The concept of planar diffusion zones. Theory of the potentiostatic transient for multiple nucleation on active sites with diffusion-controlled growth

Abstract

Most theoretical models used to describe the potentiostatic transient for the case of multiple nucleation on active sites with diffusion-controlled growth are based on the concept of planar diffusion. It is shown that the definition of a planar diffusion zone is based on an analogy with the Cottrell equation but does not involve a flux balance, as is usually stated in the literature. The current to a growing nucleus can be written in a form that presents this analogy but it remains a hemispherical current, i.e. there is no change in the diffusional regime or the associated boundary conditions. This is the key feature of the concept of planar diffusion zones because it provides a simple way to describe the transition of hemispherical diffusion to planar diffusion when the diffusion fields interfere. In essence, a model based on the concept of planar diffusion zones can only work just because it is not based on a flux balance. The concept of a planar diffusion zone usually is associated with the growth of a single nucleus but this notion is not really needed to derive the equation of the potentiostatic transient. It is better to apply this concept to the ensemble of growing nuclei as a whole since this leads in a natural way to the definition of a uniform diffusion layer, which is connected with the idea of a mean concentration field. It is this notion of a uniform diffusion layer that reduces the interference of hemispherical diffusion fields to a true two-dimensional problem so that Avrami's equation can be used correctly to describe the overlap of the planar diffusion zones.