Competitive adsorption of two species: Doublet closure approximation and simulation

Abstract

Starting from a master equation, competitive adsorption of two kinds of interacting particles on a linear chain is considered. The transition probabilities are chosen in the Arrhenius form, and the activation energy is split into two additive terms, corresponding, respectively, to the action of the substratum and to interactions between nearest neighbor adatoms. The kinetic equations are obtained by using a doublet closure approximation, writing triplet densities in terms of doublet and singlet densities. In this approximation, for the range of parameters being considered, only one stable steady state results, unlike in the case of the mean field approximation (where up to three stable steady states can exist). In view of the disagreement between the results of both approximations, a Monte Carlo simulation is carried out and results similar to those of doublet closure approximation are obtained. In neither of these two models interactions between nearest adatoms produce multistability. Thus, one may conclude that multistability resulting from the mean field model is spurious and caused by the approximations used. Therefore, the mean field approximation can be unsuitable for studying multistability in these kinds of problems.