On the rate equation of nucleation and the concept of active sites in electrodeposition

Abstract

On the basis of the assumption that on a homogeneous surface area a probability 0 < P( E, c) <: 1 for nucleation can be defined which increases with the monomer concentration c and is also dependent on the potential E, it is shown both by a schematrc computer simulation and by an approximate analytical derivation that necessarily the number of nuclei has to attain a limiting value for long times. without having to resort to the existence of active sites. It follows that this limiting number arises from a concurrence between the probability of nucleation and the processes that accompany the growth of a nucleus and that decrease supersaturation. LIST OF SYMBOLSR(L u> nucleation rate per active site, s-' monomer concentration at a radial distance r from the centre of a lone nucleus at time t, mol cmm3 monomer bulk concentration, mol cmP3 diffusion coefficient, cm2 s-l growth constant of exclusion zone, cm s-' number density of nuclei at time t, cm-2 number density of active sites, cmP2 nucleation rate probability as a function of potential E and concentration c, cme2 s-' radius of a nucleus at time t, cm radius of exclusion zone at time t belonging to a lone nucleus, which is born at time u, cm l To whom correspondence should be addressed 0022-0728/88/$03.50 0 1988 Elsevier Sequoia S.A.

A complementary survey of staircase voltammetry with metal ion deposition on macroelectrodes

“…Under this condition, the phenomenon can be treated as in chronoamperometry except that the nucleation constant is likely to vary with time. With the conventional wisdom [11][12][13][14][15][16][17], it is assumed that around a growing hemispherical nucleus created at t = s from the beginning of nucleation at t = t 1 , because of the ingestion of active sites, a circular area free of other nuclei develops which surface is proportional to t-s. This area was identified to an equivalent area needed to sustain the growth of the hemispherical nuclei by planar diffusion.…”

Nucleation phenomena in electrochemical systems: kinetic models

“…Here I will mention only the pioneering work of Erdey-Gruz and Volmer [31], who were the first to notice that nuclei of the new phase were formed on some preferred sites on the electrode surface, the work of Fleischmann and Thirsk [32], who considered the case of equally active sites and the works of Kaischev and Mutaftschiev [33], Markov et al [34][35][36] and Fletcher et al [37][38][39][40][41][42], who examined the nucleus formation on active sites with different activities with respect to the process of nucleus formation. Attention should be paid also to the works of Sharifker and Mostany [43], Sluyters-Rehbach et al [44,45], Mirkin and Nilov [46], Heerman and Tarallo [47][48][49][50] and Danilov et al [51][52][53], who contributed essentially to this very important subject, too (see also Ref. [30] and the references cited therein).…”