Diffusion currents to (ultra)microelectrodes of various geometries - Ellipsoids, spheroids and elliptical 'disks'

The literature contains many static field formulas for capacitors of various geometries. The mathematical theory for these problems is analogous to diffusion theory for these geometries. We show how to obtain expressions for steady-state diffusion currents and local current densities of various microelectrode geometries via this analogy. Starting with the result for an ellipsoidal electrode, equations are obtained for the diffusion currents at oblate and prolate spheroidal, spherical electrodes, elliptical disk electrodes and circular disk electrodes. The results for micro elliptical disk electrodes are given in tabular form in terms of their major and minor axes. The significance of the elliptical disk's eccentricity is discussed for potentiodynamic and potentiostatic conditions.