14130
J. Phys. Chem. 1996, 100, 14130-14136
ECE and DISP Processes at Channel Electrodes: Analytical Theory Wayne M. Leslie, John A. Alden, and Richard G. Compton* Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford OX1 3QZ, United Kingdom
Toomas Silk Faculty of Physics and Chemistry, Tartu UniVersity, Jakobi 2, EE2400 Tartu, Estonia ReceiVed: April 2, 1996; In Final Form: May 31, 1996X
Analytical theory is developed for ECE and DISP1 reactions occurring at channel electrodes. Simple expressions are presented which allow the ready mechanistic interpretation of experimental data and the deduction of corresponding rate constants. These are shown to be in excellent agreement with numerical simulations and with experiments conducted on the reductions of o-bromonitrobenzene in dimethylformamide solution and of p-bromonitrobenzene in acetonitrile in the presence of light of wavelength 325 nm.
A-C in time (t) and space (x,y) are as follows.
Introduction Channel electrodes (Figure 1) have found widespread application for the resolution of electrode reaction mechanisms in which heterogeneous electron transfer reactions are coupled with homogeneous chemical reactions.1 A particular merit of conducting experimental investigations with this choice of electrode geometry is that the electrode response is readily predicted for a generality of mechanistic types by established numerical procedures.2,3 In this manner chemical realistic mechanisms may be postulated and assessed by the experimentalist who is thus not restricted to the consideration of “model” mechanisms. Nevertheless a large number of electrode processes follow relatively simple mechanistic pathways. Accordingly it is valuable if the simple analytical expressions for the current/flow rate are available to permit the interpretation of experimental data without recourse to computation. Equally such expressions may be used to verify any computations pursued. In this paper, the analytical theory of ECE and DISP1 processes at channel electrodes is developed. These mechanisms may be understood with reference to the following general scheme which describes the overall transformation of A to products in a two-electron process.4,5
E step: C step: E step: DISP step:
A ( e- f B BfC -
C ( e f products B + C f A + products
(i) (ii) (iii) (iv)
Steps i-iii define a pure ECE mechanism, while steps i, ii, and iv correspond to a DISP mechanism. Within the latter, two possibilities exist according to whether step ii or step iv is rate determining, and these separate cases are distinguished by the labels DISP1 and DISP2, respectively. Both steps ii and iv are deemed chemically irreversible. Theory We consider the ECE and DISP1 mechanisms as defined above and consider the transport-limited discharge of A. The convective-diffusion equations describing the distributions of X
Abstract published in AdVance ACS Abstracts, July 15, 1996.
S0022-3654(96)00975-6 CCC: $12.00
ECE Mechanism ∂2[A] ∂[A] ∂[A] ) DA 2 - Vx ∂t ∂x ∂y
(1)
∂[B] ∂2[B] ∂[B] ) DB 2 - Vx - k(ii)[B] ∂t ∂x ∂y
(2)
∂2[C] ∂[C] ∂[C] ) DC 2 - Vx + k(ii)[B] ∂t ∂x ∂y
(3)
DISP1 Mechanism ∂2[A] ∂[A] ∂[A] ) DA 2 - Vx + k(ii)[B] ∂t ∂x ∂y
(4)
∂2[B] ∂[B] ∂[B] ) DB 2 - Vx - 2k(ii)[B] ∂t ∂x ∂y
(5)
where DX is the diffusion coefficient of species X () A, B, or C), k(ii) is the rate constant corresponding to reaction ii, and the Cartesian coordinates x and y can be understood with reference to Figure 1. Vx is the solution velocity in the x direction; the components in the y and z directions are zero. Given laminar flow conditions and that a sufficiently long lead-in length exists upstream of the electrodes so as to allow the full development of Poiseuille flow then Vx is parabolic:
[
Vx ) V0 1 -
]
(h - y)2 h2
(6)
where h is the half-height of the cell and Vo is the solution velocity at the center of the channel. Equations 1-5 assume that axial diffusion effects may be neglected; this is valid provided the electrodes considered are not of microelectrode dimensions.6 © 1996 American Chemical Society
ECE and DISP Processes at Channel Electrodes
J. Phys. Chem., Vol. 100, No. 33, 1996 14131 of the electrode (xe, Figure 1) so that
{(2h)2/D} . (xe/V0)
(14)
As a result, concentration changes induced by the electrode are confined to distances in the y direction which are close to the electrode surface. The velocity profile in the x direction, Vx, may be simplified as follows by approximation near y ) 0 with
(
Vx ) V0 1 -
Figure 1. (a) Practical channel flow cell for mechanistic electochemical studies. (b) Schematic diagram which defines the coordinate system adopted in the text.
) (
(h - y)2 2
h
) V0 1 -
ECE Mechanism
∂[A] ∂[B] ∂[C] y ) 2h, all x, DA ) DB ) DC ) 0, ∂y ∂y ∂y
ξ ) (2Vo/hDxe) y K ) k(ii)(h xe /4Vo D) 2
2
2
(9)
-
∂[B] - K[B] ∂χ
(17)
-
∂[C] + K[B] ∂χ
(18)
-
∂[A] + K[B] ∂χ
(19)
∂[B] - 2K[B] ∂χ
(20)
∂ξ
-
∂2[C] 2
∂ξ
DISP1 Mechanism (10) 0)
0)
(13)
where 2h is the channel depth and xe is the electrode length (Figure 1). Next we note that all practical channel flow cells designed for photochemical studies1,8 operate under conditions where the time to diffuse across the the depth (2h) of the cell is long compared to the time taken to convect along the length
∂2[A] 2
∂ξ
∂2[B] 2
-
∂ξ
where we have further assumed that
D ) DA ) DB ) DC
(21)
We focus first on the ECE mechanism and apply the Laplace transform technique10 defining the Laplace transform, with respect to χ, of the concentration of A as follows, where p is the transformed variable of χ:
L[A] ) ∫0 exp(-pχ)[A] dχ ∞
(22)
Application of the Laplace transform10 to eqs 1-3 and the use of the boundary conditions (eqs 7-10) gives7
[A]bulk [A]bulk Ai(p1/3ξ) p p Ai(0)
(23)
[A]bulk Ai′(0) Ai(p-2/3K + p1/3ξ) p Ai(0) Ai′(p-2/3K)
(24)
[A]bulk Ai′(0) Ai(p-2/3K) Ai(p1/3ξ) p Ai(0) Ai′(p-2/3K) Ai(0)
(25)
L[A] ) L[B] )
(12) 1/3
2
0)
(11) 1/3
(16)
∂ξ
∂2[B]
0)
∂[A] ∂χ
2
(8)
Note that for the DISP1 case the species C is ignored. The two sets of mass transport eqs 1-3 and 4 and 5 can be solved under the sets of the above-specified boundary conditions by direct application of an implicit finite-difference method previously optimized for the solution of mass transport problems in the channel electrode geometry.2,3 References 2 and 3 contain a fully comprehensive account of the computation of the concentration profiles within a channel electrode; the interested reader is directed to those sources for further detail. In the present work such simulations are used for comparison with the analytical results developed below; these were performed using programs written in FORTRAN 77, available on request from the authors, and executed on a Sun 670 MP. In typical computations 500 grid points were used over the electrode length (xe) and 1500 over the channel depth (2h). Steady-state concentration profiles were computed for various rate constants, k(ii), and for different channel electrode geometries; each profile typically required ca. 8 s of CPU time. We next consider the analytical solution of eqs 1-3 and 4 and 5 under steady-state conditions. We begin by introducing the normalized variables χ, ξ, and K given7 by
χ ) x/xe
∂2[A]
0)
all y, x < 0, [A] ) [A]bulk, [B] ) 0, [C] ) 0 (7)
y ) 0, 0 < x < xe, [C] ) 0
)
This linearization of the parabolic velocity profile near y ) 0 is the Le´veˆque approximation.9 The mass transport equations then simplify to the following.
The boundary conditions relevant to the case of the transportlimited electrolysis of A are as follows:
∂[A] ∂[B] y ) 0, 0 < x < xe, [A] ) 0, DA ) -DB ∂y ∂y
)(
(h - y) (h - y) 1+ ≈ h h 2V0y for y ≈ 0 (15) h
L[B] + L[C] )
where Ai(x) denotes the Airy function11,12
Ai(x) )
1 2/3
∞
∑0
3 π
Γ(1/3n + 1/3) n!
sin[2/3(n + 1)π](31/3x)n
(26)
14132 J. Phys. Chem., Vol. 100, No. 33, 1996
Leslie et al.
which is the solution to the differential equation
d2Ai(x) dx2
) xAi(x)
(27)
Ai′(x) denotes the first derivative of Ai(x). Equations 23-25 permit the deduction that
[A]bulk Ai′(0) ∂L[A] ) - 2/3 ∂ξξ)0 Ai(0) p
(28)
[
]
∂L[C] [A]bulk Ai′(0) Ai′(0) Ai(p-2/3K) -1 ) 2/3 ∂ξξ)0 Ai(0) Ai(0) Ai′(p-2/3)K p
(29)
Equations 31 and 32 are related to the Laplace transformed fluxes of the electroactive species A and C at the electrode surface. It follows that the effective number of electrons transferred is given by
Figure 2. Working curve showing the relationship of Neff and K for an ECE process as calculated from numerical simulation (s) and from eqs 37 and 40 (2), respectively.
and
Ai′(x) ∼ -1/2π-1/2ξ1/4 exp(-2/3ξ3/2) ×
Neff ) L-1∫0 (∂L[C]/∂ξ)ξ)0 dχ + L-1∫0 (∂L[A]/∂ξ)ξ)0 dχ 1
∞
1
L-1∫0 (∂L[A]/∂ξ)ξ)0 dχ 1
(6k + 1)
∑0 (-1) (1 - 6k) k
(30)
Γ(3k + 1/2)
(2/3x3/2)-k (36)
54 k!Γ(k + /2) k
1
can be utilized to give L-1
signifies the inverse Laplace transform operation. where Neff takes values between 1 and 2. The lower value corresponds to slow rate constants (k(ii)) or conditions of fast mass transport, the latter to fast kinetics or slow transport. Performing the integrals of eq 30 in Laplace space10 gives
Neff ) -1
-1
[L (1/p)(∂L[C]/∂ξ)ξ)0]χ)1 + [L (1/p)(∂L[A]/∂ξ)ξ)0]χ)1 [L-1(1/p)(∂L[A]/∂ξ)ξ)0]χ)1
Neff ) 2 - 0.736K-1/2 + 0.0613K-2
(37)
We now turn to the DISP1 mechanism. Laplace transformation of eqs 19 and 20 permits the deduction that
L[B] )
2[A]bulk p
[
Ai(p-2/32K + p1/3ξ) Ai(0) Ai(p-2/32k) + Ai′(p-2/32K) Ai′(0)
]
(38)
(31) Equations 28, 29, and 31 permit the deduction of Neff, in principle, for any value of K. In practice we seek approximations for small and large K. For small K we note that
Ai(p-2/3K) ) ∑cnp-2n/3Kn
(32)
0
where the coefficients cn may be inferred from eq 26. This together with the standard inverse Laplace transform result
L
-ν-1
Γ(ν + 1) p
)χ
(ν > -1)
ν
(33)
permits the deduction of the following low-K approximation for Neff:
Neff ) 1 + 0.552K -0.309K + 0.150K 2
3
Ai(x) ∼ /2π
-1/2 1/4
ξ
∞
3/2
(6k + 1)
∑0 (-1) (1 - 6k) k
Γ(3k + 1/2)
(2/3x3/2)-k (35)
54 k!Γ(k + /2) k
1
1
(39)
If the integrations are again conducted in Laplace space and equ 32 is used to develop a low-K approximation, then
Neff ) 1 + 0.552K - 0.379K2 + 0.237K3 - 0.132K4
(40)
while eqs 35 and 36 give, at high K,
Neff ) 2 - 1.04K-1/2 + 0.479K-1 -
(34)
exp(- /3ξ ) × 2
[L-1∫0 (∂L[B]/∂ξ)ξ)0 dχ]K)0
0.183K-3/2 + 0.0782K-2 (41)
Alternatively at high K the asymptotic expansions11 1
L-1∫0 (∂L[B]/∂ξχ)ξ)0 dχ 1
Neff )
∞
-1
In this case the effective number of electrons transferred may be deduced from the equation
Theoretical Results and Discussion Figure 2 shows a working curvesa plot of Neff against Ksfor an ECE process as deduced by numerical solution of eqs 1-3. Also shown are the behavior calculated from the series in eq 37 using the terms up to, and including, that in K3 and that deduced from eq 40 retaining terms of no higher order than K-2. Comparison of the analytical and numerical predictions
ECE and DISP Processes at Channel Electrodes
J. Phys. Chem., Vol. 100, No. 33, 1996 14133 3.96 the simulated working curve was found to be described by the equation
Neff ) 1.358 + 0.483 log K
Figure 3. Working curve showing the relationship of Neff and K for a DISP1 process as calculated from numerical simulation (s) and from eq 43 and 44 (2), respectively.
shows that the low-K approximation holds to within 0.4% for K < 0.59 while the high-K equation describes the simulated data to within 0.4% for K > 3.96. In the range 0.59 < K
3.32. In the range 0.49 < K < 3.32 the simulated working curve was found to be described by the equation
Neff ) 1.331 + 0.428 log K
(43)
to within 0.3%.
Figure 4. Concentration profiles simulated for an ECE process at a channel electrode. The latter is positioned in the right-hand wall of the plot, and the direction of flow in the x direction is marked. The y coordinate shown corresponds to a fraction 0.4 of the total channel depth. The following cell geometry was used in the simulations: xe ) 0.4 cm, w ) 0.4 cm, 2h ) 0.04 cm, D ) 2 × 10-5 cm2 s-1. In a, both sets of profiles relate to a volume flow rate of 0.0177 cm3 s-1. The upper set of figures is for k(ii) ) 0.3 s-1 (giving K ) 0.260 and Neff ) 1.132) and the lower for k(ii) ) 13 s-1 (giving K ) 11.283 and Neff ) 1.787). In b, both sets relate to a fixed rate constant of k(ii) ) 13 s-1. The upper set correspond to a flow rate of 0.1773 cm3 s-1 (K ) 2.431, Neff ) 1.544) and the lower set to 0.0177 cm3 s-1.
14134 J. Phys. Chem., Vol. 100, No. 33, 1996
Leslie et al.
Figure 5. Concentration profiles simulated for a DISP1 process at a channel electrode. The latter is positioned in the right-hand wall of the plot and the direction of flow in the x direction is marked. The y coordinate shown corresponds to a fraction 0.4 of the total channel depth. The following cell geometry was used in the simulations: xe ) 0.4 cm, w ) 0.4 cm, 2h ) 0.04 cm, D ) 2 × 10-5 cm2 s-1. In a, both sets of profiles relate to a volume flow rate of 0.0177 cm3 s-1. The right-hand set of figures is for k(ii) ) 0.3 s-1 (giving K ) 0.260 and Neff ) 1.127) and the left for k(ii) ) 13 s-1 (giving K ) 11.283 and Neff ) 1.730). In b, both sets relate to a fixed rate constant of k(ii) ) 13 s-1. The upper set corresponds to a flow rate of 0.1773 cm3 s-1 (K ) 2.431, Neff ) 1.489) and the lower set to 0.0177 cm3 s-1. Figure 5a also shows a difference plot obtained by subtracting the A concentration profile for a rate constant of 0.3 s-1 from that for a value of 13 s-1 to demonstrate the build up of A near the electrode.
It is interesting to identify the differences between the ECE and DISP1 mechanisms in the context of channel electrode voltammetry since for cyclic voltammetry experiments under one-dimensional diffusion-only conditions their current-voltage behavior is indistinguishable.4,5 Figure 4a shows simulated concentration profiles for the species A-C for an ECE mechanism for two different rate constants, k(ii), using a typical cell geometry and a fixed flow rate. It can be seen that as the rate constant increases there is an enhanced loss of B which generates a greater amount of C; the concentration of A is unchanged since it depends solely of the rate of mass transport and is unaffected by the following kinetics. Comparison of the steepness of the C profiles adjacent to the electrode indicates that there is a greater flux of C to the electrode with the faster rate constant. The corresponding values of the dimensionless K in the two cases are 0.26 and 11.3, respectively, corresponding to Neff values of 1.132 and 1.787. Figure 4b shows analogous concentration profiles, but now the data have been simulated
for a fixed rate constant (of 13 s-1) for two flow rates which differ by a factor of 10. It can be seen that the depletion of A occurs over a greater fraction of the channel depth at lower flow rates. Moreover at the slower flow rate the concentration of B is more depleted signaling that the process is more nearly twoelectron as can be seen if it is noted that the dimensionless rate constants and corresponding Neff values are 2.4 and 1.54 for the faster flow rate and 11.3 and 1.79 for the slower flow rate. Turning next to the DISP1 mechanism, Figure 5a,b are analogous to Figure 4a,b in that they refer to comparisons under conditions of (a) fixed flow rate and avarying k(ii) and (b) fixed rate constant and varying flow rate. Only A and B are shown since these are the only species which control the electrode current. Close examination of Figure 5a, as assisted by the difference plot, reveals an increased buildup of A near the electrode as the value of k(ii) is increased from 0.3 to 13 s-1. A corresponding loss of B is also evident. The values of K and Neff in the two situations are 0.260 and 1.127 (slow kinetics)
ECE and DISP Processes at Channel Electrodes
Figure 6. Difference plot of Neff(ECE) - Neff(DISP1) against log10 K showing that the ECE mechanism passes a greater current for a corresponding value of k(ii).
and 11.283 and 1.73 (fast kinetics). Figure 5b again emphasizes that depletion of A occurs over a great fraction of the channel depth but that a slower flow rate permits time for a greater turnover of B and hence a greater Neffsthe values of Neff corresponding to the two figures shown are 1.489 (fast flow rate) and 1.730 (slow flow rate) corresponding to K values of 1.730 and 2.431, respectively. The different behavior between ECE and DISP1 for similar rate constants as revealed by Figures 4 and 5 suggests that the channel electrode will respond differently to the two mechanisms, thereby possibly allowing their discrimination. As noted above, this distinction is impossible with conventional cyclic voltammetry. Figure 6 shows a difference working curve in which the Neff values for the DISP1 process have been subtracted from those for the ECE mechanism. The latter always passes a larger current for corresponding values of k(ii). The different response amounts to 0.06 electrons at the most, but the difference varies nonsystematically with K (and hence the flow rate), suggesting that mechanistic discrimination is indeed possible under favorable circumstances. Experimental Section All standard photovoltammetry experiments were conducted using a platinum channel electrode made of optical quality synthetic silica to standard construction and dimensions.1 Solution (volume) flow rates between 10-4 and 10-1 cm3 s-1 were employed. Working electrodes were fabricated from Pt foils (purity of 99.95%, thickness 0.025 mm) of approximate size 4 × 4 mm2, supplied by Goodfellow Advanced Materials. Precise electrode dimensions were determined using a traveling microscope. A silver pseudo-reference electrode (Ag) was positioned in the flow system upstream, and a platinum gauze counter electrode located downstream, of the channel electrode. Electrochemical measurements were made using an Oxford Electrodes potentiostat modified to boost the counter electrode voltage (up to 200 V). Other methodological details were as described previously.1 Irradiation was provided by an Omnichrome continuous wave 3112XM He-Cd source (Omnichrome, Chino, CA) which gave light of wavelength 325 nm at 20 mW absolute power with a minimum beam diameter of 1.6 mm. The laser was used in conjunction with a beam expander (Optics for research, Caldwell, NJ) which gave a 25fold increase in beam area and a radiative power of 55 mW cm-2. Experiments were performed using solutions of the electroactive substrate (ca. 10-4-10-3 M) in dried13 acetonitrile (Fison’s dried, distilled) solution containing 0.1 M (recrystallized) tetrabutylammonium perchlorate (TBAP) (Kodak) as
J. Phys. Chem., Vol. 100, No. 33, 1996 14135
Figure 7. Plot of K vs (flow rate)-2/3 for the photo-electroreduction of p-bromonitrobenzene as deduced from the full working curve (see text).
Figure 8. Plot of Neff - 1 vs (flow rate)-2/3 for the photoelectroreduction of p-bromonitrobenzene as suggested by eq 34.
supporting electrolyte. Solutions were purged of oxygen by outgassing with prepurified argon prior to electrolysis. p-Bromonitrobenzene was used as received from Aldrich (>99%). Experimental Results and Discussion Preliminary experiments reducting p-bromonitrobenzene in 0.1 M TBAP/acetonitrile solution at a platinum channel electrode indicated a one-electron wave with a half-wave potential at -0.77 V (vs Ag). Measurements of the transport-limited current as a function of electrolyte flow rate gave a diffusion coefficient of 2.0 × 10-5 cm2 s-1. These observations are in excellent agreement with literature reports.14,15 When the electrode was illuminated with light of wavelength 325 nm photocurrents were observed to flow. These have been previously14,15 demonstrated to result from a photochemical ECE process and not from a DISP1 reaction:
Ar-Hal + e- f [Ar-Hal]•[Ar-Hal]•- + hν f Ar• + HalAr• + HS f Ar-H + S• Ar-H + e- f [Ar-H]•HS denotes the solvent/supporting electrolyte system and Ar ≡ p-NO2C6H4-. Values of Neff were recorded as a function of electrolyte flow rate by comparing the current flowing in the presence and absence of light at a potential (-0.95 V) corresponding to the transport-limited current. The range of flow rates examined was 0.003-0.08 cm3 s-1, corresponding
14136 J. Phys. Chem., Vol. 100, No. 33, 1996
Leslie et al. ECE mechanism wiht a rate constant of 250 s-1. Figure 9 shows the predictions of eq 40 for three values of k(ii) (200, 250, and 300 s-1) together with Wellington’s data. The high-K approximation is seen to be consistent with the data for values of k(ii) close to the value obtained from the full analysis. It may be concluded that eqs 38 and 40 provide an easy means for the analysis of experimental ECE channel electrode data provided the measured values of Neff are small or large enough for the low-K or high-K approximation to hold. Acknowledgment. We thank the EPSRC for a studentship for J.A.A. and the Royal Society for supporting a Joint Project between Oxford and Tartu Universities. References and Notes
Figure 9. Data of Wellington et al.16 for the reduction of obromonitrobenzene in acetonitrile solution and the theoretical behavior predicted by eq 40 for rate constants of 200, 250, and 300 s-1.
to Neff values between 1.15 and 1.02. The data were analyzed in two ways. First the full working curve (Figure 2) was used to generate values of K from the measured Neff. Next, as shown in Figure 7, K was then plotted against (flow rate)-2/3 as suggested by eq 16. The good straight line passing through the origin confirmed the ECE mechanism and the slope of the plot permitted the inference of a rate constant of 0.133 s-1 for the light-induced halide loss from the radical anion under the conditions employed. Second the data were analyzed using eq 37 truncated to retain only the term in K, as shown in Figure 8 where Neff - 1 is plotted against (flow rate)-2/3. Again a reasonable straight line is found the slope of which suggests a value of 0.125 s-1 for k(ii). The good agreement of the low-K expression with the full analysis further supports the veracity of the latter. Last the high-K expression, eq 40 was assessed by using data published by Wellington et al.16 for the reduction of onitrobenzene in dimethylformamide solution in the absence of light using a gold channel electrode. Rigorous analysis using the full working curve procedure suggested the operation of an
(1) Compton, R. G.; Dryfe, R. A. W. Progr. React. Kinet. 1995, 20, 245. (2) Compton, R. G.; Pilkington, M. B. G.; Stearn, G. M. J. Chem. Soc., Faraday Trans. 1 1988, 84, 2155. (3) Fisher, A. C.; Compton, R. G. J. Phys. Chem. 1991, 95, 7538. (4) Amatore, C.; Save´ant, J. M. J. Electroanal. Chem. 1977, 85, 27. (5) Amatore, C.; Gareil, M.; Save´ant, J. M. J. Electroanal. Chem. 1983, 147, 1. (6) Compton, R. G.; Fisher, A. C.; Wellington, R. G.; Dobson, P. J.; Leigh, P. A. J. Phys. Chem. 1993, 345, 273. (7) Compton, R. G.; Page, D. J.; Sealy, G. R. J. Electroanal. Chem. 1984, 161, 129. (8) Compton, R. G.; Dryfe, R. A. W.; Eklund, J. C. Res. Chem. Kinet. 1994, 1, 239. (9) Le´veˆque, M. A. Ann. Mines. Mem. Ser. 1928, 12/13, 201. (10) Miles, J. Integral Transforms in Applied Mathematics; Cambridge University Press: London, 1971. (11) Copson, E. T. Asymptotic Expansions; Cambridge University Press: Cambridge, U.K.,1965. (12) Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions; Dover: New York, 1970. (13) Coetzee, J. F. Recommended Methods for Purification of SolVents; IUPAC; Pergamon Press: Oxford, U.K., 1982. (14) Compton, R. G.; Dryfe, R. A. W.; Fisher, A. C. J. Electroanal. Chem. 1993, 361, 275. (15) Compton, R. G.; Dryfe, R. A. W.; Fisher, A. C. J. Chem. Soc., Perkin Trans. 2 1994, 1581. (16) Compton, R. G.; Wellington, R. G.; Dobson, P. J.; Leigh, P. A. J. Electroanal. Chem. 1994, 370, 129.
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