Anal. Chem. 1985, 57, 1763-1765 (6) Juergens, U. J . Chromatogr. 1984, 370, 97-106. (7) De Jong, G. J. J . Chromafogr. 1980, 183, 203-211. (8) Hux, R. A.; Mohammed, H. Y.; Cantwell, F. F. Anal. Chem. 1982, 54, 113-117. (9) Andereg, J. W. J . Am. Chem. SOC. 1955, 77, 2927. (10) Yau, W. W.; Kirkland. J. J.; Bly, D. D. "Modern Size-Exclusion Liquid Chromatography"; Why-Interscience: New York, 1979; Chapter 2. (11) Unger, K. K.; Kinkel, J. N.; Anspach, 6.; Gleshe, H. J . Chromatogr. 4QfIA .- - ., -298 - - , 3-14. - . .. (12) Schmldt, D. E.; Giese, R. W.; Conron, D.; Karger, 8 . L. Anal. Chem. lQB0. 52. 177-182. ----, (13) Pinkerton, T. C.; Hagestam, I . H. US. Patent, 6646 153, 1984. (14) Bethell, G. S.; Ayerer, J. S.; Hancock, W. S.; Hearn, M. T. J . 8/01. Chem. 1979, 254, 2572-2574. Glad, M.; Hasson, L.; Mansson, M. 0.;Ohlson, S.; Mos(15) Lasson, P. 0.; bach, U. Adv. Chromatogr. 1983, 27, 41-85. (16) Hofman, K.; Bergman, M. J . 8/0/.Chem. 1940, 734, 225. (17) Slggia, S. "Quantitatlve Organlc Analysis vla Functional Groups"; Wiley-Interscience: New York, 1949; pp 8-9.
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(18) Smith, G. F. "Analytical Appllcations of Periodic Acid and Iodic Acid"; G. F. Smith Chemical Company: Columbus, OH, 1950. (19) Stout, S. A.; Devane, C. L. J . Chromatogr. 1984, 285, 500-508. (20) Gerson, 6.; Bell, F.; Chan, S. Clin. Chem. (Winsfon-Salem, N . C . ) 1984, 30, 105-108. (21) Haroon, V.; Keith, D. A. J . Chromatogr. 1983, 276, 445-450. (22) Lunde, P. K. M.; Rane, A.; Yaffe, S. J.; et al. C/h. Pharm. Ther. 1970, 1 1 846-855. (23) Miller, T. D.; Plnkerton, T. C. Anal. Chim. Acta, In press. I
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RECENEDfor review January 28,1985. Accepted April 9,1985. The authors wish to express their appreciation to the Foremost-McKesson Foundation, Inc., for funding this research, through the Cottrell Research Grant Program of the Research Corporation.
CORRESPONDENCE Diffusion Layer Imaging: Spatial Resolution of Electrochemical Concentration Profiles Sir: We report here a spectrophotometric technique for determining concentration vs. distance profiles of absorbing solution species generated at an electrode surface. The technique can accurately describe diffusion layers as thin as 8 pm, after only 50 ms of electrolysis. In this paper, we describe the apparatus and its performance and discuss its potential for providing new information about mass transport and reaction mechanisms. The fundamental importance of mass transfer to electrochemistry has spawned a variety of theoretical and experimental examinations into diffusion (1,2), convection (3-51, and migration (6) as mechanisms for the transport of redox species t o an electrode. For several well-defined mass transport situations, the Faradaic current may be predicted from theories of diffusion and hydrodynamics, but in many cases solutions are not readily available. Diffusion to microelectrode arrays (7,8),mass transport in flowing streams (9, IO), and mixed convection/migration conditions are examples of cases where concentration vs. distance profiles are not available, and the Faradaic current is not accurately predictable from theory. Several approaches have been pursued to experimentally observe concentration- vs. distance profiles near an electrode, including interferometric methods (10-15) based on refractive index gradients near an electrode and on UV-vis absorption by electrogenerated species (16-18). The present approach is a spatidy resolved UV-vis absorption measurement which permits concentration vs. distance profiles to be obtained with better resolution and shorter time scales than those from previous methods. The cross section of a beam passing parallel to a planar electrode surface is magnified and imaged onto a photodiode array detector. Each diode samples a discrete distance from the electrode, and Beer's law may be used to directly determine a spatially resolved concentration profile. EXPERIMENTAL SECTION The cell, electrodes, and chemical systems were identical with those described previously for diffractivespectroelectrochemistry (19). Trianisylamine (TAA) in acetonitrile was oxidized at a platinum electrode to TAA+. at +0.8 V vs. aqueous SCE. The 0003-2700/85/0357-1763$01.50/0
diffusion coefficient of TAA (1.25 X 10" cm2/s) and molar absorptivity for TAA+. (11OOO & 200 M-' cm-', at 633 nm) have been reported previously (19). The optical apparatus shown in Figure 1 consists of a 2Ox magnifier producing an image of the beam cross section on the face of a 1024 element photodiode array. L1 (f = 1.48 cm), L2 (f = 5.0 cm), and a 25-pm pinhole form a collimated, spatially filtered, 2.9 mm diameter beam which passes parallel to a planar electrode surface made by polishing the edge of a Pt sheet (19). L3 (Mellis Griot LAO 126,f = 10 cm, diameter = 3.15 cm) and L4 (Space Optics Research Labs Fourier lens, f = 38 cm, diameter = 7.6 cm) form a magnifier with f = 8.67 cm. A photodiode array detector (Tracor 6112) was positioned vertically at the image plane of the magnifier, such that each element monitored a segment of the magnified beam cross section. The magnification was calibrated by using gold minigrids of known dimensions (Buckbee-Mears)and in the work reported here had a value of 20.0. The system was aligned and focused with the array scanning, with the criterion for optimum alignment being the sharpness of the magnified electrode edge. For 20X magnification, four 25 pm wide diodes fell on the rising portion of the electrode edge, indicating an apparent transition from electrode to solution of about 5 pm. On the basis of existing theories for the imaging of an edge using coherent light (20), the true electrode edge at the image plane was taken to be 25% up the rising portion of the image. This point was used as the origin of the distance axis in all plots. The Tracor Northern diode array system and PAR 173 potentiostat were triggered by an Apple 11+ microcomputer, which also stored digital data from the Tracor. The accuracy of the photodiode array was checked by using a range of calibrated neutral density filters, and absorbance error was less than f1.5% over the the absorbance range employed. For the electrochemical experiments, the array was scanned continuously, and the scans immediately before electrolysis and at the desired time after electrolysis began were stored and used to determine the absorbance as a function of channel number. The distance from the electrode sampled by a given photodiode, indicated here as x,, was calculated from the channel number by multiplying by the factor 1.25 pm/channel(25 pm divided by 20X magnification). The concentration of T U + .at a particular distance was calculated from the absorbance at that distance using Beer's law, with the path length equal to the electrode length along the optical axis (0.0150 cm). In all references to the diffusion layer thickness, it is defined as the value of x , where the T U + . concentration equals 50% of the bulk TAA concentration. 0 1985 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985
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1.05F4 k - F 20 F 4 Figure 1. Optical apparatus for diffusion layer Imaging. Electrode to L 3 dimension Is 8 cm, L3 to L4, 3 cm, and L4 to array, 175 cm. See text for further details.
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Flgure 2. Dlodie array scans of intenslty vs. channel number for the magnified image before (curve a) and after (curve b) a 2-9 electrolysls of TAA to TAA'.. Points on curve a indicate intensities at individual diodes. Irregularities in profile away from the edge are reproducible variations in beam cross section. Raw scans from the diode array are shown in Figure 2, for the generation of trianisylamine cation radical (TAA+.) from TAA in acetonitrile. The initial scan was taken immediately before the applied potential was stepped from 0 to 0.8 V vs. SCE. The lower trace was taken 2 s after the start of diffusion limited TAA+-generation and shows the attenuation of the image near the electrode edge. The points on the rising portion of the image show the intensities at discrete photodiodes. Figure 3 shows several experimental absorbance vs. x, plots, calculated from data similar to that of Figure 2. The theoretical points were calculated without adjustable parameters from eq 1 assuming the TAA+- diffusion coefficient
equals that of TAA. Good agreement between theory and experiment is observed for periods from 50 ms to 4 s after the potential step. Note that the diffusion layer thickness is 8 pm at 50 ms, indicating that the technique can accurately measure quite thin diffusion layers. At times longer than 4 s, experimental points show negative deviation from theory, an expected consequence of natural convection. Figure 4
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RESULTS AND DISCUSSION
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distance from electrode, x e , ( p m ) Figure 3. Absorbance vs. x , profiles for TAA'. generated from 2.6 mM TAA by a diffusion limited potential step. Solid lines are experimental profiles, points were calculated from eq 1 and Beer's law wlth b = 0.0150 cm and 6 = 11 000 M-I cm-'. Absorbance proflles were taken at the following times after the potential step: a, 0.05 s; b, 0.1 s; c, 0.3 s;d, 0.5 s; e, 1.0 s;f , 2.0 s;g, 4.0 s;h, 8 s; 1, 16 s. Curve j shows absorbance profile 2.0 s after the reduction of 4.5 mM benzoquinone to its radlcal anion.
shows double potential step results, converted from absorbance to concentration using Beer's law. Significant deviations between experiment and theory are apparent for x, less than 5 pm for all profiles, and this aberration is likely to be caused by diffraction of the beam as it passes along the planar electrode. This effect is substantially smaller than that ob-
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the boundary layer is often a few tens of micrometers thick or less. The present method differs from our previous work on diffractive spectroelectrochemistry (21,22) in the way the attenuated laser beam is processed optically. For the diffraction experiment, the detector is placed one focal length downstream from the lens L4, and the diffraction pattern is a Fourier transform of the beam cross section. While the diffraction pattern is related to the spatial distribution of absorber, the relationship is complex. The imaging method effectively carries out the Fourier inversion optically, forming an image while maintaining a simple one to one relationship between the position of each photodetector and the dimension
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Figure 4. Concentration of TAA’. relative to bulk TAA concentration as a function of distance from the electrode, x,: curve a, 0.1 s after second potential step; curve b, 0.4 s; curve c, 1.0 s; curve d, 3 s. Potential was stepped from 0.0 to 0.8 V vs. SCE for 2 s and then returned to 0.0 before recording absorbance profile.
served in previous work (17) due to the much shorter dimension of the electrode along the optical axis (0.015 vs. 0.19 cm). In addition to the TAA results Figure 3 shows an absorbance profile for the reduction of quinone to its radical anion at -0.8 V, a process which will generate a refractive index gradient but no absorption at 633 mm (19). This reaction produces a negligible (
