Surface Coverage Dynamics for Reversible Dissociative Adsorption on Finite Linear Lattices

Unlike molecular (or non-dissociative) adsorption, dissociative adsorption introduces correlations between neighboring sites. We study the resulting effects on surface coverage dynamics for reversible dissociative adsorption of dimers on a quasi-one-dimensional lattice system consisting of independent strips of reactive sites. We first show that the effect of finite system size on surface coverage dynamics becomes significant when dissociative adsorption is much slower or faster than the corresponding associative desorption. To this end, we derive analytic formulas for the equilibrium surface coverage and the correlation coefficient for the occupancy of neighboring sites as a function of system size (more specifically, the number of reactive sites in a strip) and the ratio of the adsorption and desorprtion rates. Second, we show that the validity of cluster-expansion-based approximations also largely depends on the ratio of adsorption and desorprtion rates. While the mean-field approximation and pair approximation predict the correct equilibrium surface coverage, they fail to predict the temporal growth of the surface coverage from an initially unoccupied lattice when adsorption is much slower than desorption. This implies that site correlation cannot be naively ignored nor approximated using a simple expression during a nonequilibrium process of dissociative adsorption. We show that the surface diffusion of adsorbed atoms can reduce correlations between sites and the fast-diffusion limit can be described by the mean-field approximation that assumes there is no correlation between sites. We also present kinetic Monte Carlo simulation results for the validation of our analytic results as well as the comparison of the surface coverage growth with the cluster-expansion-based approximations.