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J. Phys. Chem. B 2001, 105, 8963-8969

8963

Rates of Electron-Transfer Across Liquid/Liquid Interfaces. Effects of Changes in Driving Force and Reaction Reversibility† Chunnian Shi and Fred C. Anson* Arthur Amos Noyes Laboratories, DiVision of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125 ReceiVed: February 7, 2001; In Final Form: May 13, 2001

Rates of electron-transfer between redox reactants located on opposite sides of the interface between thin layers of organic solvents on graphite electrode and aqueous solutions were measured by means of steadystate electrochemistry. Changes in the overall driving forces for irreversible reactions produced changes in rate that fit no simple behavioral pattern. For reversible reactions, a regular increase in rate with driving force was obtained. Evidence for a significant effect of diffuse-layer potentials on reaction rates was not found.

Introduction Experimental investigations of the rates of electron-transfer between reactants located on opposite sides of liquid/liquid interfaces have accelerated recently, as electrochemical methods have been developed to facilitate the rate measurements.1-15 However, the increase in the quantity of experimental data has not resulted in a consistent pattern of kinetic behavior. In particular, the reported dependences of cross-phase electrontransfer rates on the overall driving force of the reactions have varied widely and include examples in which reaction rates increase, decrease, or do not vary as driving forces are varied.1-5,9,11-14 The present study was undertaken to obtain data for additional liquid/liquid interfaces with pairs of coreactants that undergo reactions with both positive and negative overall free energy changes. In addition, the rates of the reactions of a reactant in an aqueous phase with a pair of redox co-reactants in an adjacent nonaqueous phase were evaluated simultaneously at a single interface. Comparison of the new results with those from previous studies suggest that each combination of liquid/liquid interface, redox reactant pair and supporting electrolyte represents a special case. The theoretical analysis of the kinetics of cross-phase electron-transfer offered by Marcus16-18 can account for experimental data with some systems but not with others, and considerable variability persists in the patterns of reactivity observed. Experimental Section Materials. Nitrobenzene, tolunitrile, and other reagents were of the highest available purity. Various pretreatments did not alter their behavior so that they were usually used as received from commercial sources. Cylindrical graphite electrodes (Advanced Ceramics Corp) were mounted to expose 0.32 cm2 of the edge planes of the graphite as previously described.9 The electrodes were polished with 600 grit SiC paper before each experiment. Apparatus and Procedures. Conventional electrochemical cells and instrumentation were employed. Thin layers of organic solvents (usually ca. 3 × 10-3 cm thick) were created on the †

Part of the special issue “Royce W. Murray Festschrift”. * To whom correspondence should be addressed. E-mail: fanson@ caltech.edu. Telephone: (626) 395-6000. Fax: (626) 577-4088.

surfaces of roughly polished edge plane pyrolytic graphite electrodes by previously described procedures.12 The aqueous solutions in which the coated graphite electrodes were immersed were deaerated with argon. Experiments were conducted at the ambient laboratory temperature (22 ( 2 °C). Results Tolunitrile/Water Interfaces. In our previous studies of cross-phase electron-transfer across liquid/liquid interfaces, the two immiscible liquids used to create the interface were nitrobenzene (NB) and water. The rate of the reaction between Fe(CN)63- in the aqueous phase and decamethylferrocene (DMFc) in the NB phase appeared to be rather insensitive to changes in the Galvani potential difference across the interface.13,14 To investigate whether this insensitivity might be associated with the polarity of the organic solvent, the measurements were repeated at interfaces formed by a less polar solvent, tolunitrile (TN), and water, using the same thin layer electrochemical method described in the earlier report.12-14 A schematic depiction of the cell employed is shown in Figure 1. Initially, the potential of the graphite electrode was maintained at a value where the DMFc in the TN thin layer was oxidized to DMFc+. The potential was then scanned toward more negative values to reduce the DMFc+ to DMFc which diffused to the liquid/liquid interface where it was reoxidized to DMFc+ by electron-transfer to the Fe(CN)63- in the aqueous phase. The overall driving force for the electron-transfer is composed of the difference in the formal potentials of the two redox couples in their respective phases and ∆°wφ, the Galvani potential difference present at the liquid/liquid interface.19 The value of ∆°wφ was varied by changing the concentration of ClO4- (a potential-determining-ion that moves across the liquid/liquid interface) in the aqueous phase while maintaining its concentration fixed in the nonaqueous phase. Under such conditions, ∆°wφ is expected to change by 59 mV for each decadic change in the concentration of ClO4- in the aqueous phase.19 To evaluate the driving force for the reaction at each concentration of ClO4-, the averages of the anodic and cathodic cyclic voltammetric peak potentials for both the DMFc+/0 and Fe(CN)63-/4- couples were measured with respect to the reference electrode in the aqueous phase (Figure 1). The resulting potentials are the formal potential of the redox couple

10.1021/jp010465r CCC: $20.00 © 2001 American Chemical Society Published on Web 06/23/2001

8964 J. Phys. Chem. B, Vol. 105, No. 37, 2001

Shi and Anson TABLE 1: Bimolecular Rate Constants for Cross-Phase Electron-Transfer between Fe(CN)63- and Decamethylferrocene Located on Opposite Sides of a TN/H2O Interfacea aqueous phase supporting electrolyte 0.010 M NaClO4b 0.10 M NaClO4b 1.0 M NaClO4b 0.10 M NaClO4c 1.0 M NaClO4c

Figure 1. Schematic depiction of the electrochemical cell used to evaluate rates of cross-phase electron-transfer between reactants in aqueous solutions and those dissolved in thin layers of organic solvents on graphite electrodes.

EHf 2O,d mV

EfTN +∆°wφ,e mV

Keqf

ketg cm s-1 M-1

200 211 257 378 371

-33 -90 -140 -80 -129

9 × 103 1 × 105 5 × 106 6 × 107 3 × 108

0.3 0.1 0.1 0.93 0.60

a The TN thin layer contained 0.25 M tetrahexylammonium perchlorate and 0.23 mM DMFc. b The aqueous phase also contained 0.1 M NaCl and 2-5 mM Fe(CN)63-. c The aqueous phase also contained 0.1 M HCl. d Formal potential of the Fe(CN)63-/4- couple in the aqueous phase. e Apparent formal potential of the DMFc+/0 couple in the TN thin layer evaluated from the average of the anodic and cathodic cyclic voltammetric peak potentials measured with respect to the reference electrode in the aqueous phase. ∆°wφ is the Galvani potential difference across the TN/H2O interface. f Equilibrium constant of the crossphase reaction: ln Keq ) F/RT[EHf 2O - (EfTN + ∆Φ°w)]. g Calculated from eqs 1-3. Values were reproducible within ca. (25% in replicate experiments.

interface. The concentration of ClO4- in the TN phase was fixed by dissolving 0.25 M tetrahexylammonium perchlorate (THAP) in the TN used to form the thin layers. The concentration of NaClO4 in the aqueous phase was varied. In the absence of Fe(CN)63- in the aqueous phase only the reversible response of the DMFc+/DMFc couple in the TN thin layer is observed (Figure 2A). In the presence of Fe(CN)63-, the response changed to those shown in Figure 2B and 2C with steady-state cathodic plateau currents, iobs, that are jointly controlled by the rate of the cross-phase electron-transfer reaction at the liquid/liquid interface and the diffusion of the reactant that is confined to the thin layer13,14,22

(iobs)-1 ) (ik)-1 + (id)-1

(1)

where ik and id are defined by eqs 2 and 3

ik ) nFAketCH2OCorg id ) Figure 2. Current-potential responses obtained from 0.23 mM DMFc dissolved in a thin layer of tolunitrile (TN) also containing 0.25 M tetrahexylammonium perchlorate (THAP) in a cell like the one in Figure 1. The aqueous solution contained: (A) 0, (B) 2.4, (C) 5 mM Fe(CN)63-; The concentration of NaClO4 in the aqueous supporting electrolytes is given at the top of each set of curves. Each solution also contained 0.1 M NaCl. Scan rate: 5 mV s-1.

in the aqueous phase, EHf 2O, and the apparent formal potential of the redox couple in the organic phase, (EfTN + ∆°wφ). The difference between these potentials, EHf 2O - (EfTN + ∆°wφ), provides a direct measure of the driving force for the reaction. (Note that the measurement of EHf 2O at each concentration of ClO4- is preferable to the method employed in most previous studies because it includes any changes in the formal potential of the redox couple in the aqueous phase, e.g., the Fe(CN)63-/4couple, that result from factors such as ion-pairing or protonation.) Measurement of Rates of Cross-Phase Electron-Transfer. Shown in Figure 2 is a typical set of current-potential responses recorded with the DMFc-Fe(CN)63- system at the TN/H2O

nFACorgDorg δ

(2) (3)

The terms in these equations are n, the number of electrons transferred, F, the Faraday, A, the area of the liquid/liquid interface, ket, the cross-phase electron-transfer rate constant (cm s-1 M-1), CH2O and Corg, the concentrations of the redox reactants in the aqueous and nonaqueous phases, respectively, and Dorg, the diffusion coefficient of the reactant in the thin layer of thickness δ. id, the maximum current that can be carried across the thin layer by the diffusion of the reactant between the electrode surface and the liquid/liquid interface, can be calculated when Dorg and δ are known or it can be measured by increasing CH2O until iobs becomes independent of CH2O (ik . id) at which point iobs ) id (eq 1). Values of ket were calculated from eq 2 using the values of ik obtained from eq 1. The resulting rate constants, given in Table 1, show that ket depends on ∆°wφ in the more dilute supporting electrolytes (0.01-0.1 M NaClO4) but becomes less dependent on changes in ∆°wφ as the supporting electrolyte concentration increases (0.1-1 M NaClO4). A similar trend was found by Zhang et al. at the DCE/ H2O (DCE ) 1,2-dichloroethane) interface.9 An insensitivity of ket to changes in ∆°wφ was reported previously at the NB/ H2O interface.13,14 Some of the insensitivity may have been the

Changes in Driving Force and Reaction Reversibility result of the neglect of changes in the concentration of Fe(CN)63- at the liquid/liquid interface.21 Reevaluation of the rate constants using the constraints specified in a recent study to avoid such concentration changes22 yielded rate constants that were somewhat more sensitive to changes in ∆°wφ. However, the values of ket decreased as ∆°wφ increased. This behavior, which was also observed by Zhang et al.9 and is the case for the rate constants in Table 1, is not in accord with expectations based on the conventional Butler-Volmer treatment.23 By taking advantage of the pH dependence of the formal potential of the Fe(CN)63-/4- couple, it is possible to alter the thermodynamic driving force for the cross-phase electrontransfer reaction while maintaining a constant value of ∆°wφ. This tactic was adopted by comparing the reaction rates obtained when the 0.1 M NaCl in the aqueous supporting electrolyte was changed to 0.1 M HCl. As shown in Table 1, this change resulted in substantial increases in rate while ∆°wφ, as reflected in the apparent formal potential of the DMFc+/DMFc couple, (EfTN + ∆°wφ), changed very little. As with the NaClO4 + NaCl electrolytes, changes in ∆°wφ for the acidic electrolytes (produced by changes in the concentration of NaClO4) caused relatively small changes in ket that were in the opposite direction from those expected on the basis of Butler-Volmer theory. Thus, changes in the thermodynamic driving force of the electron-transfer reaction produced by changes in pH affect its rate significantly and in the expected direction, but changes in the electrostatic component of the driving force produced by changes in ∆°wφ are weaker and in the “wrong” direction. To explore the puzzling behavior more extensively, a second set of experiments was carried out in which rates of cross-phase electron-transfers at the TN/H2O interface were examined at a constant value of ∆°wφ using thin layers of TN containing both DMFc and a second hydrophobic ferrocene, 1,1′,3,3′-tetrakis(2-methyl-2-hexyl)ferrocene (MHFc).24 Electron-transfer to Fe(CN)63- in the aqueous phase was examined in two steps for the same thin layer of TN as the potential of the graphite electrode was scanned across the formal potential of each of the ferrocenium/ferrocene couples. Shown in Figure 3A are the two reversible cyclic voltammetric responses obtained in the absence of Fe(CN)63- in the aqueous phase. Addition of 3.2 mM of Fe(CN)63- to the aqueous phase produced no effect on the responses from the MHFc+/MHFc couple at +0.18 V (Figure 3B), but the response from the DMFc+/DMFc couple at -0.08 V was converted into a steady-state plateau current similar to those in the experiments of Figure 2. The rates of the cross-phase reaction between 3.2 mM Fe(CN)63- and MHFc is apparently too small to produce an effect on the cathodic currents for the reduction of MHFc+. However, by increasing the concentration of Fe(CN)63- in the aqueous phase to 150 mM (Figure 3C), a steady-state response is observed at the potential corresponding to the MHFc+/MHFc couple (Figure 3C). At the same time, the steady-state current at the potential of the DMFc+/DMFc couple increased, as expected, to id, the current that is limited by the diffusion of DMFc across the TN thin layer.13,14 The steady-state responses in Figure 3B and 3C were used to obtain rate constants of 0.8 and 2.3 × 10-3 cm s-1 M-1 for the cross-phase electron-transfer reactions of Fe(CN)63- with DMFc and MHFc, respectively. These values show a clear dependence of ket on the thermodynamic driving force of the reaction. In addition to the driving force of the reaction, values of ket are expected to depend on the self-exchange rate constants of the two reactants.18 Self-exchange rate constants for the ferrocene reactants in TN are not available but ferrocenes typically

J. Phys. Chem. B, Vol. 105, No. 37, 2001 8965

Figure 3. Current-potential curves recorded with a thin layer of TN containing 0.25 M THAP and both 0.4 mM MHFc and 0.4 mM DMFc. The aqueous phase contained 0.1 M HClO4 and (A) 0, (B) 3.2 and (C) 150 mM Fe(CN)63-. Thin layer thickness ) 2.0 × 10-3 cm. Scan rate: 5 mV s-1.

have similar self-exchange rates so that the primary origin of the difference in ket values for DMFc and MHFc is likely to be the difference in the thermodynamic driving forces of the two reactions. Thus, increases in driving force produced by changing the ferrocene reactant in the TN layer (Figure 3) or by changing the pH of the aqueous solution of Fe(CN)63- (Table 1) both produce significant changes in ket. Reversible Electron-Transfer between DMFc+/0 and Ru(NH3)63+/2+. If the redox couples in the aqueous and nonaqueous phases have equal, or nearly equal, formal potentials, it becomes possible to examine the cross-phase electrontransfer processes in both directions. This possibility was explored with the Ru(NH3)63+/2+ couple in the aqueous phase and the DMFc+/0 couple in a thin layer of nitrobenzene as the organic solvent. Shown in Figure 4 are current-potential curves obtained with this pair of redox couples. In the absence of any Ru(NH3)63+/2+ in the aqueous phase, only the response from the DMFc+/0 couple is observed (Figure 4A). Addition of Ru(NH3)63+ to the aqueous phase leads to the response shown in Figure 4B. The cathodic plateau current is the result of the crossphase reduction of Ru(NH3)63+ by electron-transfer from DMFc generated in the NB phase. The rate constant for this reaction cannot be calculated simply from the plateau current in Figure 4B using eqs 1-3 because the effect of the back reaction on the plateau current must be taken into account as will be explained. When both Ru(NH3)63+ and Ru(NH3)2+ are present in the aqueous phase, a composite current-potential curve is obtained with both cathodic (reduction of Ru(NH3)63+ by DMFc) and anodic (oxidation of Ru(NH3)62+ by DMFc+) plateau currents (Figure 4C). In this case, the current-potential curves were obtained by scanning the electrode potential from its equilibrium (open circuit) value to more negative or more positive values. Note that the cathodic plateau current in Figure 4C is smaller than that in Figure 4B even though the concentrations of Ru(NH3)63+ and DMFc are the same in both cases. This is the

8966 J. Phys. Chem. B, Vol. 105, No. 37, 2001

Shi and Anson The values of kf and kb calculated from the cathodic and anodic plateau currents, respectively, in Figure 4C are listed in Table 2. Their ratio, 0.72, is in reasonable agreement with the value of Keq (0.68) calculated from the value of ∆Ef + ∆°wφ measured for the Ru(NH3)63+/2+ and DMFc+/0 couples. (A value for Keq is required to evaluate kf (or kb) from eq 5 (or eq 6), but the rate constant(s) is much more sensitive to iobs than to Keq.) The low solubility of Ru(NH3)62+ in aqueous solutions of perchlorate prevented studies of the effect of changes in ∆°wφ on the rate of reaction 4. A different reversible reaction was therefore employed to examine this point. Reversible Electron-Transfer between TCNQ0/- and Fe(CN)63-/4-. The formal potentials of the TCNQ0/- (TCNQ ) 7,7,8,8-tetracyanoquinodimethane) and Fe(CN)63-/4- couples are also similar so that reversible electron-transfer between these two couples occurs across the NB/H2O interface (reaction 7) kf

TCNQ- + Fe(CN)3\ z TCNQ + Fe(CN)46 y 6 k

(7)

b

Figure 4. Current-potential curves for reversible electron-transfer between 0.12 mM DMFc+/0 in a thin layer of nitrobenzene containing 0.25 M THAP and Ru(NH3)63+/2+ in an aqueous solution containing 0.05 M NaClO4. (A) [Ru(NH3)63+] ) [Ru(NH3)62+] ) 0 mM; (B) [Ru(NH3)63+] ) 1.79 mM, [Ru(NH3)62+] ) 0 mM; (C) [Ru(NH3)63+] ) 1.79 mM, [Ru(NH3)62+] ) 0.98 mM. In (C), the potential was scanned from its open circuit value to more negative or more positive values. Scan rate: 5 mV s-1.

expected result: For reversible reactions such as reaction 4 kf

+ Ru(NH3)3+ \ z Ru(NH3)2+ 6 + DMFc y 6 + DMFc k

(4)

b

the relation between the plateau current and the kinetic current is no longer given by eq 1. As is shown in the Appendix, eqs 5 and 6 must be substituted for eq 1 when dealing with reversible reactions

(

-1 + (id)-1 1 + Keq-1 (iobs)-1 cat ) (ikf)

(

) )

[Red] [Ox]

[Ox] -1 (iobs)-1 + (id)-1 1 + Keq an ) (ikb) [Red]

(5) (6)

where (iobs)cat and (iobs)an are the cathodic and anodic plateau currents, ikf and ikb are the kinetic currents as defined by eq 2 after substituting kf or kb for ket, id is the diffusion-limited current for transfer of the oxidized or reduced form of the reactant in the thin layer between the electrode surface and the liquid/liquid interface, Keq is the equilibrium constant for the reversible reaction, and [Red] and [Ox] are the concentrations of the reactants in the aqueous phase at the liquid/liquid interface. These concentrations can often be equated to their concentrations in the bulk of the solution by choosing appropriate experimental conditions.22 It is clear from eqs 5 and 6 that plateau currents obtained with reversible reactions (whether or not the reaction product is initially present in the solution) will always be smaller than for irreversible reactions. Thus, the behavior shown in Figure 4 is qualitatively consistent with that expected on the basis of eqs 5 and 6.

Current-potential curves are shown in Figure 5. The rate of the reaction is rather low so that relatively high concentrations of Fe(CN)63- and Fe(CN)64- in the aqueous phase were required to obtain significant steady-state currents. As the concentration of NaClO4 in the aqueous phase was increased from 0.01 to 1.0 M, the apparent formal potential of the TCNQ0/- couple became more negative (Table 2 and lower set of curves in Figure 5) so that the equilibrium constant of reaction 7 increased. As a result, the ratio of the cathodic to the anodic plateau currents in the upper set of curves in Figure 5 increased, as expected from eqs 5 and 6. With 0.1 M NaClO4 as the aqueous supporting electrolyte the equilibrium constant for reaction 7 was calculated to be 0.92. The cathodic and anodic plateau currents for this electrolyte were almost equal (Figure 5). Values of kf and kb of 6.5 × 10-3 and 6.2 × 10-3 cm s-1 M-1, respectively, were calculated from eqs 5, 6, and 2 using the value of id (8.5 µA) calculated from eq 3. Rate constants evaluated for other concentrations of NaClO4 are listed in Table 2. The changes in ∆°wφ (and, therefore, in Keq) caused by the changes in the concentration of NaClO4 clearly affect kf and kb and the reaction rate in both directions increases with the driving force. This behavior contrasts with that of the irreversible cross-phase reaction between DMFc and Fe(CN)63- (Table 1). Discussion The rate constants summarized in Tables 1 and 2 exhibit a disparate pattern which supports the recent conclusion of Zhang et al.9 that no single explanation appears capable of accommodating the variety of experimental observations that have been reported. DMFc + Fe(CN)63-. The oxidation of DMFc by Fe(CN)63at the TN/H2O(NaClO4) interface exhibits kinetic behavior (Table 1) that is similar to that we reported previously for the same pair of reactants at the NB/H2O (NaClO4) interface.13 In particular, the rate of the reaction appears to be only weakly sensitive to changes in ∆°wφ. Although the driving force for the reaction is approximately equal at the two interfaces, the absolute values of the rate constants are smaller at the TN/H2O interface. This difference may reflect a lower self-exchange rate for the DMFc+/0 couple in TN, which is considerably more viscous than NB. The larger rate constants obtained when the driving force of the reaction was increased by acidifying the aqueous supporting electrolyte instead of by changing ∆°wφ (Table 1) show that the reaction rate is sensitive to driving force. However, the changes

Changes in Driving Force and Reaction Reversibility

J. Phys. Chem. B, Vol. 105, No. 37, 2001 8967

TABLE 2: Bimolecular Rate Constants for Reversible Cross-Phase Electron-Transfer between Reactants Located on Opposite Sides of a NB/H2O Interfacea aqueous phase reactantb [NaClO4], M

EHf 2O,c mV

NB phase reactant

EfNB + ∆°wφ,d mV

Keq e 0.68 1.5 0.017 59 0.92 1.1 28 0.036

Ru(NH3)63+/2+

0.05

-150

DMFc+/0

-140

Fe(CN)63-/4-

0.01

151

TCNQ0/-

256

Fe(CN)63-/4-

0.10

196

TCNQ0/-

198

254

0/-

169

3-/4-

Fe(CN)6

1.0

TCNQ

102 ket,f cm s-1 M-1 23 (kf) 32 (kb) 0.043 (kf) 2.5 (kb) 0.65 (kf) 0.62 (kb) 1.7 (kf) 0.06 (kb)

a The NB thin layer contained 0.25 M tetrahexylammonium perchlorate and either 0.12 mM DMFc+/0 or 0.22 mM TCNQ 0/-. b Reactant concentrations correspond to Figures 4 and 5. c Formal potential of the redox couple in the aqueous phase. d Apparent formal potential of the redox couple in the NB phase. e Equilibrium constant of the cross-phase reaction: ln Keq ) (F/RT[EHf 2O - (EfNB + ∆°wφ)]; the + and - signs correspond to the forward and reverse reaction directions, respectively. f Rate constant calculated from eqs 5, 6, and 2 using the values of id calculated from eq 3 with the diffusion coefficients for DMFc and TCNQ measured by rotating disk voltammetry with solutions of the reactants in NB. (id)DMFc ) 3.7 µa; (id)TCNQ ) 8.5 µa. Values were reproducible within (25% in replicate experiments.

Figure 5. Reversible electron-transfer between the TCNQ0/- and Fe(CN)63-/4- couples across the NB/H2O interface. The NB used to prepare the thin layer contained 0.22 mM TCNQ and 0.23 M THAP. For the three lower curves, the aqueous solution contained only the indicated concentrations of NaClO4. For the three upper curves, the aqueous solution contained 60 mM Fe(CN)63- and 60 mM Fe(CN)64-. The electrode potential was scanned from its open circuit value at 5 mV s-1.

in the aqueous reactants produced by adding protons to the aqueous phase affects the composition and ionic charge carried by the transition state complex, which complicates the interpretation of the rate differences. The relatively weaker sensitivity of the rate to changes in ∆°wφ might reflect the effect of reactant separation on reaction rate. If, in order for cross-phase electron-transfer to occur, the two reactants must be separated by a distance significantly smaller than that across which the interfacial potential difference falls, the observed behavior could be understood. Girault and Schiffrin24 and Schmickler20 have previously suggested essentially the same notion. The idea is that little or no reaction occurs until the reactants sit at sites where the difference in electrostatic potential, ∆red ox φ, is smaller, and less sensitive to changes in the concentration of supporting electrolyte than is ∆°wφ. Under such conditions, the values of ket would be expected to be relatively insensitive to changes in ∆°wφ, as observed.

Recently, Zhang et al. measured rate constants for the same interface and reactant pair using the scanning electrochemical microscopy method.9 They obtained a rate constant similar to that in Table 1 in 0.1 M NaClO4 but a substantially higher rate constant in 0.01 M NaClO4. An important difference between measurements of the rate of cross-phase electron-transfer by the scanning electrochemical microscopy and the steady-state thin-layer methods is that cross-phase ion-transfer accompanies electron-transfer in the former but not the latter method.14 This difference might be one factor contributing to the disagreement between the results of Zhang et al. and those reported in these studies in more dilute supporting electrolytes. Both Zhang et al. and we observed that changes in ∆°wφ cause ket for the reaction between Fe(CN)63- and DMFc to decrease as the overall driving force for the reaction (as measured by Keq) increases. That ion-pair formation between the reactants and the supporting electrolytes within the mixed solvent media present at the liquid/liquid interface may play a more dominating role than the overall driving force in controlling the rate of electron-transfer, as suggested by Zhang et al.,9 seems a reasonable working hypothesis on which to base the additional experiments that are clearly needed to obtain a more satisfying explanation of the observed patterns of kinetic behavior. Results have been presented4,26 that indicate that inverse ratedriving force dependences for electron-transfer at liquid/liquid interfaces may reflect entry into the inverted region of Marcus theory. However, such cases involve considerably larger driving forces than are present with the DMFc-Fe(CN)63- system. Thus, the behavior of this system, observed by both Zhang et al. and us, seems not to be an example of electron-transfer kinetics in the inverted region of Marcus theory. Fe(CN)63-/4 + TCNQ0/-. In the reaction between TCNQand Fe(CN)63-, the two anionic reactants are likely to be prevented by mutual repulsion from approaching each other as closely as was possible for the reaction between neutral DMFc and Fe(CN)63-. As a result, the values of kf are considerably smaller and they are sensitive to changes in ∆°wφ (Table 2). A greater distance separating the reactants would account for the smaller values of kf. And if the reactants occupied sites where ∆ox redφ was a significant fraction of ∆° wφ, the greater dependency of kf on changes in ∆°wφ would also be understandable. In the reaction between TCNQ and Fe(CN)64-, the lack of charge on the oxidant in the NB phase might allow the two reactants to approach each other more closely in the interface (as proposed for the Fe(CN)63--DMFc reactant pair). However, the rate constant for the (reverse) reaction, kb, exhibits a

8968 J. Phys. Chem. B, Vol. 105, No. 37, 2001

Shi and Anson uncharged reactants in the organic phase, ket values that do change substantially with ∆°wφ have been reported (Figure 6 and ref 9), so that some aspects of the behavior described in ref 5 remain puzzling. Conclusions

Figure 6. Forward and reverse rate constants for reaction 7 vs the driving force for the reaction. Data from Table 2. (b) kf; (0) kb.

significant sensitivity to changes in ∆°wφ (Table 2), which indicates that ∆red ox φ for the reverse reaction changes along with ∆°wφ. The changes in log kf and log kb with changes in driving force, i.e., [EHf 2O - (EfNB + ∆°wφ)], are linear and approximately equal (Figure 6). The behavior can be regarded as an indication that ∆°wφ makes a significant contribution to the overall driving force for the reaction with corresponding affects on the rates of the reaction in both directions. The change in kf with changes in ∆°wφ (produced by changes in [ClO4-] in the aqueous phase) shown in Figure 6 is also in the direction expected from a diffuse-layer effect. For example, increases in [ClO4-] cause ∆°wφ to decrease, which would increase the concentration of TCNQ- at the interface and cause the observed value of kf to increase, as is observed. There should be no diffuse-layer effect on kb because, for the reverse reaction, the reactant in the oil phase (TCNQ) is neutral. However, the changes in kb caused by changes in [ClO4-] are similar to the changes in kf (Figure 6). Thus, diffuse-layer effects appear not to be important for the TCNQ0/--Fe(CN)63-/4- system. The rate of the cross-phase reaction between TCNQ and Fe(CN)64- has also been examined at the DCE/H2O (DCE ) 1, 2-dichloroethane) interface in previous studies.8,26,27 The present results are in qualitative agreement with those from these previous studies. Quantitative comparisons are not warranted because of differences in the composition of the interfaces and the supporting electrolytes. The slopes of the lines in Figure 6 correspond to transfer coefficients of 0.50 and 0.51 for the forward and reverse directions of reaction 7, respectively. The smaller values of transfer coefficients for this reaction reported in ref 8 is the result of a numerical error. After correction (multiplication by 2.303) the transfer coefficients measured previously agree with those measured in this study. A more important point is that all studies concur that the reaction rate is sensitive to changes in ∆°wφ without evidence of a significant diffuse-layer effect. Liu and Mirkin5 recently concluded that a significant diffuselayer effect was present in the reversible reaction between the Ru(CN)63-/4- and ZnPor+/0 couples (where ZnPor is zinc tetraphenylporphyrin) at the benzene/H2O interface. However, the reported increase in the rate constant for the oxidation of Ru(CN)4- by ZnPor+ as ∆°wφ increased5 is compatible with a driving force effect as well as a diffuse-layer effect. The rate of the reverse reaction (reduction of Ru(CN)63- by ZnPor) was found to be insensitive to changes in ∆°wφ5 which is compatible with the lack of a diffuse-layer effect (in the organic phase) when the reactant is neutral but one would still expect to observe a dependence of kb on driving force. In other cases involving

Additional experimental data on the kinetics of cross-phase electron-transfer at liquid/liquid interfaces have revealed disparate patterns of kinetic behavior which do not lead to broadly applicable generalizations. However, the following restricted conclusions suggest themselves: (i) Variability in the sensitivity of reaction rates to changes in the Galvani potential differences at interfaces may reflect differences in reactant separations when electron-transfer occurs. (ii) For reactions with rates that are sensitive to changes in ∆°wφ, the contribution of ∆°wφ to the overall driving force for the electron-transfer appears to be the most significant factor. Unambiguous evidence for diffuse-layer effects was not encountered. (iii) The kinetics of reversible reactions, which are readily accessible to the thin-layer electrochemical method, can provide useful insights into electrontransfer mechanisms at liquid/liquid interfaces. (iv) In experiments on electron-transfer at liquid/liquid interfaces in which the concentrations of supporting electrolytes in the aqueous phase are varied, it is wise to measure the formal potential of the aqueous redox couple in each supporting electrolyte rather than assuming that it remains constant. Acknowledgment. This work was supported by the National Science Foundation. We appreciated receiving a pre-print of reference 26 prior to its publication. APPENDIX We seek the steady-state plateau currents to be expected when a reversible cross-phase electron-transfer reaction (reaction A1) is examined in a cell like the one in Figure 1 kf

(Red)o + (Ox)w y\ z (Ox)o + (Red)w k

(A1)

b

(Red)o and (Ox)o refer to the redox couple confined to the thin layer of nonaqueous (oil) solvent and (Red)w and (Ox)w are the corresponding reactants in the aqueous (water) phase. At steady-state, the net rate of reaction A1 is equal to the diffusive supply of (Red)o to the liquid/liquid interface

kf[Red]o[Ox]w - kb[Ox]o[Red]w )

DoCo(iobs)cat (A2) δid

where kf and kb are the rate constants for the forward and reverse direction of reaction A1, Do is the diffusion coefficient of the reactant in the nonaqueous thin layer of thickness δ, Co ) [Red]o + [Ox]o is the total concentration of reactant in the thin layer, (iobs)cat is the observed cathodic plateau current and id is defined by eq 2. The reactant concentrations on the lhs of equation A2 refer to their values at the liquid/liquid interface. For the aqueous phase reactants, it is assumed that the experimental measurement time is sufficiently short and the concentrations of Ox and Red in the bulk of the aqueous phase are sufficiently large that they can be assumed to remain unchanged at the liquid/liquid interface. The values of [Red]o and [Ox]o are given by equation A3 and A4

(

[Red]o ) Co

)

id - (iobs)cat id

(A3)

Changes in Driving Force and Reaction Reversibility

(iobs)cat [Ox]o ) Co id

J. Phys. Chem. B, Vol. 105, No. 37, 2001 8969

(A4)

Combining equations A1-A4 leads to eq 5 in the text. An analogous analysis of the situation for the anodic plateau current leads to eq 6 in the text. References and Notes (1) Wei, C.; Bard, A. J.; Mirkin, M. V. J. Phys. Chem. 1995, 99, 16033. (2) Tsionsky, M.; Bard, A. J.; Mirkin, M. V. J. Am. Chem. Soc. 1997, 119, 10785. (3) Delville, M.-H.; Tsionsky, M.; Bard, A. J. Langmuir 1998, 14, 2774. (4) Tsionsky, M.; Bard, A. J.; Mirkin, M. V. J. Phys. Chem. 1996, 100, 17881. (5) Liu, B.; Mirkin, M. V. J. Am. Chem. Soc. 1999, 121, 8352. (6) Barker, A. L.; Unwin, P. R.; Amemiya, S.; Zhou, J.; Bard, A. J. J. Phys. Chem. B 1999, 103, 7260. (7) Zhang, J.; Slevin, C. J.; Unwin, P. R. Chem. Commun. 1999, 1501. (8) Zhang, J.; Unwin, P. R. J. Phys. Chem. B 2000, 104, 2341. (9) Zhang, J.; Barker, A. L.; Unwin, P. R. J. Electroanal. Chem. 2000, 483, 95. (10) Barker, A. L.; Unwin, P. R. J. Phys. Chem. B 2000, 104, 2330.

(11) Zhang, J.; Unwin, P. R. J. Electroanal. Chem. 2000, 494, 47. (12) Shi, C.; Anson, F. C. Anal. Chem. 1998, 70, 3114. (13) Shi, C.; Anson, F. C. J. Phys. Chem. B 1998, 102, 9850. (14) Shi, C.; Anson, F. C. J. Phys. Chem. B 1999, 103, 6283. (15) Shafer, H. O.; Derback, T. L.; Koval, C. A. J. Phys. Chem. B 2000, 104, 1025. (16) Marcus, R. A. J. Phys. Chem. 1990, 94, 1050. (17) Marcus, R. A. J. Phys. Chem. 1990, 94, 4152. (18) Marcus, R. A. J. Phys. Chem. 1991, 95, 2010. (19) (a) Girault, H. H.; Schiffrin, D. J. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1989; Vol. 15, p 1. (b) Volkov, A. G.; Deamer, D. W.; Tanelian, D. L.; Markin, V. S. Liquid Interfaces in Chemistry and Biology; Wiley: New York, 1998; Chapter 4. (20) Schmickler, W. J. Electroanal. Chem. 1997, 428, 123. (21) Barker, A. L.; Unwin, P. R J. Phys. Chem. B 2000, 104, 2341. (22) Shi, C.; Anson, F. C. J. Phys. Chem. B 2001, 105, 1047. (23) Amemiya, S.; Ding, Z.; Zhou, J.; Bard, A. J. J. Electroanal. Chem. 2000, 483, 7. (24) Clark, J. F.; Clark, D. L.; Whitener, G. D.; Schroeder, N. C.; Strauss, S. H. EnViron. Sci. Technol. 1996, 30, 3124. (25) Girault, H. H. J.; Schiffrin, D. J. J. Electroanal. Chem. 1988, 244, 15. (26) Ding, Z.; Quinn, B. M.; Bard, A. J. J. Phys. Chem. B, submitted. (27) Ding, Z.; Fermin, D. J.; Brevet, P. F.; Girault, H. H. J. Electroanal. Chem. 1998, 458, 139.