The theory of chronoamperometry for the investigation of electrocrystallization : Mathematical description and analysis in the case of diffusion-controlled growth

A critical study is made of the mathematics needed to describe the current response towards a potential step perturbation of an electrode at which phase formation takes place by the process of nucleation and diffusion-controlled hemispherical growth. As a result, an expression for the current-time transient is derived which is more general than the expressions for the limiting cases used hitherto. Procedures are discussed for fitting experimental data to this new expression in order to obtain the number density of nucleation sites and the nucleation rate constant. The theory is extended to cases where overlap of growing nuclei has to be accounted for, resulting in a new expression as well. From a comparison with existing theories it is concluded that the present derivation, and its result, although also not rigorous, is to be preferred because it is unique in extrapolating to both short-time and long-time limiting behaviour exactly