Cooperative sequential adsorption with nearest-neighbor exclusion and next-nearest neighbor interaction

A model for cooperative sequential adsorption that incorporates nearest-neighbor exclusion and next-nearest neighbor interaction is presented. It is analyzed for the case of one-dimensional dimer and two-dimensional monomer adsorption. Analytic solutions found for certain values of the interaction strength are used to investigate jamming coverage and temporal approach to jamming in the one-dimensional case. In two dimensions, the series expansion of the coverage $\theta(t)$ is presented and employed to provide estimates for the jamming coverage as a function of interaction strength. These estimates are supported by Monte Carlo simulation results.