Monomer adsorption on a square lattice with first- and second-neighbor interactions

Abstract

A year ago, we reported a number of crystallization patterns ~phases! of monomers with nearest- ~first-! neighbor interaction on a multilayered semi-infinite square lattice @1#. This article goes a step further, analyzing the more realistic model of monomer surface adsorption including nearest- and next-nearest- ~second-! neighbor interactions. Lattice models have been used for a very long time; a brief summary of lattice calculations done by others can be found in Ref. @1#, and the notation used here is very similar to that of Ref. @1#. The surface is a semi-infiniteM3N square lattice ~N!‘! in the presence of a gas containing one molecular species and the adsorbed molecules occupy one site. For this reason, we refer to them as monomers. The system is at thermal equilibrium and the chemical potential energy m of a monomer depends on the external gas pressure. The interaction energies of an adsorbed monomer are V0 with the lattice, V with any first-neighbor monomer at a distancea, and W with any second-neighbor monomer at a distance a &. The activities associated with these three interactions are