Two-dimensional nucleation and growth on spherical electrodes

Abstract

The average current transients are derived for nucleation and growth of circular islands on the surface of a spherical electrode, for the cases of instantaneous and progressive nucleation. For large numbers of nuclei or for short times, these expressions reduce to the familiar expressions for a planar surface. For small numbers of nuclei, the nucleation density and the growth rate constant can in principle be separately extracted from the experimental data. A conceptual distinction must be made between the case where the number of nuclei on the surface is exactly specified and where only the mean value is known: these lead to different expected instantaneous nucleation and growth transients. The Avrami theorem is shown to be exact on spherical electrodes, provided the expected coverage is interpreted as an ensemble average over experiments in which the number of nuclei is a random variable.