Anal. Chem. 1992, 64, 3064-3067
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UV-Visible Reflection Absorption Spectroscopy in the Presence of Convective Flow Ming Zhao and Daniel A. Scherson. Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106
A spectroelectrochemlcal technlque Is hereln descrlbed In whlch the surface of a rotatlng dlsk electrode Is used as a mlrror to reflect a focused beam of Hght In the UV-VIS range at a near normal Incidence angle. Thls approach makes lt possible to probe quantltatively the presence of absorttlng specles In the dlffurrlon boundary layer under welMeflned hydrodynamic condltlons. Good agreement between theory and experhnentswasobtalned usingthe oxIdationof Fe(CN),,& as a model system. I n partlcular, the absorbance dlfference at the dlffuslon llmltlng current was found to be proportlonal to the reactant concentration, a,for a fixed rotatlon rate, w , and proportional to w-"* for a flxed a.
INTRODUCTION The advent of a variety of in situ spectroscopic techniques has opened new prospects for the further understanding of heterogeneous electron transfer and other interfacial proce8ses.l In their present stage of development, however, most of these methods lack sufficient time resolution to enable the detection and identification of short-lived reaction intermediates. Attempts have been made over the past 15 years to overcome some of these limitations by using forced conve~tion."~With the exception of the rotating disk electrode/ optically transparent (insulating) ring arrangement introduced by Debrodt and Heusler3 and later rigorouslyanalyzed by Dorr and Grabner) the hydrodynamic characteristics of the fluid flow have not been well defined. This work describes a novel strategy in which in situ UVvisible reflection absorption spectroscopy has been coupled to a rotating disk electrode. As will be shown, this approach makes it possible to monitor the concentration of (sufficiently) absorbing electroactive species present in the diffusion boundary layer. Furthermore, experiments involving the oxidation of Fe(CN)64-to Fe(CN)e3- have indicated that the technique can indeed yield quantitative data.
THEORETICAL CONSIDERATIONS 1. Hydrodynamics. Within the framework of approximations discussed el~ewhere,~ the steady-state concentration profile of a species in the presence of the convective flow generated by a rotating disk electrode is given by [c(E) - co]/[cs- co] = 1- (l/0.8934)texp(-E3) d t
(1)
where c([) is the (local) concentration of the species and the (1) Electrochemical Interfaces: Modern Techniques for In-situ Interface Characterization; Abruna, H. D. Ed.;VCH New York, 1991. (2) Roth, J. D.; Weaver, M. J. Anal. Chem. l991,63,1603andreferences therein. (3) Debrodt, H.; Heusler, K. E. Ber. Bunsen-Ges. Phys. Chem. 1977, 81, 1172. (4) Dorr, R.; Grabner, E. W. Ber. Bunsen-Ges. Phys. Chem. 1978.82, 164. (5) Riddiford, A. C. In Advances in Electrochemistry and Electrochemical Engineering; Delahay, P., Ed.;Wiley: New York, 1966; Vol. 4.
superscripts o and s refer to the magnitudes of c in the bulk of the solution and a t the electrode surface, respectively. The variable t = y/6 in eq 1is a dimensionless coordinate normal to the electrode surface, where y is the actual distance from the surface (in centimeters) and 6 = 1.805D1/3v1/6w-1/2, the thickness of the diffusion boundary layer, in which D is the diffusion coefficientof the species (in square centimeters per second), Y is the kinematic viscosity of the solution (in square centimeters per second), and w is the rotation rate of the disk in radians per second. Consider a cell such as that shown in Figure 1,in which the axis of rotation is normal to the bottom of the cell placed at a distance L (E = L/6)from the electrode surface ([ = 0). The total amount of the species (per unit cross-sectional area) along the [axis can be obtained by rearranging and integrating eq 1 between the appropriate limits to yield
soLiacd t = c"L/6 + [ c ~ c"1 soL/6[1- (1/0.8934)J:exp(-F3)
dt'l d[ (2)
In pactice, L is on the order of centimeters and therefore 3 orders of magnitude larger than 6, which is on the order of tens of microns. The integral on the right-hand side of eq 1 is rapidly convergent reaching a limiting value for [ of about 2 and, thus, much smaller than L/6. Therefore, and to a good degree of approximation, one can replacethe upper integration limit by infinity and thus obtain a universal constant B, defined as
B = Lm[l - (1/0.8934)~e~p(-['~) dF1 d t
(3)
Evaluation of this constant by a simple numerical method yielded a value of 0.5055. On the basis of simple algebraic manipulations, eq 2 can be rewritten to read f c dy = c"L + [cs - c0]6B
(4)
This implies that in the case of a very fast heterogeneous electron-transfer reaction, so that cs is prescribed solely by the applied potential, the integrated profile at a constant potential is a linear function of the thickness of the diffusion boundary layer, which in turn is proportional to w-ll2. This treatment implicitly assumes that despite the passage of current the bulk composition of the solutionremains unaltered over the full duration of the experiments. Such conditions can be approximately fulfilled provided the current is small, the volume of solution is large, and the measurement time is short. 2. Optics. According to Lambert-Beer's law, the absorbance of a sample is directly proportional to the concentration of the absorbing species. Hence, along the axis of rotation, Y
d I / I = kecdy (5) where I is the intensity of the light, k = 2.303, and e is the extinction coefficient of the electroactivespecies. Notice that
0003-2700/92/0364-3064$03.00/0 0 1992 Amerlcan Chemical Society
ANALYTICAL CHEMISTRY, VOL. 64, NO. 23, DECEMBER 1, 1992
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obtained by adding the contributions arising from both species. Hence, from eq 9 A(E)
+
2to(Co0L + [Con- Coo]6$) - &R(CR~L [CR'
- cRo]6RB)- log r(E) (11)
where the subscripts 0 and R refer to the oxidized and reduced species. 3. Potential Difference UV-Visible Reflection Absorption Spectroscopy under Forced Convection. Consider a situation in which the absorbance for a system consisting of the reduced and oxidized forms of the redox couple introduced above is measured at two arbitrary potentials E1 and Ez. Based on the arguments put forward earlier, the difference in the absorbance at the two potentials will be given by
rt
in out Figure 1. Schematic diagram of the experimental arrangement for reflection absorption UV-vlsible spectroscopy on a rotating disk electrode at near normal incidence angle. In and out refer to the incoming and outgoing beams, respectively. Other componentshave been omitted for clarity.
the sign of one of the terms in eq 5 has been reversed to account for the fact that the incoming light is attenuated in the direction of decreasing y values to conform to the orientation of the axis defiied for the hydrodynamics. Hence, for the incoming beam denoted as (in)
A(&) = log [Z~(out82)/Z~(0~t81)1 = 2c4@CcoS(E1) - cos(E2)1 ~&B[CR'(E~)- c$(E,)I log [@i)/r(&)I (12) As indicated, this general expression is independent of ZL(in), the intensity of the incoming beam, and also of L. A particularly convenient choice of E2 is a value at which no reaction takes place, denoted as EO,in which case the righthand side of eq 12 becomes
A(E1) -A(Eo) = 2t063[coS(E1)- Coo] + 2t~bRB[c$(E1)CRol
where Z ~ ( i n is ) the intensity of the beam entering the cell (at y = L) and Zo(in) is that of the beam impinging of the electrode surface (at y = 0) after traversing the whole solution. Therefore, using eq 4 the total absorbance of the incoming beam can be obtained by integrating eq 6 to yield
In (ZL(in)/Zo(in))= ke(coL + [cB- co]6B)
(7) In direct analogy with the previousanalysis,the absorbance of the outgoing (out) or reflected beam may be shown to be given by
In (zo(out)/z,(out)) = kt(cOL+ [cB- c"16B)
(8) From an optical viewpoint, metals such as gold are not perfect reflectors in the UV-visible spectral range; hence, the intensity of the light followingreflection is, in general, smaller than that of the original beam just before reaching the electrode surface. Also to be considered is the fact that the reflectivity is also a function of the applied potential (vide infra). Therefore, the total absorbance A, as defined in the conventional sense, can be written as A(E) = log [ZL(in)/ZL(out)l= 2c(c0L + [cs - c"16B) logr(E) (9) where r(E) = Zo(out)/Zo(in)represents the reflectivity loss at the specified potential. The absorbance in eq 9 has been written as A(E) to stress the fact that cs and therefore ZL(out) (although not explicitly labeled) are potential dependent. Equation 9 is a general expressionthat applies for an electrode polarized at any arbitrary potential E. For example, if no electrochemical reaction takes place for E = EO,the concentration profile will be constant throughout the cell. Hence cs = co and eq 9 reduces to A(Eo) = log [ZL(in)/IL(out)]= 2tcOL - log r(Eo) (10)
-
For a simple redox process (R 0 + ne-) in which both R and 0 may be optically active, an expression for the total absorbance at a specific wavelength and potential can be
- log [r(El)/r(Eo)l (13)
EXPERIMENTAL SECTION All measurements were carried out at a near normal incidence angle using an all-quartz electrochemical cell, consisting of a cylinder fused to a flat optical window, and a Pine Rotator/ rotating gold electrode system (diskarea: 0.16 cm2). The optical system employed was essentially identical to that developed in this laboratory for in situ reflection absorptionmagnetic circular dichroism! AU experiments were performed in We(CN)a/0.5 M KzSOd aqueous solutions at room temperature. We(CN)6 (Fisher,reagent grade)was recrystallized from water, and K&O4 (Baker Analyzed reagent) was used aa received. For most of the runs, the monochromator was set at 420 11111, a wavelength at which Fe(CN)p* exhibitsan absorptionmaximum and the absorptivity of Fe(CN)6" is negligibly small. This provides ideal conditions for verifying experimentally the predictions of the theoretical analysis (vide infra). Reflection absorption data were acquired as the electrode potential was scanned linearly between 0.0 and 0.4 V vs SCE in a repetitive fashion by feeding the output signal of the photomultiplier into a signal averager (Nicolet 1170). About 10cycles were often found sufficientto obtain an adequate signal-to-noise ratio. Measurements were conducted as a function of the concentration of the species in solution and the rotation rate.
RESULTS AND DISCUSSION A number of conditions were chosen for the forced convectionreflection absorption experiments so as to simplify somewhat the analysis of the data and thus test the predictions made by the theory. Specifically, (i) only the reduced form of the redox couple,i.e. Fe(CN)e4-,waspresent in the solution, and (ii) X was set at the absorption maximum of Fe(CN)p3in this spectral region, i.e. 420 nm, a wavelength at which c[Fe(CN)s4-lis essentially zero. Furthermore, the potential range in which the redox transition occurs is within the double layer region of gold in this electrolyte; hence, r(E1) r(Eo) and the last term in eq 13 becomes negligibly small.
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(6) Zhao, M.;Kim, S.; Bae, I. T.; Rosenblatt, C.; Scherson, D. A. AMI. Chem. 1991,63, 2990.
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