J . Phys. Chem. 1994,98, 1270-1275
1270
Hydrodynamic Voltammetry with Channel Microband Electrodes: Potential Step Transients Richard G. Compton,' Robert A. W. Dryfe, John A. Alden, and Neil V. Rees Physical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
Peter J. Dobson and Peter A. Leigh Department of Engineering Science, Oxford University, Parks Road, Oxford OX1 3PJ, United Kingdom Received: September 14, 1993; In Final Form: November 2, 1993"
The current transients induced by a potential step a t a microband electrode located in a rectangular channel through which solution is pumped under laminar flow conditions are described by theory which accounts for convection axially through the flow cell and diffusion normal, and parallel, to the electrode surface. The hopscotch algorithm is used to predict numerically the form of the chronoamperometric transients as a function of the flow cell/electrode geometries and as a function of flow rate. Experiments are reported for the reduction of p-chloranil in acetonitrile solution using gold channel microbands: the effect of electrode size and solution flow rate is found to be in excellent agreement with the theoretical predictions. Computed concentration profiles showing the depletion of the electroactive material as a function of time after a potential step are presented and reveal that axial diffusion leads to significant depletion of material a t large distances upstream of the electrode.
Introduction The advent of microelectrodes has transformed the scope and applicability of voltammetric practice within a period of only a few years.',* One particular merit resulting from the greatly enhanced rates of mass transport, as compared to electrodes of larger dimensions, is the opportunity for studying very fast chemical reactions coupled with heterogeneous electron-transfer processes which were traditionally too fast to be probed voltammetrically and hence simply masked by mass transport control. In particular, cyclic voltammetry using microdisc electrodes permits time scales approaching the nanosecond scale to be interrogated ele~trochemically.~,~ Such measurements have hitherto been made under conditions where mass transport occurs solely via diffusion. However, we have suggested the possible merits of enhancing the rate of mass transport to microelectrodes through the use of convection in addition to diffusion5and have given a theoretical and experimental treatment of the flow rate dependence of the steady-state transport limited currents passed at microband electrodes located in a channel flow cell. Specifically, a good description was found to be given by a model which considered axial convection through the flow cell and diffusion both axial and normal to the electrode surface. In this paper we consider transient measurementsat channel microband electrodes and report the current response induced by stepping the electrode potential between values corresponding to no current flow and to the transport-limited reduction/oxidation of the electroactive substrate. Quantitative agreement is found between theory and experiment. Theory
In this section we present a theoretical model for the potential step transient at a microband channel electrode. We suppose that the potential step occurs between two values such that the first corresponds to no current flowing and the second to the transport limited electrolysis of A: Afe---B
much larger than its length, xe, (w >> xc), so the calculation reduces to a two-dimensional problem and sufficient supporting electrolyte is present for migration effects to be neglected. Under these conditions the steady-state convective diffusion equation describing the spatial distribution of A is
where x and y are defined in Figure 1, a = [A], D is the diffusion coefficient of A, and vx is the solution velocity profile in the x direction. Under laminar flow conditions the latter is parabolic, provided that an adequately long lead-in section is present for the flow to become fully d e v e l ~ p e d . ~Quantitatively, *~
where vo is the velocity at the center of the channel and 2h is the channel depth (height). The boundary conditions pertinent to the problem of interest are as follows: t
< 0:
all x
> 0:
y=o
o
