Stochastic models for surface adsorption and reaction processes
A sophisticated description of surface reactions, including spatial correlations or ordering in the adsorbed reactant species, can be provided by lattice-gas models of Statistical Mechanics or, equivalently, by Interacting Particle Systems models of Mathematical Statistics and Probability; In this thesis, the CO-oxidation reaction is considered wherein CO adsorbs reversibly and oxygen adsorbs irreversibly onto a surface (represented by a square lattice of adsorption sites), oxygen dissociates, and the constituent atoms react with adjacent CO to form CO2. The product, CO2, immediately desorbs from the surface. A new model is developed which incorporates both the high surface mobility of adsorbed CO, and a superlattice ordering of relatively immobile adsorbed oxygen. The latter feature derives from the constraint that diatomic oxygen adsorbs on diagonally adjacent empty sites, provided that none of the six adjacent sites are occupied by adsorbed oxygen. Thus, a suitable ensemble of eight sites is required for oxygen adsorption. A comprehensive analysis of the properties of the model is provided, utilizing both kinetic Monte Carlo simulation, as well as approximate solution of the exact Master equations for this model. More specifically, the following are considered: steady state behavior including a cusp bifurcation corresponding to the loss of bistability, and a symmetry-breaking transition associated with the superlattice ordering; both percolation and coarsening phenomena associated with symmetry-breaking; enhancement of fluctuations near the cusp bifurcation and consequences for experimental systems; and some issues regarding relaxation in related but simpler adsorption models.