Anal. Chem. 1999, 71, 2939-2944
Hydrodynamic Modulation Voltammetry with a Variable-Height Radial Flow Microring Electrode Julie V. Macpherson* and Patrick R. Unwin
Department of Chemistry, University of Warwick, Coventry, CV4 7AL, U.K.
A new form of hydrodynamic modulation voltammetry (HMV), employing a radial flow microring electrode (RFMRE), is described. In the RFMRE, a nozzle, bearing a thin ring electrode (thickness 0.1-0.5 µm) is positioned close to a planar inert substrate, forming a thin-layer radial flow cell. Solution flows down the nozzle, impinging on the surface of the substrate, and is then forced into the nozzle-substrate gap whereupon it flows radially across the surface of the ring electrode. At constant volume flow rate, mass transport to the RFMRE is readily modulated by periodically varying the effective height of the flow cell, on the micrometer scale. As a result of the rapid diffusional and hydrodynamic relaxation times in this device, the modulated current in phase with the oscillation of the cell height can be described quantitatively using existing models for the variation of the mass-transfer-limited current with nozzle-substrate separation. The capabilities of RFMRE-HMV, in terms of improved amperometric detection close to the solvent window and at low concentration, are illustrated through studies of the oxidation of tris(2,2′-bipyridyl) ruthenium(II) and hexachloride iridate(III) at a Pt electrode in aqueous solution. A key feature of this modulation technique is that the in-phase currents recorded in the RFMRE-HMV configuration (which discriminate against background processes) are far in excess of the equivalent dc currents (which do not discriminate against background processes) measured at thin ring electrodes in quiescent solution. Hydrodynamic modulation voltammetry (HMV)1,2 refers to the periodic oscillation of the mass transfer rate at an electrode, under voltammetric conditions. This can be achieved in two ways, by either (i) modulating the motion of the electrode with respect to the solution, e.g., modulating the rotation frequency of a rotating disk electrode3 or vibrating the electrode4,5 or (ii) varying the solution flow rate over a static electrode.1 Subsequent extraction (1) Wang, J. Talanta 1981, 28, 369. (2) Williams, D. E.; Macpherson, J. V. In Comprehensive Chemical Kinetics; R. G. Compton, R. G., Hancock, G., Eds.; Elsevier: Amsterdam, 1999; Vol. 37, pp 369-438. (3) (a) Miller, B.; Bruckenstein, S. Anal. Chem. 1974, 46, 2026. (b) Miller, B.; Bruckenstein, S. J. Electrochem. Soc. 1974, 121, 1558. (c) Albery, W. J.; Hillman, A. R.; Bruckenstein, S. J. Electroanal. Chem. 1979, 100, 687. (4) Schuette, S. A.; McCreery, R. L. Anal. Chem. 1986, 58, 1778. (5) Williams, D. E.; Ellis, J.; Colville, A.; Dennison, S. J.; Laguillo, G.; Larsen, J. J. Electroanal. Chem. 1997, 432, 159. 10.1021/ac981397g CCC: $18.00 Published on Web 06/05/1999
© 1999 American Chemical Society
of the alternating current component of the signal allows masstransport-limited processes to be separated from those which are not, including, for example, double layer charging, solvent decomposition, and certain electrode surface reactions. Consequently, HMV has found many applications in electroanalysis, especially in detecting low concentrations and extending the potential window of a given solvent. Flowing solutions offer many desirable features for analysis, such as on-line detection, multisample analysis, and low sample consumption. By interrupting6,7 or pulsing8 the solution flow through a tubular or channel electrode, hydrodynamic modulation has been used in an attempt to improve concentration detection limits. In these experiments, the volume flow rate was simply switched between a maximum and minimum value (zero for the interrupted flow technique6,7) and the steady-state current difference measured, in dc mode only. Given the fairly low mass transport rates in these systems, it was necessary to employ lengthy cycling times, often tens of seconds, to attain the maximum steady-state current-difference signal. Moreover, experimental constraints prevented the rapid change of volume flow rate. This precludes the use of such devices as detection systems for flow injection analysis or high-performance liquid chromatography. Some improvements in measurement times were made through the adoption of a thin layer channel flow geometry,9,10 in which the relaxation distance of the concentration boundary layer, adjacent to the electrode, was decreased. Negligible attenuation of the current was observed for pulse rates up to a maximum of 0.5 Hz. We have recently introduced a novel hydrodynamic ultramicroelectrode (UME), the radial flow microring electrode (RFMRE),11 a device which is presently characterized by the highest steadystate mass transfer rate of any hydrodynamic technique (up to 2 cm s-1). This methodology has been applied to the investigation and quantification of fast, heterogeneous electron-transfer processes.12 In the RFMRE arrangement (Figure 1), solution flows from a capillary, which is positioned very close to a planar substrate (distances of 5-40 µm). The ring electrode, of typical thickness 0.1-0.5 µm, is formed around the outer edge of the capillary. As fluid leaves the capillary, it impinges on the substrate below and is forced into the nozzle-substrate gap whereupon it (6) (7) (8) (9) (10)
Blaedel, Blaedel, Blaedel, Blaedel, Blaedel,
W. W. W. W. W.
J.; J.; J.; J.; J.;
Boyer, S. L. Anal. Chem. 1971, 43, 1538. Wang, J. Anal. Chem. 1979, 51, 799. Iverson, D. G. Anal. Chem. 1977, 49, 1563. Yim, Z. Anal. Chem. 1980, 52, 564. Wang, J. Anal. Chem. 1981, 53, 78.
Analytical Chemistry, Vol. 71, No. 14, July 15, 1999 2939
significantly enhanced, compared with dc measurements with this device, in either flowing or quiescent solutions.
Figure 1. Schematic cross-section of the RFMRE arrangement. The ring electrode, which is positioned on the outer side of the capillary and electrically insulated with epoxy resin, except at the very end, completes the formation of a thin channel with the glass substrate. Solution flows down through the nozzle and then radially into the thin channel.
Figure 2. Schematic and video microscopy images of the heightmodulated RFMRE. In this configuration, the capillary shank of the ring electrode is attached to a piezoelectric positioner which modulates the position of the nozzle with respect to the underlying glass substrate. Typical modulation frequencies and nozzle-substrate halfheight modulation amplitudes of 1-5 Hz and 1-4.5 µm, respectively, are employed.
flows radially past the ring electrode. The RFMRE has been shown to represent a radical miniaturization of a channel flow electrode, operating under laminar flow conditions.11 In this paper we report the first hydrodynamically modulated UME in a flowing solution, using the RFMRE. We show that the mass transport rate can be modulated, very simply, by oscillating the position of the nozzle (( 2-9 µm about a central location) with respect to the substrate, in a periodic fashion, at a constant volume flow rate (Figure 2). Using phase-sensitive detection to measure the in-phase current component of the oscillating signal, we demonstrate that the analytical capabilities of the RFMRE are (11) Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1998, 70, 2914.
2940 Analytical Chemistry, Vol. 71, No. 14, July 15, 1999
EXPERIMENTAL SECTION Chemicals. Solutions were prepared from potassium iridate hexachloride (Sigma-Aldrich) at a concentration of 5 × 10-4 mol dm-3 in 0.2 mol dm-3 potassium nitrate (Fisons, Loughborough, AR) or tris(2,2′-bipyridyl) ruthenium(II) chloride hexahydrate (Sigma-Aldrich) at a concentration of 5 × 10-5 mol dm-3 in 0.1 mol dm-3 potassium nitrate. The potassium nitrate served as a supporting electrolyte. All solutions were prepared using Milli-Q (Millipore Corp.) reagent water and deaerated with argon. Electrodes. The procedures for the fabrication, preparation, polishing, and determination of the width of the thin platinum ring electrodes has been described in detail elsewhere.11,12 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 cell base contained a small recess which could securely accommodate a glass disk. The glass body contained an outlet pipe to prevent solution overflow in the cell and an optical window (15-mm diameter) so that video microscopy could be used to monitor the position of the capillary nozzle relative to the glass substrate. The zoom microscope was equipped with a CCD camera attachment that offered maximum on-screen resolution of 2.2 µm per pixel. Flow of electrolyte through the RFMRE nozzle was achieved with either a Gilson (Villiers-Le-Bel, France) model 305 HPLC pump equipped with a 25-W Ti pump head and model 806 manometric module or a dual syringe infusion pump (ColeParmer, Vernon Hills, Illinois). Instrumentation. The position of the RFMRE capillary normal to the glass substrate (z-axis) was controlled by mounting the nozzle on a piezoelectric translator, which incorporated a strain gauge sensor which monitored the expansion with a resolution of 0.1 µm (translator model P843 and controller E501, Physik Instrumente, Waldbronn, Germany). The piezoelectric positioner was oscillated sinusoidally, with typical amplitudes and frequencies of vibration of 2-9 µm and 1-5 Hz, respectively, using the waveform generator from a Stanford Research Systems lock-in amplifier (model SR810 DSP, Sunnyvale, CA). The positioner was attached to a Newport Corp. (Fountain Valley, CA) model 461 x, y, z stage. The stages were, in turn, located on a vibrationally isolated Newport CSD series breadboard and the cell shielded using a home-built Faraday cage. The current in phase with the position of the oscillating RFMRE was detected using the lock-in amplifier. Both the raw and in-phase current-potential characteristics were acquired with an Eco-Chemie (Utrecht, The Netherlands) Autolab Electrochemical Workstation, incorporating a preamplifier (model ECD) for low-current measurements. All voltammetric measurements were made in a two-electrode arrangement with an Ag wire serving as a quasi reference electrode (AgQRE) and the thin platinum ring electrode serving as the working electrode. Procedure. The mass transport characteristics of the RFMRE, subject to a periodic modulation in the height of the nozzlesubstrate gap, were assessed by recording both raw and in-phase (12) Macpherson, J. V.; Jones, C. E.; Unwin, P. R. J. Phys. Chem. B 1998, 102, 9891.
absence of diffusional edge effects:
( )
ilim ) 0.925nFc*
Dxew h
2/3
Vf1/3
(1)
Here, n is the number of electrons transferred per redox event, F is Faraday’s constant, c* and D are the bulk concentration and diffusion coefficient, respectively, of the electroactive species, and w is the circumference of the thin ring electrode. Equation 1 dictates that modulation of the nozzle-substrate separation should result in the following quantitative change in the limiting current, provided that Levich behavior is obeyed:
- h-2/3 ∆ilim ) [0.925nFc*(Dxew)2/3Vf1/3](h-2/3 lo hi )
(2)
Here, hlo and hhi represent the lower and upper limits of the nozzle to substrate half-height modulation. Figures 3b and 3c show, respectively, the raw and in-phase current (measured as the root-mean-square amplitude, irms, of the modulated signal) versus voltage behavior recorded with the RFMRE subject to a periodic modulation of the nozzle-substrate half-height separation, hmod ) ( 3.2 µm, about a central half-height position, hcen ) 14 µm, at a frequency of 1.00 Hz. The upper and lower steady-state currents (Figure 3b) and resulting ∆ilim of 47.9 nA, 35.1 nA, and 12.8 nA, respectively, agree well with the predicted values of 47.9 nA, 35.2 nA, and 12.7 nA, calculated from eqs 1 and 2. The limiting root-mean-square amplitude in-phase current (Figure 3c) is in quantitative agreement with the data in Figure 3b: Figure 3. (a) Analysis of the transport-limited current half-height data (9), at constant volume flow rate, in terms of eq 1. (b) Raw and (c) in-phase linear sweep voltammetric behavior recorded at a scan rate of 0.01 V s-1, with the RFMRE subject to a periodic modulation of the nozzle-substrate half-height separation, h ) 14 µm ( 3.2 µm, at a frequency of 1.00 Hz. Data were obtained for the oxidation of 5 × 10-4 mol dm-3 IrCl63- in a solution containing 0.2 mol dm-3 KNO3, with dn ) 100 µm, a ) 71 µm, Vf ) 1.67 × 10-2 cm3 s-1, and xe ) 0.28 µm.
linear sweep voltammograms for the oxidation of IrCl63-, as a function of oscillation amplitude, at a fixed volume flow rate. The initial nozzle-substrate separation, about which the RFMRE was oscillated, was established by contacting the end of the capillary with the glass disk and then retracting the nozzle from the substrate a set distance, using the piezoelectric positioner. RESULTS AND DISCUSSION Figure 3a shows the transport-limited current, ilim, versus nozzle-substrate half-height separation, h, (9), recorded at a RFMRE at constant volume flow rate, Vf ) 1.67 × 10-2 cm3 s-1. The RFMRE was characterized by an internal nozzle diameter, dn, of 100 µm, interior ring radius a ) 71 µm, and ring electrode thickness, xe ) 0.28 µm. The results were obtained with a range of nozzle-substrate half-height separations, h, between 5 µm (highest limiting current) and 17.2 µm (lowest limiting current). As expected and rationalized fully, earlier,11,12 the experimental data closely follow the theoretical Levich behavior (solid line) predicted for fully developed laminar channel flow,13,14 in the
irms, lim )
∆ilim 2x2
(3)
The close agreement between experiment and theory is not unexpected, given the inherently high diffusion and convection rates associated with the RFMRE. As a consequence, the hydrodynamic and diffusional relaxation times following a perturbation in the convective rate are very small. In response to a step change in the flow, the velocity distribution near a wall relaxes with a characteristic time scale2,15
τH ) δH2/4v
(4)
where δH is the size of the hydrodynamic boundary layer and v is the kinematic viscosity. For fully developed laminar parabolic flow which generally applies to the RFMRE in the vicinity of the thin ring electrode,13 δH is of the order of the nozzle-substrate halfheight separation. The characteristic time, τD, for diffusional relaxation of the concentration boundary layer is as follows:2 (13) Levich. V. G. Physicochemical Hydrodynamics; Prentice Hall: Engelwood Cliffs, NJ, 1962; p 32. (14) Unwin, P. R.; Compton, R. G. In Comprehensive Chemical Kinetics; Compton, R. G., Hamnett, A., Eds.; Elsevier: Amsterdam, 1989; Vol. 29, pp 173-296, and references therein. (15) Schlichting, H. Boundary Layer Theory, 7th ed.; McGraw-Hill: New York, 1979.
Analytical Chemistry, Vol. 71, No. 14, July 15, 1999
2941
τD ) δD2/2D
(5)
δD is the thickness of the concentration boundary layer, which is given by:
δD ) D/kt
(6)
Here, kt the mass transfer coefficient for the RFMRE geometry is as follows:
kt )
0.925(Dxew)2/3h-2/3Vf1/3 A
Table 1. Calculated kt, δD, τD, and τH Values for a RFMRE Systema h/µm
kt/cm s-1
δD/cm
τD/s
τH/s
10.8 17.2
0.80 0.59
0.94 × 10-5 1.27 × 10-5
5.9 × 10-6 10.8 × 10-6
29.2 × 10-6 74.0 × 10-6
a System characterized by d ) 100 µm, a ) 71 µm, V ) 1.67 × n f 10-2 cm3 s-1, and xe ) 0.28 µm, at two nozzle-substrate half-height separations, which represent the upper and lower limits of the halfheight modulation, specific to the data shown in Figure 3(b).
(7)
A is the area of the ring electrode, given by:
A ) π(a + xe)2 - πa2 ≈ 2πaxe(a . xe)
(8)
Table 1 displays the calculated kt, δD, τD, and τH values for hlo ) 10.8 µm and hhi ) 17.2 µm, for the experimental conditions cited above, with DIrCl63- ) 7.5 × 10-6 cm2 s-1,12 and assuming a typical v ) 0.01 cm2 s-1. With extremely short diffusion and hydrodynamic relaxation times, of the order of tens of microseconds, and a moderate modulation frequency of 1.00 Hz, the diffusion layer and convective flow profile is able to readjust faster than the rate at which the nozzle-substrate separation is modulated. Thus the instantaneous limiting currents follow the h dependence as defined in eq 1. The effect of modulation amplitude on the in-phase current signal was investigated over the range, hmod ) ( 1 - 4.5 µm, chosen to accommodate the typical nozzle-substrate separations which are employed in the RFMRE arrangement.11,12 Figure 4 shows the (a) raw and (b) in-phase current-voltage characteristics, recorded for the same RFMRE employed for the data in Figure 3, subject to a periodic modulation of the nozzle-substrate half-height separation, h ) 15 µm ( 1.9 µm, at a frequency of 1.00 Hz. Equation 2 predicts irms,lim ) 2.3 nA, which again agrees well with the value observed. Importantly, Figure 4 demonstrates the advantages of employing HMV with phase-sensitive detection to significantly reduce non mass transport-controlled components of the current signal. At electrode potentials greater than +0.9 V versus AgQRE, the effect of solvent electrolysis becomes appreciable in the dc signal, with the current rapidly increasing as the potential is raised (Figure 4a). However, in contrast, over the same potential range, the in-phase component of the modulated current signal shows an almost constant steady-state current plateau. These results represent a significant improvement on earlier interrupted6,7 and pulsed8 flow modulation techniques in which only the current difference in dc mode was used to extract analytical information. Figure 5a displays typical in-phase current-voltage curves recorded at hmod values of (i) (3.8 µm, (ii) (3.2 µm, (iii) (2.6 µm, (iv) ( 1.9 µm, and (v) ( 1.3 µm about hcen ) 15 µm, at a frequency of 1.00 Hz. Also given is a plot, Figure 5b, demonstrating the close correspondence between the theoretical limiting in-phase root-mean-square amplitude current (solid line), predicted using Levich theory (eq 2) and the experimental steady-state response 2942 Analytical Chemistry, Vol. 71, No. 14, July 15, 1999
Figure 4. (a) Raw and (b) in-phase linear sweep voltammetric behavior recorded at a scan rate of 0.01 V s-1, for the oxidation of 5 × 10-4 mol dm-3 IrCl63- in a solution containing 0.2 mol dm-3 KNO3. The RFMRE configuration, characterized by dn ) 100 µm, a ) 71 µm, Vf ) 1.67 × 10-2 cm3 s-1, and xe ) 0.28 µm, was subject to a periodic modulation of the nozzle-substrate half-height separation, h ) 15 µm ( 1.9 µm, at a frequency of 1.00 Hz.
(0), as a function of modulation amplitude. Figure 5b clearly shows that, over the range of modulation amplitudes investigated, the mass transport characteristics of the height-modulated RFMRE can be described quantitatively (eqs 2 and 3). This is an important aspect of the technique, compared with many other HMV methodologies in flowing solutions, which require the calibration of effective mass transport rates with solutions of known concentration. In contrast, it is possible to employ RFMRE-HMV quantitatively without such constraints, provided that the geometry of the RFMRE is characterized. As a result of the relatively low resonant frequency of the piezoelectric positioner and controller employed, which was expected to be further compromised by the additional mass of the electrode-bearing nozzle, the effect of frequency on the in-
Figure 5. (a) In-phase linear sweep voltammetric behavior recorded at a scan rate of 0.01 V s-1, for the oxidation of 5 × 10-4 mol dm-3 IrCl63- in a solution containing 0.2 mol dm-3 KNO3. The heightmodulated RFMRE configuration is characterized by dn ) 100 µm, a ) 71 µm, Vf ) 1.67 × 10-2 cm3 s-1, and xe ) 0.28 µm. The halfheight modulation amplitudes employed were h ) 15 µm ( (i) 3.8 µm, (ii) 3.2 µm, (iii) 2.6 µm, (iv) 1.9 µm, and (v) 1.3 µm, all recorded with a modulation frequency of 1.00 Hz. (b) Analysis of the experimental (0) limiting in-phase current versus half-height modulation amplitude, in terms of the predicted behavior, eqs 2 and 3.
phase current signal was not investigated significantly. However, for the limited range of modulation frequencies used, 1-5 Hz, mass transfer to the oscillating ring electrode in the RFMRE geometry was always found to follow the predicted convectivediffusive response. Moreover, the upper limit of the frequencies adopted here is still almost an order of magnitude greater than those used in the pulsed flow methodologies8 and approaches being fifty times larger than those employed in the interrupted flow techniques.6,7 To further emphasize the capabilities of the height-modulated RFMRE as an analytical tool, both static and position-modulated current-voltage data were recorded for the oxidation of 5 × 10-5 mol dm-3 Ru(bipy)32+ in 0.1 mol dm-3 KNO3. Figure 6a displays the steady-state current-voltage behavior recorded with a constant volume flow rate and nozzle-substrate separation for a RFMRE configuration characterized by dn ) 110 µm, a ) 74 µm, Vf ) 1.67 × 10-2 cm3 s-1, xe ) 0.40 µm, and h ) 13.8 µm. With the low concentration of Ru(bipy)32+ species employed in this experiment, solvent decomposition begins to interfere with the limiting current for the oxidation of the electroactive species. Although the steady-state current is discernible from the background signal, accurate determination of this value is compromised by the solvent signal. In the absence of convective flow (with the electrode placed far from the glass substrate), this measurement is even more difficult. Since the steady-state current, which flows at the thin ring in stationary solution, is given by the following16,17
π2(a + b) iring ) nFDc* (b + a) ln 16 (b - a)
[
]
(9)
Figure 6. Steady-state linear sweep voltammograms recorded for the oxidation of 5 × 10-5 mol dm-3 Ru(bipy)32+ in 0.1 mol dm-3 at (a) a constant nozzle-substrate half-height separation, h ) 13.8 µm, and (b) a modulated nozzle-substrate half-height separation, h ) 13.8 µm ( 4.5 µm, at a frequency of 1.00 Hz. (c) The in-phase current-voltage response recorded under the same experimental conditions as (b). In all three cases, the RFMRE configuration was characterized by dn ) 110 µm, a ) 74 µm, xe ) 0.40 µm, and Vf ) 1.67 × 10-2 cm3 s-1.
Here, b is the exterior radius of the ring electrode; the calculated transport-limited current under quiescent conditions is only 0.39 nA, an order of magnitude smaller than with flow, for DRu(bipy)32+ ) 4.8 × 10-6 cm2 s-1. The latter value was determined from the steady-state diffusion-limited current recorded at a 25µm diameter Pt disk ultramicroelectrode in a solution containing 1 × 10-3 mol dm-3 Ru(bipy)32+ in 0.1 mol dm-3 KNO3. Figures 6b and 6c show the raw and in-phase current-voltage characteristics, respectively, for the oxidation of 5 × 10-5 mol dm-3 Ru(bipy)32+, with hmod ) ( 4.5 µm about hcen ) 13.8 µm, at a frequency of 1.00 Hz. Direct comparison of Figures 6a and 6c clearly illustrates the strength of the height-modulated RFMRE coupled with in-phase current detection. The in-phase currentvoltage wave for the oxidation of Ru(bipy)32+ is much clearer. Notably, the limiting current plateau is extended further into the positive potential window, enabling an accurate determination of the steady-state limiting current. This result demonstrates the considerable promise of this technique for the detection of electroactive species in a region of the potential window normally Analytical Chemistry, Vol. 71, No. 14, July 15, 1999
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obscured by solvent. The experimental value of irms,lim ) 0.76 nA, again, agrees well with that predicted by eqs 2 and 3. Thin ring electrodes with sizable interior radii are particularly attractive geometries for UMEs as they offer the advantages of both high current densities and high mass transfer characteristics.16,17 As such, even under stationary solution conditions, the ring electrode has been advocated as an electrochemical tool for both improving analytical detection limits and studing electrode kinetics. It is, thus, interesting to note that the limiting in-phase current (which discriminates against background processes), measured in the above example, is twice as large as the transportlimited dc current (which does not discriminate against background processes) predicted for this ring electrode in quiescent solution. CONCLUSIONS The variable-height RFMRE coupled with in-phase current detection represents a new hydrodynamic modulation technique. Over the range of modulation amplitudes and frequencies employed, the results presented herein demonstrate that the mass transfer characteristics of the height-modulated RFMRE are welldefined and calculable in terms of steady-state laminar radial channel flow theory. This predicted behavior can be rationalized as a consequence of the extremely high mass transport rates and correspondingly short times in which the diffusion layer and (16) Symanski, J. S.; Bruckenstein, S. J. Electrochem. Soc. 1985, 135, 1985. (17) Szabo, A. J. Phys. Chem. 1987, 91, 3108.
2944 Analytical Chemistry, Vol. 71, No. 14, July 15, 1999
convective flow profile relaxes in the RFMRE configuration. Thus, the system is able to attain steady state faster than the rate of mass transfer modulation. The technique has been shown to be useful for the detection of electroactive species in both low concentration and in a region of the potential window normally obscured by solvent electrolysis, considerably extending and developing the capabilities of existing RFMRE methodology. The device offers several improvements over earlier modulation techniques in flowing streams. In particular, the fast response time of the device, coupled with in-phase current detection, and the experimental simplicity of modulating the nozzle-substrate separation, makes the variable-height RFMRE an extremely attractive prospect as an end-of-column electrochemical detector for flow injection analysis or HPLC with electrochemical detection. ACKNOWLEDGMENT We appreciate support from the EPSRC (GR/K97011). J.V.M., in particular, would like to thank Prof. D. E. Williams (University College London) for many interesting discussions on hydrodynamic modulation voltammetry.
Received for review December 17, 1998. Accepted April 14, 1999. AC981397G
