Application of the Bethe-Peierls approximation to a lattice-gas model of adsorption on mesoporous materials.

We calculate adsorption and desorption isotherms in models of several classes of porous materials using a lattice-gas model solved in the Bethe-Peierls (quasichemical) approximation. Isotherms and fluid density profiles from the Bethe-Peierls and Bragg-Williams approximations are compared with grand-canonical Monte Carlo simulation results. The Bethe-Peierls approximation produces both more accurate adsorption and desorption isotherms and more realistic fluid density profiles than the Bragg-Williams approximation. Details of the application of the Bethe-Peierls approximation applied to a three-dimensionally inhomogeneous system are given. We show that the numerical solution of this theory can be accomplished using a self-consistent iterator very similar to that currently used in studies employing the Bragg-Williams approximation. This iterative scheme is substantially more efficient than the numerical optimization method used in many previous studies of lattice-gas models in the quasichemical approximation. We find that use of the Bethe-Peierls approximation is only slightly more computationally demanding than the Bragg-Williams approximation, and thus recommend it for use in future work on this class of models.