8448
J. Phys. Chem. 1996, 100, 8448-8453
Diffusion Coefficients of Intrinsically Electroactive Polyelectrolytes and of Counterions Bound to Them Osamu Hatozaki and Fred C. Anson* Arthur Amos Noyes Laboratories, DiVision of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125 ReceiVed: December 15, 1995; In Final Form: March 4, 1996X
An electroactive label was attached to poly(acrylic acid) (molecular weight ) 5000) by reaction with ferrocenylethanol. The resulting ferrocene label was stable when the polymer was dissolved in aqueous solutions, and the diffusion coefficient of the labeled polymer was estimated from the currents obtained as the ferrocene was oxidized at a rotating disk electrode. Although strong adsorption of the polymer on the electrode surfaces depressed the oxidation currents below the convection-diffusion controlled values at rotating disk electrodes, it was still possible to estimate diffusion coefficients by appropriate analysis of the rotation rate dependences of the measured currents. At pH values where the labeled polymer became a polyanion, its diffusion coefficient was also estimated from the reduction currents for Ru(NH3)63+ or Co(NH3)63+ counterions bound electrostatically to the polyelectrolyte. Good agreement was obtained between the diffusion coefficients estimated by the two independent routes.
Measurements of diffusion coefficients of polyelectrolyte molecules in aqueous solutions can be useful in discerning the ways in which the structures of the molecules in solution are altered in response to changes in the ionic strength, pH or counterion composition of the supporting electrolytes. Relatively simple electrochemical techniques offer convenient means for estimating diffusion coefficients of electroactive molecules.1 In previous reports from this laboratory the use of electroactive counterions to study the diffusion of oppositely charged, electroinactive polyelectrolytes has been described.1-7 With concentrations of the polyelectrolyte sufficient to cause essentially all of the multiply charged electroactive counterions to bind to the polyelectrolyte, the electrochemically evaluated diffusion coefficients of the counterions were assumed to match that of the polyelectrolyte. Although considerable circumstantial evidence in support of this assumption has been obtained, it remained an assumption. In the present study, an intrinsically electroactive polyelectrolyte was synthesized and used in similar experiments with small, electroactive counterions. Electrochemical measurements were employed to evaluate two diffusion coefficients: one for the electroactive polyelectrolyte alone and a second for electroactive counterions bound to the polyelectrolyte. Good agreement between the two diffusion coefficients provided direct evidence in support of the previous assumption that the electrochemical responses obtained from counterions bound to polyelectrolytes offer a reliable means for measuring diffusion coefficients of the polyelectrolytes themselves. In addition, the labeling of poly(acrylic acid) with an electroactive ferrocene center allowed the diffusion of the polymer to be inspected at (low) pH values and (high) ionic strengths where the binding of electroactive counterions was absent or too weak to be useful for this purpose. Experimental Section Materials. Poly(acrylic acid) (PAA) having a specified molecular weight of 5000 was obtained from Polysciences, Inc., as a 50% aqueous solution. To obtain a solid sample, the X
Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(95)03740-3 CCC: $12.00
solution was rotoevaporated at 70 °C under reduced pressure to obtain a sticky material which was redissolved in dimethylformamide (DMF). The resulting solution was added to ethyl acetate, and the precipitate that formed was dried under vacuum at 80-90 °C. Ferrocenylethanol was prepared from ferroceneacetonitrile (Aldrich) following a literature procedure.8 Other chemicals were obtained from commercial sources and were used as received, except for DMF which was dried over molecular sieves. Aqueous solutions were prepared with laboratory deionized water that was further purified by passage through a Millipore Milli-Q Plus purification train. Ferrocene-Labeled PAA. Ferrocene groups were attached to PAA chains by reaction with ferrocenylethanol in the presence of dicyclohexylcarbodiimide (DCC). A 1.0 g sample of dry PAA was dissolved in dry DMF by heating to 80 °C. The solution was cooled to room temperature, and 0.13 g of ferrocenyl ethanol was added followed by 0.14 g of DCC in 3 mL of dry DMF. The resulting solution was stirred for 10 h at 62 °C followed by cooling in a refrigerator overnight. The precipitated dicyclohexylurea was removed by filtration, and the filtrate was added dropwise to a large volume of vigorously stirred diethyl ether at room temperature. The precipitated polymer was purified by repeating the dissolution-precipitation step two more times. The resulting pale yellow solid was dried under vacuum at 80 °C and stored under argon in a desiccator to avoid air oxidation of the ferrocene groups. The ferrocene content of the labeled polymer was determined by atomic absorption using aqueous solutions of the polymer and ferrocenylethanol as a standard. The results showed that, on average, one ferrocene group was present on each PAA chain, which corresponded to one ferrocene group and ca. 69 carboxylic acid groups randomly distributed along each PAA chain of molecular weight 5000 (Figure 1). To obtain samples with more or fewer ferrocene groups, the quantity of ferrocenylethanol in the reaction mixture was varied without changing the quantities of DCC or PAA. Apparatus and Procedures. Conventional electrochemical cells and instrumentation were employed. Edge plane pyrolytic graphite disk electrodes (0.20 cm2), used as working electrodes, © 1996 American Chemical Society
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Figure 1. Composition of the ferrocene-labeled poly(acrylic acid), PAA-Fc, examined in this study.
Figure 3. (A) Cyclic voltammograms for PAA-Fc and ferrocenylethanol in aqueous 0.2 M NaCl. (1) PAA-Fc at pH 2.8; (2) PAA-Fc at pH 8.2, and (3) ferrocenylethanol + 5 mM PAA at pH 8.2. The response was the same in the absence of PAA and at all pH values between 2 and 9. The concentration of ferrocene centers in all solutions was 0.07 mM. The initial potential was -0.2 V. The scan rate was 10 mV s-1. (B) Scan rate dependences of the anodic peak currents for voltammograms like those in (A): (O) pH 2.8, (4) pH 8.2.
Figure 2. Absorption spectra of 0.5 mM ferrocenylethanol (- - -) and PAA-Fc containing 0.5 mM ferrocene groups (s). The solvent was DMF and the optical path length ) 1 cm.
were mounted on stainless steel shafts by means of heat shrinkable polyolefin tubing. For rotating disk measurements, the electrode was rotated with a rotator from Pine Instrument Co. Potentials were measured and are reported with respect to a sodium chloride saturated calomel electrode (SSCE). Solutions were deaerated by bubbling with prepurified argon. The pH of test solutions was measured with an Orion pH meter and was adjusted by addition of HCl or NaOH. The PAA present acted as a buffering agent. Experiments were carried out at 22 ( 2 °C. Spectra were recorded with a Hewlett-Packard Model 8452 spectrophotometer. Atomic absorption measurements were performed with a Perkin-Elmer Model 3100 instrument. Results and Discussion Labeling PAA with Ferrocene. The ferrocene-labeled PAA (PAA-Fc) shown in Figure 1 proved to be a stable, useful material. We restricted our measurements to PAA that contained fewer than two ferrocene groups per polymer chain so that the properties of the labeled material could be reasonably assumed to match those of unlabeled PAA. The UV-vis absorption spectrum of the PAA-Fc is compared with that of ferrocenylethanol in Figure 2. The large difference in the intensities of the band at 324 nm could arise from the known sensitivity of this band to the environment experienced by the ferrocene ring9 and to the nature of the ring substituents.10 The band at 440 nm results from a transition localized on the iron center and is much less sensitive to changes in ring substituents.10 We also explored the possibility of preparing ferrocenelabeled PAA by carrying out copolymerizations of acrylic acid and vinylferrocene. Although copolymers containing ferrocene labels were obtained, their electrochemical responses frequently indicated that two different types of ferrocene groups were present. Because of this complication in their electrochemistry, we chose not to use these copolymers in evaluating the diffusion coefficients of ferrocene-labeled PAA.
Cyclic Voltammetry of the Ferrocene-Labeled PAA. The PAA-Fc was readily soluble in aqueous media, except in solutions containing high concentrations of salt (>0.8 M) at pH values below 3. Previous measurements with unlabeled PAA showed that the carboxylate groups are largely undissociated below pH 3 and essentially fully dissociated at pH 7.5.6 (pH titrations confirmed that the labeled PAA behaved similarly.) The cyclic voltammetric response obtained from the ferrocene label was very different at pH values where the carboxylate groups were dissociated than at values where they were not. A cyclic voltammogram for a solution of PAA-Fc containing 5 mM carboxylic acid groups and 0.07 mM ferrocene groups is shown in curve 1 of Figure 3A with a supporting electrolyte consisting of 0.2 M NaCl adjusted to pH 2.8 with HCl. The difference between the anodic and cathodic peak potentials is significantly smaller than the 59 mV expected for a Nernstian, diffusion-controlled process, which suggests that the response is strongly influenced by PAA-Fc that is adsorbed on the electrode surface. This surmise is supported by the dependence of the anodic peak current on the potential scan rate (Figure 3B). The peak current in curve 1 of Figure 3A is enhanced significantly by contributions from the adsorbed reactant. Voltammogram 2 in Figure 3A was obtained when the pH of the supporting electrolyte was increased to 8.2 to convert the PAA-Fc into a polyanion. The larger separation in peak potentials and peak currents that were proportional to (scan rate)1/2 (Figure 3B) indicate that the polyanion is much less extensively adsorbed on the electrode at this pH. Smaller peak currents are obtained at pH 8.2 both because the diffusion coefficient of the polyanion is smaller than that of undissociated PAA-Fc (vide infra) and because the decreased adsorption of the polyanion at pH 8.2 diminishes contributions to the peak current from the adsorbed reactant. Voltammogram 3 in Figure 3A was obtained from a solution of ferrocenylethanol containing the same concentration of ferrocene centers as the solutions used to record voltammograms 1 and 2. The peak potentials and peak currents for ferrocenylethanol were independent both of the pH of the supporting electrolyte between pH 2 and 9 and of the presence of 5 mM PAA. The more negative formal potential for the Fc+/Fc couple of PAA-Fc at pH 8.2 than at pH 2.8 (Figure 3A) seems most likely to reflect a stabilization of the oxidized Fc+ centers by intramolecular interaction with the high local concentration of anionic carboxylate groups present at pH 8.2. The formal potential of the Fc+/Fc couple of ferrocenylethanol remained
8450 J. Phys. Chem., Vol. 100, No. 20, 1996
Hatozaki and Anson involved in the electrode reaction, A is the electrode area, ν is the kinematic viscosity of the solution, ω is the rate of rotation of the electrode (rpm), C is the concentration of the electroactive reactant (mol cm-3), and D is its diffusion coefficient. At higher pH, where both the adsorbed and dissolved PAAFc became polyanionic, the plateau currents were smaller and the Levich plots were nonlinear. Shown in Figure 4C is a set of current-potential curves obtained at pH 8.2, and the corresponding Levich plot is shown by the triangles in Figure 4B. The lack of linearity in the Levich plot at pH 8.2 indicates that the oxidation of the polyanionic PAA-Fc in solution is not diffusion-convection controlled. In contrast with its behavior at lower pH values, the adsorbed layer of polyanion is apparently unable to mediate the oxidation of the PAA-Fc in solution as rapidly as it arrives at the electrode surface. As a result, some of the PAA-Fc must move through the polyanionic adsorbed layer to be oxidized. Electrostatic repulsion (as well as possible steric interferences) evidently diminishes the net rate of the oxidation to values that are below the diffusion-convectioncontrolled value given by eq 1. To cope with the nonlinear Levich plots, we resorted to Koutecky-Levich plots based on eq 212
Figure 4. (A) Current-potential curves for the oxidation of PAA-Fc at a rotating graphite disk electrode in 0.2 M NaCl at (A) pH 2.8 and (C) pH 8.2. The concentration of ferrocene groups was 0.07 mM. (B) Levich plots of the plateau currents from (A) (O) and (C) (4). (D) Koutecky-Levich plot of the plateau currents from (C).
unchanged when 5 mM PAA was added to the supporting electrolyte at pH 8.2 where electrostatic binding of the Fc+ cations could occur. This behavior indicates that intramolecular electrostatic interactions are probably responsible for the difference in the formal potential exhibited by the Fc+/Fc couple of PAA-Fc at pH 8.2 and 2.8 (Figure 3A). Rotating Disk Voltammetry with PAA-Fc. The adsorption of PAA-Fc on the graphite electrode surfaces posed potential problems in experiments designed to estimate the diffusion coefficients of the dissolved PAA-Fc because of the sluggish rate of electron transfer across the adsorbed layers, especially at high pH (vide infra). The problems were minimized by employing steady-state electrochemical methods for these measurements. As might be anticipated from the cyclic voltammetric behavior shown in Figure 3A, plateau currents for the oxidation of PAA-Fc at a rotating graphite disk electrode depended on the pH of the supporting electrolyte. A set of current-potential curves recorded at pH 2.8 is shown in Figure 4A, and the corresponding Levich plot11 of the plateau currents vs electrode (rotation rate)1/2 is shown in Figure 4B. To eliminate any contribution to the currents from the adsorbed reactant, the plateau currents used to prepare the Levich plots were measured at 0.4 V and at an effective scan rate of 0 mV s-1. The linearity of the Levich plot measured at pH 2.8 (Figure 4B) showed that the adsorbed PAA-Fc did not interfere with the electrooxidation of the PAA-Fc in solution. Evidently, the layer of adsorbed polymer can mediate the electron transfer between the underlying electrode and the dissolved reactant at a rate that exceeds the rate of its arrival at the electrode surface at the rotation rates employed. The slopes of linear Levich plots like the one in Figure 4B were used to calculate diffusion coefficients for PAA-Fc in acidic solutions from the Levich equation11
IL ) 1.94 × 104nCAν-1/6ω1/2D2/3
(1)
where IL is the Levich current, n is the number of electrons
I-1 ) IL-1 + Ik-1
(2)
where I is the measured plateau current, IL is the Levich current given by eq 1, and Ik is a “kinetic current” that measures the rate of the process that is responsible for the depression of the plateau currents to values below the diffusion-convectioncontrolled Levich currents. Ik is independent of the electrode rotation rate so that plots of I-1 vs ω-1/2 are expected to be linear with slopes proportional to D-2/3 and intercepts equal to Ik-1. The plateau currents that deviated from linearity in the Levich plot in Figure 4B are replotted in the Koutecky-Levich format in Figure 4D. The data points now lie on a straight line in accord with eq 2. The slopes of plots such as the one in Figure 4D were used to estimate diffusion coefficients under conditions where Levich plots were not linear. Diffusion Coefficients for PAA-Fc. In Figure 5A are shown the values of diffusion coefficients for PAA-Fc obtained in supporting electrolytes of varying pH and ionic strength. Shown in Figure 5B is the fraction of total carboxyl groups that are dissociated at each pH calculated from a titration of unlabeled PAA of the same molecular weight. The decrease in the diffusion coefficient as the pH increases in Figure 5A is clearly correlated with the increase in the anionic charge of the polymer which is well-known to result in the conversion of the polymer structure from entangled chains to more extended conformations because of electrostatic repulsion among the carboxylate groups. The larger effective diameter of the extended chains and their likely greater hydration produces smaller diffusion coefficients. The error bars in Figure 5A reflect the fact that the reproducibility of the values of D obtained at low pH was poorer than at high pH despite the nicely linear Levich plots obtained at low pH. The reproducibility in separate measurements at a given pH was good, typically (10-15%. However, when two solutions were prepared separately by dissolution of the solid and adjustment of the pH to the same value, variations in D as large as 40% were not uncommon at pH values between 3 and 4.5. The origin of this limited precision in the estimation of D at low pH is unclear. To check that the changes in D shown in Figure 5A were not the result of changes in the viscosity of the solution with pH, the diffusion coefficient of ferrocenylethanol was measured in solutions containing unlabeled PAA at the same series of pH values. The diffusion coefficient remained constant at 6.3
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Figure 5. (A) Diffusion coefficients of PAA-Fc in 0.2 M NaCl (b) and 0.05 M NaCl (O) as a function of pH. The error bar shown at pH 2.8 also applies to the other points up to pH 5. The error bar shown at pH 8.2 also applies between pH 5 and 8.2. (B) Extent of dissociation of the carboxylate groups of PAA-Fc in 0.2 M NaCl. (C) Dependence of the diffusion coefficients of PAA-Fc upon the ionic strength of the supporting electrolyte at pH 2.8 (O) and 8.2 (b).
TABLE 1: Diffusion Coefficients of PAA-Fc with Varying Ratios of Ferrocene (Fc) to Carboxylate (PAA) Groups 106 D/cm2 s-1 b Fc/PAAa
pH ) 2.8
pH ) 8.2
0.7 1.0 1.3 2.0
1.3 ( 0.4 1.4 ( 0.4c 1.3 ( 0.4 1.1 ( 0.4
0.88 ( 0.1 0.85 ( 0.1c 0.89 ( 0.1 0.91 ( 0.1
a Average number of ferrocene groups attached to each PAA chain that initially contained an average of ca. 70 carboxylic acid groups. b Evaluated in 0.2 M NaCl as supporting electrolyte. c Differences between these values of D and those in Figure 5A reflect the reproducibility of the measurements in separate experiments.
× 10-6 cm2 s-1, independent of pH, indicating that any viscosity changes were minor. The fact that the values of D obtained for PAA-Fc remained well below that for ferrocenylethanol at all pH values showed that the ester bond between the PAA and ferrocene groups was stable throughout the range of pH values investigated. The diffusion coefficients in Figure 5A were calculated by assuming that all of the ferrocene centers attached to the PAA chains were fully electroactive. To check this assumption, diffusion coefficients were evaluated with additional samples of PAA-Fc in which a larger number of ferrocene groups were present (on average) on each polymer chain. The results, summarized in Table 1, show that, within the range investigated, the values of D were independent of the number of ferrocene
labels per chain, as expected if all of the attached ferrocene centers remained fully electroactive. The diffusion coefficient of PAA-Fc at pH 8.2 exhibited a considerable dependence on the ionic strength of the supporting electrolyte as shown in Figure 5C. The increase in the diffusion coefficient with ionic strength up to ca. 0.2 M probably reflects the conversion of the PAA-Fc molecules from extended to more tangled chains as the electrostatic repulsion between carboxylate groups is partially shielded. However, the effect of the added electrolyte appears to saturate at about 0.2 M, and further increases do not cause the diffusion coefficient to increase to the values observed at low pH where the molecules are essentially uncharged (Figure 5A). The diffusion coefficients evaluated at pH 2.8 were much less dependent on ionic strength (solid points in Figure 5C). Association of Electroactive Countercations with PAAFc. At pH values where the PAA-Fc molecules are polyanionic, multiply-charged cations are strongly attracted by the polyanions, and at sufficiently high concentrations of the polyelectrolyte, essentially all of the multiply charged cations are bound to the polyanion, even in the presence of large excesses of Na+ cations. When the multiply charged cations are electroactive, the electrostatic association can be monitored by observing the decrease in the diffusion coefficient of the countercations that results from their binding to the polyanion molecules. Experiments of this type were carried out in our previous study of mixtures of unlabeled PAA with Ru(NH3)63+ or Co(NH3)63+ as counterions.6 Repetition of such measurements with the ferrocene-labeled PAA produced the results shown in Figure 6. In Figure 6A is shown a current-potential curve obtained at a rotating disk electrode in a solution containing both Ru(NH3)63+ and PAA-Fc. The cathodic wave with a half-wave potential near -0.2 V arises from the reduction of Ru(NH3)63+ (both bound and unbound), and the anodic wave with a halfwave potential near 0.1 V arises from the oxidation of the ferrocene centers in the PAA-Fc. The plateau currents for both waves were measured at a constant electrode rotation rate as the concentration of PAA-Fc was increased, and the results are shown in Figure 6B. The increases in the plateau current for the oxidation of the Fc centers with their concentration were essentially linear because, at the low rotation rate employed, the deviation of the corresponding Levich plots from linearity was small. The plateau currents for the reduction of the Ru(NH3)63+ counterions diminished as the concentration of PAAFc increased because more and more of the cation was bound by the more slowly diffusing PAA-Fc molecules until a steady current was obtained. This is the expected behavior when the concentration of the polyelectrolyte becomes high enough to produce essentially complete association of the Ru(NH3)63+ cations with the polyanionic molecules. Linear Levich plots were obtained for the reduction of Ru(NH3)63+ (Figure 6C). The slopes of these plots were used to evaluate an apparent diffusion coefficient for the Ru(NH3)63+ at each concentration of PAAFc. The Levich plots for the oxidation of the Fc centers were nonlinear in the presence of Ru(NH3)63+ (Figure 6C) just as they were in the absence of Ru(NH3)63+ (Figure 4B), so the slopes of Koutecky-Levich plots (which were linear) were used to evaluate diffusion coefficients for the PAA-Fc at each concentration. The resulting values of the diffusion coefficients are plotted in Figure 6D. An analogous set of experiments carried out with Co(NH3)63+ instead of Ru(NH3)63+ as the electroactive counterion produced the diffusion coefficients plotted in Figure 6E. The values of D for the PAA-Fc polyanion (circle points) are essentially independent of its concentration and about the same as the values obtained in the absence of
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Figure 6. (A) Current-potential curve at a rotating graphite disk electrode in a solution containing 0.15 mM ferrocene groups of PAA-Fc and 0.1 mM Ru(NH3)63+ in 0.05 M NaCl at pH 8.2. The electrode rotation rate was 240 rpm. (B) Anodic (O) and cathodic (4) plateau currents from curves like the one in (A) for 0.1 mM Ru(NH3)63+ and varying concentrations of PAA-Fc expressed in terms of the carboxylate groups present. (C) Levich plots of the plateau currents for the two waves in mixtures of PAA-Fc and Ru(NH3)63+: (4) reduction of Ru(NH3)63+; (O) oxidation of Fc groups in PAA-Fc. (D) Diffusion coefficients for Ru(NH3)63+ (4) and PAA-Fc (O) in solutions containing 0.1 mM Ru(NH3)63+ and varying concentrations of PAA-Fc. The [PAA-Fc] is expressed in terms of carboxylate groups. (E) as in (D) for Co(NH3)63+ instead of Ru(NH3)63+.
Ru(NH3)63+ or Co(NH3)63+ (Figure 5). More important is the observation that the steady value of the diffusion coefficients for the Ru(NH3)63+ and Co(NH3)63+ counterions (triangle points in Figure 6, D and E) obtained at the highest concentrations of PAA-Fc match the diffusion coefficient of the polyanion itself as measured by the oxidation of the ferrocene label. This is the result required by the assumption that all of the Ru(NH3)63+ or Co(NH3)63+ cations are bound to the polyanion at concentrations above ca. 3 mM in Figure 7D. The very good agreement between the two independently measured diffusion coefficients for both electroactive counterions constitutes strong support for this assumption. It was somewhat puzzling to obtain linear Levich plots for the reduction of Ru(NH3)63+ under conditions where essentially all of the counterion was bound electrostatically to the PAAFc polymer while the covalently bound ferrocene centers in the same molecules exhibited nonlinear Levich plots (Figure 6C). We attribute this apparent anomaly to differences in the mechanisms by which the two types of electroactive centers react at the electrode surface on which a layer of adsorbed PAAFc is present. As suggested earlier, we believe that oxidation of the Fc centers covalently bound to the PAA-Fc molecules in solution at pH 8.2 requires that the polymer move through the adsorbed layer of PAA-Fc on the electrode surface and that the rate of this motion is below the diffusion-convection-controlled value, except at very low electrode rotation rates. By contrast, the electrostatically bound Ru(NH3)63+ counterions are free to move along the polyanionic chains and to hop from chain to chain which could facilitate their reduction either by rapid diffusion in and out of the adsorbed layer or by self-exchange between Ru(NH3)62+ counterions bound in the adsorbed layer and Ru(NH3)63+ counterions bound to PAA-Fc molecules in solution. This latter possibility seems less likely because the
Figure 7. Cyclic voltammograms in pure supporting electrolytes for PAA-Fc adsorbed on the graphite electrode. (A) Response from an electrode like the one used to record curve 1 in Figure 3A after transfer to 0.2 M NaCl at pH 2.8: (s) recorded immediately after the transfer; (- - -) recorded 3 h later. (B) Response from an electrode like the one used to record curve 2 in Figure 3A after transfer to 0.2 M NaCl at pH 8.2. (C) Response from the electrode used to record (B) after transfer to 0.2 M NaCl at pH 2.8.
behavior of Ru(NH3)63+ and Co(NH3)63+ counterions was similar (Figure 6, D and E), and the lifetime of Co(NH3)62+ in the solutions employed is much too short to support significant self-exchange between the reduced and oxidized complex.13 Thus, we believe that the Ru(NH3)63+ and Co(NH3)63+ cations are able to reach the electrode surface by moving through the adsorbed polyanion layer. However, whatever the mechanism of the electroreduction, the agreement between the two diffusion coefficients in Figure 6, D and E demonstrates both the utility
Intrinsically Electroactive Polyelectrolytes and the reliability of electroactive counterions in estimating diffusion coefficients of polyelectrolytes to which they are bound. Adsorption of PAA-Fc on the Graphite Electrode Surface. In a previous study the adsorption of unlabeled PAA on the surface of graphite electrodes in the presence of multiply charged electroactive countercations was established.6 However, it was not possible to measure the quantities of the electroinactive PAA that were adsorbed. With PAA-Fc, the adsorption of the polyelectrolyte could be monitored directly. The solid curve in Figure 7A was obtained by transferring the electrode used to record curve 1 in Figure 3A to a pure supporting electrolyte solution at pH 2.8. The peak current is about two-thirds as large as that of curve 1 in Figure 3A, showing that the adsorbed reactant made a major contribution to that voltammogram, as deduced previously from its shape and the scan rate dependence of its peak current. The area under the anodic peak in Figure 7A corresponds to 3.5 × 10-10 mol cm-2 of ferrocene groups, and ca. 70 times as many carboxylate groups accompany each ferrocene group so that the adsorbed polymer coating must contain multiple molecular layers. The solid curve in Figure 7A is the response obtained immediately after the electrode was transferred to the pure supporting electrolyte. After 3 h of continuous cycling of the potential, the response had changed only slightly (dotted curve) so the PAA-Fc adsorbed at pH 2.8 is retained on the surface for extended periods. Electron propagation across the relatively thick adsorbed layers present at low pH probably involves electron hopping between adjacent ferrocene and ferrocenium sites which is apparently facile judging from the shape of Figure 7A. Figure 7B is the response obtained when the electrode used to record curve 2 in Figure 3A at pH 8.2 was transferred to a pure supporting electrolyte at the same pH. The voltammetric response contains no evidence of the presence of irreversibly adsorbed PAA-Fc. However, when the pH of the supporting electrolyte was decreased to 2.8 by addition of HCl, a small response from adsorbed PAA-Fc appeared (Figure 7C). Evidently, electron hopping between the ferrocene sites in the adsorbed polymer on the electrode surface is more facile when the polymer is uncharged rather than polyanionic. The implication of these results is that the adsorption of PAA-Fc from solutions where it exists as a polyanion is much less extensive than the adsorption from solutions where it exists as the uncharged acid. In addition, charge propagation within the smaller quantity of PAA-Fc that is adsorbed at pH 8.2 is much less facile (Figure 7B) than is true at pH 2.8 (Figure 7A), perhaps because the motion of the polymer chains required to bring the ferrocene centers sufficiently close together to allow electron hopping between them to occur is less hindered when repulsion between the anionic carboxylate groups is removed. Electrostatic repulsion is also the likely reason that the adsorption of the soluble, highly charged polyanionic form of PAA-Fc is less extensive than that of the uncharged, less soluble form.14 At low pH, the electrooxidation of the ferrocene centers in PAA-Fc molecules in solution seems likely to occur by electron self-exchange between ferrocenium centers in the thick, adsorbed layer of PAA-Fc and the ferrocene centers of the dissolved polymer. At high pH, where electron hopping among the ferrocene centers in the adsorbed PAA-Fc is slow (Figure 7B), the dissolved polymer probably must move through the
J. Phys. Chem., Vol. 100, No. 20, 1996 8453 thinner layer of adsorbed polymer for the oxidation of the ferrocene centers to occur. Concluding Remarks Although the results shown in Figure 6 are encouraging with respect to the use of electroactive counterions for assessing the mobilities of polyelectrolyte molecules with which they associate, the limitations inherent in such experiments need to be recognized. If the polyelectrolyte being studied consists of an array of molecular weights, the diffusion coefficient obtained will be an average value in which the lower molecular weight components contribute disproportionately to their concentrations because they diffuse more rapidly. If the association of the electroactive counterions with the polyelectrolyte molecules is not statistical, e.g., if higher molecular weight polyions bound the counterions preferentially, the average diffusion coefficients obtained from the electrochemical measurements would not reflect the true average diffusion coefficient of the array of polymer molecules present. In the present experiments this possible source of confusion was apparently not important because the diffusion coefficient based on the covalently linked ferrocene label matched that based on the electroactive counterions. Such agreement would not be expected unless both types of label were distributed statistically among the polymer molecules present. Finally, the extensive adsorption of the polyelectrolyte molecules on electrode surfaces is a generally undesirable complicating feature when electrochemical methods are employed to estimate diffusion coefficients. The use of rotating disk voltammetry and Koutecky-Levich plots can sometimes circumvent the problems introduced by polymer adsorption, but these tactics may not always prove successful. However, labeling polymers with electroactive groups can facilitate estimation of the extent of their adsorption with electrochemical techniques. In addition, the same polymer adsorption that may interfere in the estimation of diffusion coefficients might be exploited to measure the rates of electron transfer through polymer coatings labeled with redox groups. Acknowledgment. This work was supported in part by the U.S. Army Research Office (Durham). References and Notes (1) Ohyanagi, M.; Anson, F. C. J. Electroanal. Chem. 1989, 285, 469. (2) Ohyanagi, M.; Anson, F. C. J. Phys. Chem. 1989, 93, 8377. (3) Kobayashi, J.; Anson, F. C. J. Phys. Chem. 1991, 95, 2595. (4) Jiang, R.; Anson, F. C. J. Phys. Chem. 1991, 95, 5701. (5) Jiang, R.; Anson, F. C. J. Phys. Chem. 1992, 96, 452. (6) Jiang, R.; Anson, F. C. J. Phys. Chem. 1992, 96, 10565. (7) Yoshikawa, M.; Anson, F. C. J. Phys. Chem. 1996, 100, 4199. (8) Lednicer, D.; Lindsay, J. K.; Hauser, C. R. J. Org. Chem. 1958, 23, 653. (9) Kaplan, L.; Kewster, W. L.; Katz, J. J. J. Am. Chem. Soc. 1952, 75, 5531. (10) Scott, D. R.; Becker, R. S. J. Chem. Phys. 1961, 35, 516. (11) Levich, V. G. In Physicochemical Hydrodynamics; Prentice-Hall: Englewood Cliffs, NJ, 1962; pp 345-57. (12) Koutecky, J.; Levich, V. G. Zh. Fiz. Khim. 1956, 32, 1565. (13) Geselowitz, D. A.; Taube, H. Comments Inorg. Chem. 1982, 1, 391. (14) Fleer, G. J.; Stuart, M. A. C.; Scheutjens, J. M. H. N.; Cosgrove, T.; Vincent B. In Polymers at Interfaces; Chapman and Hall: London, 1993, p 343.
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