Microdisc radius

Kinetic and mechanistic information may be gleaned through examination of the effective number of electrons transferred, as a function of microdisc radius. Figure 33 shows that Nett varies between 1 and 2. The former limit corresponds to the case of fast mass transport (small radius) since B is lost to... 

Hemispherical electrodes are experimentally realized using hanging mercury drops for macroelectrodes and mercury-coated microdisc electrodes for microhemispheres. The lower radius limit is thus governed by the microdisc radius the upper limit has been chosen as 70 fim above which natural convection becomes significant. 

Table 6.1 Linear sweep and cyclic voltammetry characteristics associated with the four categories (see text), where 5 is the size of the diffusion zone, Rb is the microdisc radius, d is the center-to-center separation, /p is the peak current, lum is the limiting current, and V is the scan rate [35].

The latter is defined by x = where re is the microdisc radius and t is time. 

Of course, in order to vary the mass transport of the reactant to the electrode surface, the radius of the electrode must be varied, and this unplies the need for microelectrodes of different sizes. Spherical electrodes are difficult to constnict, and therefore other geometries are ohen employed. Microdiscs are conunonly used in the laboratory, as diey are easily constnicted by sealing very fine wires into glass epoxy resins, cutting... 

For the disk-shaped bead mound and an x scan over the center of the bead spot, the lateral distance of the UME position from the center is r = Ax = x—x0, where x0 is the x coordinate of the spot center. The factor 9 is proportional to the steady-state concentration distribution over a microdisc electrode and assumes the following form, where rs is the radius of the bead spot ... 

Note that the peak current densities (Aippp = A/ppp /Ao) of microspheres and microdiscs of the same radius fulfill Aipppyphe peak = (w/4)Aippp lsc peak. 

Cyclic voltammograms can be presented in an alternative format to that shown in Fig. 5 by using a time rather than potential axis, as shown in Fig. 8. The equivalent parameters in steady-state voltammetric techniques are related to a hydrodynamic parameter (e.g. flow-rate, rotation speed, ultrasonic power) or a geometric parameter (e.g. electrode radius in microdisc voltammetry). 

Consideration of Fig. 32 implies that chemical information may be extracted from microelectrode experiments either via steady-state measurements or via transient, often cyclic voltammetric, approaches. In the former approach, measurements are made of the mass transport limited current as a function of the electrode size - most usually the electrode radius for the case of a microdisc electrode. This may be illustrated by reference to a general ECE mechanism depicted by (23a)-(23c) where k is the rate constant for the C step. 

The above discussion applies to spherical geometry. Unfortunately, no analytical solution can be found for the finite disc configuration however, we saw earlier that, for simple reversible electron transfer reactions, the limiting current density at the microdisc electrode was identical to that at a sphere of radius nrm/4. Fleischmann et al. [21] have investigated whether this analogy can be extended to systems with coupled chemical reactions. The system chosen for this study was the oxidation of anthracene in very dry acetonitrile at platinum electrodes. This reaction is thought to proceed by the ece mechanism [22]... 

A microdisc electrode is a micron-scale flat conducting disc of radius r. that is embedded in an insulating surface, with the disc surface flush with that of the insulator. It is assumed that electron transfer takes place only on the surface of the disc and that the supporting smlace is completely electroinactive under the conditions of the experiment. These electrodes are widely employed in electrochemical measurements since they offer the advantages of microelectrodes (reduced ohmic drop and capacitive effects, miniaturisation of electrochemical devices) and are easy to fabricate and clean for surface regeneration. In Chapter 2, we considered a disc-shaped electrode of size on the order of 1 mm. In that case we could approximate the system as one-dimensional because the electrode was large in comparison to the thickness of the diffusion layer, such that the current was essentially uniform across the entire electrode surface. Due to the small size of the microdisc, this approximation is no longer valid so we must work in terms of a three-dimensional coordinate system. While the microdisc can... 

Fig. 9.1. The (r, z, ) cylindrical polar coordinate system used to model a microdisc electrode. The disc radius is re.

In these transformed coordinates, the radius of the microdisc is 1. The definitions of T and C are unchanged so that the dimensionless Fick s second law in this space is... 

As discussed for the case of (hemi)spherical microelectrodes in Chapter 4, the response in cyclic voltammetry at microdiscs varies from a transient, peaked shape to a steady-state, sigmoidal one as the electrode radius and/or the scan rate are decreased, that is, as the dimensionless scan rate, a = Y r lv/TZTD, is decreased. The following empirical expression describes the value of the peak current of the forward peak for electrochemically reversible processes [11] ... 

A randomised algorithm could be used that would take as input the disc radius, r, the electrode area, A, and the surface coverage, 0, and would generate a surface with randomly distributed microdiscs alternatively the... 

Fig. 3 Relationship between the RC cell time constant and the radius of platinum microdiscs in which the supporting electrolyte is 0.1 M HCl. Cell time constants were measured using chronoamperometry conducted on a microsecond to submicrosecond timescale by stepping the potential from 0.200 to 0.250 V versus Ag/AgCl.

Fig. 5 Theoretical limitations on ultrafast cyclic voltammetry. The shaded area between the slanted lines represents the radius that a microdisc must have if the ohmic drop is to be less than 15 mV and distortions due to nonplanar diffusion account for less than 10% of the peak current.

Dimension given is the radius of a microdisc electrode unless otherwise stated. 

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