18818
J. Phys. Chem. 1996, 100, 18818-18822
Electrochemistry of Organic Redox Liquids at Elevated Pressures Keith J. Stevenson and Henry S. White* Department of Chemistry, UniVersity of Utah, Salt Lake City, Utah 84112 ReceiVed: June 17, 1996X
The effect of hydrostatic pressure on the 1-e- reductions of acetophenone (AP) and nitrobenzene (NB) in the absence of an inert solvent is reported. Steady-state voltammetric responses for these redox systems are obtained at a 12.5 µm radius Pt microdisk in a three-electrode, high-pressure electrochemical cell. Reduction of 8.0 M AP and 9.1 M NB in solutions containing only a small quantity of supporting electrolyte (0.2 M [(n-butyl)4N]PF6) yields well-defined sigmoidal-shaped voltammetric waves over the range of pressures investigated (P ) 1-1000 bar). Transport-limited currents for both AP and NB reduction are shown to decrease linearly with increasing pressure. Apparent (or integral) diffusion coefficients (Dapp) are computed from the voltammetric limiting currents for AP and NB reduction and compared to bulk solution molecular diffusivities (D) measured for a redox-active molecule (decamethylferrocene) added to the solutions at low concentration (∼16 mM). The relative decreases in Dapp and D with increasing pressure are essentially identical in both NB and AP solutions for pressures up to 1000 bar. The results indicate that transport-limited currents for the reduction of these organic liquids are determined solely by diffusive processes.
Introduction In previous investigations, our laboratories have developed methodologies using electrodes of micrometer dimensions (i.e., microelectrodes) for quantitative investigations of organic electrochemical reactions in the absence of an inert solVent.1-6 In these systems, the solution comprises a polar organic liquid, e.g., nitrobenzene,1,2 and a small quantity of a dissociated supporting electrolyte, e.g., 0.2 M tetra-n-butylammonium hexafluorophosphate. Well-defined voltammetric responses have been obtained by ourselves and others7,8 for the reduction or oxidation of several organic redox liquids (e.g., propanol,7 methanol,7 4-cyanopyridine,3 acetophenone,6 benzophenone,8 benzonitrile,2 and nitrobenzene1,2), firmly establishing the feasibility of performing electrochemical investigations in the absence of a solvent. Microelectrode techniques have also been successfully used to explore the electrochemical behavior of undiluted, redox-active, ambient temperature molten salts9 and melts.10 The ability to explore electrochemistry in highly concentrated solutions is especially relevant to the scale-up of electrosynthetic reactions11 and electroanalyses,7 but also raises a number of interesting conceptual issues regarding interfacial structure, electron-transfer dynamics, and molecular transport. For instance, in a dilute solution of a redox-active species, every reactant molecule transported to the electrode/solution interface may be electrochemically oxidized or reduced if a sufficiently large potential is available to drive the reaction at its masstransport-limiting rate. Applying this principle to redox reactions in the absence of a solvent suggests that the reduction or oxidation of a redox liquid generates an interfacial region containing molar quantities of product ions (as well as chargecompensating counterions from the supporting electrolyte). Thus, unlike the reduction or oxidation of a dilute redox species, the Faradaic reaction alters the chemical composition of the solution phase in contact with the electrode. The large gradient in solution composition at the electrode/solution interface produces interesting phenomena in concentrated organic solutions, including organic solution-phase electronic conductivity12 and magneticfield-enhanced molecular transport.4,6 X
Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)01787-X CCC: $12.00
Of special interest in the current studies is the compressibility of the interfacial region in the absence of a solvent and the effect of pressure on molecular transport rates. A high-pressure electrochemical cell has been developed that allows the use of microdisk techniques that are necessary for voltammetric measurements in the absence of a solvent. Electrochemical measurements at elevated pressures have been performed for over a century13 and continue to be utilized in investigations of heterogeneous charge-transfer mechanisms.14-21 However, to our knowledge, only recent reports by Flarsheim et al.22 and Golas et al.23 have described the use of microdisk electrodes in high-pressure electrochemical investigations. This is somewhat surprising since microelectrode techniques allow measurement of electrochemical phenomena over a much wider range of materials and experimental conditions than are accessible using conventional macroscopic electrodes. In the present report, we describe the influence of pressure on the reduction of acetophenone and nitrobenzene without solvent. Apparent molecular diffusivities obtained from voltammetric measurements using an ∼12.5 µm radius Pt microdisk are compared to values obtained for the oxidation of a dilute redox species (e.g., decamethylferrocene) in the same solutions. Our results suggest that the reduction of an organic redox liquid in the absence of a solvent is controlled by a diffusive transport mechanism. In addition, pressure-dependent diffusive fluxes for undiluted acetophenone and nitrobenzene are shown to be inversely proportional to the viscosity of the bulk solution phase and essentially independent of the viscosity of the interfacial boundary layer. Experimental Section High-Pressure Electrochemical Cell. The high-pressure cell and the electrochemical cell are drawn approximately to scale in Figure 1. The high-pressure cell is cylindrical (12 cm o.d., 7 cm i.d.) with a 3 cm thick lid that is held in place by eight 3/8 × 1 in. hex-head bolts (labeled as A in Figure 1). The lid is sealed to the base using a Buna O-ring (B). A pressure fluid inlet (C) connects the cell to a screw-type high-pressure pump, similar to the system developed by Spitzer et al.24 The cell pressure was measured using a pressure gauge with an estimated uncertainty of (3 bar. Three insulated electrical feedthroughs © 1996 American Chemical Society
Electrochemistry of Organic Redox Liquids
J. Phys. Chem., Vol. 100, No. 48, 1996 18819
Figure 1. Schematic drawing of the electrochemical cell enclosed in the high-pressure cell: (A) bolt holes; (B) Buna O-ring; (C) pressure fluid inlet; (D) electrical feedthroughs; (E) brass cell holder; (F) electrochemical cell body (Ke1-F); (G) Ag/AgxO reference electrode; (H) Pt counter electrode; (I) Pt microdisk electrode; (J) heptane pressure fluid; (K) solution inside electrochemical cell; (L) Teflon diaphragm; (M) Teflon diaphragm set screw; and (N) Viton O-ring.
(D) in the top of the high-pressure cell provide contact to the electrodes in the electrochemical cell (the electrical wires inside the cell are not shown). A brass collar (E), attached to the lid of the high-pressure cell, holds the electrochemical cell (F) in position. A hex screw is used to mount the cell into the brass collar, allowing the cell to be detached from the lid for modification and cleaning. The electrochemical cell is a singlecompartment 3 mL Ke1-F cell equipped with a Ag/AgxO reference electrode (G), a Pt wire counter electrode (∼1 cm in length) (H), and a Pt microdisk electrode (nominal radius ) 12.5 µm) (I). Machined Ke1-F fittings, which thread into cell ports containing Teflon O-rings, were heat pressed onto the electrodes to prevent leaks. Pressure transfer between the heptane (J) in the high-pressure cell and the electrochemical solution (K) is achieved using a thin Teflon diaphragm located (L) on the bottom of the electrochemical cell. A threaded Teflon set screw (M) affixes the Teflon diaphragm against a Viton O-ring (N) on the electrochemical cell. The pressure exerted by the heptane causes the diaphragm to compress the electrochemical solution until the pressure inside and outside the electrochemical cell is equal. The Pt microdisk electrodes were constructed by sealing a 12.5 µm radius Pt wire in a glass tube and grinding one end of the tube on sandpaper to expose a Pt disk. The glass tube was then heat sealed in the Ke1-F fitting (see above), polished with Al2O3 powder (down to 0.01 µm particle size), sonicated in H2O, and rinsed with CH3CN. Voltammetric measurements were performed at 25 °C using a BAS Model CV-27 potentiostat and a Kipp & Zonen Model BD 90 XY recorder. All voltammetric responses reported in this article are insensitive to dissolved O2. Thus, the solutions were not purged with an inert gas. Precise values of Pt microdisk radii were computed from voltammetric limiting currents measured for ferrocene (Fc) oxidation in an acetonitrile solution containing 2 mM Fc and 0.2 M [(n-butyl)4N]PF6.25 The literature value26 for the diffusion coefficient of Fc was employed in this calculation (D ) 2.4 × 10-5 cm2/s). Chemicals. Nitrobenzene (NB; Aldrich, HPLC grade) was dried over activated 3 Å molecular sieves. Acetophenone (AP; EM Science, 98+%), decamethylferrocene (DMFc; Aldrich, 97%), and heptane (Mallinckrodt, 97%) were used as received. Tetra(n-butyl)ammonium hexafluorophosphate ([(n-butyl)4N]PF; Aldrich) was recrystallized twice and dried under vacuum.
Figure 2. Voltammetric response of a 12.5 µm Pt disk in NB (9.1 M at ambient pressure) containing 0.2 M [(n-butyl)4N]PF6 and 16 mM DMFc; a ) 11.9 µm. (a) NB reduction; scan rate ) 50 mV/s. (b) DMFc oxidation; scan rate ) 5 mV/s. Pressures: (i) 1 bar; (ii) 210 bar; (iii) 410 bar; (iv) 620 bar; (v) 830 bar; and (vi) 1030 bar.
Figure 3. Voltammetric response of a 12.5 µm Pt disk in AP (8.0 M at ambient pressure) containing 0.2 M [(n-butyl)4N]PF6 and 16 mM DMFc; a ) 11.2 µm. (a) AP reduction; scan rate ) 5 mV/s. (b) DMFc oxidation; scan rate ) 2 mV/s. Pressures: (i) 1 bar; (ii) 210 bar; (iii) 410 bar; (iv) 620 bar; (v) 830 bar; and (vi) 1030 bar.
Results and Discussion Figures 2 and 3 show the voltammetric response of a 12.5 µm radius electrode as a function of pressure in NB and AP solutions containing 0.2 M [(n-butyl)4N]PF6 and 16 mM DMFc. The sigmoidal-shape voltammetric curves observed for the 1-ereductions of 9.1 NB and 8.0 M AP (eqs 1 and 2) and the 1-eoxidation of 16 mM DMFc (eq 3) are anticipated for the microdisk electrode geometry. Limiting currents for
NB + e- f NB•-
(1)
AP + e- f AP•-
(2)
DMFc f DMFc+ + e-
(3)
NB and AP reduction are greater than 2 orders of magnitude
18820 J. Phys. Chem., Vol. 100, No. 48, 1996
Stevenson and White
larger than the corresponding value for DMFc oxidation, consistent with the relative concentrations of the redox-active species (CNB/CDMFc ≈ 570 and CAP/CDMFc ≈ 500). The hysteresis apparent in the i-V response for DMFc oxidation, Figures 2 and 3, indicates that a true steady-state response is not obtained at the 12.5 µm radius electrode, even at scan rates as slow as 2 mV/s. Although this hysteresis is small, it introduces significant error in measurements of the standard redox potential E° and molecular diffusivities. According to Zoski,27 the criterion for ensuring a steady-state voltammetric response is given by eq 4:
νa2 nF e 6.25 × 10-4 D RT
( )
(4)
where a is the radius of the disk electrode, D is the reactant diffusion coefficient, n is the number of electrons transferred per molecule, F is Faraday’s constant, and ν is the voltammetric scan rate. The maximum scan rate (νmax) allowable in obtaining a steady-state voltammetric response is readily computed from eq 4. Both AP and NB are relatively viscous, and molecular diffusivities for small solute molecules in these liquids are typically ∼10-6 cm2/s. Using this value yields νmax ) 0.01 mV/s for a 12.5 µm radius disk. Thus, for the conditions employed in our investigations, it is impractical to attempt to obtain a true steady-state response. From the theoretical description of the i-V response of a microdisk (for instance, see discussion in ref 27), we estimate that limiting currents for DMFc oxidation in the NB and AP solutions are ∼5% larger than the true steady-state masstransport-limiting currents (ilim) that would be obtained at very slow scan rates (ν e 0.01 mV/s). However, our primary interest is in the relative values of ilim as a function of the hydrostatic pressure. Throughout this work, we assign the current measured at the positive potential limit of the voltammogram as ilim, since there is no ambiguity in experimentally defining this value. The reader should keep in mind that this value is slightly larger (∼5%) than the true ilim. The error in relative values of the limiting current, measured as a function of pressure, should be significantly smaller. As shown in Figures 2 and 3, values of ilim for the reduction of NB and AP and for the oxidation of DMFc decrease at elevated pressures. This dependency reflects a decrease in the transport-limited fluxes of these molecules to the electrode surface. The limiting current at a microdisk electrode of radius a is given by eq 5,28 where C* is the concentration of the
ilim ) 4nFDappC*a
(5)
reactant in the bulk solution, and Dapp is an apparent diffusion coefficient. Values of Dapp were computed from ilim values and are shown in Figure 4. The increase in redox concentration due to compression of NB (∼4% at 1000 bar) was accounted for using the Tait equation and compressibility constants evaluated by Gibson and Loeffler for pure NB.29 Unfortunately, we are unable to find the compressibility constants for AP. However, the relative error due to neglecting the solvent compression should not be greater than a few percent. Dapp values for DMFc are essentially equal in NB and AP solutions for pressures between 1 and 1000 bar, Figure 4. Although the viscosities of pure NB and AP differ only by ∼20% at ambient conditions (ηNB ) 2.014 cP30 and ηAP ) 1.617 cP31), the finding that the diffusivity of DMFc is nearly identical in these solutions is somewhat fortuitous. On the other hand, Dapp for NB and AP are approximately 3 and 10 times smaller, respectively, than the corresponding value of Dapp for DMFc.
Figure 4. Plot of Dapp as a function of pressure computed from ilim (eq 5) for the reduction of NB and AP and the oxidation of DMFc. Values of Dapp for NB and DMFc in NB solutions are corrected for compression of solvent.
Figure 5. Plot of Dapp/Dapp(1 bar) versus pressure for NB, AP, and DMFc. Values of Dapp are presented in Figure 4.
On the basis of their relative sizes, the diffusivities of the dilute and concentrated redox species in each solution are not expected to be significantly different. Our finding that the apparent diffusivity of the concentrated organic redox species is significantly smaller than that of the dilute redox species suggests that eq 5, derived for a dilute redox system, does not adequately describe the limiting currents for the highly concentrated redox systems. In Figure 5, values of Dapp/Dapp(1 bar) for each redox system are plotted as a function of pressure (where Dapp(1 bar) ) Dapp measured at ambient pressure). This presentation of the data clearly demonstrates that the percent relative changes in Dapp as a function of pressure are very similar for the concentrated and dilute redox systems. For instance, within error, Dapp/Dapp(1 bar) values are identical for 9.1 M NB and 16 mM DMFc in the NB solution. In contrast to the large differences in absolute values of Dapp, this behavior clearly suggests a common transport mechanism for the dilute and concentrated redox species. The similarity in the dependencies of Dapp/Dapp(1 bar) on pressure for NB, AP, and DMFc is surprising given the vast difference in the concentrations of the reactants. To rationalize this behavior, we recall that eq 5 is derived on the basis of the assumption that Dapp is constant throughout the solution. The assumption of a constant-valued Dapp for redox reactions in the absence of a solvent is highly questionable, since the chemical composition of the depletion layer is significantly different from that of the bulk solution. Intuitively, one expects the diffusion coefficient of the electroactive reactant to vary as a function of
Electrochemistry of Organic Redox Liquids
J. Phys. Chem., Vol. 100, No. 48, 1996 18821
distance across the depletion layer (which has a thickness of ∼5a, or 60 µm) if the properties of the reactant phase (in the bulk) and product phase (at the surface) are significantly different. We believe that this must be the situation for NB and AP reduction, since the reaction generates molar quantities of an ionic product at the electrode surface (NB•- or AP•-, and (n-butyl)4N+). In a previous investigation,3 we have considered the voltammetric behavior of such systems, using various types of empirical mixing rules to esimate the molecular diffusivities as a function of concentration. For instance, an arithmetic mixing rule, eq 6, can be written to approximate the variation in diffusivity across the depletion layer.
Dmix(r) ) (CR(r)/C*)D + (CP(r)/C*)Ds
(6)
In eq 6, CR(r) and CP(r) are the local concentrations of the electroactive reactant and product, respectively (e.g., NB and NB•-), and D and Ds are the values of the diffusivity in the bulk and at the electrode surface. The steady-state-limited current can be obtained for this case by solving the continuity equation using the appropriate boundary conditions. To simplify the mathematics, we approximate the microdisk geometry by a microhemisphere of radius r0. Thus, the continuity equation is
(
)
dCR d 0 ) r-2 r2Dmix(r) dr dr
which is readily integrated, after substitution of eq 6, using the boundary conditions
CR(r) ) 0 at r ) r0 CR(r) ) C* as r f ∞ Combining the resulting expression for CR(r) with ilim ) 2πnFr02(∇CR(r)|r0) yields the limiting current, eq 7, in terms of the ratio of bulk and surface diffusivities (D/Ds ≡ ξ).
ilim ) -πnFDC*r0
(
)
1 - ξ2 ξ(ξ - 1)
(7)
To apply eq 7 to the analysis of experimental data obtained using a microdisk, we recall the equivalency of steady-state currents32 between a microdisk of radius a and a hemisphere of radius r0 ) 2a/π. Substituting r0 ) 2a/π into eq 8 yields ilim for the microdisk geometry in terms of ξ.
(
ilim ) -2nDFC*a
)
1 - ξ2 ξ(ξ - 1)
(8)
Equation 8 reduces to eq 5 for the special case where the reactant diffusion coefficient is independent of the concentrations of reactant and product in the depletion layer, i.e., ξ ) D/Ds ) 1.33 Thus, eq 8 can be considered as a general equation for ilim in both dilute and concentrated redox solutions. For a concentration-independent diffusivity, Dapp is clearly identified as the molecular diffusivity of the reactant in the bulk solution, D. This latter value is independent of the interfacial solution properties. Figure 6 shows a plot of ilim as a function of ξ, calculated according to eq 8. Values of ilim are normalized to the current obtained assuming a constant diffusivity (ξ ) 1, ilim ) 4nFDC*a), allowing the effect of varying ξ to be easily visualized. For ξ < 1 (corresponding to the diffusivity being larger at the electrode surface than the bulk solution), the limiting current is always larger than the corresponding value based on a constant-valued diffusivity, i.e., ilim/4nFDC*a > 1.
Figure 6. Normalized limiting current (ilim/4nFDC*a) versus ξ (≡D/ Ds, the ratio the bulk and surface diffusivities).
In this regime, ilim/4nFDC*a increases without bound as ξ decreases. Conversely, when ξ > 1, ilim/4nFDC*a is < 1 and asymptotically decreases to a value of 1/2. Figure 6 shows that values of ilim/4nFDC*a are relatively insensitive to ξ when this value is greater than ∼2. Physically, the weak dependence of ilim/4nFDC* on ξ results from the small near surface diffusivity being offset by a concurrent increase in the reactant concentration gradient (dCR/dr).3 For instance, it can be shown that as ξ f ∞ (corresponding to Ds f 0), the concentration gradient at the surface becomes infinitely large in order to maintain a finite value of ilim. We note that the weak dependence of ilim/ 4nFDC*a on ξ is not unique to the arithmetic mixing rule. For instance, employing a geometric mixing rule in computing the variation in diffusivity within the depletion layer (i.e., Dmix(r) ) (DR)CR(r)/C*(DP)CP(r)/C*) yields a plot of ilim/4nFDC*a vs ξ that is quantitatively similar to that shown in Figure 6.3 It is appropriate to use eq 5 to compute Dapp for DMFc as a function of pressure given that the diffusivity will be essentially constant across the depletion layer for this dilute redox species. In this case, Dapp computed from the limiting current yields a true molecular diffusivity for DMFc in the NB and AP solutions (i.e., D ) Dapp). The decrease in D of DMFc at high pressure can thus be interpreted as resulting from an increase in the solution viscosity, the two quantities being inversely related by the Stokes-Einstein equation. For instance, the viscosity of pure NB at 30 °C is reported to increase by a factor of 1.9 upon increasing the pressure from ambient conditions to 980 bar.34 We observe that D at 25 °C for DMFc decreases by 2.1 over the same pressure (Figure 4). Although the measurement conditions for the viscosity and diffusion data are slightly different, the correspondence between these values is very good. Equation 8, rather than eq 5, appears to be a more appropriate description of ilim for NB reduction, since ξ is most likely not equal to unity. Inspection of eq 5 and 8 yields Dapp in terms of D and ξ.
Dapp ) -
(
)
D 1 - ξ2 2 ξ(ξ - 1)
(9)
In this form, Dapp is aptly defined as an integral diffusivity that reflects the graded variation in diffusivity across the depletion layer. From eq 9, Dapp ≈ (1/2)D when ξ > 2. The finding that Dapp for NB and DMFc have the same dependency on pressure, Figure 5, suggests that the quantity (1 - ξ2)/ξ(ξ - 1) is independent of pressure. Physically, this can occur if either (i) ξ is independent of pressure, implying that an increase in pressure results in identical decreases in Ds and D, or (ii) ξ is sufficiently large (>2) that (1 - ξ2)/ξ(ξ - 1) is not sensitive to pressure-dependent variation in ξ. Given that D is equivalent
18822 J. Phys. Chem., Vol. 100, No. 48, 1996 to the self-diffusivity of NB and Ds is the diffusivity of NB in the concentrated ionic interfacial layer, it seems highly unlikely that these two quantities would have the identical dependencies on the applied pressure. Thus, the latter explanation (ii) appears more reasonable. Conclusion The use of microdisk electrodes in a high-pressure electrochemical cell provides a means of investigating the dependence of pressure on the reduction or oxidation of organic liquids in the absence of an inert solvent. A well-behaved voltammetric response is observed for the reductions of undiluted nitrobenzene and acetophenone for pressures up to 1000 bar. We have shown that the apparent diffusivities of these liquids, computed from values of ilim, have the same dependency on pressure as the molecular diffusivity for a dilute solute (DMFc). These data also suggest that the dependence of limiting current on pressure for undiluted organic redox liquids can be predicted a priori from bulk viscosity data over the same pressure range. Based on a model that assumes a concentration-dependent molecular diffusivity within the depletion layer, our results are consistent with the near surface diffusivity, Ds, being at least a factor of 2 smaller than the corresponding bulk value, D. Acknowledgment. This research was supported by the National Science Foundation/Electric Power Research Institute and The Office of Naval Research. The authors gratefully acknowledge Mr. Yanlong Shi and Dr. Xiaoping Gao for assistance in the construction of the electrochemical cell and Prof. E. M. Eyring’s research group at the University of Utah for the use of their high-pressure pump. References and Notes (1) Malmsten, R. A.; White, H. S. J. Electrochem. Soc. 1986, 133, 1067. (2) Malmsten, R. A.; Smith, C. P.; White, H. S. J. Electrochem. Chem. 1986, 215, 223. (3) Morris, R. B.; Fischer, K. F.; White, H. S. J. Phys. Chem. 1988, 92, 5306. (4) Lee, J.; Gao, X.; Hardy, L. D.; White, H. S. J. Electrochem. Soc. 1995, 142, L90. (5) Paulsen, S. C.; Okerlund, N. D.; White, H. S. Anal. Chem. 1996, 68, 581. (6) Ragsdale, S. R.; Lee, J.; Gao, X.; White, H. S. J. Phys. Chem., in press. (7) Ciszkowska, M.; Stojek, Z. J. Electroanal. Chem. 1993, 344, 135. (8) Paulsen, S. C.; Lee, J.; White, H. S.; Feldberg, S. W. Unpublished results, Univ. of Utah, 1995. (9) Carlin, R. T.; Osteryoung, R. A. J. Electrochem. Chem. 1988, 252, 81.
Stevenson and White (10) (a) Hatazawa, T.; Terrill, R. H.; Murray, R. W. Anal. Chem. 1996, 68, 597. (b) Pindertown, M. J.; LeMest, Y.; Zhang, H.; Wantanabe, M.; Murray, R. W. J. Am. Chem. Soc. 1990, 112, 3730. (11) Montenegro, M. I.; Pletcher, D. J. Electroanal. Chem. 1988, 248, 229. (12) Norton, J. D.; White, H. S. J. Phys. Chem. 1992, 96, 3. (13) (a) Bichat, E.; Blondlot, R. Ann. Chim. Phys. 1883, 2, 503. (b) Amagat, E. H. Compt. Rend. 1885, 100, 633. Articles of historical interest concerning high-pressure electrochemistry are given in the following: Bridgman, P. W.; The Physics of High Pressure; Macmillan: New York, 1931; p 372. Hills, G. J.; Ovenden, P. J. Electrochemistry at High Pressure; Advances in Electrochemistry and Electrochemical Engineering, Vol. 4; Interscience Publishers: New York, 1966; p 185. (14) (a) Conway, B. E.; Currie, J. C. J. Electrochem. Soc. 1978, 125, 252. (b) Conway, B. E.; Currie, J. C. Ibid. 1978, 125, 257. (15) (a) Hills, G. J. Talanta 1965, 12, 1317. (b) Hills, G. J. In AdVances in High Pressure Research; Bradley, R. S., Ed.; Academic Press: London, 1969; Vol. 2, pp 169, 225. (c) Fleischmann, M.; Gara, W. B.; Hills, G. J. J. Electroanal. Chem. 1975, 60, 313. (d) Hills, G. J.; Kinnibrugh, D. R. J. Electrochem. Soc. 1966, 113, 1111. (16) Claesson, S.; Lundgren, B.; Szwarc, M. Trans. Faraday Soc. 1970, 66, 135. (17) (a) Franklin, T.; Mathew, S. A. J. Electrochem. Soc. 1987, 134, 760. (b) Franklin, T.; Mathew, S. A. Ibid. 1988, 135, 2725. (c) Franklin, T.; Mathew, S. A. Ibid. 1989, 136, 3627. (18) Krasinski, P.; Tkacz, M.; Baranowski, B.; Galus, Z. J. Electroanal. Chem. 1991, 308, 189. (19) (a) Sachinidis, J.; Shalders, R. D.; Tregloan, P. A. J. Electroanal. Chem. 1992, 327, 219. (b) Sachinidis, J.; Shalders, R. D.; Tregloan, P. A. Inorg. Chem. 1994, 33, 6180. (20) (a) Doine, H.; Whitcombe, T. W.; Swaddle, T. W. Can. J. Chem. 1992, 70, 81. (b) Takagi, H.; Swaddle, T. Inorg. Chem. 1992, 31, 4669. (c) Sun, J.; Wishart, J. F.; van Eldik, R.; Shalders, R. D.; Swaddle, T. W. J. Am. Chem. Soc. 1995, 117, 2600. (d) Swaddle, T. W. Can. J. Phys. 1995, 73, 258. (21) Cruanes, M. T.; Drickamer, H. G.; Faulkner, L. R. Langmuir 1995, 11, 4089. (22) Flarsheim, W. M.; Bard, A. J.; Johnston, K. P. J. Phys. Chem. 1989, 93, 4234. (23) Golas, J.; Drickamer, H. G.; Faulkner, L. R. J. Phys. Chem. 1991, 95, 10191. (24) Spitzer, M.; Gartig, F.; van Eldik, R. ReV. Sci. Instrum. 1988, 59, 2092. (25) Values of electrode radii (a) are computed using eq 5 in the text. (26) Kuwana, T.; Bublitz, D. E.; Hoh, D. E. J. Am. Chem. Soc. 1960, 82, 5811. (27) Zoski, C. G. J. Electroanal. Chem. 1990, 296, 317. (28) Saito, Y. ReV. Polarogr. 1968, 15, 177. (29) Gibson, R. E.; Loeffler, O. H. J. Am. Chem. Soc. 1939, 61, 2515. (30) Viswanath, D. S.; Natarajan, G. Data Book on the Viscosity of Liquids; Hemisphere Publishing Corp.: New York, 1989; p 517. (31) Handbook of Chemistry and Physics; Weast, R. C., Astle, M. J., Eds.; CRC Press, Inc.: Boca Raton, FL, 1981-1982; Vol. 62. (32) Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. 1988, 256, 11. (33) The function (1 - ξ2)/(ξ(ξ - 1)) is indeterminate at ξ ) 1, but is evaluated as ξ f 1 using l’Hospital’s rule. (34) Bridgman, P. W. The Physics of High Pressure; MacMillian: New York, 1931; p 344.
JP961787B
