The long-time transient of two- and three-dimensional diffusion in microelectrode chronoamperometry

We consider the long-time transient of current to a microelectrode following a large step change in potential after which transport is diffusion-limited. For the three-dimensional problem of a spatially bounded microelectrode of arbitrary shape, in the absence of insulating surfaces, the three-term asymptotic series for the total charge transferred, already known in the context of heat transfer, is extended by one term, giving a third term in the series for the current itself. For the two-dimensional problem of a cylindrical microelectrode of arbitrary cross-section, the previously known two-term series in inverse powers of the logarithm of time is replaced by a single asymptotic expression which includes all the logarithmic terms. Using a symmetry argument the results can also be applied to microelectrodes mounted on insulating planes. Examples include spheroidal microelectrodes (e.g. the inlaid disc), thin ring microelectrodes and cylinders of elliptical cross section. The relationship between the long-time current to circular cylinder and band microelectrodes is confirmed and quantified.