Voltammetry and electrodeposition in the presence of attractive interactions: II. from Monte Carlo simulations to the KJMA–ECNT approach F. Berthier a, * , B. Legrand b , I. Braems a , J. Creuze a , R. Te ´tot a a LEMHE, Universite ´ Paris XI, Bat 413, Orsay Cedex 91405, France b SRMP-DMN, CEA Saclay, Gif-sur-Yvette Cedex 91191, France Received 7 April 2004; received in revised form 2 July 2004; accepted 10 July 2004 Available online 13 October 2004 Abstract Electrodeposition voltammograms are studied by Monte Carlo simulations when strong attractive interactions exist between the adsorbed atoms. The existence of a phase transition in the electrosorption isotherm leads to a nucleation and growth process when electroplating takes place for temperatures lower than the critical temperature for phase separation. In that case, we show that the voltammograms derived from the Monte Carlo simulations differ strongly from those obtained within the mean-field approach, par- ticularly for low sweep rates. Thus, the potential, the asymmetry and, above all, the current density at the peak appearing in the voltammograms are widely overestimated in the mean-field approach. However, by using an approach based on the Kolmogo- rov–Johnson–Mehl–Avrami formalism and on a generalization of the classical nucleation theory, we are able to reproduce all the peak characteristics very well. Moreover, we show that they depend very little on temperature, contrary to what is obtained within the mean-field approximation. Furthermore, the divergence of the dimensionless current density as (1/m b ) predicted by the mean-field approach for low sweep rates m b is substituted by a much slower divergence in (1/m b ) 2 . Ó 2004 Elsevier B.V. All rights reserved. Keywords: Electrodeposition; Voltammetry; Monte Carlo simulations; Classical nucleation theory; Langmuir isotherm; Frumkin isotherm 1. Introduction In the first part of this study, we analyzed the influ- ence of attractive interactions between electrodeposited atoms on the voltammograms under a linear potential sweep [1]. The mean-field approximation allowed us to express the main characteristics of the peak that appears in the plot of current density versus electrode potential, as a function of the parameters of the kinetic model. For high temperatures, the dimensionless current density at the peak potential turns out to converge towards two different limits for low and high sweep rates, which dis- tinguish the reversible and irreversible regimes. At low temperatures, the presence of a first-order phase transi- tion in the equilibrium isotherm (Frumkin isotherm) leads to different voltammograms relative to the direc- tion of the sweep, whichever the regime may be [1]. In the reversible regime, when the potential sweep rate con- verges towards 0, the peak potential tends towards the limit of the spinodal instability of the equilibrium iso- therm, while the dimensionless current density at the peak now diverges as (1/m b ) [1]. In which range can the mean-field approach be used to model the voltammetry in the presence of attractive interactions? For temperatures high enough, relative to the critical temperature T c of the equilibrium isotherm, 0022-0728/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2004.07.037 * Corresponding author. Tel.: +33 1 69 15 50 77; fax: +33 1 69 15 48 19. E-mail address: fabienne.berthier@lemhe.u-psud.fr (F. Berthier). www.elsevier.com/locate/jelechem Journal of Electroanalytical Chemistry 573 (2004) 377–389 Journal of Electroanalytical Chemistry