7096
J. Phys. Chem. 1995, 99, 7096-7101
Voltammetry under High Mass Transport Conditions. A High Speed Channel Electrode for the Study of Ultrafast Kinetics Neil V. Rees, Robert A. W. Dryfe, Jonathan A. Cooper, Barry A. Coles, and Richard G. Compton* The Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford, OX1 3QZ, United Kingdom
Stephen G. Davies and Tom D. McCarthy The Dyson Perrins Laboratory, Oxford University, South Parks Road, Oxford, OX1 3QY, United Kingdom Received: January 3, 1995@ The design, construction, and application of a miniature channel electrode operating with very high flow conditions, of up to ca. 10 cm3 s-l, are reported. The channel cell has approximate cross-section dimensions of 0.2 cm x 100 p m so that the axial velocity of the solution through the channel can reach values as high as 75 m s-l (270 km h-l, 167 mi h-l) at the channel center. The electrode takes the form of a microband electrode presently of length ca. 5-10 pm. With this arrangement voltammetry can be performed under flow conditions where the mass transport coefficient approaches 1.O cm s-l. Voltammetric measurements utilizing the new cell are reported, and the mass transport is shown to be quantitatively consistent with a model in which the dominant transport is by diffusion normal to the electrode and by convection axially through the cell. Axial diffusion effects are relatively insignificant. The cell is applied to the study of ECE processes, and it is shown that homogeneous rate constants as high as lo5 s-* are readily measureable from steady-state experiments.
Introduction During the last decade there has been a dramatic shrinkage of the voltammetric time scale brought about the the introduction, and now widespread adoption, of microelectrodes of diverse geometries-discs, hemispheres, bands, etc.-which possess at least one dimension of a size no more than the micron The rate of mass transport to such electrodes is appreciably greater than to electrodes of conventional sizes, and this permits the kinetic interrogation of processes, both heterogeneous and homogeneous, which were previously masked by transport control and therefore outside the scope of measurement by voltammetric means. The use of microelectrodes for kinetic measurements has been recently reviewed3 and the feasibility demonstrated of accessing nanosecond time scales through the use of fast scan ( 5 lo6 V s-') cyclic v~ltammetry.~.~ Under steady-state conditions the variation of the voltammetric response with electrode radius has been exploited to provide kinetic data and, for microdisc electrodes, is applicable to those reactions whose rate constants are comparable to Dla2, where a is the electrode radius and D the diffusion coefficient of the electroactive species.6 In practice this implies that processes with first-order rate constants in the 102-104 s-l range are accessible with electrodes of radii on the order of 1 pm in size.3 The kinetic microelectrode measurements discussed above have generally been made under conditions where mass transport occurs solely via diffusion. However, we have suggested the possible merits of enhancing the rate of mass transport to microelectrodes through the use of convection in addition to d i f f u ~ i o nand ~ , ~discussed the theoretical modeling of microband electrodes located in a channel flow cell as schematically shown in Figure 1 with the anticipation that hydrodynamic microelectrodes in which mass transport occurs predominantly via convection rather than diffusion should be especially advantageous for the study of electrode processes coupled to ultrafast chemical steps. Similar ideas have been advocated by Macpher@Abstractpublished in Advance ACS Abstracts, April 1, 1995.
-
flow Figure 1. Schematic diagram showing a channel microband electrode.
son, Marcar, and U n ~ i n who , ~ have introduced a wall-tube microelectrode and demonstrated its merits in the study of fast heterogeneous kinetics. The purpose of this paper is to report the design, construction, and application of a new channel microelectrode cell which seeks to optimize the rate of mass transport within this cell geometry through the maximization of the convective flow rate through the cell and over the electrode surface. We anticipate that this design should be capable of measuring rate constants under steady-state and transient conditions which are significantly greater than those alluded to above in the context of diffusion-only measurements. This prediction is realized in the context of experiments reported for the decomposition of the radical anion of p-bromobenzophenone electrogenerated in dimethylformamide solution, which is shown to fragment with a rate constant for the formation of benzophenone, which is close to lo5 s-l.
Cell Design Figures 2 and 3 give schematic representations of both the high speed channel electrode cell and the associated pressurized system designed to force solution through the flow cell so as to induce velocity gradients at the electrode surface which are as high as possible. Practically, this involves a compromise to keep solution consumption and the driving pressure drop within reasonable bounds. For a given pressure drop and at constant channel width, neglecting edge effects, the volume flow rate,
0022-365419512099-7096$09.0010 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 18, 1995 7097
Voltammetry under High Mass Transport Conditions Perspectiveview A
.............. ........ ......................
...................... ....... .............
Figure 2. High speed channel flow cell showing a perspective view (not to scale) and the principal dimensions. I.
I
...............................................i - .I---. ,. ,........................................ I
interlaces
channel height involves a 16-fold increase in solution consumption for only a 4-fold increase in shear rate; conversely, halving the channel height would require a 4-fold increase in pressure to maintain the same shear rate but with one-quarter of the solution consumption. The dimensions chosen for the channel of 2 mm x 0.1 mm will achieve shear rates of 3 x lo6 s-l with a flow of only 10 cm3 sP1 if laminar flow is maintained. The flow cell (Figure 2) is constructed from fused blocks of silica (Optiglass Ltd., Hainault, Essex, U.K.) and is designed to minimize flow resistance and to maintain a smooth flow from the cell inlet to the start of the channel by using large bore connection tubes with low flow velocities; this flow is then accelerated very rapidly by a factor of 35 as it enters the channel through a taper section. The cell is completed by the addition of a cover plate which carries the microband working electrode or electrodes. The length of the channel is 2 mm to establish a stable flow pattern and to allow space for multiple electrode assemblies, while keeping the pressure drop required within practicable values of 150-200 kPa. To avoid problems of operating delicate cell assemblies at high pressure, the pressure differential is applied by enclosing the entire apparatus comprising the solution reservoir, cell, and reference and counter electrodes inside a pressure vessel with the waste solution being discharged at atmospheric pressure (Figure 3). Thus, large pressure differences are only applied to the outlet end of the cell and to the counter electrode housing, and as these forces act inwardly, there is no problem with construction or in making satisfactory joints. The chamber is pressurized by cylinder nitrogen under computer control using two fast-acting electromagnetic valves (Clippard Inc., Cincinnati, OH), with pressure being measured by a silicon diaphragm pressure sensor (Entran Ltd., Watford, U.K.). Oxygen may be removed from the chamber by repeated cycles of pressurizing and venting. A separate valve controls deoxygenation of the solution by bubbling, which is carried out with the chamber at atmospheric pressure to avoid supersaturation with nitrogen. Flow rate is controlled by the combination of chamber pressure with one of three capillaries through which the waste solution flows, selected by electromagnetic Teflon valves (Neptune Research Inc., Maplewood, NJ). These valves are normally closed so that solution is only consumed during the few seconds required for a potential scan. The cell is mounted at one end of the pressure chamber in front of a silica window to allow inspection of the electrode surface and to allow irradiation of the electrode, if desired, for photoelectrochemical studies.
Experimental Section
Figure 3. Schematic diagram showing the essential features of the high speed channel flow system. Pressure sensors are marked P, electromagnetic valves X.
Vf, will vary as the fourth power of the channel depth (h4,Figure l), while the shear rate at the wall, (&&yyX=o varies as h2,where the coordinates x and y are defined in Figure 1 and v, is the solution velocity in the x-direction. Thus, doubling of the
Gold microband electrodes were fabricated on an oxidized silicon substrate using standard semiconductor processing techniques as described p r e v i o ~ l y . ~Platinum microband electrodes were made by a metal-glass sealing procedure to avoid the use of adhesives, which would have restricted the choice of solvents amenable to study. A platinum foil strip (Goodfellow Metals, Cambridge, U.K., 99.95% purity) was sandwiched between two 9 mm diameter Pyrex rods, and the junction heated until the assembly fused. The section of glass carrying the electrode was then cut out and ground to a rectangular shape (Figure 4) using standard glassworking diamond tools, leaving a free end of the foil protruding on one side, which was subsequently soldered to a copper clip attached to the glass with Araldite epoxy resin for making the electrical connection to the potentiostat. The face forming the electrode was lapped to a flat surface and polished using a sequence of silicon carbide and alumina abrasives. Atomic force microscopy
7098 J. Phys. Chem., Vol. 99, No. 18, 1995
Rees et al.
t
Pt foil (pm thick)
6.0 -
a =L
4.0-
H \
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
(vf/cm3 Cu contact (soldered to Pt foil) Figure 4. Schematic diagram depicting the single high-temperature annealed band electrode.
was used to monitor the lapping and polishing procedure to ensure that this did not cause undercutting of the electrode. The precise dimensions of the electrodes were measured using either a scanning electron microscope or a Park Instruments AFM. The solvent used throughout was dried dimethylformamide (Sigma- Aldrich, HPLC Grade) or acetonitrile (Fisons, dried, distilled); tetrabutylammonium perchlorate (TBAP, Kodak, puris) served as the background electrolyte. Ferrocene, pchloranil, benzophenone, and p-bromobenzophenone (all Aldrich, 99%) were used as received. m-Bromobenzophenone was prepared using a literature procedure.lo Solutions were thoroughly purged of oxygen as described above by outgassing with predried nitrogen. Supporting theory was generated from programs written in FORTRAN 77 on a Sun IPC workstation.
Results and Discussion We consider first experiments performed using the oxidation of ferrocene, CpzFe, in 0.1 M TBAPDMF, which is a wellestablished simple one-electron oxidation process. Experiments were conducted using approximately millimolar concentrations of the substrate and a gold electrode of length 12 pm. Electrochemically reversible voltammetric waves were recorded, with a half-wave potential of +0.325 V (vs Ag/AgCl pseudoreference electrode) and the variation of the mass transport limited current, Ilim, with electrolyte flow rate investigatedusing a range of flow rates up to ca. 3.5 cm3 s-l. Figure 5 shows that Ilim depends in a direct linear fashion on the cube root of the flow rate. The data depicted in Figure 5 was analyzed in terms of the Levich equation:12
Ilim = 0 . 9 2 5 F [ C p , F e ] , , ~ ~ ~Vdh2d} D ~ ~ (1'3
(1)
where F is the Faraday constant, D the diffusion coefficient of the electroactive species CpzFe, Vf the volume flow rate, xe the electrode length, w the electrode width, h the half-height of the channel, and d the channel width. Using measured values of xe = 12 pm, w = 0.2 cm, 2h = 116 pm, and d = 0.2 cm, a value of 9.4 x cm s-l for D was deduced. This value corresponds exactly to the accepted literature value for the diffusion coefficient of ferrocene. A similar exercise conducted on the reduction of p-chloranil in acetonitrile solution gave analogous conclusions. The foregoing suggests that eq 1 quantitatively describes the rate of mass transport to the channel electrode surface. The basis of the Levich equation is that the dominant forms of mass transport are convection axially through the cell and diffusion
Figure 5. Transport limited current (Z~i,,,)/flow rate (Vf) data obtained for the oxidation of ferrocene (1.15 mM) using a 12 p m gold channel electrode. The channel dimensions were d = 0.2 cm, w = 0.2 cm, and 2h = 1.16 x lo-* cm.
normal to the electrode surface so that the relevant convectivediffusion equation is
where the coordinates n and y are depicted in Figure 1 and v, is the solution velocity in the x-direction. Provided the solution flow is laminar and fully developed in the vicinity of the electrode, v, is a parabolic function of y.12 Quantitatively,
(3) where vo is the velocity at the center of the channel. The entrance length, XL, for the establishment of the equilibrium laminar flow pattern between parallel plates when the entry flow is planar is estimated by13
xL/2hx 0.04Re
+ 0.5
(4)
where 2h is the separation of the plates and Re is the Reynolds number. The value for a channel of high aspect ratio may be expected to be similar, and thus for larger Reynolds numbers excessive lengths of channel would be required to establish equilibrium flow. The present cell design is therefore based on equilibrium flow being present in the entry tubing to the cell, and as this is accelerated in the taper section, the smooth flow pattern should be preserved so that the entry flow to the channel will be close to parabolic instead of planar. Thus, the two boundary layers will already be fully developed, and the minimum distance is required for re-equilibration. At very high Reynolds numbers the flow will become turbulent after a transition distance xt. In the case of a tube an expression has been given:l4
where r is the radius and qt = (VO - V ) f i , vo and V being the axial and mean velocities. Assuming an analogous behavior for the channel, where qt = 0.5 and using the hydraulic diameter Dh = 4h for 2r, suggests for example that for Re = lo4 the value of xt would be on the order of 4 mm, and thus turbulence would not occur until after the electrode position, which would normally be 1 mm from the channel entrance. Therefore, laminar flow conditions may exist in this cell at flow rates above
Voltammetry under High Mass Transport Conditions
J. Phys. Chem., Vol. 99, No. 18, 1995 7099
the critical value of Re, as demonstrated above for the reduction of p-chloranil in acetonitrile, where Reynolds numbers up to 9050 (volume flow rate 3.7 cm3 s-l) were achieved without any observed deviation from eq 1. We next consider the mass transport coefficient, kT, which quantifies the rate of mass transport to the electrode surface:
where j is the mean flux to the electrode of area A. Examination of the currents flowing in Figure 1 under fast flow conditions enables us to estimate the mass transport coefficient, k ~ for , these flow rates. For an electrode ca. 10 pm long, kT can be as high as 0.5 cm s-l. We note that a reduction in the electrode length to 1 pm, or less, would increase this quantity by 1 order of magnitude or more. We turn next to the application of the high speed channel electrode to the study of fast kinetic processes coupled with voltammetrically visible electron transfer processes and examine, first, the reduction of m-bromobenzophenone (mBBP) in 0.1 M TBAPDMF solution. This has previously been studied using fast scan cyclic ~ o l t a m m e t r yunder ~ ~ corresponding conditions, on which basis the following mechanism was inferred:
+ e- - [m-BrPhCOPh1'[m-BrPhCOPh1'- - Br- + 'C,H,COPh 'C,H,COPh + "H' - PhCOPh
m-BrPhCOPh
+ e- - [PhCOPh]'-
O=
O=D
ay2
a2[mBBP'-]
aY2
- 'x
a[mBBP] - ' x ax
a[mBBP'-] - k[mBBP'-] ax
-E/V(vs pseudo R.E.1
(iii)
(iv)
-EIV(vs pseudo R.E.1
2.0
1.6
Figure 6. Hydrodynamic voltammograms measured for the reduction of m-bromobenzophenone in 0.1 M TBAPDMF solution using a 12 pm gold channel electrode using flow rates of (a, top) 0.020 cm3 s-', (b, middle) 0.042 cm3 s-I, and (c, bottom) 0.172 cm3 s-l.
x < 0, ally, [mBBPl = [mBBP],,,,,
[mBBP'-l = 0, [BPI = 0
0 < x < x,, y = 0, [mBBPl = 0, a[mBBP]/ay = -a[mBBP'-]/ay,
(7)
(8)
2.4
- E N (vs pseudo R.E.)
[BPI = 0
all X, y = 2h, a[BBP/ay = a[mBBP'-]/@ = a[BP]/@ = 0 The result of the above ECE problem is known,16 and it has been demonstrated that Neff is a unique function of the dimensionless rate constant
K = k(4h4x~d2/9V~D)1'3 subject to the boundary conditions
2.4
(ii)
The generation of the radical anion, [PhCOPh]'-, effectively proceeds via an ECE mechanism, and the ratio of the total current arising from botht waves to the current due to the first wave only provides a measure of the effective number of electrons transferred in the ECE reaction, ne^, which lies in the range 1 < Neff < 2. The prediction of Nefffor the mass transport conditions suggested above for the high-speed channel requires the solution of the following mass transport equations: a2[mBBP]
I
2.0
1.6
(1)
where initially the radical anion mBBP- is formed, but undergoes rapid debromination with the ultimate formation of benzophenone, Ph2CO (BP). The source of the hydrogen, "H', was thought to be the solventhpporting electrolyte system. A rate constant, k, of 740 f 200 s-l for the formation of benzophenone was reported. l5 Figure 6 shows three hydrodynamic voltammograms obtained for the reduction of mBBP at the high speed channel electrode using a 12 pm gold electrode. In each case two reduction waves are apparent. The first, with a half-wave potential of ca. -1.73 V (vs pseudo-Ag/AgCl) relates to the reduction of the parent material, while the second, which has a reduction potential of ca. - 1.90 V, corresponds to the simple one-electron reduction of benzophenone: 15.16 PhCOPh
0.0
(10)
The relationship between ne^ and K has been presented in the
7100 J. Pkys. Ckem., Vol. 99, No. 18, 1995
Rees et al. I
I
/
1.q-
1.01
r
2
6
4
8
x)
12
14
16
18
C V/cm ~ 3sV'~ Figure 7. Analysis of N&flow rate data obtained from voltammograms
such as those shown in Figure 5 .
Figure 9. Analysis of N,&low rate data obtained from a 12.5 pm platinum microband electrode.
been reported as undergoing reduction via an ECE process analogous to that suggested for the meta-i~omer:'~
+ e- - [p-BrPhCOPh1'[p-BrPhCOPh1'- - Br- + 'C6H4COPh 'C6H4COPh + "H' - PhCOPh PhCOPh + e- - [PhCOPh]'-
p-BrPhCOPh
0.2
0.L
0.6
0.8
1.0
1.2
1.4
( ~ f / c m s.')''~ Figure 8. Typical currendflow rate data obtained at a 12.5 pm platinum microband electrode for the reduction of mBBP (0.97 mM) in 0.1 M TBAPDMF solution.
form of a working curve.17 This permits the analysis of experimental data via the following protocol: Neff values are measured as a function of Vf and the working curve used to generate corresponding values of K, which are then plotted against Vf-2/3, yielding a straight line through the origin if the data so analyzed do indeed correspond to an ECE process.'' Consideration of the data shown in Figure 6 revealed first that the reduction wave with a half-wave potential of ca. -1.73 V obeyed eq 1, with D = 7.4 x cm2 s-l, consistent with literature data.15 Second, analysis of the second wave in terms of an ECE mechanism using the procedure given above produced the good direct dependence between K and Vf-2'3 required for an ECE process." The data are given in Figure 7, the gradient of which permits the inference of the magnitude of k: 830 zt 200 s-l. Next, the experiment was repeated using a 12.5 pm platinum microband electrode. Analogous results were obtained except that the voltammetric waves of mBBP and BP were merged into a single voltammetric feature, perhaps implying a slight degree of electrochemical irreversibility in the reduction of mBBP at platinum. Figure 8 shows typical limiting current/flow data obtained at the platinum microband, and Figure 9 shows a typical analysis of such results in ir form analogous to that used in Figure 7. The slope of plots such as that in Figure 9 permitted the following value of k to be deduced: 710 f 150 s-l (mean of three separate experiments). The two values obtained for k from the two electrode types are in excellent agreement with that noted above from literature cyclic voltammetry data.15 This result further confirms the convectivediffusion model proposed above for the fast channel. Last, we turn to consider the reduction of p-bromobenzophenone (pBBP), again in 0.1 M TBAPDMF solution. This has
(9 (ii) (iii)
(iv) However, cyclic voltammetry shows that the rate of benzophenone formation from the radical anion is much faster than for the case of the meta-species: k,,, = 80 000 zt 24 000 s-l.15 Figure 10 shows two hydrodynamic voltammograms obtained for the reduction of pBBP at the high speed channel electrode using a 12 pm gold electrode. As with the case of the metacompound, two reduction waves are again apparent. The first, with a half-wave potential of ca. - 1.78 V (vs pseudo-Ag/AgCl), relating to the reduction of pBBP is now closer to the second wave, corresponding to the one-electron reduction of BP,18 and the two waves merge into each other, although a point of inflexion is apparent at the midpoint between the two respective half-wave potentials. The magnitude of the total current passed on the second wave was analyzed using the same general approach as used above. Experiments using large (ca. 3 mm) channel electrodes, at which the ne^ value for the second wave is accurately equal to 2, showed that pBBP had a diffusion coefficient of 7.4 x cm2 s-l, equal to that of the metaisomer. This enabled the magnitude of the total current recorded under fast-flow conditions to be converted into an Neffvalue and hence analyzed as before. The resulting plot of K against (flow is shown in Figure 11. A good straight line fit through the origin is apparent, as expected for an ECE process. The slope of the line permitted a value of 73 000 s-l to be deduced for kPara.Confirmation of this value was obtained by further experiments conducted using a 5 pm platinum microband electrode. In this case useful quantitative data was only obtained from the first few (five or six) voltammograms recorded after the mechanical polishing of the electrode. Figure 12 shows the analysis of typical data. Note that the values of K are much smaller than depicted in Figure 11, corresponding to the smaller electrode size and hence the correspondingly lower values of Neff. The slope of Figure 12 permits the following value for k,,, to be inferred: 76 500 s-l. Again, excellent agreement with the published cyclic voltammetry data is apparent from the experiments made with both the platinum and gold microband electrodes. In conclusion, two merits of the high speed channel cell are
Voltammetry under High Mass Transport Conditions
J. Phys. Chem., Vol. 99, No. 18, 1995 7101
1.2 1.0-
0.8-
a a 2 0.6-
t
0’4 0.2 0.0
-1.5
-2.0
E/V(vs pseudo R.E.) I
a . 1
c1
-1.5
-2.0
E / V ( v s pseudo R.E.) Figure 10. Hydrodynamic voltammograms measured for the reduction of p-bromobenzophenone in 0.1 M TBAPDMF solution using a 12 cm3 p m gold channel electrode using flow rates of (a, top) 4.2 x s-’ and (b, bottom) 3.4 cm3 s-’.
Figure 11. Analysis of Ne&low rate data obtained from voltammograms such as those shown in Figure 7.
evident. First, it is described by a simple mass transport model in which axial convection and diffusion normal to the electrode are dominant. The necessary theory for the interpretation of experiments in the channel geometry is well-developed, and recipes exist for the analysis of all the familiar mechanisms of electrode reactions (EC, CE, EC’, ECE, DISP, etc.).lg Moreover, if mechanisms present themselves which are not covered by existing theory, then simple numerical methods are available for the routine solution of equations such as (l), (7), (8), and (9), which can treat cases of considerable ~omplexity.~ Second, the very fast rate of mass transport in the cell permits the study of ultrafast kinetic processes coupled to the electrochemical events. In particular, the above shows that a rate constant as large as ca. lo5 sP1 may be measured using a ca. 10
0.4
0.8
1.2
1.6
( Vf /cm 3~41-2’3 Figure 12. Analysis of N,&low rate data obtained from voltammograms measured at a 5 p m microband electrode.
pm microband electrode. Equation 10 suggests that by shrinking the electrode length below 1 pm, a further order of magnitude should be attainable, so giving access to the microsecond time scale by means of steady-state experiments alone in which kinetics are deduced through the variation of currents (Ne# values) or half-wave potentials (in the case of EC processes, for example) with the rate of mass transport (flow rate). We note that transient experiments (potential steps, cyclic voltammetry) are entirely viable in the high-speed channel and may be predicted to lower the time scale yet further. Acknowledgment. We thank EPSRC for financial support (Grant No. GR/H9988), NERC for a studentship for R.A.W.D., and John Alden for his interest in our activities. R.A.W.D. would also like to thank St. Edmund Hall, Oxford, for their award of a graduate scholarship and the Edinburgh University Club of Oxford for further financial support.
References and Notes (1) Fleischmann, M.; Pons, S. Ultramicroelectrodes; Datatech Morgantown, NC, 1987. (2) Wang, J. Microelectrodes; VCH: New York, 1990. (3) Montenegro, M. I. Res. Chem. Kinet. 1994, 2, 1-80. (4) Amatore, C.; Lefrou, C. Port. Electrochim. Acta 1991, 9, 311. (5) Amatore, C.; Jutand, A.; Pfluger, F. J . Electroanal. Chem. 1987, 218, 361. (6) Oldham, K. B. J . Electroanal. Chem. 1991, 313, 3. (7) Compton, R. G.; Fisher, A. C.; Wellington, R. G.; Dobson, P. J.; Leigh, P. A. J . Phys. Chem. 1993, 97, 10410. (8) Compton, R. G.; Dryfe, R. A. W.; Alden, J. A.; Rees, N. V.; Dobson, P. J.; Leigh, P. A. J . Phys. Chem. 1994, 98, 1270. (9) Macpherson, J. V.; Marcar, S.; Unwin, P. R. Anal. Chem. 1994, 66, 2175. (10) Koopal, S. A. Recl. Trav. Chim. Pay-Bas 1915, 34, 152. (11) Sharp, P. Electrochim. Acta 1983,28, 301. Schull, H.; Sochaj, K. Electrochim. Acta 1989, 34, 915. (12) Levich. V. G. Phvsicochemical Hvdrodvnamics: Prentice-Hall: , , Englewood Cliffs, NJ, 1962. (13) White. F. M. Viscous Fluid Flow: McGraw-Hill: New York. 1974. (14) Idelchik, I. E. Handbook of Hydraulic Resistance; Hemisphere Publishing Corp.: Bristol, PA, 1986. (15) Nadjo, L.; SavCant, J. M. J . Electroanal. Chem. 1971, 30, 41. (16) The formation of the radical anion, and its stability on the channel electrode time scale, was c o n f i i e d by means of in situ electrochemical ESR experiments in which a conventional channel electrode was located in the cavity of an X-band spectrometer. The spectrum obtained by the electrolysis at -2.0 V of m-bromobenzophenone was identical to that obtained from an authentic sample of benzophenone. The methodology used for these experiments is described in the following: Waller, A. M.; Compton, R. G.Compr. Chem. Kinet. 1989, 29, 297. (17) Compton, R. G.; Dryfe, R. A. W.; Eklund, J. C. Res. Chem. Kinet. 1993,1,260. Compton, R. G.; Pilkington, M. B. G.; Steam, G. M. J . Chem. Soc., Faraday Trans. 1 1988, 84, 2155. (18) In situ electrochemical ESR was used, as with the meta-isomer, to confirm the formation of the radical anion of BP as the sole product of the electroreduction of pBBP. (19) Unwin, P. R.; Compton, R. G. Compr. Chem. Kinet. 1989,29, 171. JP950011S
