In Situ Solution-Phase Raman Spectroscopy under Forced Convection

Anal. Chem. 2007, 79, 8004-8009

In Situ Solution-Phase Raman Spectroscopy under Forced Convection Huanfeng Zhu, Jun Wu, Qingfang Shi, Zhenghao Wang, and Daniel A. Scherson*

Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106-7078

In situ Raman spectra of solution-phase electrogenerated species have been recorded in a channel-type electrochemical cell incorporating a flat optically transparent window placed parallel to the channel plane that contains the embedded working electrode. A microscope objective with its main axis (Z) aligned normal to the direction of flow was used to focus the excitation laser beam (λexc ) 532 nm) in the solution and also to collect the Raman scattered light from species present therein. Judicious adjustment of the cell position along Z allowed the depth of focus to overlap the diffusion boundary layer to achieve maximum detection sensitivity. Measurements were performed using a Au working electrode in iron hexacyanoferrate(II), [Fe(CN)6]4-, and nitrite, NO2-, containing aqueous solutions as a function of the applied potential, E. Linear correlations were found between both the gain and the loss of the integrated Raman intensity, IR, of bands, attributed to [Fe(CN)6]3- and [Fe(CN)6]4-, respectively, recorded downstream from the edge of the working electrode, and the current measured at the Au electrode as a function of E. The same overall trend was found for the gain in the IR of the NO3- band in the nitrite solution. Also included in this work is a ray trace analysis of the optical system. Applications of an expanding array of in situ spectroelectrochemical techniques continue to afford valuable insights into the mechanisms of heterogeneous electron-transfer reactions of both fundamental and technological importance.1,2 Coupling of these methodologies to forced convection systems enables acquisition of spectral data under steady-state conditions, thereby improving conditions for detection and identification of intermediates. Such tactics have been implemented in this and other laboratories for UV-visible transmission spectroscopy for rotating disk3 and channel-type electrodes (ChEC),4-6 as well as for attenuated total reflection Fourier transform infrared spectroscopy7,8 and electron * To whom correspondence should be addressed. E-mail: [email protected]. (1) Bard, A. J.; Stratmann, M.; R. Unwin, P. R. Encyclopedia of Electrochemistry;Wiley-VCH: Weinheim, 2003; Vol. 3. (2) Amatore, C.; Bonhomme, F.; Bruneel, J.-L.; Servant, L. Electrochem. Commun. 2000, 2, 235-239. (3) Shi, P.; Scherson, D. A. Anal. Chem. 2004, 76, 2398-2400. (4) Wang, Z. H.; Zhao, M.; Scherson, D. A. Anal. Chem. 1994, 66, 4560-4563. (5) Tolmachev, Y. V.; Wang, Z. H.; Scherson, D. A. J. Electrochem. Soc. 1996, 143, 3539-3548. (6) Wang, Z. H.; Scherson, D. J. Electrochem. Soc. 1995, 142, 4225-4229. (7) Barbour, R.; Wang, Z. G.; Bae, I. T.; Tolmachev, Y. V.; Scherson, D. A. Anal. Chem. 1995, 67, 4024-4027.

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Figure 1. Schematic diagram of the channel-type electrochemical cell employed for in situ Raman measurements. WE, working electrode, RE, reference electrode; CE, counter electrode, R , reflecting surface. 2h ) 0.3, Lc )12, d )3.6, e )5, xe )0.9, w ) 0.6, l ) 0.7, and s ) 0.1. All dimensions are given in cm.

spin resonance for channels.9,10 The present contribution describes an experimental arrangement that allows acquisition of Raman data of solution-phase electrogenerated products at a ChEC downstream of the working electrode surface. The excitation laser beam was focused within the diffusion boundary layer using a microscope objective with its main axis aligned normal to the direction of flow downstream from the edge of the working electrode, which also served to collect the Raman scattered light from species present therein. This configuration generates a depth of focus (dof) within the solution for which its length and position can be adjusted to optimize interaction of the excitation beam with (8) Tolmachev, Y. V.; Wang, Z. H.; Scherson, D. A. J. Electrochem. Soc. 1996, 143, 3160-3166. (9) Cooper, J. A.; Compton, R. G. Electroanalysis 1998, 10, 141-155. (10) Webster, R. D.; Dryfe, R. A. W.; Eklund, J. C.; Lee, C. W.; Compton, R. G. J. Electroanal. Chem. 1996, 402, 167-174. 10.1021/ac070573v CCC: $37.00

© 2007 American Chemical Society Published on Web 10/04/2007

Figure 2. Schematic diagrams of the optical systems incorporating an objective and two (panel A, from refs 11 and 12) or three media (panel B), where the symbols define all metrical parameters involved in the ray tracing analysis (see text).

the diffusion boundary layer to achieve highest Raman collection sensitivity. As will be shown, the oxidation currents at the Au electrode measured in unbuffered iron hexacyanoferrate(II), [Fe(CN)6]4-, solutions were found to be proportional to the integrated Raman intensity, IR, of the main spectral feature of [Fe(CN)6]3- centered at 2132 cm-1, I2132, and also to the loss in IR of the bands due to [Fe(CN)6]4-. The same overall behavior was found for experiments involving oxidation of nitrite in buffered aqueous electrolytes, for which the oxidation currents were found to be proportional to IR for the Raman nitrate band centered at 1044 cm-1. EXPERIMENTAL SECTION The ChEC (12 cm in length, Lc, 3.6 cm in width, d, and 0.3 cm in height, 2h), shown schematically in Figure 1, incorporates three flat rectangular Au pieces embedded in epoxy resin placed along an axis parallel to the direction of fluid flow to render, following polishing, a smooth common plane, which constitutes the bottom plate of the channel. These pieces include: a working electrode (WE), 0.9 cm in length, xe, and 0.6 cm in width, w, placed 5 cm from the entrance of the channel, e, and a 1 cm × 1 cm counter electrode (CE, see top view). The third Au piece, denoted as R in the side view, of length l ) 0.7 cm, and the same width as the working electrode, was placed at a distance s ) 0.1 cm, downstream from the working electrode, directly below the focused laser beam. The use of this auxiliary reflecting surface, R, was found to be necessary to avoid contributions to the Raman signal derived from the resin, which degraded significantly the spectral quality. The reference electrode (RE, see side view) was placed at the exit of the channel so as not to disturb the hydrodynamic flow within the cell. The upper plate of the channel is a flat glass plate glued via a gasket to the bottom plate to yield the height, 2h, specified above. The laser beam was aligned along an axis normal to direction of flow and placed above R. To achieve maximum Raman sensitivity, the distance between the cell window and the objective was adjusted using a micrometer while the Au working electrode was polarized at a sufficiently positive potential for the oxidation of [Fe(CN)6]4- to proceed under diffusion-limited conditions. Once the Raman feature characteristic of [Fe(CN)6]3centered at 2132 cm-1 reached maximum intensity, the cell was locked in that position for the rest of the experiments. The same tactic was employed for studies involving oxidation of nitrite in

aqueous electrolytes. Raman spectra were obtained with a Chromex Raman 2000 equipped with an Olympus microscope attachment (1-UM345, with an objective of working distance, WD ) 1.2 cm) and a cooled CCD detector using a laser excitation wavelength of λ ) 532 nm (Verdi,Coherent Corp.). The power on the sample was on the order of 50 mW. Measurements were performed in aqueous solutions of either K4Fe(CN)6 (99%, Aldrich, ACS reagent) in 0.5 M KCl (Fisher, Certified ACS), or NaNO2/0.1M NaClO4 (98%, Aldrich, ACS reagent) pH 4.3 aqueous acetate buffer (NaAc‚3H2O, Fisher, Certified ACS; glacial acetic acid, Certified ACS PLUS) at room temperature. All solutions were prepared with ultrapure water. The proper electrochemical operation of the ChEC was assessed by measuring the limiting current, ilim (µA), as a function of the volume flow rate, Vf (mL/s), over the range ∼0.025-0.4 mL/s, as determined from the volume delivered by the cell at prescribed periods of time using gravity feed. Optical Considerations. Consider a parallel beam of monochromatic light traveling along the main axis (Z) of a microscope objective of radius rmax immersed in a nonabsorbing media with index of refraction n1 (e.g., air) aimed normal to the surface of a second transparent media (n3, e.g. water) placed at a distance H from the flat end of the objective (see panel A, Figure 2). Ray trace analysis of such a configuration yields a dof along Z, where each point within dof, Zm, can be related back to a ring of radius rk on the objective, 0 < rk < rmax, where rmax is its actual radius (see panel B in this figure)

Zm ) ∆

x

n2 +

m2NA2(n2 - 1) 1 - NA2

(1)

In this equation, n ) n1/n3, m ) rk/rmax, is a dimensionless radius, NA ) sinθmax is the numerical aperture of the focusing lens, where θmax is defined in panel A, Figure 2, and ∆ is the distance between the interface between the two media and the focus point in the second or lower medium (n3, e.g., water). It thus follows, as shown by Everall,11,12 that dof is given by (11) Everall, N. J. Appl. Spectrosc. 2000, 54, 1515-1520. (12) Everall, N. J. Appl. Spectrosc. 2000, 54, 773-782.

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dof ) Zm)1 - Zm)0 ) ∆

(x

n2 +

NA2(n2 - 1) 1 - NA2

-n

)

(2)

Assuming the cross-sectional intensity distribution of the laser beam can be represented by a Gaussian, and also that the fill factor is unity, the radial distribution function along dof, mI(m), will be given by,

mI(m) ) me-2m

2

(3)

where I(m) is the normalized intensity. Based on this formalism, it becomes possible to obtain plots of mI(m) versus Zm to yield intensity profiles for prescribed values of n, NA, and ∆, such as those provided in Figure 5 in ref 12, where the integrated intensity was normalized to a constant area. The situation, in our case, is complicated by the introduction of a third medium (n2, glass) of finite thickness L interposed between the two phases as depicted in panel B, Figure 2. A tedious, albeit straightforward application of ray trace analysis, yielded, for this geometry, explicit expressions for Zm and dof given in eqs 4 and 5 below:

Zm ) L + ∆

x

n32 + L

m2NA2(n32 - 1) 1 - NA2

x

-

n32(1 - NA2) + m2NA2(n32 - 1) n22(1 - NA2) + m2NA2(n22 - 1)

dof ) Zm)1 - Zm)0 ) ∆

(x

n32 +

L

NA2(n32 - 1) 1 - NA2

(x

)

- n3 -

n32 - NA2 2

n2 - NA

(4)

2

-

)

n3 (5) n2

Shown in panel A, Figure 3 is a plot of mI(m) versus Zm for values of the metrical parameters involved in our experiments, namely, NA ) 0.4, L ) 0.1 cm, and n1 ) 1 (air), n2 ) 1.517 (glass), and n3 ) 1.332 (water), for three different values of ∆ ) 0.07, 0.18, and 0.27 cm, which are close to the top, center, and bottom of the channel, respectively. Also shown as in inset in this figure is a gray scale that represents the intensity of the laser beam for ∆ ) 0.27 cm, which is within the dof region. It becomes evident from this simple analysis that the objective must be placed close to the surface of the glass plate in order for dof to reach the bottom of the cell. In addition, dof must be long enough to overlap the diffusion boundary layer and thus achieve optimum detection conditions for species present therein. Based on eq 5, dof can be increased either by decreasing L, i.e., using a thinner glass window, or by increasing ∆, i.e., displacing the entire cell toward the objective. For the experiments to be presented herein, the value of ∆ was optimized by varying the distance between the end of the objective and the upper plate of the cell until a maximum intensity of the Raman signal for the product was achieved, ∆ ∼0.27 cm. Spectroscopic Analysis. Contributions of [Fe(CN)6]4- and [Fe(CN)6]3- to the spectra of mixtures generated electrochemi8006

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Figure 3. Plot of the normalized laser intensity vs Z for three different values of ∆ as specified. Inset: Gray scale plot of the laser intensity as a function Z for ∆ ) 0.27 cm within the dof region. The parameter values are specified in the caption of Figure 2.

cally were determined by multilinear regression (Matlab) analysis in the region 2000-2200 cm-1, using data collected for pure of K4[Fe(CN)6] solutions in the channel cell while the working electrode was disconnected, and pure 5 mM K3[Fe(CN)6] solutions in a quartz cuvette under the same spectral collection conditions, as reference spectra. Analysis of the NO3- band in the case of experiments involving NaNO3 solutions was performed by fitting the spectral feature with a Lorentzian function (Origin) using the spectra collected at 0.5 V versus SCE as a background reference. RESULTS AND DISCUSSION Shown in Figure 4 are dynamic polarization curves recorded with the channel cell at a scan rate of 1 mV/s in aqueous 5 mM K4Fe(CN)6/0.5 M KCl (panel A) for Vf ) 56, 79, 132, 237, and 358 µL/s, and 5 mM NaNO2/0.1M NaClO4 in pH 4.3 acetate buffer solutions (panel B) for Vf ) 46, 81, 108, and 124 µL/s. Based on Levich’s formalism, the diffusion limiting current ilim (in µA) is given by9

ilim ) 9.25 × 105nF[A]bulkxe2/3D2/3w(dh2)-1/3Vf1

/3

(6)

where Vf (mL/s) is the volume flow rate, n (not to be confused with the relative index of refraction above) is the number of electrons transferred in redox reaction, F is Faraday’s constant, [A]bulk (mol/cm3) and D (cm2/s) are the bulk concentration and diffusion coefficient of the reactant, either [Fe(CN)6]4- or NO2-, respectively, and all other symbols refer to geometric parameters defined above. As predicted by theory, plots of ilim versus Vf1/3, based on the data in panels A and B, Figure 4, yielded straight lines (see panels C and D, in this figure). Values of D extracted from the slopes of the best linear fits to the data were found to be in relatively good agreement with those reported in the literature (lit), i.e. Dcal ) 5.7 × 10-6 cm2/s, Dlit ∼6.8 × 10-6 cm2/s for [Fe(CN)6]4-,3 and Dcal ) 1.76 × 10-5 cm2/s, Dlit ∼1.73 × 10-5 cm2/s for NO2-.13 (13) Piela, B.; Wrona, P. K. J. Electrochem. Soc. 2002, 149, E55-E63.

Figure 4. Dynamic polarization curves as a function of flow rate in 5 mM K4Fe(CN)6/0.5 M KCl (panel A) and in 5 mM NaNO2/0.1 M NaClO4 in pH 4.3 acetate buffer solutions (panel B) at a scan rate of 1 mV/s obtained with the channel cell described in Figure 1. Plots of the limiting /3 current, ilim, vs Vf1 based on these data are shown in panels C and D for K4Fe(CN)6 and NaNO2, respectively. Statistical best linear fits to the data yielded a slope, S ) 184 µA(s/mL)1/3, intercept, I ) 5.94 µA, and R ) 0.999 52 (for K4Fe(CN)6, C), and S ) 740 µA(s/mL)1/3, I ) 19.8 µA, and R ) 0.995 (for NaNO2, D). Based on the values of the slopes, the diffusion coefficients of [Fe(CN)6]4-and NO2- in the specified solutions, were found to be 5.7 × 10-6 and 1.76 × 10-5 cm2/s.

Figure 5. (A) In situ Raman spectra collected at steady state at a distance of ∼0.11 cm from the downstream edge of the Au working electrode polarized at a constant volume flow rate Vf ) 57 µL/s in 5 mM K4Fe(CN)6/0.5 M KCl solutions, at fixed potentials (panel A) in the sequence defined by the arrow, (from the bottom) E ) 0.0, 0.05, 0.08 V vs SCE. Subsequent curves were recorded in 0.02 V intervals in the range 0.08 V < E < 0.42 V. (B) Corresponding data collected at Vf ) 25 µL/s in 20 mM NaNO2/0.1 M NaClO4 in pH 4.3 acetate buffer solutions in the range 0.5 V < E < 1.2 V vs SCE at intervals of 0.1 V (see text for details). Excitation wavelength, 532 nm; accumulation time for all spectral data, 2 min.

Panels A and B in Figure 5 display Raman spectra collected under steady-state conditions following position optimization (see Experimental Section above) for Vf ) 57 µL/s, and 25 µL/s for the [Fe(CN)6]4- and [NO2-] solutions specified above, respectively, following polarization of the Au working electrode at various potentials, E. As clearly seen, polarization at values of E over the range in which [Fe(CN)6]4- undergoes oxidation (panel A) gave rise to two Raman bands at 2130 (ν3, Eg) and 2135 cm-1 (ν1, A1g) characteristic of the Oh symmetric [Fe(CN)6]3- ion centered at 2132 cm-1 for the first solution14,15 and to the emergence of a strong band centered at 1044 cm-1 due to the symmetric NO

stretching vibration of nitrate ion16 for the second solution (panel B). Particularly noteworthy from a quantitative viewpoint, is the fact that the integrated intensities of the overall dual feature centered at 2132 cm-1, to be denoted as I2132(E), normalized by the corresponding value obtained at the limiting current I2132(Elim) (left ordinate, solid circles in panel A, Figure 6), and the current (14) Lowry, R. B. J. Raman Spectrosc. 1991, 22, 805-809. (15) Loo, B. H.; Lee, Y. G.; Liang, E. J.; Kiefer, W. Chem. Phys. Lett. 1998, 297, 83-89. (16) Ianoul, A.; Coleman, T.; Asher, S. A. Anal. Chem. 2002, 74, 1458-1461.

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Figure 6. (A) Integrated intensity of the [Fe(CN)6]3- band centered at 2132 cm-1, I2132 normalized by the corresponding value measured at the limiting current (left ordinate, solid circles) as a function of the applied potential, E. The corresponding values for the loss of integrated intensity of the [Fe(CN)6]4- bands centered at 2058 and 2095 cm-1, I2158,2095 are shown in open circles, left ordinate, in this panel. The half-filled circles (right ordinate) represent the current normalized by ilim as a function of E, based on the data shown in panel A, Figure 5. (B) Plots of I1044 for the NO3- band (left ordinate, solid circles) and of the current normalized by ilim (right ordinate, half-filled circles) vs E, based on the data shown in panel B, Figure 5. The bars in panel A for potentials E g 140 mV, represent the square root of the MSE (see text for details), and those in panel B the uncertainties as determined by the fitting routine (see Spectroscopic Analysis subsection).

Figure 7. Raman spectra of K3Fe(CN)6 aqueous solutions in the concentration range 50 µM-5 mM recorded in the channel cell under quiescent conditions without potential control. Excitation wavelength, 532 nm; accumulation time, 10 min. Inset: Plot of the integrated intensity of the band centered at 2132 cm -1 I2132 vs [Fe(CN)6]3concentration. Statistical best linear fits parameters, S ) 0.978, I ) 2.40, and R ) 0.999 68. The error bars in the inset represent the root of the MSE, of the difference between the spectrum of the most concentrated solution (5 mM) multiplied by the dilution factor, and the actual spectra of the corresponding more dilute solution.

normalized by ilim (right ordinate, half-filled circles, in panel A, Figure 6) were found to coincide when plotted as a function of the applied potential (E). Furthermore, a plot of the decrease in the normalized integrated intensity of the two [Fe(CN)6]4- CtN stretching bands centered at 2058 (ν3, Eg) and 2095 cm-1 (ν1, A1g) (left ordinate, open circles, in panel A, Figure 6), versus E, were also found to be in very good agreement with the other two sets of data displayed in panel A, Figure 6. In other words, the spectroscopic and electrochemical data are proportional to one another both for the reactant and for the product. The bars in panel A, Figure 6, for potentials more positive than 140 mV, represent the square root of the mean-squared error (MSE). For most of the spectra, the error was smaller than the symbol, i.e., on the order of 0.5%. The same overall behavior was found for the oxidation of nitrite in buffered aqueous electrolytes. The integrated intensities of the main spectral feature of nitrate NO3-, centered at 1044 cm-1, I10448008 Analytical Chemistry, Vol. 79, No. 21, November 1, 2007

Figure 8. Theoretical simulation of the overlap between the laser intensity within the dof region (right ordinate) and the concentration profile of a product generated at steady state on the surface of a channel type electrode at a distance of ∼0.11 cm from the downstream edge of the Au working electrode polarized at 0.4 V at a constant volume flow rate Vf ) 34 µL/s in 5 mM K4Fe(CN)6/0.5 M KCl solution as a function of ∆ (see Figure 2).

(E), normalized by the corresponding value obtained at ilim, I1044(Elim) (left ordinate, solid circles in panel B, Figure 6), and the current normalized by ilim (right ordinate, half filled circles, in panel B, Figure 6) tracked each other when plotted as a function of E. The error bars in the plot represent uncertainties as determined by the fitting routine described in the Spectroscopic Analysis subsection above and ranged from ∼3 to 4% for E g 0.8 V and ∼10.5% for E ) 0.7 V versus SCE. It is useful to note in this regard that Raman spectra recorded for fully homogeneous solutions of K3Fe(CN)6, in the range 50 µM-5 mM (see Figure 7) obtained in the channel cell under quiescent conditions without potential control, yielded I2132 for proportional to [Fe(CN)6]3- (see inset in the same figure). The bars in the inset plot represent the root of the MSE, of the difference between the spectrum of the most concentrated solution (5 mM) multiplied by the dilution factor, and the actual spectra of the corresponding more dilute solution. It is important to note that the concentration profile of the product downstream of the working electrode surface is highly

Figure 9. (A) Raman spectra as a function of ∆ for the working electrode under conditions employed in Figure 8. The zero point was set arbitrarily at a position at which the image of the electrode as measured with the microscope was the sharpest. (B) Plot of I2132 vs ∆ based on the data in panel A in this figure.

inhomogeneous along axes normal (and also parallel) to the direction of fluid flow; hence, the magnitude of the spectroscopic signal is a convolution of the laser intensity spatial profile and the spatially dependent concentration. Shown in Figure 8 (left ordinate), as a means of illustration, is a plot of θ ) 1 - Cs/C∞, the dimensionless concentration of a species generated at the surface of a channel electrode at diffusion-limited rates along an axes parallel to the light path, Z, at a distance of 0.11 cm downstream of the electrode edge, obtained from theory.8 The symbol Cs in this expression represents the concentration of the electrogenerated species in solution along the axis Z. The distance of 0.4 cm in Figure 8 corresponds to the plane where the electrode is embedded. The parameters used for this calculation are those of the actual cell used in our experiments (see above and also caption Figure 1) assuming a mean volume velocity Um ) Vf/2dh ) 3.14 × 10-2 cm/s, which corresponds to Vf ) 34 µL/s, a value well within those achievable with our experimental setup. Also displayed in Figure 8 (see right ordinate) are theoretical plots of the intensity of the laser beam along the Z axis as a function of ∆, where the area of overlap provides a measure of the expected Raman signal to be collected by the arrangement shown in Figure 1. Evidence in support of the behavior predicted in Figure 8 was provided by the Raman spectra shown in panel A, Figure 9, recorded as a function of ∆ (as derived from H, the distance between the objective and the top of the glass slide (see panel B, Figure 2), under diffusion-limited conditions. As indicated in panel B in this figure, the integrated intensities of the features centered at 2132 cm-1, attributed to the electrogenerated product, normalized by the maximum value observed, increased with ∆ up to ∆ ) 0.27 cm. Although lacking quantitative rigor, as the model (17) Akkermans, R. P.; Suarez, M. F.; Roberts, S. L.; Qiu, F. L.; Compton, R. G. Electroanalysis 1999, 11, 1191-1202. (18) Mo, Y. B.; Scherson, D. A. J. Electrochem. Soc. 2003, 150, E39-E46.

proposed does not account for diffraction and other possible effects, the experimental and predicted data appear to follow the same trend. The decrease in the Raman signal for larger ∆ may be due to light scattering or absorption due to interactions of the excitation light with the reflecting Au surface R. In fact, care was exercised not to focus the laser on the electrode to avoid local heating effects such as those reported by the group of Compton17 for quiescent solutions, which can lead to local convection and thus to enhanced rates of mass transport, i.e., larger currents, compared to a dark electrode, especially when the power of the laser beam exceeds a few tenths of W/cm2. It is interesting to note that, for the typical conditions employed in our experiments, i.e., 5 mM K4Fe(CN)6/0.5 M KCl and Vf ) 56 µL/s, the increase in ilim recorded at the channel electrode induced by laser illumination above R amounted to only ∼2.6%. In other words, possible local heating in the vicinity of the working electrode does not seem to propagate very far into the solution. In summary, the results shown in panels A and B, Figure 6, provide unambiguous evidence that the integrated Raman intensities of the bands characteristic of electrogenerated products [Fe(CN)6]3- and NO3- are directly proportional to the currents associated with their generation at a channel working electrode. The theoretical analysis presented should serve as a basis for defining an effective optical collection efficiency, in much the same way as that introduced for an optical ring concentric to a solid rotating disk in prior work in this laboratory.18 ACKNOWLEDGMENT This work was supported by NSF. Received for review March 22, 2007. Accepted August 21, 2007. AC070573V

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