Kinetic lattice gas model for adsorption, desorption and diffusion: An investigation of truncation schemes.

摘要

The lattice gas model of an adsorbate, which assigns adsorbed particles to a regular array of sites of a substrate, permits a succinct description of the equilibrium properties of the adsorbate. To rigorously describe its evolution, specifically adsorption from and desorption to its gas phase and surface diffusion, in the presence of lateral interactions, a kinetic lattice gas model is set up. From the master equation a hierarchy of equations of motion is derived for the coverage and the higher-order particle correlators. A manageable set of evolution equations is derived by examining different methods of truncation of this hierarchy and factorizations of the correlators. These equations are developed with a set of computer codes.; From these we calculate the equilibrium correlators of a gas adsorbed on a square-latticed substrate. These, as well as thermodynamic quantities of interest (isosteric heat of adsorption, chemical potential), are compared with quasi-exact results obtained using the transfer matrix method and with existing analytic approximation methods. We explore thermal desorption under quasi-equilibrium and nonequilibrium conditions induced by limited surface diffusion. We show that a five-correlator basis on a square lattice gives very good results. The extension of the basis to fifteen functions improves the quality even further. The latter is now the best available analytic approximation for a description of the evolution of a lattice gas with interactions. The approach can be generalized to multi-component adsorbates and other surface processes.