Anal. Chem. 1998, 70, 2914-2921
Radial Flow Microring Electrode: Development and Characterization Julie V. Macpherson* and Patrick R. Unwin*
Department of Chemistry, University of Warwick, Coventry, U.K. CV4 7AL
The radial flow microring electrode (RFMRE), a new hydrodynamic ultramicroelectrode, is described. In the RFMRE, solution flows from a capillary nozzle, which is positioned very close to a planar substrate using micropositioners. The RFMRE can be operated in one of two configurations: either (a) with the ring electrode on the capillary or (b) with the ring electrode positioned in the plane of the substrate directly underneath the capillary. In both arrangements, as fluid leaves the capillary, it is forced into the nozzle/substrate gap and flows radially past the ring electrode. Under these conditions, the RFMRE is effectively analogous to a microband channel electrode. The RFMRE is shown to be characterized by well-defined, variable, and high mass-transfer rates under steady-state voltammetric conditions. Mass-transfer coefficients in excess of 2 cm s-1 have been readily achieved with the RFMRE operating at relatively low volume flow rates (1.67 × 10-2 cm3 s-1). The device thus has considerable promise for electroanalysis and the study of fast electrode kinetics. The ability to characterize both heterogeneous electrode reactions and coupled homogeneous solution reactions with increasingly faster kinetics is a major challenge in electrochemical research.1 The attainment of this goal requires the availability and development of techniques that are able to deliver the necessary high mass-transfer rates to compete with the reaction kinetics, under defined and controllable conditions. Hydrodynamic techniques,2,3 where the electrode moves with respect to the solution, as with rotating (or vibrating) disks,3 rings,4 wires,5 and photoelectrodes,6,7 or where solution is forced past a stationary electrode, as exemplified by conical,8 band,9 and (1) Andrieux, C. P.; Hapiot, P.; Save´ant, J. M. Chem. Rev. 1990, 90, 723 and references therein. (2) Bard, A. J., Faulkner, L. R. Electrochemical Methods; Wiley: New York, 1980. (3) Albery, W. J.; Jones, C. C.; Mount, A. R. In Comprehensive Chemical Kinetics; Compton, R. G., Hamnett, A., Eds.; Elsevier: Amsterdam, 1989; Vol. 29, p 129-146 and references therein. (4) (a) Levich, V. G. Physicochemical Hydrodynamics; Prentice-Hall: Englewood Cliffs, NJ, 1962; pp 102, 313. (b) Napp, D. T.; Johnson, D. C.; Bruckenstein, S. Anal. Chem. 1967, 39, 481. (5) (a) Laitinen, H. A.; Kolthoff, I. M. J. Phys. Chem. 1941, 45, 1079. (b) Pratt, K. W.; Johnson, D. C. Electrochim. Acta 1982, 27, 1013. (6) (a) Albery, W. J.; Archer, M. D.; Edgell, R. G. J. Electroanal. Chem. 1977, 82, 199. (b) Albery, W. J.; Bowen, W. R.; Fisher, F. S.; Turner, A. D. J. Electroanal. Chem. 1980, 107, 1. (7) Johnson, D. C.; Resnick, E. W. Anal. Chem. 1972, 44, 637. (8) Kirowa-Eisner, E.; Gileadi, E. J. Electrochem. Soc. 1976, 123, 22.
2914 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
tubular10 electrodes in fluid streams, have long been used as a means of enhancing mass transport in electrochemical systems. With conventional-sized hydrodynamic electrode systems under laminar solution conditions, maximum mass-transfer rates up to ∼0.05 cm s-1 are typically reached. The advent of ultramicroelectrodes (UMEs), electrodes with at least one dimension in the micrometer or submicrometer range, has had a major impact on both electroanalysis and the voltammetric investigation of electrode kinetics and coupled chemical reactions.1 In particular, since the steady-state diffusion-limited current density at a UME varies reciprocally with the characteristic electrode dimension,11 very high mass-transfer rates can be attained by using small electrodes in quiescent solution.11b,c The thin-ring geometry is particularly attractive for an UME because although, in the main, the current is determined by the surface area of the ring, the mass-transfer coefficient is controlled by the ring thickness.12-18 Hence, the construction of very thin rings results not only in high mass-transport rates but also sizable currents. This high current density compared with that of the more widely used disk UME has merit for both improved analytical detection limits and the study of electrode kinetics. Recently, several workers have demonstrated that the employment of UMEs in conjunction with hydrodynamic voltammetric techniques results in greatly enhanced and variable mass-transfer rates, typically under steady-state conditions. For example, work from our group introduced the microjet electrode (MJE),19 in which a high-velocity jet of solution was fired through a fine nozzle positioned directly over a disk UME. In addition to the MJE being (9) Unwin, P. R.; Compton, R. G. in Comprehensive Chemical Kinetics; Compton, R. G., Hamnett, A., Eds.; Elsevier: Amsterdam, 1989; Vol. 29, pp 173-209 and references therein. (10) Blaedel, W. J.; Olson, C. L.; Sharma, L. R. Anal. Chem. 1963, 35, 2100. (11) (a) Saito, Y. Rev. Polarogr. 1968, 15, 177. (b) Penner, R. M.; Heben, M. J.; Longin, T. L.; Lewis, N. S. Science 1990, 250, 1118. (c) Shao, Y.; Mirkin, M. V.; Fish, G.; Kokotov, S.; Palanker, A.; Lewis, A. Anal. Chem. 1997, 69, 1627. (12) Szabo, A. J. Phys. Chem. 1987, 91, 3108. (13) (a) Fleischmann, M.; Bandyopadhyay, S.; Pons, S. J. Phys. Chem. 1985, 89, 5537. (b) Russell, A.; Repka, K.; Dibble, T.; Ghoroghchian, J.; Smith, J. J.; Fleischmann, M.; Pitt, C. H.; Pons, S. Anal. Chem. 1986, 58, 2961. (c) Fleischmann, M.; Pons, S. J. Electroanal. Chem. 1987, 222, 107. (14) Phillips, C. G.; Stone, H. A. J. Electroanal. Chem. 1995, 396, 277. (15) (a) Kalapathy, U.; Tallman, D. E.; Cope, D. K. J. Electroanal. Chem. 1990, 285, 71. (b) Cope, D. K.; Tallman, D. E. J. Electroanal. Chem. 1990, 285, 85. (c) Kalapathy, U.; Tallman, D. E.; Hagen, S. J. Electroanal. Chem. 1992, 325, 65. (d) Tallman, D. E. Anal. Chem. 1994, 66, 557. (16) Symanski, J. S.; Bruckenstein, S. J. Electrochem. Soc. 1985, 135, 1985. (17) MacFarlane, D. R.; Wong, D. K. Y.; Wong, J. Electroanal. Chem. 1985, 185, 197. (18) Khoo, S. B.; Gunasingham, H.; Ang, K. P.; Tay, B. T. J. Electroanal. Chem. 1987, 216, 115. S0003-2700(98)00166-8 CCC: $15.00
© 1998 American Chemical Society Published on Web 06/04/1998
characterized by well-defined and variable mass-transfer rates, it was demonstrated that the steady-state mass-transfer rate to a 25µm diameter disk electrode could be enhanced by more than 2 orders of magnitude in the MJE configuration,19a,b making this configuration extremely attractive for the study of fast kinetics.19b,c Work by Compton and co-workers resulted in the development of the fast flow channel flow electrode.20 In this case, solution was pumped at high speed and pressure (volume flow rates up to 10 cm3 s-1 were employed) over a microband electrode in a channel geometry. This technique has been used to measure fast heterogeneous electron-transfer kinetics20b and homogeneous chemical reactions coupled to electron-transfer events.20a,c To date, there is only a little documented work on the use of hydrodynamic ring UMEs. Vielstich et al. investigated fast electron-transfer processes using a micro-ring electrode in turbulent pipe flow.21 The geometry adopted was equivalent to a microscale version of the tubular electrode.9,10 It was predicted that the system would allow steady-state measurements of fast reactions with rate constants approaching 5 cm s-1. Unfortunately, the necessary working conditions involved high-pressure equipment to deliver volume flow rates between 2 and 60 cm3 s-1. Symanski and Bruckenstein16 introduced a thin rotating ring electrode. They observed negative deviations from the predicted mass-transport behavior due to difficulties in constructing the electrode coplanar with the insulating material. In this paper, we suggest a new approach for achieving enhanced and variable steady-state mass-transfer rates at a ring UME by deploying it in a thin-layer radial flow cell. In this arrangement, solution flowing out of a capillary nozzle is forced radially into the gap between a substrate and the capillary and over the ring electrode. The radial flow microring electrode (RFMRE) can be operated in one of two configurations, with the ring electrode (a) on the capillary or (b) positioned on the substrate, directly underneath the capillary. A video microscopy image (a) and schematic diagram (b) are presented in Figure 1 to illustrate the essential features of these two arrangements. In the present study, experimental conditions were such that the nozzle/substrate separation was in the range 5-40 µm and the radius of the ring electrode was always greater than the radius of the nozzle. Under practical hydrodynamic conditions, it is demonstrated that mass-transfer to the RFMRE is analogous to that to the channel flow electrode under laminar conditions.9 Under relatively low volume flow rates and pressure conditions, it is shown that mass-transfer rates in excess of 2 cm s-1 can be readily achieved, (19) (a) Macpherson, J. V.; Marcar, S.; Unwin, P. R. Anal. Chem. 1994, 66, 2175. (b) Macpherson, J. V.; Beeston, M. A.; Unwin, P. R. J. Chem. Soc., Faraday Trans. 1995, 91, 899. (c) Martin, R. D.; Unwin, P. R. J. Electroanal. Chem. 1995, 397, 325. (d) Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1997, 69, 5045. (20) (a) Rees, N. V.; Dryfe, R. W.; Cooper, J. A.; Coles, B. A.; Compton, R. G.; Davies, S.; McCarthy, T. D. J. Phys. Chem. 1995, 99, 7096. (b) Compton, R. G.; Fisher, A. C.; Wellington, R. G.; Dobson, P. J.; Leigh, P. A. J. Phys. Chem. 1995, 99, 14813. (c) Coles, B. A.; Dryfe, R. W.; Rees, N. V.; Compton, R. G.; Davies, S. G.; McCarthy, T. J. Electroanal. Chem. 1996, 411, 121. (d) Prieto, F.; Aixill, J.; Alden, J. A.; Coles, B. A.; Compton, R. G. J. Phys. Chem. 1997, 101, 5540. (21) (a) Bernstein, Ch.; Heindrichs, A.; Vielstich, W. J. Electroanal. Chem. 1978, 87, 81. (b) Bernstein, Ch.; Vielstich, W. Proc. Electrochem. Soc. 1980, 9, 350. (c) Dreeson, E. W.; Vielstich, W. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 6. (d) Dreeson, E. W.; Vielstich, W. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 12.
a
b
Figure 1. (a) Video microscopy image of the RFMRE. In this configuration, the ring electrode is positioned on the outer side of the capillary and is exposed at the end. The epoxy coating provides electrical insulation and completes the formation of a thin channel with the glass substrate through which solution flows radially. The nozzle/substrate separation is ∼20 µm, the nozzle radius is 50 µm, and the mean radius of the ring electrode is 66 µm. (b) Schematic cross section of the RFMRE with the ring electrode positioned centrally underneath the capillary nozzle.
making this technique very attractive for electroanalysis and kinetic studies. EXPERIMENTAL SECTION Chemicals. All solutions were prepared from Milli-Q (Millipore Corp.) reagent water. Solutions were prepared from potassium ferrocyanide trihydrate (Aldrich, ACS grade) at a concentration of either 0.002 or 0.005 mol dm-3 in 0.2 mol dm-3 potassium chloride (Fisons, AR grade) solutions, the latter serving as a supporting electrolyte. Electrodes. The procedure for the fabrication of the thin platinum ring capillary electrodes is outlined in Figure 2. Borosilicate capillary tubes (Clark Electromedical, Reading, U.K., 2.0mm o.d., 1.2-mm i.d.; Chance Glass, Leicester, U.K., 2.0-mm o.d., 0.5-mm i.d.) were heated and pulled to a fine point using a Narishighe (Tokyo, Japan) PB7 vertical micropipet puller. The capillary was then attached to a home-built motor that rotated the horizontally held capillary about its cylindrical axis, and the narrower end was coated evenly with a platinum organometallic complex (Bright Platinum Paint, Cookson Matthey Ceramics, Stoke-on-Trent, U.K.). This was achieved by running a paintbrush slowly down the rotating shank. The procedure was, in some instances, repeated up to two further times in order to increase the thickness of the platinum Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
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Figure 2. Schematic of the stages in the construction of the thinring platinum electrode. (a) The capillary is pulled to a fine point and (b) rotated using a motor and coated evenly with platinum paint. (c) After curing the platinum paint film, the pulled end of the capillary is insulated using epoxy resin and (d) polished flat using a home-built polishing wheel, equipped with micropositioners.
film. In these cases, it was found that heating the capillary at 70 °C for 15 min between successive paint applications aided the subsequent coating process. A thin strip of platinum paint was applied down the side of the capillary to provide an electrical connection. Reduction of the organometallic complex to platinum was achieved by baking the capillaries in a pyrolysis oven at 600 °C for 15 min. The thinner shank of the pulled capillary was placed in a shortened (∼1.5-cm length) nylon pipet tip (Labsystems, Helsinki, Finland), so that the end protruded out of the tip, and was secured in a central position using sealing wax. The nylon tip was filled with epoxy resin (Delta Resins, Stockport, U.K.) and left to cure for 48 h. With the end of the capillary placed outside the nylon tip, it was possible to electrically insulate the sides of the ring electrode without simultaneously backfilling the capillary with epoxy resin. Tips of the electrodes were cut with a scalpel, typically to reveal a capillary with an inner diameter in the range 60-110 µm, and polished flat using a home-built polishing wheel, fabricated from a PC hard disk. The electrode was mounted vertically above the wheel using a Newport Corp. (Newbury, CT) model 461 x,y,z stage. The z-axis (normal to the polishing wheel surface) was controlled by a differential micrometer (model DM-13), and the x- and y-axes were moved with AJS-05 fine adjustment screws. The ring capillary electrode was lowered slowly onto the wheel until contact was made and polishing proceeded using a succession of polishing pads (240 grit, 15-, 9-, and 6-µm diamond) all from Buehler (Coventry, U.K.). The latter three pads had the lapping compound impregnated into the film, thus preventing blockage of the capillary during polishing. The use of pads with smaller sized diamond particles was found to result in the “tearing” of the epoxy surface and a gross deterioration of the platinum-epoxy seal. 2916 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
At this stage, the outer edges of the probe (capillary plus epoxy coating) were “coned” until the radius of the probe was approximately 3 times the outer radius of the capillary. The end of the electrode was finally polished with 0.05-µm alumina on a polishing pad, made slightly damp with water. Removal of any alumina particles that accumulated in the capillary during this procedure was achieved by forcing Milli-Q reagent water through the nozzle using a syringe. Occasionally, the particle removal process was aided by placing the capillary in an ultrasonic bath. Adoption of the above procedure in most cases produced optically flat probes, i.e., the electrode, glass wall of the capillary, and epoxy were all in the same plane, free from recession, at magnifications up to ×1000. Differential polishing is a possibility due to the different abrasive properties of the insulator and metalcoated fiber (be the fiber a glass rod, capillary, or optical fiber). However, driving the electrode into the polishing pad, in a controlled manner, appeared to force the whole probe to polish at the same rate. Thin-ring electrodes on glass substrates were fabricated as described above, with the glass capillary replaced by a glass rod (2.0-mm-diameter borosilicate, Chance Glass). Visual inspection of the ring electrodes was carried out using an Olympus BH2 light microscope equipped with a PM-10AK photomicrographic system (magnifications ×100-×1000). For accurate determination of the width of the electrodes, a JEOL JSM6100 scanning electron microscope (SEM) was used. For each ring sampled, width measurements were recorded at three different, widely spaced positions. RFMRE Apparatus. The RFMRE cell comprised a fully detachable Teflon base, cylindrical glass body, and Teflon lid, with a total volume of 25 cm3. The glass body contained an outlet pipe to prevent solution overflow in the cell and an optical window (15mm diameter) so that video microscopy could be used to monitor the position of the capillary nozzle relative to the appropriate substrate and aid in the alignment procedure. This was of particular importance for the configuration depicted in Figure 1b, where it was essential that the nozzle of the capillary was positioned directly above the center of the ring electrode. The video microscope comprised a zoom microscope with a CCD camera attachment that offered maximum on-screen resolution of 2.2 µm/pixel. The camera was attached to a video recorder and video capture card (model Win-TV Celebrity, Hauppage, NY) that allowed images to be transferred to a PC. In configuration a (Figure 1a), the cell base contained a small recess which could securely accommodate a glass disk. For configuration b (Figure 1b), the platinum thin-ring electrode was positioned through the center of the cell base such that it sat well below the level of the solution outlet, ensuring that the hydrodynamics in the vicinity of the electrode were not affected by solution outflow. Flow of electrolyte (at rates in the range 1.67 × 10-4-3.33 × -2 10 cm3 s-1) through the nozzle was achieved with a Gilson (Villiers-Le-Bel, France) model 305 HPLC pump equipped with a 25 WTi pump head and model 806 manometric module. Instrumentation. For all RFMRE configurations, the position of the capillary normal to an interface (z-axis) was controlled with 0.1-µm resolution by mounting the nozzle on a piezoelectric translator, incorporating a strain gauge sensor (translator model
P843 and controller E501, Physik Instrumente, Waldbronn, Germany). The positioner was attached to a Newport Corp. model 461 x,y,z stage, described above. The stages were, in turn, located on a vibrationally isolated bench, and the cell was shielded using a home-built Faraday cage. Current-potential characteristics were recorded with an EcoChemie (Utrecht, Holland) Autolab Electrochemical Workstation, incorporating a preamplifier (model ECD) for low-current measurements. All voltammetric measurements were made in a twoelectrode arrangement with an Ag wire serving as a quasireference electrode (AgQRE) and the thin-ring platinum electrode serving as the working electrode. Procedure. To assess the mass-transfer characteristics of the RFMRE in configurations a and b, the limiting current for the oxidation of Fe(CN)64- at the ring electrode was determined as a function of both the nozzle/substrate separation (for a fixed volume flow rate) and the volume flow rate (for a fixed nozzle/ substrate separation). The nozzle/substrate distance was established typically by contacting the end of the capillary with the substrate and then retracting the nozzle from the substrate a set distance. RESULTS AND DISCUSSION Characterization of Thin Platinum Ring Capillary Electrodes. Figure 3 shows typical SEM images of the end-on views of (a) a thin-walled platinum ring capillary and (b) a thick-walled platinum ring capillary. Figure 3c depicts a section from a ring capillary, at higher resolution, that was coated with only one layer of platinum paint. From Figure 3c, and measurements taken at different points on the same ring (under higher resolution conditions), it was possible to estimate the thickness of this particular electrode as 0.18 (( 0.02) µm. From many SEM measurements taken on different rings, it was apparent that increasing the number of coatings of platinum (up to a maximum of three in total) increased the ring thickness to ∼0.50 µm. The corresponding linear sweep voltammogram (LSV) for the ring capillary electrode shown in Figure 3c in an aqueous solution containing 0.005 mol dm-3 Fe(CN)64- and 0.2 mol dm-3 KCl, at a sweep rate of 0.05 V s-1, is given in Figure 4. For a very thin ring electrode, in which a/b > 0.91, where a and b are the interior and exterior radii of the ring, respectively, the predicted steadystate current, iring, can be represented as12,16
iring ) nFDc*
π2(a + b) ln[16(b + a)/(b - a)]
(1)
where n is the number of electrons transferred per redox event, F is Faraday’s constant, D is the diffusion coefficient, and c* is the bulk concentration of the electroactive species. Armed with a knowledge of the electrode width (i.e., (b - a) ) 0.18 ( 0.02 µm, as determined above), the expected diffusionlimited current for the oxidation of Fe(CN)64- under the conditions of the experiment is deduced readily from eq 1. For the case where n ) 1, a ) 66 µm, and the value of (b - a) is as cited, the theoretical diffusion-controlled current is calculated as 45.0 ( 0.5 nA. DFe(CN)64- ) 6.7 × 10-6 cm2 s-1 was used, given the literature value under similar solution conditions.22
Figure 3. Typical scanning electron micrographs of (a) the end-on view of a thin-walled platinum-coated thin-ring capillary, (b) the endon view of a thick-walled platinum-coated thin-ring capillary, and (c) a section from a ring capillary electrode, coated with one layer of platinum paint.
Generally, the time taken to attain a limiting, steady-state current is of the order of l2/D, where l is the largest characteristic dimension of the electrode.16 For a ring electrode, l equates to a, suggesting an approximate time of 6.5 s for the electrode shown in Figure 3c. Given the scan conditions employed in Figure 4, the plateau of the LSV should thus approach a steady state. The experimentally determined value for iring is 45.1 nA, demonstrating (22) Adams, R. N. Electrochemistry at Solid Electrodes; Marcel Dekker: New York, 1969.
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where Re, the Reynolds number, for a channel flow geometry can be represented as24
Re ) U h h/ν
(3)
In eq 3, ν is the kinematic viscosity of the solution and U h is the mean solution velocity. The expression for the Reynolds number is usually written with υo, the fluid velocity in the center of the channel, as the characteristic velocity, but for the approximate approach here it is reasonable to use U h . This analysis holds provided that Re < 2000.9,24,25 Under these conditions, the masstransport-limited current to the electrode in the absence of diffusional edge effects is given by the Levich equation:9,25
ilim ) 0.925nFc* Figure 4. Steady-state voltammogram recorded at 0.05 V s-1 for the oxidation of 0.005 mol dm-3 ferrocyanide in 0.2 mol dm-3 KCl at a platinum ring capillary electrode characterized by a ) 66 µm and (b - a) ) 0.18 µm.
Figure 5. Schematic diagram showing the geometry of a typical channel flow electrode.
le ≈ (0.08Re + 1)h 2918 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
(2)
Dxe h
2/3
Vf d
1/3
w
(4)
where ilim is the limiting steady-state current and Vf is the volume flow rate. In the RFMRE arrangement, solution flows out of the capillary nozzle and is forced radially into the gap between the glass substrate and the capillary, past the thin-ring electrode. Provided that laminar flow is established, the mass-transport-limited current at the RFMRE will be as described by eq 4, since the thickness of the ring is sufficiently small that the ring electrode effectively “sees” a constant local velocity. For the RFMRE, 2h is the distance between the glass substrate and ring capillary electrode, xe ) (b - a), and w is now equivalent to d, where
(a + b) ≈ 2πa 2
d ) 2π good agreement with the predicted value, based on the SEM measurement. This suggests that all the ring is exposed and, importantly, evenly coated with platinum paint, verifying SEM micrographs, such as those shown in Figure 3a,b. Sputter coating is a widely used method to produce thin, even metal films, but it is clearly evident that the painting procedure offers a very low cost and valid alternative, as suggested by previous workers.13,15a,16,18 Mass Transfer in a Radial Flow Regime. Ring on the Capillary. Although at constant volume flow rate the mean radial solution velocity in the RFMRE cell decreases with the radial coordinate from the central axis of symmetry, it will be shown that the arrangement depicted in Figure 1a, with a thin electrode, is, in fact, a radical miniaturization of the (constant velocity) channel flow electrode. The geometry of this related device is given schematically in Figure 5. The terms used in Figure 5 have the following definitions: xe and w are the length and width, respectively, of the band electrode, d is the width of the channel flow cell, and 2h is the distance between the plane bearing the electrode and the roof of the cell. The geometry of a practical channel is such that 2h , d and w < d, so that the electrode effectively sees a two-dimensional flow profile (characteristic of the x,y plane). In typical experimental practice, h (the half-height) is in the range 0.05-0.5 mm, d in the range 6-12 mm, and w ≈ 0.8 d. Flow is fully developed and Poiseuille at a distance defined as the entrance length, le, from the inlet:23
( )()
(5)
Figure 6 gives the experimental ilim versus Vf1/3 (0) response for a RFMRE characterized by an internal nozzle diameter, dn ) 100 µm, a ) 115 µm, h ) 8 µm, and xe ) 0.35 µm. The solution contained 0.002 mol dm-3 Fe(CN)64- and 0.2 mol dm-3 KCl. The electrode length was determined using both SEM and eq 1, from the limiting current recorded with the ring capillary electrode placed far from the substrate in quiescent solution. Equation 4, represented as (s), provides a very good description of the experimental data over a range of volume flow rates, clearly demonstrating that mass-transfer to the ring capillary electrode in RFMRE geometry obeys the Levich equation. It has been shown that, for a channel microband electrode operating at low volume flow rates, diffusional edge effects may be significant.26-28 Figure 5 also shows the current-flow rate behavior predicted by Alden and Compton26a (‚‚‚) and Aoki et al.27 (- - -) when mass transport to a rectangular channel electrode includes axial (edge) diffusion. It can be seen that such effects (23) (a) Compton, R. G.; Coles, B. A. J. Electroanal. Chem. 1983, 144, 87. (b) White, F. M. Viscous Fluid Flow; McGraw-Hill: New York, 1974. (24) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; Wiley: New York, 1960; p 47. (25) Levich, V. G. Physicochemical Hydrodynamics; Prentice-Hall: Englewood Cliffs, NJ, 1962; p 32. (26) (a) Alden, J. A.; Compton, R. G. J. Electroanal. Chem. 1996, 404, 27. (b) Compton, R. G.; Fisher, A. C.; Wellington, R. G.; Dobson, P. J.; Leigh, P. A. J. Phys. Chem. 1993, 97, 10410. (27) Aoki, K.; Tokuda, K.; Matsuda, H. J. Electroanal. Chem. 1987, 217, 33. (28) Newman, J. J. Electroanal. Chem. 1973, 6, 279.
(a)
Figure 6. Analysis of transport-limited current-flow rate data, in terms of eq 4 for a RFMRE system characterized by dn ) 100 µm, a ) 115 µm, h ) 8 µm, and xe ) 0.35 µm. Also shown is the theoretical transport-limited current-flow rate behavior using the models of (‚‚‚) Alden and Compton26a and (- - -) Aoki et al.27 for the inclusion of diffusional edge effects.
are minimal, with the parameters cited above, at the RFMRE. Moreover, it is questionable as to whether the treatment of edge effects for a conventional channel geometry is strictly applicable for the RFMRE. For the rectangular flow geometry, it has been demonstrated that the predominant diffusional edge effect is that upstream of the electrode (the edge closest to the inlet). Moving upstream of the RFMRE, the effective velocity increases and the cross-sectional area through which diffusion can occur decreases due to the cylindrical geometry. Both of these factors may minimize the extent to which edge diffusion is important for the RFMRE compared to a microband in a rectangular channel. Further evidence for the inferred hydrodynamic profile is provided by considering the likely entrance lengths. Although the overall hydrodynamics of the RFMRE are not identical to those in a rectangular duct, the analysis in eq 2 and 3 will give a reasonable representation of the entrance length requirements. For this analysis, U h ) Vf/4πah and ν ) 0.01 cm2 s-1. Even at the highest flow rate (where le attains the greatest value) the flow profile is considered “fully developed” at distances of only 15 µm from the entrance of the channel. This value is much smaller than the shortest radial pathway for solution traveling from the capillary to the electrode, i.e., the thickness of nozzle wall, which for this particular electrode is 65 µm. In a conventional fixed volume channel flow cell, a constraint imposed by the cell design is that the volume flow rate is usually the only parameter that can be changed to alter the mass-transfer rate.9 Some work has considered the use of an array of electrodes of different lengths to give different mass-transfer coefficients, but this practice has not been widely adopted.26b A unique feature of the RFMRE is the ease with which the nozzle/substrate separation (i.e., the cell height) can be varied, in addition to the volume flow rate, thus providing an additional parameter with which to vary the mass-transfer rate at a single electrode. Figure 7a depicts a typical series of steady-state voltammograms obtained with the ring capillary in a RFMRE configuration, at a fixed volume flow rate, for a range of nozzle electrode/glass substrate separations between 5.8 (highest wave) and 17.8 µm
(b)
Figure 7. (a) Steady-state voltammograms, recorded at a scan rate of 0.1 V s-1, for the oxidation of 0.005 mol dm-3 ferrocyanide in 0.2 mol dm-3 KCl at a platinum RFMRE employing half-heights of (a) 2.9, (b) 3.4, (c) 3.9, (d) 4.4, (e) 4.9, (f) 5.4, (g) 6.4, and (h) 8.9 µm. Data were obtained with dn ) 88 µm, a ) 66 µm, Vf ) 1.67 × 10-2 cm3 s-1, and xe ) 0.14 µm. (b) Analysis of the transport-limited current- half-height data (from Figure 7a), in terms of eq 4.
(lowest wave). These results were obtained with dn ) 88 µm, a ) 66 µm, Vf ) 1.67 × 10-2 cm3 s-1, and xe ) 0.14 µm, in a solution containing 0.005 mol dm-3 Fe(CN)64- and 0.2 mol dm-3 KCl, at a sweep rate of 0.1 V s-1. Given the high mass-transfer rate of the RFMRE, it is possible to obtain limiting current values at relatively high potential scan speeds, enabling experimental measurement times to be minimized. As h decreases, solution is forced radially past the ring at increased velocities, resulting in a larger flux of electroactive material to the electrode and, hence, an increase in the limiting current. Decreasing h below 2.9 µm caused a notable increase in the back pressure of the system, due to the restriction of fluid flowing in the RFMRE cell. Under the conditions of this experiment, changing h by distances as small as 0.5 µm can have a significant effect on the mass-transport-limited current. It should be possible to build on this observation and introduce a new form of hydrodynamic modulation voltammetry (HMV),29 in which the cell height is modulated. Work in this area is currently in progress. (29) Wang, J. Talanta 1981, 28, 369.
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Table 1. Calculated U h and le Values for the RFMRE System Characterized by dn ) 88 µm, a ) 66 µm, Vf ) 1.67 × 10-2 cm3 s-1, xe ) 0.14 µm, and Re ) 20, at Different Half-Height Separations h/µm
U h /cm s-1
le/µm
h/µm
U h /cm s-1
le/µm
2.9 3.4 3.9 4.4
705 600 522 462
7.4 8.7 10.0 11.3
4.9 5.4 6.4 8.9
414 376 317 227
12.6 13.9 16.5 23.0
For comparison with other steady-state techniques, the highest mass-transfer coefficient, kt, attained in this study,
kt )
ilim nAFc*
(6)
where A is the area of the electrode, in conjunction with the limiting current measured at the closest nozzle/substrate separation in Figure 7a, is ∼2.3 cm s-1. This is equivalent to the rate of mass-transfer at a disk UME with a radius of ∼40 nm,11a while a rotating disk electrode would have to rotate at speeds in excess of 3.7 × 106 Hz in order to achieve the same mass-transfer rate! The latter value is more than 4 orders of magnitude greater than the maximum rotation speed typically attainable with commercial devices. With the mass-transfer coefficients attainable, the RFMRE is analogous to the high-speed channel flow electrode20 but has the advantages that (i) both h and Vf are adjustable parameters in a single experiment and (ii) the device is easy to assemble and employs volume flow rates some 2 orders of magnitude smaller than in the high-speed channel flow electrode. This generally avoids the need to work under high-pressure conditions and minimizes the consumption of solutions. Full analysis of the ilim versus h data taken from Figure 7a in terms of the Levich equation (s) is shown in Figure 7b. The results closely obey the predicted theoretical response. Table 1 provides information on the calculated le values at each nozzle/ substrate separation. Re ) 20 remains constant for this system for all values of h. These results demonstrate that the fluid flow profile at the nozzle/substrate separations considered will be predominantly laminar and locally Poiseuille when the solution reaches the electrode. Capillary above the Ring Electrode. An alternative arrangement for the RFMRE is to position the ring electrode directly underneath the capillary, as depicted in Figure 1b. Again, provided that the radial distance between the inner edge of the nozzle and electrode exceeds le and Re < 2000, flow in the vicinity of the electrode should be laminar and effectively Poiseuille in nature. Figure 8 gives the log(ilim) versus log(h) relationship for a system characterized by dn ) 84 µm, a ) 133.5 µm, Vf ) 3.33 × 10-2 cm3 s-1, and xe ) 0.24 µm, in a solution containing 0.002 mol dm-3 Fe(CN)64- and 0.2 mol dm-3 KCl. The slope of the plot is determined as 0.658, with a correlation coefficient of 0.984, which agrees well with the expected dependence of 2/3 as determined from eq 4. Compared to the RFMRE arrangement a, discussed above, the geometry of this present configuration requires that both the 2920 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
Figure 8. Log(limiting current) versus log(half-height) for a RFMRE of design (b) characterized by dn ) 84 µm, a ) 133.5 µm, Vf ) 3.33 × 10-2 cm3 s-1, and xe ) 0.24 µm.
epoxy-coated glass nozzle and the ring electrode be polished flat. For the ring on the glass rod, this was technically challenging, due to the large area of glass. This made it difficult to produce a reasonable parallel-walled flow cell at very close nozzle/substrate separations. In the worst cases, deviations from the predicted mass-transport behavior were seen, similar to that observed by Symanski and Bruckenstein for their recessed rotating thin-ring electrode.16 For this arrangement, it is also essential that the nozzle is located centrally over the ring electrode in order to ensure equivalent velocity profiles all the way around the ring. This alignment procedure requires the use of video microscopy. In contrast, configuration a has no such positioning requirements in the x,y plane and thus represents the simpler, user-friendly version of the RFMRE. One advantage of arrangement b over a, however, is the exciting possibility of replacing the platinum-coated glass rod with a metal-coated optical fiber. Various workers have used microoptical ring electrodes (MOREs)30-32 to investigate a wide variety of photochemically activated processes, but only in quiescent solutions. A hydrodynamic optical ring electrode has been used to detect photolytic intermediates under steady-state conditions, but on the macroscale, limiting the technique to the detection of longer-lived intermediates (lifetimes greater than 10-2 s).7 Clearly, the introduction of a hydrodynamic MORE (by simple adaptation of the RFMRE) would significantly increase the temporal resolution, enabling the study of shorter-lived photogenerated intermediates. CONCLUSIONS The RFMRE represents a new hydrodynamic approach for achieving significantly enhanced and variable mass-transfer rates at UMEs. It can be operated in one of two configurations: (a) (30) Pennarun, G.; Boxall, C.; O’Hare, D. Analyst 1996, 121, 1779. (31) (a) Kuhn, L. S.; Weber, A.; Weber, S. G. Anal. Chem. 1990, 62, 1631. (b) Cohen, C. B.; Weber, S. G. Anal. Chem. 1993, 65, 169. (32) (a) Casillas, N.; James, P.; Smyrl, W. H. J. Electrochem. Soc. 1995, 142, L16. (b) James, P.; Casillas, N.; Smyrl, W. H. J. Electrochem. Soc. 1996, 143, 3853.
with the thin-ring electrode on the capillary or (b) with the thinring electrode situated coaxially in the plane of a substrate underneath the capillary. In both arrangements, the electrode is characterized by well-defined mass-transfer, which is analogous to that for the conventionally sized channel flow electrode, operating under laminar Poiseuille flow conditions. The RFMRE thus represents a radical miniaturization of the channel flow electrode. At present, the highest mass-transfer coefficient attainable with the electrode is in excess of 2.3 cm s-1 (for a typical value of D ) 6.7 × 10-6 cm2 s-1), making the electrode attractive for the study of fast kinetics under steady-state conditions. Under these conditions, the RFMRE is comparable with the high-speed channel flow electrode20 but, very favorably, requires drastically reduced volume flow rates while achieving higher mass-transfer coefficients. The thin-ring electrode can also operate at much lower pressures and is very easy to assemble. Furthermore, there may be scope for increasing the available mass-transfer rates by employing smaller nozzles and electrodes in the thin-layer radial flow cell arrangement. (33) (a) Macpherson, J. V.; Unwin, P. R. Prog. React. Kinet. 1995, 20, 185. (b) Unwin, P. R.; Macpherson, J. V. Chem. Soc. Rev. 1995, 24, 109.
Given the simple and versatile nature of the flow cell design, there are substantial opportunities for developing the methodology. Two areas highlighted above that we plan to investigate are (1) hydrodynamic modulation voltammetry, to increase analyte detection limits and the potential window, and (2) the use of thin metal-coated optical fibers to investigate short-lived photochemically produced species. There may also be opportunities for downstream electrochemical detection of reactions at solid/liquid interfaces,9,33 using the RFMRE as a probe of surface reactions at the microscale under high mass-transfer conditions. ACKNOWLEDGMENT We thank the EPSRC for support (GR/K97011), Mr. Steve York (Department of Physics, University of Warwick) for providing the scanning electron micrographs, Dr. Marshall Pope for helping with the construction of the polishing wheel, and Dr. Rachel Martin for her initial work on thin-ring electrode preparation.
Received for review February 12, 1998. Accepted April 22, 1998. AC9801667
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