Some Consequences of the Significantly Different Mobilities of

Some Consequences of the Significantly Different Mobilities of Hydrophilic and Hydrophobic Metal Complexes in Perfluorosulfonated Ionomer Coatings on ...
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Anal. Chem. 1997, 69, 2653-2660

Some Consequences of the Significantly Different Mobilities of Hydrophilic and Hydrophobic Metal Complexes in Perfluorosulfonated 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

Thin coatings of Nafion on glassy carbon rotating disk electrodes were saturated with hydrophilic [Ru(NH3)63+, Co(NH3)63+] or hydrophobic [Ru(bpy)32+] counterions. With both types of counterions, the plateau currents obtained when the electrodes were rotated in solutions of the cations matched the currents obtained with the uncoated electrodes in the same solutions at all accessible rotation rates. The high rates of cross-coating charge propagation demonstrated by these results involved physical diffusion of the hydrophilic complexes and electron hopping between adjacent, immobile pairs of the hydrophobic complexes. The approximate concentration profiles that develop within, and just outside of, Nafion coatings on disk electrodes that are rotated in solutions of electroactive counterions are depicted. In several previous studies, much higher rates of diffusion within Nafion coatings have been reported for hydrophilic complexes such as Ru(NH3)63+ than for hydrophobic complexes such as M(bpy)32+ (M ) Fe, Ru, Os; bpy ) 2,2′-bipyridine).1-8 Some of the values of the diffusion coefficients reported in the various studies have disagreed, sometimes by orders of magnitude, and these discrepancies have been traced, at least in part, to differences in the states of hydration of the Nafion coatings employed in various studies.9-11 In continuing studies of modes of charge propagation both within Nafion coatings and at Nafion solution interfaces, we undertook a comparison of the behavior within Nafion coatings of redox couples with fast and slower rates of electron self-exchange in solution. One initial objective was to measure the rates of electron self-exchange reactions between half of a redox couple incorporated in Nafion coatings and the other half in solution. Attempts to conduct such measurements with the Ru(NH3)63+/2+ couple were not successful because only diffusion-controlled responses were obtained at Nafion-coated (1) White, H. S.; Leddy, J.; Bard, A. J. J. Am. Chem. Soc. 1982, 104, 4811. (2) Martin, C. R.; Rubinstein, I.; Bard, A. J. J. Am. Chem. Soc. 1982, 104, 4817. (3) Buttry, D. A.; Anson, F. C. J. Am. Chem. Soc. 1983, 105, 686. (4) Anson, F. C.; Blauch, D. N.; Saveant, J.-M.; Shu, C.-F. J. Am. Chem. Soc. 1991, 113, 1922. (5) Sharp, M.; Lindholm, B.; Lind, E.-L. J. Electroanal. Chem. 1989, 274, 35. (6) Yeager, H. L.; Steck, A. J. Electrochem. Soc. 1981, 128, 1880. (7) Samec, Z.; Trojanek, A.; Samcova, E. J. Phys. Chem. 1994, 98, 6352. (8) Martin, C. R.; Dollard, K. A. J. Electroanal. Chem. 1983, 159, 127. (9) Pourcelly, G.; Oikonomou, A.; Gavach, C.; Hurwitz, H. D. J. Electroanal. Chem. 1990, 287, 43. (10) Shi, M.; Anson, F. C. J. Electrochem. Soc. 1995, 142, 4205. (11) Shi, M.; Anson, F. C. J. Electroanal. Chem. 1996, 415, 41. S0003-2700(97)00137-6 CCC: $14.00

© 1997 American Chemical Society

rotating disk electrodes in solutions of Ru(NH3)63+. In arriving at an interpretation of this somewhat surprising result, it was necessary to consider the concentration profiles of reactants and products that develop inside and outside of Nafion coatings on rotating disk electrodes that are placed in solutions containing half of an electroactive redox couple that is strongly incorporated by the coating. The situation is different from that encountered in most previous studies and is the subject of this report. EXPERIMENTAL SECTION Materials. [Ru(NH3)6]Cl3 (Strem Chemical Co.), [Ru(bpy)3]Cl2 (GFS Chemical, Inc.), and a 5 wt % solution of 1100 equiv wt Nafion (Aldrich Chemical Co.) were obtained from the commercial sources indicated and were used as received. [Os(bpy)3]Cl2 was prepared by the conventional procedure.12 Other chemicals were reagent grade and were used as received. Laboratory-deionized water was further purified by passage through a purification train (Millipore Ultrapure). Cylindrical glassy carbon electrodes (Tokai Carbon Co.) were mounted on stainless steel shafts with heatshrinkable polyolefin tubing. The exposed area was 0.2 cm2. The Ag/AgCl (KCl satd) reference electrode employed had a potential of 0.20 V vs the standard hydrogen electrode. Apparatus and Procedures. Conventional electrochemical cells and commercial instrumentation were employed except for a computer-controlled potentiostat and data acquisition system that has been previously described.10 Before each experiment, the glassy carbon rotating disk electrodes were polished with 0.05 µm alumina, sonicated in pure water for 5 min, and dried in air. Nafion coatings were applied to the dry electrode by spreading 15 µL of the 5 wt % solution of Nafion in an alcoholic solvent across the surface of the inverted electrode followed by rotation in air at 3000 rpm for 30 s. The resulting coating was allowed to dry in air for 2-5 min before it was immersed in pure water for 1-2 h to hydrate the Nafion fully.10 This spin-coating procedure yielded coatings that appeared uniform and that contained quantities of Nafion that could be reproduced from run to run within (5%. The quantity of Nafion sulfonate groups in the coatings was determined by loading them to saturation with Os(bpy)32+, cycling the coating over the Os(bpy)33+/2+ wave (at 11.6 mV s-1 in pure supporting electrolyte) until a steady response was obtained, and integrating the area under the cathodic peak.4,10 The Nafion coatings prepared by the spin-coating method employed in this study were (12) Creutz, C.; Chou, M.; Netzel, T. L.; Okumura, M.; Sutin, N. J. Am. Chem. Soc. 1980, 102, 1309.

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Figure 1. (A) Cyclic voltammograms for Ru(NH3)63+. Dotted curve, 0.5 mM Ru(NH3)63+ at the bare glassy carbon electrode. Scan rate, 93 mV s-1. Solid curve, Nafion coating loaded to saturation with Ru(NH3)63+ and transferred to the pure supporting electrolyte. Scan rate, 11.6 mV s-1. (B) Current-potential curves for the reduction of 0.2 mM Ru(NH3)63+ at a Nafion-coated disk electrode rotated at the indicated rates. The potential was scanned at 1.45 mV s-1. The dashed curve was recorded at the uncoated electrode at a rotation rate of 3600 rpm. (C) (b) Levich plot of the plateau currents in (B) vs the electrode (rotation rate)1/2. (O) Corresponding plateau currents measured at the bare electrode. All coatings contained 3.8 × 10-8 mol cm-2 Nafion sulfonate groups and were fully hydrated by soaking in pure water for 1-2 h before exposure to the Ru(NH3)63+ solutions. Supporting electrolyte, 0.1 M CH3COOH/0.1 M CH3COOLi.

found to contain 3.8 × 10-8 mol cm-2 sulfonate groups. Their thicknesses were estimated from profilometric measurements as (3 ( 0.5) × 10-5 cm. Experiments were conducted at the ambient laboratory temperature, 23 ( 2 °C. RESULTS AND DISCUSSION Nafion Coatings Saturated with Ru(NH3)63+. The incorporation of Ru(NH3)63+ into Nafion coatings produces a significant negative shift in the formal potential of the Ru(NH3)63+/2+ couple because of the stronger binding of the more highly charged cation by the Nafion sulfonate groups.13,14 The magnitude of the shift depends upon the ionic strength of the supporting electrolyte.15,16 A typical example is shown by the pair of cyclic voltammograms in Figure 1A. The dotted curve was recorded at a bare GC electrode in a 0.5 mM solution of Ru(NH3)63+, and the solid curve was obtained with a Nafion coating loaded to saturation with Ru(NH3)63+ and transferred to the same supporting electrolyte solution used to record the dotted curve. The difference between the formal potentials of the Ru(NH3)63+/2+ couple as determined from the average of the cathodic and anodic peak potentials is 116 mV. This difference in the potentials results in a net driving force for reaction 1 to proceed from left to right so that it becomes a cross-reaction instead of a self-exchange reaction. The subkf

[Ru(NH3)62+]Nf + [Ru(NH3)63+]S y\ z k b

3+

[Ru(NH3)6 ]Nf + [Ru(NH3)62+]S (1) scripts, Nf and S in reaction 1 indicate that the ions are present in the Nafion coating or the supporting electrolyte solution, respectively. The kinetics of reactions such as (1), in which two different redox couples are involved (typically a cation in Nafion (13) Tsou, Y.-M.; Anson, F. C. J. Electrochem. Soc. 1984, 131, 595. (14) Szentirmay, M. N.; Martin, C. R. Anal. Chem. 1984, 56, 1898. (15) Naegeli, R.; Redepenning, J.; Anson, F. C. J. Phys. Chem. 1986, 90, 6227. (16) Redepenning, J.; Anson, F. C. J. Phys. Chem. 1987, 91, 4549.

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and a nonincorporating anionic or uncharged reactant in solution), have been investigated for a variety of systems by means of rotating disk voltammetry using Nafion-coated disk electrodes.17-19 We attempted to employ the same approach with reaction 1. A set of current-potential curves recorded with a Nafion-coated electrode in a solution of Ru (NH3)63+ is shown in Figure 1B. (The curves were recorded at a very low scan rate to diminish the contribution to the current from the Ru(NH3)63+ present in the saturated Nafion coating.) A Levich plot20 of the plateau currents in Figure 1B vs the electrode (rotation rate)1/2 is shown by the solid points in Figure 1C. Even at the highest rotation rate, the currents lie on a straight line that extrapolates to the origin, which matches the behavior obtained at an uncoated electrode (open points in Figure 1C). Thus, the plateau currents in Figure 1B are diffusion-convection limited and provide no information about the kinetics of reaction 1. The Nafion coating used to record the curves in Figure 1B was initially saturated with Ru(NH3)63+; i.e., the coating contained one Ru(NH3)63+ cation as the counterion for every three Nafion sulfonate groups. At potentials on the plateau of each currentpotential curve the counterions in the coating are mostly Ru (NH3)62+ cations, but Ru(NH3)63+ cations are also present and their concentration gradient determines the magnitude of the plateau currents. The nearly ideal permselectivity of Nafion coatings16 meant that only cations that were serving as counterions for the sulfonate groups were present in the coating. As a result, reaction 1 could occur only at the coating/solution interface where Ru(NH3)62+ ions in the outermost layer of counterions in the Nafion could transfer electrons to Ru(NH3)63+ ions in solution. (17) Molecular Design of Electrode Surfaces; Murray, R. W., Ed.; John Wiley: New York, 1992. (18) Genborg, A.; Sharp, M. Electrochim. Acta 1993, 38, 1321 and references cited therein. (19) Xie, Y.; Anson, F. C. J. Electroanal. Chem. 1993, 349, 325 and references cited therein. (20) Levich, V. G. Physicochemical Hydrodynamics; Prentice Hall: Englewood Cliffs, NJ, 1962.

Figure 2. (A) Cyclic voltammograms for Co(NH3)63+. Dotted curve, 0.5 mM Co(NH3)63+ at the bare glassy carbon electrode. Scan rate, 93 mV s-1. Solid curve, Nafion coating loaded to saturation with Co(NH3)63+ and transferred to the pure supporting electrolyte. Scan rate, 23.2 mV s-1. Dashed curve, Second scan with the Nafion-coated electrode. (B) Repeat of Figure 1B using Co(NH3)63+ in place of Ru(NH3)63+. The dotted curve was recorded at a scan rate of 0.18 mV s-1. (C) (b) Levich plot of the plateau currents in (B). (O) Corresponding plateau currents measured at the bare electrode. Other conditions as in Figure 1.

When the rate of such interfacial electron-transfer reactions is substantially slower than rate of electron propagation across the Nafion coating, the measured plateau currents are expected to obey eq 2,21 where i is the plateau current, iL is the diffusion-

i ) iLik/(iL + ik)

(2)

convection-limited Levich current and ik is a kinetic current that is controlled by the rate of reaction 1

ik ) kfFAC°Γm

(3)

where kf is rate constant of reaction 1 in the forward direction, F is the faraday, A is the electrode area, C° is the concentration of Ru(NH3)63+ in the solution, and Γm is the quantity of Ru(NH3)63+/2+ in the outermost layer of the coating that is exposed to the solution. The value of ik that corresponds to the experimental conditions of Figure 1B can be calculated for particular assumed values of kf. The rate constant for electron self-exchange between Ru(NH3)63+ and Ru(NH3)62+ in solution is kex ) 3.2 × 103 M-1 s-1.22 With one of the reactants confined within Nafion coatings, the 116 mV difference in apparent formal potentials of the two redox couples (Figure 1A) could conceivably enhance the rate constant for reaction 1 by 1 order of magnitude (assuming a Brønsted coefficient of 0.5). If kf is assigned a value 10 times larger than kex, Γm is taken as ∼1 × 10-10 mol cm-2, and C° is the value employed in Figure 1B, 0.2 × 10-3 M, the calculated value of ik is 12 µA. With a diffusion coefficient of Ru(NH3)63+ of 6 × 10-6 cm2 s-1,23 the Levich current, iL, is calculated as 11 and 38 µA at electrode rotation rates, ω, of 400 and 4900 rpm, respectively. Since the calculated value of ik, 12 µA, is not much greater than iL, eq 2 predicts that Levich plots like the one in Figure 1C should be (21) Andrieux, C.-P.; Saveant, J.-M. J. Electroanal. Chem. 1982, 134, 163. (22) Brown, G. M.; Sutin, N. J. Am. Chem. Soc. 1979, 101, 883. (23) Kovach, P. M.; Caudill, W. L.; Peters, D. G.; Wightman, R. M. J. Electroanal. Chem. 1985, 185, 285.

nonlinear. The fact that a linear Levich plot that matches the one obtained at the uncoated electrodes was obtained (Figure 1C) means that either the value of ik must be much larger than that calculated, even though an exaggerated value was chosen for kf, or that reaction 1 does not describe the processes actually occurring at the Nafion-coated electrode. An alternative possibility is that the rate of reaction 1 does not control the magnitude of the plateau currents because the Ru(NH3)63+ cations move across the Nafion coating to be reduced directly at the underlying electrode surface. The resulting Ru(NH3)62+ cations would then move in the opposite direction and be released from the coating at the Nafion/solution interface to create counterion vacancies that could be occupied by additional Ru(NH3)63+ cations by means of a cation-exchange reaction. If the physical exchange of cations and their movement across the Nafion coating were more rapid than the rate of reaction 1, the linear Levich plot in Figure 1C could be explained because the plateau currents would be determined not by processes occurring within the Nafion coating but by the mass transfer processes occurring in the Levich layer that extends into the solution from the coating/solution interface. To test this possibility, a set of parallel experiments was conducted in which Co(NH3)63+ was substituted for Ru(NH3)63+. The Co(NH3)62+ produced by reduction of Co(NH3)63+ decomposes very rapidly into electroinactive aquaammine complexes which eliminates the possibility of electron exchange between the oxidized and reduced halves of the redox couple as depicted in eq 1 for the Ru(NH3)63+/2+ couple. The dotted curve in Figure 2A is a cyclic voltammogram recorded with an uncoated electrode in a solution of Co(NH3)63+. The solid curve was obtained with the Nafion-coated electrode in which Co(NH3)63+ was incorporated to saturation. The dashed curve shows the absence of any response during the second voltammetric scan with the Nafion-coated electrode. The rapid decomposition of the Co(NH3)62+ formed at the electrode surface is responsible for the absence of anodic peaks in all of the voltammograms as well as the lack of a cathodic peak in the second scan of the Nafion-coated electrode. Analytical Chemistry, Vol. 69, No. 14, July 15, 1997

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Figure 3. (A) Chronocoulometric charge-t1/2 plots for the reduction of 4.3 × 10-9 mol cm-2 of Ru(NH3)63+ incorporated in a Nafion coating on the glassy carbon electrode. The electrode potential was stepped from 0 to -0.55 V. The data obtained between 15 and 45 ms after the step were used to evaluate the chronocoulometric slopes. The dashed curve was obtained before the Ru(NH3)63+ was incorporated in the Nafion. (B) Apparent diffusion coefficients, Dap, for Ru(NH3)63+ in Nafion calculated from eq 4 and the slopes of plots like the solid line in (A). (C) Apparent diffusion coefficients for Ru(bpy)32+ in Nafion determined as in (A) except that the electrode potential was stepped from 0.75 to 1.35 V.

The set of current-potential curves in Figure 2B was recorded with a Nafion-coated rotating disk electrode in a solution of Co(NH3)63+. The anomalous peak just ahead of the current plateau is caused by the decomposition of the Co(NH3)62+ generated in the coating. Some of the products of the decomposition, e.g., Co(OH)2, apparently precipitate within the Nafion coating because saturation of the coating with the Co(NH3)63+ complex effectively prevents the acetate buffer present in the supporting electrolyte from controlling the pH within the permselective Nafion coating. The presence of the peak in the current-potential curve did not affect the steady-state plateau current that develops at more negative potentials. The peak could be eliminated entirely by recording the curves at a sufficiently slow scan rate (dotted curve in Figure 2B). The Levich plot of the plateau currents in Figure 2B is shown by the solid points in Figure 2C. It is linear and matches the plot obtained at an uncoated electrode (open points in Figure 2C). Thus, the behavior of Co(NH3)63+ and Ru(NH3)63+ at Nafion-coated rotating disk electrodes is essentially the same. As electron selfexchange reactions are not possible with the former complex, the similarity of its behavior to that of the latter complex supports the proposal that both complexes are reduced by the same mechanisms: The oxidized complex is reduced directly at the electrode surface, which it reaches by physical motion through the Nafion coating along pathways defined by the positions of the sulfonate groups for which the cationic complexes and their reduced counterparts are the only counterions present in the coatings. The rates of both the physical motion within the Nafion and the cation place exchange at the Nafion/solution interface (tripositive cations entering the coating as dipositive cations leave) must be higher than the convective diffusion of the cations across the Levich layer that separates the Nafion coating from the bulk of the solution to account for the linear Levich plots in Figures 1C and 2C. To check this assertion, apparent diffusion coefficients for Ru(NH3)63+ incorporated in Nafion were estimated from the slopes 2656

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of chronocoulometric charge-(time)1/2 (t1/2) plots24 obtained with Nafion coatings loaded with increasing quantities of Ru(NH3)63+ by successive brief immersions in a 0.1 mM solution of the complex. The loaded coating was transferred to a pure supporting electrolyte solution to record the charge-time response that resulted when the electrode potential was stepped from 0 to -0.55 V. The data were analyzed for times between 15 and 45 ms to assure that the mass-transport layer was much thinner than the coating thickness. The charge-t1/2 plots were reasonably linear (a typical example is shown in Figure 3A) and the apparent diffusion coefficient was calculated from eq 4, where S is the

(Dap)1/2 ) Sφπ1/2/2FΓRu

(4)

chronocoulometric slope (C cm-2 s-1/2), φ is the coating thickness, and ΓRu is the quantity of Ru(NH3)63+ present in the coating as determined from the area under the cathodic peaks in cyclic voltammograms recorded at a low scan rate (23 mV s-1). The resulting values of Dap are plotted in Figure 3B as a function of ΓRu. With coatings that were not saturated with Ru(NH3)63+, reasonably constant values of Dap were obtained, but there was a major decrease in Dap for coatings that were 60-100% saturated with Ru(NH3)63+. The decrease in Dap probably results from the previously demonstrated partial dehydration of Nafion coatings that are highly loaded with Ru(NH3)63+ (and many other multiply charged counterions).25 The value of Dap obtained for the saturated coating, Dap ∼ 4 × 10-9 cm2 s-1, is the parameter needed to compare the relative rates of mass transfer in Nafion coatings and Levich layers at rotating disk electrodes. The mass-transferlimited current within the Nafion, iNf, can be calculated from eq 5, which is based on an analogous equation given by Andrieux and Saveant.21 The appropriate diffusion coefficient to be used in eq 5 is the one that measures diffusional rates under steady-state conditions (24) Anson, F. C.; Osteryoung, R. A. J. Chem. Educ. 1983, 60, 293. (25) Shi, M.; Anson, F. C. J. Electroanal. Chem. 1997, 425, 117.

iNf ) FAΓRuDap/φ2

(5)

where the composition of the coating through which the diffusion is proceeding is fixed. The values of Dap obtained from transient potential-step experiments such as those employed in Figure 3 measure diffusional rates through a small portion of the coating closest to the electrode surface in which the counterion composition is changing as the diffusion coefficients are being measured. In the following paper, it is shown that the difference between diffusion coefficients measured under steady-state or transient conditions can be substantial and some of the consequences of the difference are examined. In the present paper, the use of diffusion coefficients obtained as in Figure 3 seemed acceptable because the calculated and experimental currents being compared were drastically different. Thus, for AΓRu ) 2.5 × 10-9 mol, Dap ) 4 × 10-9 cm2 s-1, and φ ) 3 × 10-5 cm, the calculated value of iNf is 1072 µA. The Levich current measured at an uncoated electrode in a 0.2 mM Ru(NH3)63+ solution at the highest rotation rate of 4900 rpm was 40 µA. Thus, the surmise that the reacting cations can move across the Nafion coating at much higher rates than they move across the Levich layer in solution is clearly the case for Ru(NH3)63+ and very likely for Co(NH3)63+ as well. It should be noted that the half-wave potentials of the currentpotential curves obtained with the Nafion-coated rotating disk electrode in Figure 1B match the half-wave potential obtained when an uncoated electrode is used in the same solution (dashed curve in Figure 1B). This agreement might appear surprising because the formal potentials of the Ru(NH3)63+/2+ couple are clearly different in solution and within Nafion coatings (Figure 1A). However, for the same reason that bare and Nafion-coated electrodes must adopt the same equilibrium potential at open circuit in a solution containing equal concentrations of the oxidized and reduced forms of a redox couple, the half-wave potentials obtained at rotating disk electrodes in solutions of, say, the oxidized reactant must be the same at both bare and Nafion-coated electrodes. This assertion is true in general, no matter which half of a redox couple is more strongly incorporated by the coating, so long as the currents at the rotating disk electrode are diffusionconvection limited and the redox couple inside the coating is in equilibrium with the couple just outside the coating. The equilibration can be achieved by ionic place exchange, electron exchange, or both. In the case of the Ru(NH3)63+/2+ couple, where Ru(NH3)63+ is much more strongly bound by Nafion coatings than is Ru(NH3)62+, the ratio of the concentration of Ru(NH3)63+ to Ru(NH3)62+ at the electrode/coating interface is much greater than unity at the half-wave potential of the solid curves in Figure 1B. This concentration ratio is unity at the half-wave potential at uncoated electrodes (dashed curve in Figure 1B). The reason that the half-wave potentials are the same despite the unequal concentration ratios of the Nernstian redox couple at the surface of the two electrodes is because, at equilibrium, the difference in Nernstian potentials at the surfaces of the bare and coated electrodes is just compensated by the potential that is developed at the coating/solution interface. The solid curve in Figure 1A was recorded in a pure supporting electrolyte solution where equilibrium between the Ru(NH3)63+/2+ couple in the Nafion coating and the solution just outside is not established. (If it were, the Ru(NH3)63+/2+ would be driven from the coating by ion exchange with the Li+ cations of the supporting electrolyte.) No compensating potential develops at the coating/

solution interface, and the average of the two peak potentials provides a measure of the formal potential of the Ru(NH3)63+/2+ couple within the Nafion coating. Nafion Coatings Saturated with Ru(bpy)32+. The mechanism of charge propagation within Nafion coatings containing the hydrophobic Ru(bpy)32+ [or Os(bpy)32+] complexes at levels below saturation has been ascribed to electron hopping between essentially immobile pairs of Ru(bpy)32+ and Ru(bpy)33+ counterions in a number of previous studies.1-5 We have concluded that physical motion instead of electron hopping is the operative mechanism for the hydrophilic Ru(NH3)63+/2+ couple in Nafion coatings. It was therefore of interest to examine the behavior of the Ru(bpy)33+/2+ system in Nafion coatings saturated with Ru(bpy)32+ or Ru(bpy)33+ for comparison with the behavior of the coatings saturated with Ru(NH3)63+/2+. Shown in panels A and B of Figure 4 are cyclic and rotating disk voltammograms for Ru(bpy)32+ similar to those for Ru(NH3)63+ in Figure 1A and B. The plateau currents for the oxidation of Ru(bpy)32+ to Ru(bpy)33+ match those obtained at the uncoated electrode, and the Levich plot is linear (Figure 4C). Thus, just as was true for the reduction of Ru(NH3)63+ at Nafion-coated electrodes, the oxidation of Ru(bpy)32+ proceeds at the diffusion-convection-controlled rate. However, the mechanism of charge propagation within Nafion coatings containing the Ru(bpy)33+/2+ couple is not likely to involve the type of physical motion of the cations that we believe occurs with the Ru(NH3)63+/2+ couple. Charge propagation by physical motion without loss of Ru(bpy)33+/2+ from the coating would require that the oxidized and the reduced halves of the redox couple enter and leave the coating, respectively, at a rate corresponding to the steady-state plateau current. However, the rates at which Ru(bpy)32+ and Ru(bpy)33+ enter and leave Nafion coatings are much lower than those for Ru(NH3)63+ and Ru(NH3)62+. For example, shown in Figure 5 are the cyclic voltammetric responses obtained when a freshly prepared Nafion coating was placed in a solution containing both 5 × 10-5 M Ru(NH3)63+ and 5 × 10-5 M Ru (bpy)32+. The response from the latter complex near 1.2 V develops much more slowly than that for the Ru(NH3)63+ complex near -0.2 V (curves 1-4 in Figure 5). However, the more strongly bound Ru(bpy)32+ complex eventually displaces the Ru(NH3)63+ complex until equilibrium is achieved and the response is dominated by the Ru(bpy)33+/2+ couple (curves 5-8 in Figure 5). Similarly, coatings loaded with Ru(bpy)32+ can be placed in pure supporting electrolyte and cycled between 0.6 and 1.2 V for extended periods without significant diminishment of the peak currents for the Ru(bpy)33+/2+ couple, showing that neither oxidation state departs from the coating at a significant rate. Thus, the propagation of charge across Nafion coatings loaded with Ru(bpy)33+/2+ is ascribed to electron hopping between adjacent pairs of the largely immobile oxidized and reduced complex. Shown in Figure 3C are apparent diffusion coefficients for Ru(bpy)3+/2+ as a function of the quantity present in the Nafion coating. The behavior resembles that reported in previous studies of both Ru(bpy)33+/2+ and Os(bpy)33+/2+.4,5,26 The increase in Dap with loading has been ascribed to decreases in the extent of tight ion pairing of the multiply charged complexes with the Nafion sulfonate groups as the loading increases as well as to increases in the rate of electron self-exchange at higher concentrations of the reactants in the Nafion.4 For the purposes of the present study (26) He, P.; Chen, X. J. Electroanal. Chem. 1988, 256, 253.

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Figure 4. (A) Cyclic voltammograms for Ru(bpy)32+ analogous to those for Ru(NH3)63+ in Figure 1A. (B) Current-potential curves for the oxidation of 0.2 mM Ru(bpy)32+ at a Nafion-coated rotating disk electrode. (C) Levich plots for the oxidation of Ru(bpy)32+ analogous to those in Figures 1C and 2C.

Figure 5. Cyclic voltammograms for the Ru(NH3)63+/2+ and Ru(bpy)33+/2+ couples recorded with a Nafion-coated electrode at various times after it was placed in a solution containing 5 × 10-5 M Ru(NH3)63+ and 5 × 10-5 M Ru(bpy)32+. Curve 1 was recorded immediately, and curves 2-8 were recorded 4, 14, 20, 30, 50, 90, and 350 min after the coated electrode was placed in the solution. The electrode was maintained at 0.3 V between each scan. Scan rate, 93 mV s-1. Supporting electrolyte, 0.1 M CH3COOH/0.1 M CH3COOLi.

the noteworthy point is the contrast between the changes in Dap for Ru(NH3)63+ and Ru(bpy)32+ (Figure 3B and C), which we believe reflects the fundamental difference in the mode of charge propagation within Nafion for the two cations. The linearity of the Levich plot up to rotation rates of 4900 rpm in Figure 4C 2658

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requires that ik for the Ru(bpy)33+/2+ system be much larger than iL in eq 2. There is rather little difference in the formal potential of the Ru(bpy)33+/2+ couple in solution and within Nafion coatings (Figure 4A). If the rate constant for electron self-exchange for the Ru(bpy)33+/2+ couple in solution, 2 × 109 M-1 s-1,27 is used to calculate ik from eq 3, the value obtained, ik ) 7.7 × 105 µA, is much larger than iL at the highest rotation rate in Figure 4B, iL ) 27 µA, so that, in contrast with the Ru(NH3)63+/2+ couple, the calculated rate of electron propagation by self-exchange between Ru(bpy)32+ and Ru(bpy)33+ is rapid enough to be compatible with self-exchange instead of physical motion as the mechanism for charge propagation across the coatings. Concentration Profiles near and within Nafion Coatings on Rotating Disk Electrodes. The steady-state plateau currents at Nafion-coated electrodes in solutions of Ru(NH3)63+ or Ru(bpy)32+ flow in response to concentration gradients of the reacting cations within the Nafion coating that are coupled to the corresponding gradients in the Levich layer separating the coating from the bulk of the solution. In Figure 6 are shown highly schematic depictions of the concentration profiles. They are drawn as linear within the coating, as would be true in lightly loaded coatings. With fully loaded coatings, all of the current must be carried by the reactants and the electric field present in the coating could lead to nonlinear profiles. The effect of the electric field on the profiles was neglected to obtain the approximate profiles within the Nafion shown in Figure 6. The concentration profiles in the hydrodynamic Levich layer just outside the coating/ solution interface are also approximated as linear in the conventional way.28 With these approximations, the difference in the reactant concentrations between the electrode surface and the outer edge of the coating can be described by eq 6, where Ds

∆C )

Ds φ C° Dap δ

(6)

and Dap are diffusion coefficients in the solution and the Nafion (27) Young, R. C.; Keene, F. R.; Meyers, T. J. J. Am. Chem. Soc. 1977, 99, 2468. (28) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; Wiley: New York, 1980; p 289.

Figure 6. Schematic depictions of the steady-state concentration profiles that develop at Nafion-coated disk electrodes rotated in a solution of a counterion reactant. The electrode potential corresponds to a point on the plateau of the current-potential curve. Solid lines, concentration of the reactant counterion; dotted lines, concentration of the product counterion. The electrode rotation rate increases from lines 1 to 3. φ is the thickness of the coating; δi is the rotation ratedependent thickness of the Levich layer. The inset shows an expanded view of the coating/solution interface. C and C° are the concentrations just outside the coating and in the bulk of the solution, respectively.

coating, respectively, φ and δ are the thicknesses of the coating and the Levich layer, respectively, and C° is the concentration of the reactant in the bulk of the solution. The concentration gradients in the coating are steeper the larger the value of Ds/ Dap. The gradients also become steeper as the electrode rotation rate increases (δ decreases) because larger currents must flow across the coating to accommodate the larger flux of reactant at the coating/solution interface as δ becomes smaller (Figure 6). The inset in Figure 6 is a magnified view of the profiles on the solution side of the coating/solution interface. The concentration of the reactant must remain close to zero at the interface because the measured plateau currents remain essentially equal to the Levich current. However, the concentration just inside the coating/solution interface must increase as the electrode rotation increases to provide the higher cross-coating currents that match the Levich current. The partitioning that controls the concentrations of the reactant on either side of the interface is assumed to remain at equilibrium so that both concentrations must increase with the rotation rate as shown in the two parts of Figure 6. However, the increases in the reactant concentration in the solution at the coating/solution interface do not cause it to become significant compared with the bulk concentration because the equilibrium constant that governs the partitioning of the reactant into the coating is very large. Effect of Dehydration of Nafion Coatings on Their Current Carrying Capacity. The linear Levich behavior shown in Figure 1C for the freshly prepared and hydrated Nafion coating did not persist if the coating was exposed to solutions of Ru(NH3)63+ for longer times. Plotted in Figure 7 are the values of the plateau currents for the reduction of Ru(NH3)63+ at a Nafion-coated rotating disk electrode as a function of the time the coating had been exposed to the solution of Ru(NH3)63+. The substantial decrease in the plateau current to values well below the Levich current was caused by large decreases in the Dap. The hydrated

Figure 7. Time dependence of the cathodic plateau current measured at -0.4 V with the Nafion-coated disk electrode rotated at 4900 rpm in a 1 mM solution of Ru(NH3)63+. Between measurements the electrode was at open circuit and not rotated. Supporting electrolyte, 0.1 M CH3COOH/0.1 M CH3COOLi.

coating became saturated with Ru(NH3)63+ within a few minutes and remained so. However, water is driven from such Nafion coatings by prolonged exposure to solutions of strongly incorporating cations,25 and cation diffusion coefficients in the resulting dehydrated coatings are smaller than those in more highly hydrated coatings. Eventually, the diffusion coefficients become too small to provide charge propagation rates corresponding to the Levich current in solutions, and behavior such as that shown in Figure 7 results.

CONCLUSIONS New evidence has resulted from this study to demonstrate that different mechanisms are involved in charge propagation across Nafion coatings by the Ru(NH3)63+/2+ and the Ru(bpy)3+/2+ redox couples incorporated in the coatings as counterions. Physical motion is the dominant mechanism for the Ru(NH3)63+/2+ couple while electron hopping is utilized by the much less mobile Ru(bpy)33+/2+ couple. This difference in the mechanism of charge propagation causes the apparent diffusion coefficients of Ru(NH3)63+ and Ru(bpy)32+ in Nafion to change in opposite directions as the quantity of counterion present in the coating increases. The rates of incorporation of the two counterions by Nafion coatings are also significantly different. From mixtures of Ru(NH3)63+ and Ru(bpy)32+, the more mobile Ru(NH3)63+ cations enter Nafion coatings more rapidly but they are ultimately displaced by the less mobile but more strongly bound Ru(bpy)32+ cations. The initial incorporation of either counterion by freshly hydrated Nafion coatings produces coatings through which relatively large steady-state currents can be passed. However, prolonged exposure to solutions of the cations leads to the gradual dehydration of Nafion coatings and produces a large decrease in the magnitudes of the currents that can be passed through them. The partitioning of the redox couples into Nafion coatings is much stronger for Ru(bpy)33+/2+ than for Ru(NH3)63+/2+. However, the higher oxidation state is much more strongly bound than its redox partner in the case of Ru(NH3)63+/2+ but not of Ru(bpy)33+/2+. As a result, the electron-exchange reaction beAnalytical Chemistry, Vol. 69, No. 14, July 15, 1997

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tween Ru(NH3)62+ incorporated in Nafion and Ru(NH3)63+ in solution is a cross-reaction with a significant driving force while the corresponding reaction for the Ru(bpy)33+/2+ couple is much closer to a self-exchange reaction. It was not possible to measure the rates of these electron-transfer reactions because both exceeded the convection-diffusion-limited rate at which the two reactants were brought into contact at freshly prepared coatings, and the diminished rates obtained with older, dehydrated coatings were limited by diffusion across the coating rather than electron transfer at the coating/solution interface.

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ACKNOWLEDGMENT This work was supported by the National Science Foundation. Received for review February 5, 1997. Accepted April 30, 1997.X AC970137G

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