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semblies of octadecyltrichlorosilane and N-methyl-Af'-octa- decyl-4,4'-blpyrldinlum chloride. Voltammetrlc and chrono- coulometrlc studies in dilutefe...
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Anal. Chem. 1988, 60, 1168-1176

1168

Microporous Aluminum Oxide Films at Electrodes. Dynamics of Ascorbic Acid Oxidation Mediated by Ferricyanide Ions Bound Electrostatically in Bilayer Assemblies of Octadecyltrichlorosilane and an Octadecylviologen Amphiphile Cary J. Miller and Marcin Majda* Department of Chemistry, University of California, Berkeley, California 94720

Electrode films of porous alumlnum oxlde are used as mlcrostructural templates for the lmmobllratlon of bilayer assemblles of octadecyHrlcMorosllane and N-methyl-N’octadecyl-4,4’-blpyrldlnlum chlorlde. Voltammetrlc and chronocoulometrlc studles In dllute ferrocyanlde solutlons reveal lon+xchange bhwlhg of ferrocyanide In the head group region of the Mlayer assembly. The maxlmm quantity of the bound Ions Is reached near the polnt of complete charge neutrallratlon of the vlologen surfactant by ferrocyanlde. Dlffuslon of ferrocyanide along the bHayer assembly Is Independent of Its dlffuslon In the solution as a result of an Insuffklently hlgh rate of electron exchange between the bound and the solution specles. The dynamlcs of the ferrlcyanlde-medlated electrooxklatlon of ascorbic ackl were lnvestlgated In vlew of the SavCant-Andrleux theory wJth a plmary goal of obtalnlng the rate constant of the medlation reactlon. An enhancement of the rate constant was observed and Interpreted In terms of the electrostatic shleldlng effect. The presence of octanol In solutlon and its Intercalatlon Into the bilayer assembly decrease the electrostatic Interactions between the ferrkyankle andvlobgengroupg. Conslstentiywlththkgeneralconcl~ and our previous Investlgatlons, we observed an Increase of ferrocyanide moMllty and a decrease of the rate constant of ascorblc acld oxldatlon.

Thin filmsof ion-exchange polymers and other ion-exchange materials have been used extensively to modify electrode surfaces ( I ) . The universal ability of these coatings to incorporate electrochemically active ions proved to be useful in the development of analytical sensors (2-5) and in the design of electrocatalyticsystems (6-15). The elements of film behavior crucial to its performance in electrocatalysis have been particularly emphasized. These are, besides the type of the immobilized electrocatalyst, the transport of a solution reactant to the catalytic sites within the electrode film and the electron transport, a process responsible for the regeneration of the catalytically active oxidation state of the catalyst. Both of these transport problems have a strong intrinsic dependence on the physical and chemical structure of the electrode film. The modes of charge transport of species immobilized within ion-exchange films have been an object of particular interest (16-22). A large variation in the apparent diffusion coefficients (in the range of to lo4 cm2/s) has been reported for ionic species bound within different ion-exchange materials (23-25). Recently, the role of microscopic heterogeneity of the electrode films has been the main focus of these studies (18, 20-24,26-31). The presence of well-segregated hydrophobic and hydrophilic domains of vastly dif*Author to whom correspondence should be addressed. 0003-2700/88/0360-1168$01.50/0

ferent composition and properties, and their influence on the charge transport processes were first observed in Ndion films (18, 28). More recently, Anson and co-workers have investigated a number of random, ternary polymers and block polymers, which strongly self-segregate into microscopic hydrophilic and hydrophobic domains (23,29-31). Significant improvements in the ion binding capacity and retention as well as faster rates of charge diffusion have been observed in these systems and related directly to their heterogenous structure (23). Specifically, Anson and co-workers postulated that diffusion of the electrostatically bound ions along the charged “Donnan” domains of the hydrophilic regions constitutes an efficient means of charge propagation within these electrode films (22). A more complete understanding of the charge transfer dynamics within such polymeric systems will require a detailed knowledge of the internal structure of the polymer films. Films of porous aluminum oxide, developed in this laboratory, constitute a special case of electrode films of microheterogeneous character (27). Their structure, consisting of a dense array of cylindrical pores of controllable diameter in the range of 20-200 nm which propagate normal to the oxide surface, is well suited for electrocatalytic and sensor applications. Adsorption of polymers or attachment of reagents along the inner surfaces of the oxide films does not alter the films’ overall porous structure while induces at the same time desired chemical properties. In a previous report, we have described the impregnation of the electrode films of porous aluminum oxide with thin, ca. 20-80 A, adsorbed layers of poly(viny1pyridine)(PVP) (27). In that system, the diffusion of ferrocyanide ions bound within a thin, protonated PVP layer was similar to that observed for the bulk polymer. Clearly, the impregnation of the oxide films with P W did not change the properties of the polymer with respect to its ionexchange binding and charge transport properties (27). A different method of reagent immobilization in the porous aluminum oxide films was demonstrated recently. We have shown that the spontaneous organization of amphiphiles onto the inner surfaces of the oxide films can be used as a general method for the formation of bilayer assemblies of various electroactive amphiphiles (32, 33). A unique system with ion-exchange properties and a high degree of spatial ordering is produced when the surfactant layer of the bilayer assembly is ionic. An example of such a system is the recently reported bilayer assembly consisting of octadecyltrichlorosilane (OTS) and N-methyl-N‘-octadecyl-4,4‘-bipyridiniumchloride (C18MV2+) supported on the inner surfaces of a porous aluminum oxide fdm at an electrode. We have demonstrated that the charged, bipyridinium head groups of this amphiphile are strongly ion-paired and that they are capable of binding ferricyanide ions through ion-exchange equilibria (33). In this paper we carry out a systematic analysis of the performance of a complex, multimolecular system consisting of a rigid aluminum oxide film of microscopically heteroge0 1988 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988

neous structure, which supports an organized amphiphilic bilayer assembly with ion-exchange properties. Despite this level of chemical and structural complexity, we are able to dissect the system's performance into ita individual functions and provide their detailed characterization. The ultimate goal of these types of investigations is to develop synthetic procedures and analytical methods of investigation needed to build systems for sensor and electrocatalytic applications. Specifically, we give a detailed description of the ferricyanide binding in the OTS/C18MV+bilayer assemblies. We show that the charge transport in this system of the ion-paired ferricyanide ions involves their lateral diffusion along the OTS/C18MV+bilayer to the electrode surface. Furthermore, the immobilized ferricyanide ions serve as an example of an electrocatalyst in the investigations of the mediated electrooxidation of L-ascorbic acid. The rate constant of the mediation reaction, besides its usual pH variation, depends also on the microstructural features of the bilayer assembly and on the strength of ferricyanide binding. This finding is rationalized in terms of the electrostatic shielding effect and related to previous investigations of this mediation reaction (15).

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RESULTS AND DISCUSSION The exposure of a porous aluminum oxide film to an OTS solution in hexadecane renders its surface hydrophobic due to the self-assembly of an OTS monolayer on the inner surfaces of the oxide film. Subsequent exposure of the OTStreated porous aluminum oxide coated electrode to an aqueous solution of C18MV2+results in the formation of an OTS/ C18MV2+bilayer supported on the internal surfaces of the electrode film (32, 33). The C18MV2+layer of the electrode assembly is completely electroactive, displaying diffusion coefficients within the range (4 to 7) X cm2/s (33). Translational diffusion of the viologen surfactant along the bilayer assembly was shown to be the dominant mechanism responsible for the observed electroactivity and charge transport (34). Figure 1A shows a cyclic voltammogram of

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EXPERIMENTAL SECTION Reagents. N-Methyl-Nf-octadecyl-4,4'-bipyridinium chloride was synthesized as described previously (33). Octadecyltrichlorosilane (OTS)(Petrach, Inc.) was vacuum distilled into glass ampules; a fresh ampule was opened for each series of experiments. Hexadecane (Aldrich)has passed through a column of activated alumina (ICN Biochemicals grade Super I neutral). All other chemicals were reagent grade and used as received. A stock solution of L-ascorbicacid was freshly prepared by using deaerated electrolyte prior to each experiment and kept under a positive pressure of argon. Aliquots of this solution were transferred to the electrochemicalcell by means of a gas-tight syringe in order to minimize the oxidation of the ascorbic acid by oxygen. Oxide Films. The aluminum oxide films were produced from high-purityaluminum foils or vapor-deposited aluminum on glass slides by anodization at 65 V in 4% H3P04as described previously (27). The oxide films produced by this procedure were 3-4 pM in thickness having an average pore diameter of ca. 800 A. After the chemical dissolution of the barrier layer, the oxide films were derivatized with octadecyltrichlorosilaneby exposure to a freshly made 2% solution (v/v) of OTS in hexadecane and subsequently washed with toluene and 2-propanol. The details of this procedure were described earlier (33). Vapor deposition of gold onto one side of an oxide f i i and the fabrication of the electrodes followed the OTS treatment. Surfactant incorporation into the OTStreated porous aluminum oxide coated electrodes involved exposing the electrodes wetted with isopropyl alcohol to an aqueous solution of the surfactant in 0.1 M KC1. Electrochemical Instrumentation and Procedures. Electrochemical experiments were done with the PAR Model 173, 175,and 179 instruments and a BAS 100 electrochemical analyzer. An IBM Model EC/219 rotating disk electrode system was used for the determinations of film porosity and in the experiments involving the mediation of ascorbic acid oxidation.

1169

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0.4 0.2 0 -0.2 -0.4 -06 E vs. A g / A g C I , sat. K C I

Figure 1. Cyclic voltammograms of an OTS/C,8MV2+assembly Immobillzed in a porous aluminum oxide film at a gold electrode ( A = 0.071 Cm'): (A) 0.1 M KCI, scan rate 50 mV/s; (B) 0.1 M KCI, 5 pM

K,Fe(CN),, scan rate 50 mV/s. such an electrode assembly in surfactant-free electrolyte. A typical coverage of C18Mv2+on the OTS-treated A1203 surface is 2.0 X mol/cm2. A t this coverage the electrode assemblies show good stability with a loss of the viologen surfactant of less than 15% per hour. Ferrocyanide Binding and Stability. Introduction of ferrocyanide ions at a 5.0 pM level to the 0.1 M KC1 electrolyte results in their preconcentration in the electrode film as shown in Figure 1B. The quantity of bound ferrocyanide reaches steady state after approximately 10 min in a stirred solution. The magnitude of the ferrocyanide voltammetric peak current in Figure 1B is due essentially just to the ions bound along the OTS/C18MV2+assembly, since the electrooxidation of ferrocyanide present in the electrolyte solution at this concentration level produces a negligible signal. The formal redox potential of the C18MV+/C18MV'+couple is shifted 50 mV in the negative direction upon ion-pairing with ferrocyanide. As expected, the dicationic C l a w +species binds ferrocyanide ions more strongly compared to the singly charged cation radical, C18MV'+. When the viologen surfactant is reduced by one electron, there is an approximately 30% loss of bound ferrocyanide due to a diminished binding capacity of the viologen assembly in its reduced state. Similar differences in the binding capacity were noted in the literature (35,36). The voltammetric peaks of C18MV2+in Figure 1B are smaller and bear stronger diffusive character than those in Figure 1A prior to ferrocyanide addition. This is due to a decrease of the C18MV+diffusion coefficient in the assembly upon ferrocyanide binding as described below.

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ANALYTICAL CHEMISTRY. VOL. 60. NO. 11, JUNE 1. IS88

Table I. Ion-Exchange Binding and Diffusion Coefficients of Ferrocyanide Ions in OTS/C18MV'+Assemblies in Porous Aluminum Oxide films at Gold Electrodes

0

8 16 32 64

0.34 0.37 0.42 0.43

5.5 1.1 1.1 1.2 1.1

4.6 4.4 5.2 5.3

4.1 4.6 5.5

5.9

3.5 3.3 4.0 4.2

"The measured diffusion coefficients. 'Diffusion coefficients of ferrocyanide bound in the C I I I M Passembly. (The values in the previous column corrected for the translational diffusion of CIBMV2+(column 3). Upon transfer of the O T S / C I 8 W * electrode from the 5.0 pM ferrocyanide solution to ferrocyanide-free supporting electrolyte, 80% of the bound ferrocyanide is lost from the film within ca. 5 min. The voltammogram of the C18MV2* species reverts back to the one obtained before the introduction of the ferrocyanide shown in Figure 1A. The lack of stability of the ion-paired ferrocyanide upon transfer to ferrocyanide-free electrolyte solution is reminiscent of the hehavior of the PVP-impregnated porous aluminum oxide film electrodes in acidic electrolytes, which we investigated previously (27).In both these cases, the nearly two-dimensional character of the ion-exchange domains populated with cation sites and the open structure of the electrode films facilitate rapid equilibration between the hound and the solution ferrocyanide ions. Consequently, a small concentration of K,Fe(CN), ( 5 6 5 pM) was always maintained in the electrolyte solution to stabilize the binding level of ferrocyanide in the OTS/ClsMV2+ bilayer assembly. In order to measure the extent of ferrocyanide binding as a function of its concentration in solution, we did a series of long p h t i m e chronocoulometric experimentswith electrodes coated with porous aluminum oxide films containing the OTS/C18MVzC bilayer assemblies. The self-assembly of CIaMV+was carried out in a 0.5 mM ClsMV2+,0.1 M KCI solution. This produced a stable coverage of 2.0 X mol/cm2 upon transfer of the electrode to a 0.1 M KCI electrolyte free of C18MV2+. Subsequently, small aliquots of a concentrated K,Fe(CN), solution were added to the solution so that the resulting ferrocyanide concentration increased in four steps from 8 to 64 pM (see Table I). After each addition, and and equilibration time allowing partitioning of the ferrocyanide ions into the C & W + assembly, two 10-8 potential step experiments were done to measure the quantity of both the hound ferrocyanide and the assembled C18MVzcin the bilayer. Each of these experiments began at 0.0 V where C,MV2* and ferrocyanide are the stable redox forms. The potential pulses were applied in the positive and the negative directions beyond the redox potentials of the ferri-/ferrocyanide and the Cl8MV2+/ClsMV'+redox potentials, respectively. A representative Anson plot of the data of the oxidizing pulse is shown in Figure 2. The initial linear portion of the plot is due to the diffusion of ferrocyanide ions under the semiinfiiite diffusion conditions along the OTS/C,&W* bilayer. The second linear region, a t longer times, reflects the Current due to the solution component of the ferrocyanide flux to the electrode surface. By extrapolating the long time portion of the plot and the initial linear region of the plot to zero time. one obtains the total charge due to the oxidation of hound ferrocyanide, Qb,as marked in Figure 2. Determination of the bound electroactive species by integration of the voltammetric current due to the ferri-/ferrocyanide couple as in Figure 1B produces, as expected, results in g d agreement with the chronocoulometricmethod. The latter is preferred because it offers better means of subtracting the background charge and because it eliminates the additional

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FWra 2. A representative Anson plot of a 10-6 potential step ckonocoulometric experiment done at a orous aluminum oxme coated Au elechode wiih the OTSIC,.MV2 P bilayer assembly in 64 pM K,Fe(CNh+, 0.1 M KCI. The electode potenllal was stepped from 0.0 to +0.40 v vs AglAgICl (saturated KCI). The exkapolation of the nrst and the second linear regions of the plot to t = 0 gives 0,. the equivalent charge of the bound ferrocyanide Ions. as shown in the figure.

Figure 3. A &matic rspresenlalion of llm OTSIC,.MV* bilayer aasembly bMing ferrocyanide Ions. The OTS mnolayer is rhown to be attached to the AI& d a c e of a porws aluminum oxide Rlm. The bilayer assembly is perpendicular to llm electrode surtace as a resuk of the prpendicular Orientation of the microscopic pores of llm oxide template.

integration step in the voltammetric assay. Qualitatively, identical Anson plots were obtained hy stepping the electrode potential to a large negative value to quantify C 1 8 Wspecies in the assembly. The results of these measurements covering the full series of ferrocyanide concentrations in solution are gathered in Table I. As the ferrocyanide concentration in solution increases, the mole ratio of the bound ferrocyanide ions to ClaMV2*increases. At the highest concentration level, the mole ratio approaches 0.5, which is equivalent to the unity charge compensation ratio. On the basis of these measmments, one can construct a simple model of the structure of the electroactive assembly as shown in Figure 3. The bound ferrocyanideions are confined to the head group region of the OTS/CI8MVZ* bilayer and compete with Cl- ions of the supporting electrolyte for the binding sites in the charged region of the assembly. This region, equivalent to Donnan domains of an ion-exchange polymer, is essentially two dimensional as it is limited by the

ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988

structure of the porous aluminum oxide f i i and the particular arrangement of the molecules in the OTS/C18MV+assembly. This unique geometry of the system gives us a chance to measure the rate of two-dimensional ion diffusion along the charged surfaces with ion-exchange properties. Charge Transport i n the OTS/ClsMV2+/Fe(CN)64Assembly. The data from the chronocoulometricexperiments described in the previous section were also interpreted in terms of the diffusion coefficients of the lateral transport of the bound ferrocyanide ions and the ClsMV2+along the bilayer assembly. Specifically, the slope values of the initial linear region of the Anson plots, such as that in Figure 2, were used to calculate the diffusion coefficients according to the integrated form of the Cottrell equation

D = rS2d2/4Qb2 (1) where Qbis the charge due to the complete reduction or oxidation of the bound ferrocyanide (or ClsMV2+)within the electrode film, S is the slope value of an Anson plot, and d is the film thickness. As seen in Table I, the apparent diffusion coefficients of the bound ferrocyanide ions, DFe(CNp-, increase only slightly ((4.7 to 5.9) X cm2/s) as the bulk concentration of ferrocyanide increases &fold. The magnitude of this diffusion coefficient indicates that physical motion of the ferrocyanide ions rather than electron hopping is the mechanism of charge propagation; this conclusion involved the evaluation of the rate constant of the electron self-exchange for the ferri-/ferrocyanide couple in terms of the electron diffusion coefficient and was discussed in detail elsewhere (15). The apparent diffusion coefficient of the CIsMV2+amphiphile, D s ~ also , listed in Table I, decreasm dramatically with the first addition of ferrocyanide ions to the electrolyte solution. After this initial drop, it remains constant in spite of the increasing level of ion-pairing with ferrocyanide ions. On the basis of our previous investigations of the OTS/ ClsMV2+system, we know that the translational diffusion of the ClsMV2+molecules is the operating mechanism of the charge transport in this case (34). The decrease of DclsMVz+ upon ion-pairing with ferrocyanide ions was attributed to electrostatic cross-linking and a lower microfluidity of the C18MV2+layer (33). Two-Phase Diffusion of Ferrocyanide Ions. The analysis of the apparent diffusion coefficients of ferrocyanide (Table I) is complicated by the heterogeneous nature of the system and the resulting biphasic character of the ferrocyanide diffusion processes in the electrode films. This means that ferrocyanide ions are present and diffuse simultaneously in two phases, the electrolyte solution phase in the central part of the oxide pores, and the ion-exchange, Donnan region of the OTS/ClSMV+bilayer assembly (see Figure 3). Diffusion of ferrocyanide in both diffusion channels either may be coupled or may proceed independently of each other. The coupling of the two diffusion channels involves fast electron and/or mass exchange between two members of the ferri-/ ferrocyanide redox couple present in the different phases across their boundary. Such coupling results in an equal rate of expansion of the diffusion front in both phases in the electrochemical experiments such as chronocoulometry, despite the fact that the intrinsic values of the diffusion coefficients of ferrocyanide ions are different in the two phases. In other words, the slower ferrocyanide transport in the ionexchange phase is, effectively, mediated by the ferricyanide ions in the faster diffusion channel of the electrolyte solution. Lack of such coupling allows a more rapid expansion of the diffusion front in the electrolyte phase, where ferrocyanide ions are more mobile. We have dealt with the biphasic diffusion problem before in the case of ferrocyanide diffusion in PVP impregnated

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Table 11. Effect of Ferrocyanide Concentration in Solution on Its Lateral Diffusion Coefficients in OTS/C18MV2+ Assemblies CFe(CN)g'-/ pM

QF~(cN)~c/

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0

16 31 62 124 242 356 466 572

0.30 0.30 0.32 0.35 0.39 0.42 0.45 0.46

4.5 4.4 4.5 4.8 5.2 5.1 6.5 1.5

4.4 4.9 5.1 7.0 9.2 11 13 14

4.2 4.4 4.1 5.3 6.4 7.4 8.3 9.3

4.3 4.0 3.8 3.6 3.1 2.8 2.8 2.9

a Calculated values of the ferrocyanide diffusion coefficient based on the model assuming coupling between the ion-exchange and the solution phases. Calculated values of the ferrocyanide diffusion coefficient assuming uncoupled diffusion in the two phases. Diffusion coefficients of ferrocyanide bound in the ClpMVZ+assemblv.

porous aluminum oxide films at electrodes (27). The mathematical formalism describing the system under potential step conditions was derived there for two limiting cases: (i) full coupling (very fast cross-phase electron and/or mass transport exchange) and (ii) lack of coupling between phases. If the cross-phase exchange is fast, one would expect the measured diffusion coefficient, D,, to be given by

Dc = XgD,

+ X@b

(2)

where x , and xb are the mole fractions of ferrocyanide within the solution and the ion-exchange domains, respectively, and D, and Db are the ferrocyanide diffusion coefficients in the two phases (37). In the limiting case of no cross-phase exchange, one expects the total flux to the electrode surface to be the sum of the two independent contributions, which leads to the following expression for D,, (27):

(3) In order to make a mechanistic assignment of our system to one of these two cases, we examined more carefully the dependence of the apparent diffusion coefficient on the solution concentration of ferrocyanide. The results are shown in Table 11. In column 4 of this table are listed calculated values of D, based on the coupled diffusional channels model of eq 2. D, was a literature value of 6.7 X lo4 cmz/s and Db = 4.0 X was chosen to maximize the agreement with the experimental data for the low ferrocyanide concentrations. The choice of the Db in this column does not affect the final mechanistic conclusion. The x , and xb values were obtained based on the knowledge of the quantity of the bound ferrocyanide ions, their solution concentration, and the film porosity of 0.4. Column 5 of Table I1 lists the calculated values of Du, according to the model of independent diffusion of ferrocyanide in both channels. To obtain these values, we first calculated the total slope value, S,, of an Anson plot as the sum of two components: s b , the component due to the diffusion of bound ferrocyanide, and S,, the component due to the diffusion in the solution phase

(4)

S , = 2nFAC*D,1/2/.lr1/2

(5)

Both equations are based on the integrated form of the Cottrell equation. In eq 4 Qb equals nFACb/d, where Cb is the concentration of bound ferrocyanide averaged over the

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ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988

Table 111. Ion-Exchange Binding and Diffusion Coefficients of Ferrocyanide Ions in OTS/C18MV2+Assemblies in Porous Aluminum Oxide Films in the Presence of Octanol in the Electrolyte CFe(CN)6'/

fiM in solution

QFe(CN)&/

Qc~~Mv~+

0

8 16 32 64

0.38 0.43 0.46 0.49

108Dcpv2+,0

cm / s

108DFep64-'0 cm /s

14 7.7 7.7 7.6 7.6

14 14 14 14

106Db,b cmz/s 14 14 13 13

108Db Wrrt C cm2/s 6.3 6.3 5.4 5.4

The measured diffusion coefficients. Diffusion Coefficients of ferrocyanide bound in the C18MV2+assembly. The d u e s in the previous column corrected for the translational diffusion of C18MVz+(column 3). upon transfer of an electrode to a ferrocyanide-free solution, it appears that the binding of ferrocyanide in the C18MV2+ monolayers is less labile than that observed in the system involving PVP (27). However, we do not know whether this effect contributed, in parallel with the slower electron exchange rate, to the lack of coupling in the present case. Another interesting observation that can be made from the analysis of the data in Table I is that the diffusion coefficient for the bound ferrocyanide, Db, is several times larger than the translational diffusion coefficient of ClsMV2+molecules. This means that the ferrocyanide ions can hop from one The method of calculating D , described here was used since viologen head group to another along the assembly. The last eq 3 is applicable only as long as the diffusion front of the column in Table I gives the values of Db corrected for the ferrocyanide ions in the solution phase remains within the diffusion of (ClsMV2+)2/Fe(CN)64ion pairs. electrode film,which in our case is ca. 15 ms. As mentioned Effect of 1-Octanol on the Diffusion of Fe(CN)64-. above, most of the data in Figure 2 were collected at times Addition of 1-octanolto the electrolyte solution has a dramatic far exceeding this range. The comparison of the experimental values of D F ~ ( cas N ) ~ ~ effect on the voltammetry of the OTS/ClSMV2+bilayer assembly in the aluminum oxide films (32-34). To summarize a function of ferrocyanide concentration and those calculated only the most relevant elements of this effect, the addition for the two limiting cases leads to the conclusion that the two of octanol at close to its saturation level (ca. 3 mM) results diffusion channels of ferrocyanide in the OTS/ClsMV2+/ in 2- to 3-fold increase of the diffusion coefficients of the lateral Fe(CN)64-system are not coupled. On the basis of this ascharge transport of ClSMV+. We have postulated that octanol signment, we can extract the Db values from the measured intercalates into the C18MV2+layer increasing its fluidity by DFe(CN)sk in Table 11. This involves subtracting the calculated inducing dissociation of counterions ion-paired in the headS, values from the measured slopes of the first linear region group region (33). The effect of octanol is also seen in the of the Anson plots. The Db values are listed in the last column diffusion of the bound ferrocyanide ions. Table I11 shows the of Table I1 and also in Table I for the series of measurements results of a series of chronocoulometricexperiments identical featured there. It appears that the Db values decrease slightly with those reported in Table I done in the presence of octanol with the increasing extent of binding. This is probably due in the KCl electrolyte solution. The electrode used to obtain to the electrostatic cross-linkingeffect common for many types these data was also the same as the one used in the Table I of ion-exchange electrode films (16, 19). experiments. That the rate of electron and/or mass exchange is not rapid As expected the measured diffusion coefficients of both the enough to couple the diffusion in the ion-exchange and the ClsMV2+and bound ferrocyanide ions increase dramatically solution phases is somewhat surprising given that we observed when octanol is present in the electrolyte. The change of complete coupling of the diffusion pathways in the system of D c l s ~ v zwith + the increasing concentration of Fe(CN)64-in ferrocyanide bound in the protonated PVP layers impregnating porous aluminum oxide films (27). To explain the data solution was discussed elsewhere (33). The lack of dependence obtained here, we postulate that the electron exchange rate of the apparent diffusion coefficient of ferrocyanide on its electrolyte concentration,similarly to the case without octanol, constant involving bound ferrocyanide in the present system is lower than that in the system involving binding of ferroprovides strong evidence of the lack of coupling between the solution and the ion-exchangechannels of ferrocyanide in this cyanide by protonated pyridinium groups. It has been well established that the rate constant of electron self-exchange system. In the last two columns of Table I11 are listed the Dband the corrected values of Db for the translational diffor this couple can vary as much as 5 orders of magnitude, fusion of C18MV+,Dbco". The average value of DbMnin Table depending on the ionic strength (38) or ion-pairing in ionexchange polymer films (39). The rate enhancement is a result I11 is ca. 5.9 X cm2/s, which is approximately 60% larger of the electrostatic shielding effect (38). Small differences in than that observed without octanol. This is consistent with our earlier postulate that octanol reduces the strength of ion the electrostatic interactions of ferrocyanide with the cations pairing between the viologen head groups and the counterions in its environment can result in substantial changes of the rate constant. It would appear then that ferrocyanide ions are (33). This promotes faster motion of ferrocyanide ions along better shielded when bound in the protonated PVP matrix the ion-exchange head-group region of the bilayer. compared to the headgroup region of the C18MV2+monolayer. Mediated Oxidation of Ascorbic Acid in OTS/ C1sMV2+/Fe(CN)6" System. The oxidation of L-ascorbic This explanation is plausible considering an almost two-dimensional character of the latter system. acid by transition-metal complexes, a subject of many investigations, proceeds in two consecutive, outer-sphere, oneWe were unable to assess quantitatively the rate of massexchange between the bound and the solution ferrocyanide. electron transfer steps (40).Each electron transfer step is Judging from the rate of loss of ferrocyanide ions observed associated with a loss of a proton; the first electron transfer film volume and d is the film thickness. Conspicuously, the bulk concentration of ferrocyanide ions, C*, used in eq 5 is not corrected for the film porosity. This is because the chronocoulometricdata in the first linear region of the Anson plot (Figure 2) were obtained over the time range long enough for the diffusion front in the electrolyte solution to extend far beyond the film thickness (d = 3.0 pm). The total slope value, S,, was then used to calculate D,, as follows:

ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988

1173

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. 2.33

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2.14

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00

1 04 0.2 E I V vs Ag/AgCI. saf KCI

0.6

Fl@ure4. A series of rotating disk electrode voltammograms obtained with an OTS/C,,MV2+ electrode assembly in 0.15 pM ascorbic acid, 10 pM K,FNCN),, 0.1 M KCI, 0.1 M phosphate buffer pH 2.36 at the rotation rates noted in the figure.

is rate limiting. Among the published reports, there are several concerned with the mediated ascorbic acid oxidation at electrodes modified by attachment of a mediator. A recent report from this laboratory dealt with the immobilization of ferrocyanide ions in acrylamide/vinylpyridine gel films at electrodes and the dynamics of the ascorbic acid mediation processes. A detailed summary of earlier literature on the subject was included in that publication (15). One of our goals in the investigations presented below was to test the system's behavior under catalytic conditions. More importantly, however, the kinetics of the mediated oxidation of ascorbic acid serve as a probe of the microenvironment around the bound ferrocyanide ions in that the rate constant of the mediation reaction is sensitive to the electrostatic repulsive interactions between HA-, the monodissociated form of ascorbic acid, and ferricyanide (15). The extent of these interactions reflecta, in turn, the level of the electrostatic shielding of the ferricyanide ions by the viologen head groups. The fact that the rate constant of the oxidation is much higher for HA- than for the undissociated ascorbic acid H2A is responsible for the pH dependence of the kinetics of the oxidation reaction and allows one to calculate the km- from the experimental data (40). A series of rotating disk electrode voltammograms obtained with an OTS/C18MV2+/Fe(CN)6"electrode assembly in 0.1 M KC1,O.l M phosphate buffer, pH 2.36, containing 10 pM K4Fe(CN)6and 0.15 mM L-ascorbic acid is shown in Figure 4. At 0.3 V, the oxidation potential of the bound ferrocyanide, one observes a steady-state current wave corresponding to the mediated oxidation of ascorbic acid by the ferricyanide ions bound in the OTS/Cl&W+ bilayer assembly. Figure 5 shows a series of Levich plota of the limiting mediation currents obtained at different pH values. The magnitude of the current due to the oxidation of ferrocyanide ions present in the electrolyte solution is less than 20% of the mediation current at the highest rotation rate. The Levich plots in Figure 5 were corrected by subtracting the current due to the ferrocyanide oxidation, which was determined for each rotation rate in a blank experiment without ascorbic acid in the solution. At a more positive potential, one observes in Figure 4 a current wave due to the direct electrooxidation of ascorbic acid, which overlaps with a background current. That one observes a large

0'

0

20

40

60

80

Flguro 5. A series of Levich plots for the mediated oxidation of ascorbic acid by Fe(CN),C bound in the OTS/CI,MV2+ assembly at the pH noted in the figure. All other conditions are as in Figure 4. The magnltude of the medlation current was corrected by subtracting the current due to the direct oxidation of Fe(CN),'- at a 10 pM level. The average of the three i, values recorded at the highest rotation rates is marked by a straight Ilne.

current wave of the direct oxidation of ascorbic acid is expected given the substantial porosity of the electrode film. Analysis of the Mediation Processes in View of the Saveant-Andrieux Theory. Quantitative analysis of the dynamics of the mediation processes was done according to the Savgant-Andrieux theory for irreversible mediation reactions (41,42). According to this theory, the magnitude of the mediation current wave, il, a t 0.3 V may depend on the magnitude of three processes intrinsic to the structure and the performance of the electrode film. They are expressed below in terms of three characteristic filmcurrent densities, ik, i ~ and , is: ik

= nFCH,A*Cbkzd

(7)

where CH2A* is the H2A concentration in the bulk of the electrolyte and k2 is the apparent second-order rate constant of H2A oxidation by ferricyanide ions in the film

In eq 9, D H z A is the diffusion coefficient of ascorbic acid in the electrolyte solution, p is the film porosity. The il current bears also a dependence on the rate of H2A transport from the bulk of the electrolyte to the film/solution interface. This is expressed by the mass transport limited current, iA. In the following analysis, the mass transport dependence is eliminated from the consideration of the film processes by obtaining the value of the characteristic currents (eq 7-9) a t the limit of infinite rotation rate. It is to be expected that the mediation current is determined by one or more of the film processes, ik, iE, is of the lowest magnitude. The analysis of the experimental results involves, first of all, the measurements of the characteristic currents to make a preliminary assessment of the rate-limiting process. Only is and iE can be measured in separate experiments. The current characteristic for the mass transport of H2A in the electrode film can be, in principle, obtained from the mag-

1174

ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988

Table IV. Magnitude of the Film Currents and the Rate Constant Describing the Dynamics of the Mediated Electrooxidation of Ascorbic Acid pH

lozis, mA/cm2

lo2&, mA/cm2

102i,, mA/cm2

2.00 2.14 2.33 2.66

20 20 20 20

0.1 M 2.00 2.14 2.33 2.66

KC1, 0.1 M Phosphate 20 8.6 20 8.6 20 8.6 20 8.6

lo2&, mA/cm2

0.1 M KC1, 0.1 M Phosphate Buffer 3.4 0.61 0.67 3.4 0.94 1.1 1.5 1.8 3.4 3.4 2.5 3.6

k,, M-ls-l 160 260 430 860

1

R+E+S

/

-0.5

Buffer and ca. 3 mM Octanol 0.48 0.48 90 0.69 0.69 130 0.98 0.98 180 1.6 1.9 350

/

nitude of the second wave due to the direct oxidation of ascorbic acid in Figure 4. However, due to the poorly developed shape of this wave, we measured is with benzoquinone, which simulated H2A in its diffusion through the film. A correction was made for the difference of the diffusion coefficients of H2A and benzoquinone. Benzoquinone is a reasonable choice of a probe species because, as H2A, it is uncharged and ita diffusion through the aluminum oxide film with the OTS/C18MV+/Fe(CN),4-k assembly should be similar to H2A. The is values obtained based on the usual Koutecky-levich analysis of the rotating disk voltammograms are listed in Table lV (43). Also listed there are iE values obtained from eq 8. The diffusion coefficient of the bound ferrocyanide was measured chronocoulometricallyjust prior to the addition of the ascorbic acid to the electrolyte as described in the previous section. In order to make a preliminary assignment of the ratelimiting step, we have to consider the magnitude of the is, iE, and il currents measured thus far. It is worth pointing out, first of all, that il currents obtained for various pH values (Figure 5) become essentially independent of the rotation rate at high w, which means that the magnitude of il is significantly smaller than iA, and therefore not dependent on the mass transport rate of H2A to the film/solution interface. The average of three highest values of the il was taken as the mediation current, i, (see Figure 5). Its values, as can be noticed in Table IV, are comparable to the iE values. The comparison of is and ,i leads to the conclusion that the mass transport of H2A in the electrode film, being close to an order of magnitude higher than ,i is not rate limiting. This eliminates all the kinetic cases defied by Sav6ant and co-workers, which involve the film permeability limitation such as R S , SR, SR -+ E , S -+ E, S, and, the general case, R + S + E (41,42).In this terminology, the letters R, S, and E represent involvement of ik, is, and i ~ respectively, , in the mediation current (15,41,42). Knowing also that ,i is comparable to iE, one can deduce that ik cannot be very much smaller than iE or else it alone would be the slowest step forcing ,i to a lower value than that observed. This eliminates R case from further consideration (41,42). Similarly, we can deduce that ik cannot be very much larger than iE because in that case ,i would be equal or larger than iE. This means that ER is not the case describing these data. On the basis of this evaluation of the data and the kinetic zone diagram constructed by Sav6ant and co-workers for this class of mediation reactions (see Figure 6), we can narrow down our preliminary assignment to the R + E case. The strategy of the final kinetic assignment involves first, a calculation of the i k value based on the equation for the mediation wave, il, for R + E case (eq 10 below). In the second step, the values of the characteristic currents, is, iE, and ik are entered into the kinetic zone diagram. This defines the case

+

SR

-1.5

-1.0

/

+

SR

I 1

E/

-0.5

0.0

0.5

1 .o

Iog ( i E / i; )"2

Figure 6. A section of the Savbnt-Andrieux kinetic zone diagram. The data points 1, 2, 3, and 4 are those from Table I V corresponding to pH 2.00, 2.14, 2.33, and 2.66, respectlvely. The open and the solid symbols correspond to the conditions with and without octanol, respectively.

assignment and should agree with our preliminary assignment. In our case (42) R + E case: il

= (ik*iE)'I2 tanh

(ik*/iE)'/'

(10)

where

= ik(1 - i l / i A ) (11) An average value of the parameter (1- il/iA) was calculated based on the experimental values of il and iA. Its value ranged from 0.88 to 0.98 in all the experiments. The calculation of ik* requires the iterative fitting of the best ik* to eq 10. The i k value calculated from eq 10 and 11 for pH 2.00 was 1.1 X mA/cm2. This, indeed, leads to the R + E case as the final assignment, based on the kinetic zone diagram shown in Figure 6 and confirms our preliminary evaluation. If the latter were incorrect, plotting the data in the kinetic zone diagram would provide the correct assignment which subsequently would have to be verified by recalculating the ik value using a correct equation and replotting the new set of the characteristic currents in the kinetic diagram. The case assignment process was repeated for the remaining pH conditions. All ik values are listed in Table IV where one can find also the k2 values calculated from eq 7. The data in Table IV are also plotted in the kinetic zone diagram in Figure 6. Before we proceed with the discussion of the kinetics of the oxidation reaction, we want to point out that the experiments presented in this section were done under conditions which would maximize the accuracy of the kinetic measurements. This means that the H2A concentration and the pH of the electrolyte were chosen in a way which would decrease ik, so it became comparable with iE as the rate-limiting step. This was accomplished by using a low concentration of ascorbic acid and working in a small range of rather low pH values. Thus, the level of the mediation current in Figure 4 should not be regarded as reflecting the optimal capability of the system to mediate the ascorbic acid oxidation. ik*

Discussion of the Kinetics of the Mediation Reaction. The same types of measurements and data analysis were also done for the case of the mediated electrooxidation in the presence of octanol in the electrolyte solution. Those data are shown in the second half of Table IV and in Figure 6.

ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988

1175

Table V. Kinetics of Ascorbic Acid Oxidation by Fe(CN),3Bound in OTS/C18MV2+Bilayer Assemblies in Porous Aluminum Oxide Films at Au Electrodes

r

electrode

I

In

no.

r

I

.

aqueous electrolyte kH2A, wkm-,

M-1

s-l

M-1

s-l

aqueous electrolyte + ca. 3 mM octanol kH2A,

M-1 g-l

1w3K~~-, M-1 s-l

I

1 2 3 4 5 6 7

N

Y

7 0 44 46 29 18 15

13 21 13 9.9 21 14 11

26 17 72 15

23 f 18"

15 f 4.5"

32 f 27"

7.8 8.5 8.8 10

8.8 f 0.9O

'Average value.

"

0

100

200

300

400

500

[ H + ] - ' / M-'

Flgure 7. Pbts of the apparent rate constant, k,, of the ascorbic acid oxidation as a function of the Inverse of the hydrogen b n concentration (see eq 12). The data points are those from Table IV.

There are two important changes brought about by the addition of octanol. The first one is an increase in the iEvalues. This is not unexpected if we recall the observed increase of the ferrocyanide mobility discussed above (compare results in Tables I and 111). The second change is a decrease of the apparent rate constant of the ascorbic acid oxidation by ferricyanide. The significance of this finding is discussed below. Both these effects of octanol result in the change of the kinetic assignment of the system's behavior to the R case for most of the pH values, as seen in Figure 6. In the R case, the kinetics of the mediation reaction is the rate-limiting process, and ik alone determines the magnitude of the mediation current (compare ,i and ik in the second half of Table IV) (41, 42). In order to discuss the effect of octanol on the apparent rate constant of the mediation reaction, we need to analyze first the pH dependence of k2 As the pH of the electrolyte is increased, the rate constant of the mediation reaction increases. As expected, this results in a diagonal shift of the plotted points in the kinetic zone diagram toward the lower left corner in both series of measurements, with and without odanol (see Figure 6). These changes are consistent with the known pH dependence of the apparent rate constant of the H2A oxidation (40)

Here, K is the first dissociation constant of ascorbic acid (9.12 X (40). A typical set of k2 vs the inverse of the hydrogen ion concentration plots, obtained in the presence and in the absence of octanol, are shown in Figure 7. From their slopes and intercepts and eq 12, the values of km- and k H I A can be calculated. The summary of all kinetic measurements of the mediated electrooxidation of ascorbic acid at various electrodes is given in Table V in terms of the kH,A and kHA- values. The average value of km- in Table V should be compared with the value of this rate constant obtained by Kuwana and co-workers for the homogeneous solution conditions of 434 f 15 M-l s-l (40). As discussed above, the enhancement factor of ca. 30, obtained based on this comparison, reflects the extent of the electrostatic shielding of the bound ferricyanide ions in the O T S / C l e W + assembly. Alternatively, one could argue that the rate enhancement is merely a result of an increased concentration of HA- ions in the f i i due to its negative charge

and the ion-exchange binding in the C18MV2+head-group region. This postulate is not plausible, considering that in the pH range where these experiments were carried out, the HA- concentration is approximately 5 orders of magnitude lower than the concentration of C1- and HzPO4-ions of the supporting electrolyte. Under such conditions, if one assumes that the affinity of HA- and C1- for the ion-exchange sites in the CleMV2+head-group region are similar, it can be shown that binding of HA- is insignificant. In our recent studies of the ferricyanide-mediated ascorbic acid oxidation at electrodes coated with acrylamide/vinylpyridine (AC/VP) polymer gel films, we observed an enhancement factor ranging from 20 to 65 depending on the composition and the structure of the gel films (15). The highest enhancement factor was obtained for gel films synthesized in an acidic solution, which led to the self-segregation of the pyridine sites into domains separate from the more hydrophobic regions of the polymer. We associated the high enhancement factor of the rate constant of H2Aoxidation with the high local concentration of the pyridine groups in this type of gel films and the resulting high extent of the electrostatic shielding effect (15). It is apparent that the interactions between ferricyanide ions and the viologen groups in the OTS/C18MV2+assembly are not as strong as in the case of one of the AC/VP polymer gels. This could be due to a lower local concentration of the viologen groups in the present system compared to the pyridine group concentration in the copolymeric gel. Also the two-dimensional character of the C18MV2+assembly, and the fact that the ferricyanide ions cannot be completely surrounded by the viologen groups for steric reasons, is partially responsible for the observed differences. Based on this discussion, it is easier to understand the apparent lack of coupling between the bound ferrocyanide ions diffusing along the C18MV2+assembly and ferricyanide in solution. Such coupling may involve an increase of the electron exchange rate constant via strong electrostatic shielding of the bound ferrocyanide ions. This level of electrostatic shielding apparently does not exist in the CleMV2+ system. It could exist in PVP films where pyridinium groups are present at much higher concentration. Consequently, the coupling of the diffusional pathways was observed in the porous aluminum oxide films impregnated with PVP (27). Consistent with the electrostatic shielding effect are also the data in the second half of Table V where a significantly lower average kHA- value is reported. We have reported elsewhere that the intercalation of octanol into the CI8MV2+ assembly decreases the electrostatic interactions between the ferricyanide ions and the viologen groups (33). Part of this effect could be due to an increase in the ordering of the C18MV2+assembly, which enhances the two-dimensional

1176

ANALYTICAL CHEMISTRY, VOL. 00, NO. 11, JUNE 1, 1988

character of the assembly. This explains both the decreased electrostatic shielding, which leads to lower rate constant, and the improved mobility of the bound ferrocyanide.

CONCLUSIONS We have demonstrated the ion-exchange properties of the OTS/ClsMV2+bilayer assembly supported in porous aluminum oxide films. The investigations of ferrocyanide binding and transport processes in this system revealed that the ferrocyanide diffusion in the Donnan domain of the bilayer assembly involves physical motion of the ions along the C18MV2+assembly. Diffusion of the bound ferrocyanide is not coupled with its diffusion in the electrolyte solution phase due to an insufficiently high rate of the electron exchange between the species in the two phases. The magnitude of the diffusion coefficient of ferrocyanide in this essentially twodimensional ion-exchange system is somewhat higher than that observed in thin films of PVP, but it is not as high as that reported by Anson and co-workers for the diffusion of Fe(edta) in Donnan domains of poly-L-lysine films (22). Several factors such as charge of the diffusing species as well as the charge, concentration, and the extent of solvation of the ion-exchange groups in Donnan domains may be responsible for these differences. Further studies of the mobility of counterions in the ion-exchange films are necessary to understand all the factors limiting this process and in order to develop new systems with superior transport properties required in future applications. We have also investigated an electrocatalytic application of the OTS/Cl8MV+/Fe(CN):- assembly by measuring the kinetics of ascorbic acid oxidation. In agreement with previously reported cases, the kinetics of the oxidation reaction are enhanced compared to the homogeneous solution conditions. The enhancement is clearly related to the electrostatic shielding effect brought about by high local concentration of the viologen head groups. This, in turn, results in a decrease of the coulombic work term in the electron transfer energy of activation of HA- and ferricyanide ion. The magnitude of this effect, which is proportional to the enhancement factor of ItHA- is very sensitive to the extent of electrostatic interactions with the surrounding cation sites. For example, a higher enhancement factor was observed for this reaction carried out in a matrix of acrylamide/vinylpyridine electrode films (15). The presence of octanol in the electrolyte and its intercalation into the C18MV+assembly decreases the extent of electrostatic interactions between the ferricyanide and viologen groups. Consistent with the above statement, we observed a decrease in the rate constant of the ascorbic acid oxidation. Registry No. OTS,112-04-9;Cl&lVCl,, 75805-29-7;Fe(CN),&, 13408-63-4; A1203, 1344-28-1;L-ascorbic acid, 50-81-7;hexadecane, 544-76-3; 1-octanol,111-87-5.

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-

RECEIVEDfor review August 25,1987. Accepted February 1, 1988. The support for this research was provided by the National Science Foundation under Grant CHE-8504368.