Anal. Chem. 2004, 76, 2398-2400
Diffusion Boundary Layer of a Rotating Disk Electrode As a Thin-Layer Spectroelectrochemical Cell Ping Shi and Daniel A. Scherson*
Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106
A UV-visible rapid scan spectrophotometer (RSS) was coupled to a Au rotating disk electrode (RDE) for monitoring at near-normal incidence the reflection-absorption spectrum of the diffusion boundary layer in [Fe(CN)6]4aqueous solutions over a potential region in which [Fe(CN)6]4- oxidizes, generating highly absorbing [Fe(CN)6]3- (λmax ) 420 nm). Measurements were performed under steady-state conditions at rotation rates, ω, in the range 300 e ω e 2500 rpm, yielding well-defined spectra displaying characteristic features of [Fe(CN)6]3-. In agreement with theoretical predictions, the absorbance A at λmax, using as a reference A(λmax) for the spectrum recorded at a potential negative to the onset of [Fe(CN)6]4oxidation, was found to be proportional both to the current and also to ω1/2 under conditions in which E was positive enough for the reaction to proceed under diffusion-limited control. Interest in our laboratory has focused on the development and implementation of techniques that combine well-defined convective diffusion laminar flow with spectroscopic methods and, thereby, impart molecular specificity to the highly sensitive information derived from purely electrical measurements. As has been shown in previous work, the use of a rotating disk electrode (RDE) for this unique type of spectroelectrochemical measurements offers significant advantages over other forced convection systems. In particular, the well-defined diffusion boundary layer generated by the RDE creates a virtual spectroscopic cell bearing characteristics similar to those of optically transparent thin-layer spectroelectrochemical cells (OTTLE) introduced by Kuwana and Heineman for the detection and characterization of electrochemically generated species.1 One of the major virtues of this novel strategy is the possibility of reducing the large IR drop of the OTTLE, enabling transient measurements to be performed in a much shorter time scale. In addition, the ability to work under steady state with continuous replenishment of fresh solution might prove beneficial for the study of systems for which decomposition of electrogenerated species may impair reliable quantitative analysis. Indeed, several illustrations of the use of this technique in the single wavelength mode have reported in the literature,2-5 includ(1) (2) (3) (4)
Kuwana, T.; Heineman, W. R. Acc. Chem. Res. Zhao, M.; Scherson, D. A. J. Electrochem. Soc. Zhao, M.; Scherson, D. A. J. Electrochem. Soc. Zhao, M.; Scherson, D. A. J. Electrochem. Soc.
1976, 1993, 1993, 1993,
9, 241. 140, 2877-2879. 140, 1671-1676. 140, 729-732.
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ingmore recently, the spectroscopic determination of faradic efficiencies for the electroreduction of bisulfite to dithionite on Au in aqueous electrolytes.6 In addition, attempts were also made to couple a rapid scan spectrophotometer (RSS) to the RDE by synchronizing the wavelength scan with the rotation rate, yielding satisfactory results.7 This contribution describes further improvements toward acquisition of spectral information of the diffusion boundary at a RDE over a wide wavelength range using a stateof-the-art UV-visible RSS. As will be shown, this improved tactic made it possible to collect spectral data at fixed potentials over times of the order of seconds without the complexities associated with wavelength synchronization. EXPERIMENTAL SECTION Measurements were performed with a commercial Au rotating disk electrode (area ) 0.1642 cm2, Pine Instruments) using a three-electrode cell incorporating a flat quartz window mounted on its bottom end. As shown in Figure 1, light emerging from the UV-visible RSS (OLIS Instruments) was directed through the window at near-normal incidence toward the electrode placed at the focal plane. Upon reflection, the beam exited the cell and was then deflected via a mirror/lens assembly placed at ∼90° with respect to the axis of rotation of the disk, toward the flat end of a liquid-filled optical fiber with its other end facing a photomultiplier. Solutions of 10 mM K4Fe(CN)6 (Fisher, Certified ACS) in 0.25 M K2SO4 (Matheson Coleman & Bell, Reagent) were prepared with ultrapure water (Barnstead). As is well-known, oxidation of Fe(CN)64- in this medium yields Fe(CN)63-, a species that displays a prominent absorption peak centered at λmax ) 420 nm ( ) 1.0 × 106 cm2 mol-1).8,9 Furthermore, the diffusion coefficients of the ferric and ferrous complexes are known rather accurately,8-11 providing suitable conditions for assessing quantitative aspects of this spectroelectrochemical technique. For these experiments, (5) Zhao, M.; Scherson, D. A. Anal. Chem. 1992, 64, 3064-3067. (6) Tolmachev, Y. V.; Wang, Z.; Hu, Y.; Bae, I. T.; Scherson, D. A. Anal. Chem. 1998, 70, 1149-1155. Tolmachev, Y. V.; Scherson, D. A. J. Phys. Chem. A 1999, 103, 572-1578 (7) Wang, Z.; Zhao, M.; Scherson, D. A. Anal. Chem. 1994, 66, 1993. (8) Wei, W. Z.; Xie, Q. J.; Yao, S. Z. Electrochim. Acta 1995, 40, 1057-1061. (9) Wang, R. L.; Tam, K. Y.; Compton, R. G. J. Electroanal. Chem. 1997, 434, 105-114. (10) Bortels, L.; VandenBossche, B.; Deconinck, J.; Vandeputte, S.; Hubin, A. J. Electroanal. Chem. 1997, 429, 139-155. (11) Robertson, B.; Tribollet, B.; Deslouis, C. J. Electrochem. Soc. 1988, 135, 2279-2284. 10.1021/ac035306d CCC: $27.50
© 2004 American Chemical Society Published on Web 03/16/2004
Figure 2. (Left panel) Steady-state polarization curve for the oxidation of Fe(CN)64- on a Au rotating disk electrode in 10 mM K4Fe(CN)6 in 0.25 M K2SO4 aqueous solutions for rotation rates ω ) 300 (curve a), 400 (b), 600 (c), 900 (d), 1600 (e), and 2500 rpm (f). (Right panel) Levich plot, ilim vs ω1/2 based on the data in the left panel in this figure. The straight line represents the best fit to the data (intercept, -0.032 mA; slope, 0.074 mA s1/2).
species i () O or R), respectively. By virtue of csO ) (DRδO/ DOδR)coR ) (DR/DO)2/3coR, where δi ) 1.805Di1/3ν1/6ω-1/2 is the thickness of the diffusion boundary layer of species i and coR is the bulk concentration of R, eq 1 can be written as follows.
A[E(ilim)] - A[(Eo)] ) 3.61Boν1/6DR2/3DO-1/3ω-1/2 coR (2) Figure 1. Schematic diagram of the experimental setup for nearnormal incidence UV-visible reflection absorption measurements at a rotating disk electrode.
10 000 single-beam spectra were first collected at a rate of 1000 spectra/s, coadded and averaged at a potential negative to the onset of Fe(CN)64- oxidation (Eo), and then at a series of potentials sufficiently positive for partial or total oxidation of Fe(CN)64- to ensue, Esam, at fixed rotation rates ω in the range 300-2500 rpm. Unless otherwise indicated, the distance between the window and the electrode surface was set to a minimum (2 mm) to avoid spurious contributions to the spectra due to adventitious solutionphase Fe(CN)63-, without affecting the hydrodynamic flow and, thus, the magnitude of the limiting currents for Fe(CN)64oxidation. RESULTS AND DISCUSSION The change in absorbance, A, for normal incidence reflectionabsorption experiments at a RDE polarized at a potential positive enough to generate an optically absorbing product, O, via oxidation of a nonabsorbing reactant, R, under limiting current conditions, E(ilim), is given by5
A[E(ilim)] - A[(Eo)] ) 3.61BoDO1/3ν1/6ω-1/2csO
(1)
where Eo is a potential at which no reaction proceeds, csO is the concentration of O at the surface of the RDE for E(ilim), ν is the kinematic viscosity of the solution (cm2/s), ω is the rotation rate of the disk (radians/s), B ) 0.5055, and Di (cm2/s) and i (cm2 mol-1) are the diffusion coefficient and molar absorptivity of
As discussed elsewhere,5 eqs 1 and 2 are approximate in that possible electroreflectance effects, that is, changes in reflectance induced by corresponding changes in the applied potential, are assumed to be negligible. Shown in the left panel, Figure 2, are plots of i vs E recorded for a Au RDE in 10 mM Fe(CN)64- in 0.25 M K2SO4 aqueous solutions in precisely the same geometry as that employed for the spectroelectrochemical measurements. The associated Levich plot, that is, ilim vs ω1/2, shown in the right panel in this figure, yielded, as expected, a straight line with virtually zero intercept, with a slope of 0.074 mA s1/2, consistent with DR ) 6.8 × 10-6 cm2/s and, thus, within the range of values reported in the literature, that is, 5.9-7.4 × 10-6 cm2/s.8-11 Reflection absorption data recorded in the same solution over the spectral region where only absorption of Fe(CN)63- is significant, that is, 370-500 nm, with electrode polarized at E(ilim) () 0.4 V) using the corresponding spectra at Eo ) 0.0 V as a reference, were used to construct reflection-absorption spectra of the diffusion boundary layer for seven values of ω (see left panel, Figure 3). In agreement with eq 2, a plot of A(0.4 V) A(0.0 V) at λmax () 420 nm) vs ω-1/2 was found to be linear (see right panel, Figure 3). Measurements performed for various electrode heights in the range 2-7 mm and for the same set of rotation rates yielded an average value for the slope of 0.132 s-1/2. On the basis of the reported value for D[Fe(CN)63-]/D[Fe(CN)64-] ) 1.15 ( 0.02,12 in neutral solutions, and assuming v ) 0.01 cm2/ s, [Fe(CN)63-], determined from the slope, was of 0.86 × 106 mol-1 cm2, which is ∼15% smaller than that obtained from (12) Martin, R. D.; Unwin, P. R. Anal. Chem. 1998, 70, 276-284.
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Figure 3. (Left panel) Near-normal incidence potential difference UV-visible reflection absorption spectra for a rotating Au disk electrode in the same solution as that specified in the caption for Figure 2, for ω ) 300 (curve a), 400 (b), 600 (c), 900 (d), 1200 (e), 1600 (f) and 2500 rpm (g). The ordinate represents the difference between the single beam spectra recorded at E ) 0.40 V, a potential at which oxidation of Fe(CN)64- proceeds under diffusion-limited conditions, and that at E ) 0.0 V, a potential negative to the onset of oxidation. (Right panel) Plot of A(0.4 V) - A(0.0 V) vs ω-1/2 for λmax (420 nm) based on the data in the left panel in this figure. The straight line represents the best fit to the data. R ) 0.999; intercept ) 3.3 × 10-4; slope ) 0.153 s-1/2.
conventional absorbance measurements in the transmission mode. Similar smaller values of [Fe(CN)63-] were also obtained from spectra of bulk solutions of Fe(CN)63- by placing the RDE surface at heights in the range 2-7 mm from the window, indicating that the observed deviations are due to optical/geometrical effects derived in all likelihood from beam displacements caused by refraction. Efforts are now underway to use a cube-type prism to achieve true normal incidence conditions. Theory also predicts a direct proportionality between the absorbance (A) and current (i) at any arbitrary potential, E. As is well-known,
i ) nFa(DR/δR)[coR - csR(E)]
(3)
where a is the area of the electrode, F is Faraday’s constant, and also from previous work,
A(E) - A(E0) ) 2OδOBcsO(E)
(4)
Hence, dividing eq 4 by eq 3 and recalling DR(coR - csR(E))/δR ) DOcOs(E)/δO, one obtains
[A(E) - A(E0)]/i ) 2BOδO2/(nFaDO) ) 3.29/nFa Oν1/3DO-1/3ω-1 (5) which implies that for a fixed ω, [A(E) - A(E0)] is proportional to i. On this basis, plots of [A(E) - A(0.0V)] vs E, and also i vs E should have the same shape. Indeed, as evident from the curves in the upper panel of Figure 4 and in agreement with eq 5, a plot of [A(E) - A(0.0 V)] vs i based on these data yielded a straight line (see lower panel, Figure 4). The average slope based on three 2400 Analytical Chemistry, Vol. 76, No. 8, April 15, 2004
Figure 4. (Upper panel) Plot of A(E) - A(0.0 V) (open circles, left ordinate) vs E and i (solid circle, right ordinate) vs E for a Au rotating disk electrode in the same solution as that specified in Figure 2. The lines represent best fits to the data. (Lower Panel) Plot of A(E) A(0.0 V) vs i based on the data in the upper panel in this figure. Intercept ) 2.64 × 10-5; slope ) 30.0 A-1; R ) 0.999.
independent experiments of this type yielded a value of S ) 28.3 A-1 (A here stands for ampere not for absorbance). This value compares relatively well with that value predicted [A(E) - A(Eo)]/ i ) 30.8 A-1, assuming ν ) 0.01 cm2/s; the reported DO/DR ratio (see above); DO ) 7.8 × 10-6 cm2/s and o) 0.86 × 106 mol-1 cm2 determined in this work; and the rotation rate used in these experiments, ω ) 600 rpm () 62.83 rad/s). In summary, normal incidence reflection-absorption experiments at a RDE of the type herein described provide within a very high degree of accuracy the same information as more conventional optically transparent thin-layer electrode cells of approximately the same thickness as the (Nernst) diffusion boundary layer with at least two clear advantages: (i) a much reduced effective electrical resistance leading to a sizable increase in time resolution and (ii) fast replenishment of fresh electrolyte and, thereby, fast transport of potentially high reactive intermediates into the bulk solution; thus, their contribution to the measured spectrum would be greatly diminished. ACKNOWLEDGMENT This work was supported by a grant from NSF. Received for review November 5, 2003. Accepted February 4, 2004. AC035306D
