Transient equations for multiple nucleation on solid electrodes: A stochastic description

Abstract

We consider the phenomenon of heterogeneous nucleation in electrolytic cells. Through the proposition of a stochastic model, we derive an equation to describe the migration of solute ions and their reaction near the electrode surface. Defining particular boundary conditions, the stochastic equation is solved and the time dependent probability density is related to the flux of ions towards the growing nucleus. The flux of ions is identified as the current transient expression, which is adequate for a comparison with the experimental results. The theory is powerful enough to reproduce results obtained by electrodepositing cobalt on n-type silicon and to explain deviations from predictions of the standard model for three-dimensional nucleation diffusion limited growth.

Modelling diffusion controlled electrocrystallisation processes

“…There have been a significant number of attempts [1][2][3][4][5][6][7][8][9][10] to formulate the patterns of behaviour of current-time transients (CTTs) when the rates of crystal growth are purely governed by the diffusion of the depositing species in the electrolyte. In view of the existence of a large number of core papers, and even some review articles [11,12], we refrain from giving a lengthy introduction to the subject in hand.…”

The potentiostatic transient for 3D nucleation with diffusion-controlled growth: theory and experiment for progressive nucleation

“…Several models have been proposed for the theoretical description of the potentiostatic transient for 3D nucleation on active sites with diffusion-controlled growth [1][2][3][4][5][6][7][8][9][10][11][12]. All these models describe the rate law for the formation of nuclei on a finite number of active sites, which are distributed randomly over the electrode surface, by the equation…”

Anomalous scaling in surface roughness evaluation of electrodeposited nanocrystalline Pt thin films

“…For instance, Santos et al [24] introduced a simple model for roughening in the instantaneous electrodeposition process. D'Ajello et al [25] provided a microscopic theory based on the stochastic Langevin equation for the cations towards the substrates. A comprehensive review article on kinetic roughness of electrodeposited films is given by Schwarzacher [4].…”