). The underlying reason for the dissimilarity in the position of the transient and steady-state current-potential curves for the Os(bpy)33+/2+ and Ru(NH3)63+/2+ couples is the greater affinity of Nafion for the oxidized half of the redox couple in the case of Ru(NH3)63+/2+ but not with Os(bpy)33+/2+.1 In Figure 1D is shown a set of curves for the Ru(NH3)63+/2+ couple analogous to the set given in Figure 1B for the Os(bpy)33+/2+ couple. The summation of the individual contributions to the current (dotted curve) agrees well with the experimental curve (curve 2) except at potentials near the anodic peak. This poorer agreement compared with that for the corresponding curves obtained from solutions of Os(bpy)33+ (Figure 1B) is the result of the more rapid replacement of Ru(NH3)62+ than of Os(bpy)32+ in Nafion by cation exchange. As a result, curve 1 in Figure 1D is a less accurate depiction of the actual response from the Ru(NH3)63+/2+ couple in the Nafion coating when the supporting electrolyte also contains Ru(NH3)63+ (vide infra). Cyclic Voltammetric Comparisons of Os(bpy)33+ and Ru(NH3)63+ Incorporated in Nafion Coatings. In our previous reports, unusual features of the cyclic voltammetric behavior of the Os(bpy)33+/2+ couple in Nafion coatings have been described and analyzed.17-19 The most striking features are the positive shift in anodic peak potentials and the enhanced anodic peak currents that result when electrodes coated with Nafion that contains only Os(bpy)32+ as counterion are scanned to potentials where the Os(bpy) 32+ is oxidized to Os(bpy)33+, one-third of which is ejected from the coating in order to preserve electroneutrality within the coating.17 Two types of pseudo-steady-state cyclic voltammetric responses can be obtained. The dotted curve in Figure 2A shows the steady-state response that results when the Nafion coating on an electrode is equilibrated with Os(bpy)33+ or Os(bpy)32+ to saturate the coating with the counterion, transferred to pure supporting electrolyte and scanned repeatedly over the Os(bpy)33+/2+ couple. The peak currents and potentials are essentially equal and remain unchanged for hundreds of cycles. The two half-reactions that are responsible for the cathodic and

Figure 2. Cyclic voltammograms for the [Os(bpy)3]3+/2+ couple in Nafion coatings on glassy carbon electrodes. The coatings contained 3.8 × 10-8 mol cm-2 sulfonate groups. (A) Solid curve, steady-state response (the twelfth cycle is shown) with the coated electrode in 0.2 mM [Os(bpy)3]3+; dotted curve, steady-state response (the tenth cycle is shown) when the electrode was transferred to the pure supporting electrolyte, 0.1 M CH3COOLi/0.1 M CH3COOH; scan rate, 11.6 mV s-1. (B) Curve 1, the electrode used to record the solid curve in (A) was scanned to 0.2 V, transferred to pure supporting electrolyte and scanned continuously from 0.2 V. Curves 2 and 3 are the second and third continuous scans. The dotted curve and other conditions as in (A). (C) Dashed curve, repeat of (B) but with the transferred electrode rotated at 3600 rpm; dotted curve, as in (A). (D) Dashed curve, repeat of (B) but with the electrode transferred at 1.0 V instead of 0.2 V; dotted curve (hidden under the dashed curve), as in (A).

anodic currents are given in eq 1 where 3N is the number of

N[Os(bpy)33+]p + Ne- + NLis+ h N[Os(bpy)32+]p + NLip+ (1) sulfonate groups in the Nafion coating and the subscripts p and s refer to the Nafion polyelectrolyte and solution phases, respectively. The ionic current is carried entirely by Li+ counterions that move into and out of the coating as the potential of the coated electrode is cycled repetitively. A different response is obtained if the coated electrode is cycled at a relatively low scan rate in a solution that contains the Os(bpy)33+ counterion (solid curve in Figure 2A). Now the anodic peak current always exceeds the cathodic peak current and the two peak potentials are no longer the same. The half-reactions responsible for the cathodic peak of the solid curve are given in eq 2. The cations that are driven into the Nafion as cathodic current flows are a mixture of the much more abundant Li+ ions of the supporting electrolyte and Os(bpy)33+ ions for which the Analytical Chemistry, Vol. 69, No. 14, July 15, 1997

2663

Cathodic Peak N[Os(bpy)33+]p + (N - x)Lis+ + x/3[Os(bpy33+]s + (N + x/3)e- f (N - x/3)[Os(bpy)32+]p + (N - x)Lip+ (2)

Nafion has a much higher affinity. The Os(bpy)33+ cations are electroreduced as they are incorporated. The incorporated Li+ counterions are largely replaced by Os(bpy)32+ counterions during the time (∼40 s) required for the potential to return to the range where anodic current begins to flow. As a result, the primary half-reaction responsible for the anodic peak is given by eq 3. Half-

Anodic Peak 1.5N[Os(bpy)32+]p - 1.5Ne- f N[Os(bpy)33+]p + 0.5 N[Os(bpy33+]s (3)

reaction 3 does not account for the fact that ∼10% of the cations ejected from the saturated coating as the electrode is scanned to more positive potentials are unoxidized Os(bpy)32+ cations.17 For the purposes of the present exposition, this complicating feature was neglected. The shift of the anodic peak to more positive potentials when Os(bpy)33+ is being ejected from Nafion coatings has been demonstrated in previous reports.17,18,22 The anodic peak current is larger than the cathodic peak current because part of the reduction of the Os(bpy)33+ ions incorporated during the cathodic scan occurs at potentials beyond the cathodic peak while all of the resulting Os(bpy)32+ ions are oxidized under the anodic peak. The contributions to the peak currents from the Os(bpy)33+/2+ ions in solution have been neglected in the preceding analyses because at the low scan rate and concentrations employed these contributions amounted to less than 10% of the experimental currents. The dynamics of the conversion from the solid to the dotted curve in Figure 2A provide additional insight into the processes involved. Curve 1 in Figure 2B is the first scan recorded in the pure supporting electrolyte solution with an electrode that had been equilibrated with a 0.2 mM Os(bpy)33+ solution with the potential of the Nafion-coated electrode held at 0.2 V to generate Os(bpy)32+ at its surface and then transferred to the pure supporting electrolyte. The anodic portion of the curve is essentially identical to that of the solid curve in Figure 2A, which confirms that the coating in Figure 2A remained saturated with Os(bpy)32+ (and Os(bpy)33+) throughout the repetitive cycling. Curves 2 and 3 in Figure 2B are the responses obtained during the second and third continuous scans and the dotted curve is the persistent response obtained after three or four cycles. The transition in shapes from curve 1 to curve 3 reflects the gradual loss of a portion of the Os(bpy)32+ initially present in the coating. The loss is the result of the ejection of one-third of the Os(bpy)33+ during the first oxidative scan (half-reaction 3) followed by partial reincorporation in the reductive half of the cycle (half-reaction 2) from the ejected Os(bpy)33+ in the solution just outside the coating. After a few cycles, only Li+ cations are ejected and reincorporated by the coating during each cycle, there are no further changes in the shape of the voltammogram, and the half-reactions in eq 1 (22) Lee, C.; Anson, F. C. Anal. Chem. 1992, 64, 528.

2664

Analytical Chemistry, Vol. 69, No. 14, July 15, 1997

Figure 3. Cyclic voltammograms for the Ru(NH3)63+/2+ couple in Nafion coatings that contained 3.8 × 10-8 mol cm-2 sulfonate groups. (A) As in Figure 2A with 0.2 mM Ru(NH3)63+ replacing Os(bpy)33+. (B) The electrode used to record the solid curve in (A) was scanned to -0.55 V, transferred to pure supporting electrolyte, and scanned continuously from -0.55 V. Curves 1-3 are the first, second, and third scans. The dotted curve is the steady-state response. Other conditions as in Figure 2A. (C) Dashed curve repeat of B but with the transferred electrode rotated at 3600 rpm. Dotted curve, as in (B). (D) Dashed curve, repeat of (B) but with the electrode transferred at 0.2 V instead of -0.55 V. Dotted curve, as in (B).

apply. If the experiment is repeated while the coated electrode is rotated during the cycling in pure supporting electrolyte, the transition from the initial to the dotted curve occurs during the first cycle (Figure 2C), as expected when the Os(bpy)33+ ejected from the coating during the anodic half-cycle is swept away from the coating/solution interface and is not available for reincorporation during the cathodic half-cycle. If the coated electrode is equilibrated at 1.0 V instead of 0.2 V before transfer to the pure supporting electrolyte and the first scan is toward less positive potentials (with or without rotation of the electrode), the first scan is identical to the steady-state response (Figure 2D) because the half-reactions in eq 1 apply from the beginning. Note that at every point in every curve in Figure 2 the Nafion coating contained one Os complex for every three Nafion sulfonate groups. At potentials where the complex is present entirely as Os(bpy)33+, no other counterions are present in the coating. At potentials where the complex is present entirely as Os(bpy)32+, the coatings contain as little as none and as much as half of the same number of Li+ counterions. When the set of experiments summarized in Figure 2 was repeated using Ru(NH3)63+ instead of Os(bpy)33+ as the electroactive counterion in the Nafion coatings, the results were significantly different. The dotted curve in Figure 3A is the steady-

state response obtained from a Nafion coating that was equilibrated with 0.2 mM Ru(NH3)63+ at -0.5 V before transfer to the pure supporting electrolyte. The response is not as stable as that obtained with the Os(bpy)33+/2+ couple under the same conditions because the weaker binding and higher mobility of Ru(NH3)63+/2+ counterions in Nafion result in their more rapid replacement by Li+ counterions from the pure supporting electrolyte. However, the loss is slow enough to allow a coulometric assay of the quantity of Ru(NH3)63+ incorporated by the coating from the area under the cathodic peak. The value obtained corresponds to the same value obtained for Os(bpy)33+, demonstrating that the coatings can also be saturated with Ru(NH3)63+ from 0.2 mM solutions of the ion. Before the loss of Ru(NH3)63+/2+ from the coating becomes significant, the half-reactions responsible for the dotted curve are those in eq 4.

N[Ru(NH3)6]p3+ + Ne- + NLis+ h N[Ru(NH3)6]p2+ + NLip+ (4)

The solid curve in Figure 3A is the steady-state response recorded with the coated electrode in the 0.2 mM solution of Ru(NH3)63+. The fact that the peak potentials are shifted to more positive values than in the pure supporting electrolyte suggests that the ionic current through the coating is carried by mobile Ru(NH3)63+/2+ cations as well as Li+ cations. In contrast with the Os(bpy)33+/2+ couple (Figure 2A), the anodic peak in Figure 3A has essentially the same area as the cathodic peak, which requires that the counterions ejected from the coating during the oxidative scans must be Li+ cations, unoxidized Ru(NH3)62+ cations, or a mixture of the two. When only Li+ cations are ejected, the anodic peak occurs at somewhat less positive potentials (dotted curve) so that some Ru(NH3)62+ cations are likely to be among the ejected cations during the oxidative half of the solid curve in Figure 3A. However, the near equality of the anodic and cathodic peak areas indicates that the additional Ru(NH3)62+ that enters the coating during the reductive half of the cycle does so at potentials beyond the cathodic peak, probably as a result of reductive cation exchange in which the initially incorporated Li+ counterions are replaced by Ru(NH3)62+ cations. Thus, the half-reactions assignable to the solid curve in Figure 3A are

Cathodic Peak N[Ru(NH3)63+]p + (N - x)Lis+ + x/3[Ru(NH3)63+]s + (N + x/3)e- f (N + x/3)[Ru(NH3)62+]p + (N - x)Lip+ (5) Anodic Peak 1.5N[Ru(NH3)62+]p - Ne- f N[Ru(NH3)63+]p + 0.5N[Ru(NH3)62+]s (6) That oxidative scans result in the ejection of Ru(NH3)62+ cations from coatings saturated with this cation while Os(bpy)33+ is the primary cation ejected from coatings saturated with Os(bpy)32+ 17,22 is probably the result of the greater mobility of the Ru(NH3)62+ cations within Nafion coatings.

When the coated electrode used in Figure 3A was scanned to -0.55 V, transferred to the pure supporting electrolyte, and scanned continuously from -0.55 V, the voltammograms shown in Figure 3B were obtained. The initial response is converted into the steady-state response shown by the dotted curve more rapidly than was the case with the Os(bpy)33+/2+ system (Figure 2B) because the larger diffusion coefficients of the Ru(NH3)63+/2+ cations, both in Nafion and in solution, lead to the rapid replacement of one-third of the Ru(NH3)62+ cations initially present in the coating by Li+ cations. This replacement is even faster when the electrode is rotated in the pure supporting electrolyte solution (Figure 3C) as is also true if the electrode is transferred at 0.2 V where the coating is saturated with Ru(NH3)63+. The first scan is essentially indistinguishable from the steady-state response (Figure 3D). The anodic and cathodic responses in Figure 3C and D are the result of the forward and reverse directions of half-reaction 4. Current-Step Experiments with Nafion-Coated Rotating Disk Electrodes. The higher mobility in Nafion coatings of Ru(NH3)63+/2+ cations than of Os(bpy)33+/2+ cations is responsible for the behavioral differences in the voltammetry of these two couples as summarized in Figures 2 and 3. Another consequence of the difference in the apparent diffusion coefficients of the two redox couples in Nafion is the difference in the concentration profiles that develop within Nafion coatings when Ru(NH3)63+ or Os(bpy)33+ cations in solution are reduced at rotating disk electrodes coated with Nafion. This feature was discussed qualitatively in the previous paper.1 A more quantitative analysis is possible by utilizing current-step experiments with the coated rotated electrodes to obtain coulometric assays of the ionic composition of coatings that are saturated with electroactive counterions. In Figure 6 of ref 1, schematic depictions were given of the concentration profiles that develop within and just outside of Nafion coatings rotated in solutions of Ru(NH3)63+ at potentials on the cathodic plateaus of the current-potential curves. The profile for Ru(NH3)63+/2+ cations in the coating is determined by the coating thickness and the diffusion coefficient of the cation. However, the appropriate diffusion coefficient is the one that governs the motion of Ru(NH3)63+ cation under steady-state conditions in a coating that contains Ru(NH3)62+ as the predominant counterion. This diffusion coefficient could differ from the value obtained in the conventional, non-steady-state chronoamperometric or chronocoulometric experiments that are typically employed with unrotated electrodes to evaluate diffusion coefficients of reactants in polymer coatings, as, for example, in ref 1. The possibility that diffusion coefficients measured under transient conditions might differ from those obtained in steady-state experiments has been explored in previous experiments by Majda and Faulkner.23,24 We sought to evaluate the diffusion coefficient that is applicable to steady-state conditions by determining the quantity of Ru(NH3)63+ present in Nafion coatings on rotating disk electrodes as a function of the electrode rotation rate. The experimental protocol was as follows: The Nafion-coated electrode was soaked for 5 min in 0.2 mM Ru(NH3)63+ and rotated at 3600 rpm for 1 min at a constant electrode potential. Without disconnecting the potentiostat, the electrode was then quickly removed from the solution, disconnected from the potentiostat, and (23) Majda, M.; Faulkner, L. R. J. Electroanal. Chem. 1982, 137, 149. (24) Majda, M..; Faulkner, L. R. J. Electroanal. Chem. 1984, 169, 97.

Analytical Chemistry, Vol. 69, No. 14, July 15, 1997

2665

Figure 5. Quantities of Ru(NH3)63+ present in a Nafion coating on a disk electrode maintained at -0.5 V and rotated at various rates in a 0.2 mM Ru(NH3)63+ solution. The coating contained 3.8 × 10-8 mol cm-2 sulfonate groups. The values of Γ3 were calculated from the cathodic transition times.

Figure 4. Potential-time curves recorded with Nafion-coated electrodes that were rotated (3600 rpm) at constant potential in a 0.2 mM solution of Ru(NH3)63+ for 1 min before transfer to the pure supporting electrode solutions where a constant current was passed through the coating. The electrode remained connected to the potentiostat during the removal from the solution of Ru(NH3)63+ but was disconnected before it was inserted into the pure supporting electrolyte solution. Potentials of the rotated electrode just before the transfer: (A) 0.2; (B) -0.147; (C) -0.5 V. The left-hand insets show the position on the rotating disk current-potential curve where the electrode potential was held just before the transfers were made. The right-hand insets show schematic depictions of the steady-state concentration profiles in the Nafion coatings. The constant current applied was (20 µA in every case. The cathodic, τc, and anodic, τa, transition times are marked on the curves.

transferred to pure supporting electrolyte where a constant current was applied to the electrode and the resulting chronopotentiometric potential-time curves were recorded. The entire operation was carried out under an argon atmosphere to prevent aerobic oxidation of Ru(NH3)62+ in the coating. The chronopotentiometric transition times obtained from constant anodic and cathodic currents were measured in separate, identical experiments and used to evaluate the quantities of Ru(NH3)63+ and Ru(NH3)62+ that were present in the Nafion coating at each potential. A typical set of experiments is shown in Figure 4 to demonstrate the feasibility of the experiment. In Figure 4A, the rotated electrode was held at 0.2 V (left-hand inset) where Ru(NH3)63+ is not 2666

Analytical Chemistry, Vol. 69, No. 14, July 15, 1997

reduced so that the Nafion coating contained only Ru(NH3)63+ in a horizontal concentration profile as shown in the right-hand inset in Figure 4A. The two chronopotentiometric potential-time curves recorded (in separate experiments) after the electrode was transferred to pure supporting electrolyte have a long cathodic transition time, τc, and a negligible anodic transition time, τa (solid curves in Figure 4A), as expected for a coating that contained only Ru(NH3)63+. When the electrode potential was moved to a point on the rising portion of the reduction wave for Ru(NH3)63+ (left-hand inset in Figure 4B), the results shown in Figure 4B were obtained. The cathodic transition time was shorter than in Figure 4A and a clear anodic transition time was present, demonstrating the presence of Ru(NH3)62+ as well as Ru(NH3)63+ in the coating. The steady-state concentration profiles present in the Nafion coating just before the electrode was transferred (right-hand inset in Figure 4B) are inclined instead of horizontal. When the potential was moved to a point on the cathodic current plateau (left-hand inset in Figure 4C), the cathodic transition time became much smaller, reflecting the small quantity of Ru(NH3)63+ present in the coating and the anodic transition time was much greater (solid curves in Figure 4C). The effect of increasing the electrode rotation rate on the quantity of Ru(NH3)63+ present in the rotated Nafion coating at steady-state is shown in Figure 5. The larger plateau currents at higher rotation rates produce a steeper concentration gradient of Ru(NH3)63+ within the Nafion which requires that more Ru(NH3)63+ be present in the coating. This rotation rate dependence of the quantity of Ru(NH3)63 in the coating allowed its diffusion coefficient in the coating to be estimated under steadystate conditions. Assuming that the concentration profile in the coating is linear, the quantity of Ru(NH3)63+ in the coating, Γ3 (mol cm-2), at potentials on the plateau of the current-potential curve is given by eq 7, where φ is the thickness of the coating and Cφ is the

Γ3 ) 0.5Cφφ

(7)

concentration of Ru(NH3)63+ in the coating at the coating/solution interface. The steady-state current density through the coating, Iss, is given by eq 8, where Dap is the apparent diffusion coefficient

Iss )

DapCφF 2Γ3DapF ) φ φ2

(8)

of Ru(NH3)63+ in the coating and F is the Faraday constant. The same steady-state current density also flows across the Levich layer just outside the coating and is given by eq 9 when

IL ) DsCoF/δ

(9)

the concentration of Ru(NH3)63+ just outside the coating is close to zero. For eq 9, Ds is the diffusion coefficient of Ru(NH3)63+ in solution, C° is the concentration of Ru(NH3)63+ in the solution, and δ is the rotation rate dependent thickness of the Levich layer.25

δ ) 1.6Ds1/3ν1/6ω-1/2

(10)

where ν is the kinematic viscosity of the solution and ω is the electrode rotation rate. Since IL ) Iss, it follows that

Ds2/3C°ν-1/6φ2ω1/2 Γ3 ) 3.2Dap

(11)

or, with ν ) 10-2 cm2 s-1,

Γ3 ) 0.22Ds2/3Dap-1C°φ2ω1/2

(12)

with rpm as the units of ω. Thus, a plot of Γ3 vs ω1/2 should be linear with a slope proportional to Dap. Such a plot is shown by the points in Figure 5. The slope of the line through the data points, 1.7 × 10-11 mol cm-2 (rpm)-1/2, was used to calculate Dap from eq 12 taking Ds ) 6 × 10-6 cm2 s-1 and φ ) 3 × 10-5 cm. The result, Dap ) 7 × 10-10 cm2 s-1, is substantially smaller than the values of Dap obtained from conventional, transient potentialstep experiments with Nafion coatings loaded to saturation with Ru(NH3)63+ (cf. Figure 3B in the preceding paper). This result makes it clear that, at least with coatings containing only Ru(NH3)63+ and Ru(NH3)62+ as counterions, the value obtained for the apparent diffusion coefficient of Ru(NH3)63+ within the coating depends upon how it is measured. The value of Dap measured under steady-state conditions applies to the motion of Ru(NH3)63+ across the entire Nafion coating as driven by concentration gradients like those shown in the insets in Figure 4. In transient potential-step experiments, the value of Dap applies to motion of Ru(NH3)63+ cations only within a portion of the coating closest to the electrode surface where the diffusion is driven by much steeper concentration gradients than those depicted in Figure 4. The possibility that counterion diffusion coefficients in Nafion coatings might be different under transient and steady-state conditions has been raised in previous studies,26 (25) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; John Wiley: New York, 1980; p 288. (26) Anson, F. C.; Tsou, Y.-M.; Saveant, J.-M. J. Electroanal. Chem. 1984, 178, 113.

but to the best of our knowledge, this is the first case in which a large difference has been demonstrated experimentally. [Majda and Faulkner23,24 conducted related experiments with poly(styrenesulfonate) coatings that were not saturated with the electroactive counterions.] The reasons for the difference in apparent diffusion coefficients seem likely to involve differences in the contribution of ionic migration in the electric fields present within the coatings under steady-state and transient conditions. The simplified analysis presented here has neglected the effects of migration. A more rigorous treatment that includes migratory contributions to the ionic motion is needed before the origin of the techniquedependent differences in measured values of Dap can be fully understood. When the experiments of Figure 4 were repeated with Os(bpy) 33+ instead of Ru(NH3)63+, the quantities of Os(bpy) 33+ in the coatings on the cathodic current plateau were too small to measure, even at the highest rotation rate (3600 rpm). The slope of a plot like the one in Figure 5 was, therefore, essentially zero. This result indicates a much larger steady-state value of Dap for Os(bpy) 33+ than for Ru(NH3)63+ (cf. eqn 12), which is in accord with previous reports that show values of Dap for the Os(bpy) 33+/2+ couple in Nafion increasing dramatically when the coatings approach saturation with respect to Os(bpy) 33+.27

CONCLUSIONS This study has shown how differences in the rotating disk voltammetric patterns exhibited by Ru(NH3)63+/2+ and Os(bpy) 33+/2+ couples incorporated to saturation in Nafion coatings can be understood on the basis of the differences in the relative affinity of Nafion coatings for the oxidized and reduced halves of the couples and the differences in the mobilities of the hydrophilic and hydrophobic counterions within Nafion coatings. Also presented was the first experimental comparison of steadystate diffusion coefficients for countercations loaded to saturation levels within Nafion with corresponding diffusion coefficients measured under transient conditions. The lack of agreement between the two values of Dap can pose problems in the common practice of using values of Dap from transient experiments in analyzing the behavior of rotated, Nafion-coated electrodes at steady state, as, for example, in many kinetic studies of electrode reactions catalyzed by redox couples incorporated in Nafion.28 If the behavior of the Ru(NH3)63+/2+ couple is representative of other hydrophilic counterions, tactics like those employed in Figures 4 and 5 to evaluate Dap under steady-state conditions may be necessary before reliable analyses of kinetic data can be obtained. The modest goals of the present study were reached without taking into account the effects of electrical migration on the motion of the counterions in the Nafion coatings. However, in more ambitious studies, the contributions of the electric fields certainly present in Nafion coatings to the motions of multiply charged counterions incorporated in the coatings would have to be considered. A variety of possible approaches to dealing with such systems have been offered.10-12 However, in the case of Nafion, a serious obstacle is presented by the time dependence of coating properties that results from the significant changes in the state (27) Anson, F. C.; Blauch, D. N.; Saveant, J.-M.; Shu, C.-F. J. Am. Chem. Soc. 1991, 113, 1922. (28) Andrieux, C.-P.; Saveant, J.-M. In Molecular Design of Electrode Surfaces; Murray, R. W., Ed.; John Wiley: New York, 1992; Chapter V and references therein.

Analytical Chemistry, Vol. 69, No. 14, July 15, 1997

2667

of hydration of the coatings that accompany their loading with multiply charged cations.18,19 ACKNOWLEDGMENT This work was supported by the National Science Foundation. Dr. Iqbal Bhugun was a consistent source of insightful comments and helpful suggestions.

2668

Analytical Chemistry, Vol. 69, No. 14, July 15, 1997

Received for review February 5, 1997. Accepted April 30, 1997.X AC9701389

X

Abstract published in Advance ACS Abstracts, June 15, 1997.