Disk electrodes mass balance

With an axisymmetric electrode (like a disk or ring) only y and/or Fr are involved in the mass balance equation. Hence, according to Eq. (2-4) or (2-11) only the F variations are useful for mass transfer measurements. 

A unique small active site close to a uniformly accessible rotating disk electrode is considered in this derivation. For the sake of simplification, the geometry of the active site is rectangular with its length perpendicular to the streamline of the flow (Fig. 5-1). By neglecting diffusion in the z direction, the mathematical problem is locally reduced to two dimensions, and the complete mass balance equation is formulated as follows ... 

Fig. 5-3. Numerical integration of the complete mass balance Eq. (5-2) for a uniform disk electrode, an isolated microelectrode and two microelectrodes of same dimension but with two different gaps (.) g = 40 pm, (-----) g = 22.5 pm.

Under steady-state conditions, the rate of charge-transfer process at the disk electrode is equal to the rate of removal of R from the disk surface (According to the definition of N, there is no further reaction of R at the disk electrode and chemical decomposition of R in the electrolyte solution). Therefore, the mass balance on disk electrode surface (x = 0) can be expressed as ... 

There is a significant contrast here with Section 5.4.2(e), where we found that the results for reversible systems observed at spherical electrodes could be extended generally to electrodes of other shapes. This is true for a reversible system because the potential controls the surface concentration of the electroactive species directly and keeps it uniform across the surface. Mass transfer to each point, and hence the current, is consequently driven in a uniform way over the electrode surface. For quasireversible and irreversible systems, the potential controls rate constants, rather than surface concentrations, uniformly across the surface. The concentrations become defined indirectly by the local balance of interfacial electron-transfer rates and mass-transfer rates. When the electrode surface is not uniformly accessible, this balance varies over the surface in a way that is idiosyncratic to the geometry. This is a complicated situation that can be handled in a general way (i.e., for an arbitrary shape) by simulation. For UME disks, however, the geometric problem can be simplified by symmetry, and results exist in the literature to facilitate the quantitative analysis of voltammograms (12). 

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