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

Rafael Salazar1,2 and Lev D. Gelb1

  • 1Department of Chemistry and Center for Materials Innovation, Washington University in St. Louis, St. Louis, Missouri 63130, USA
  • 2Universidad Nacional Mayor de San Marcos, Fac. Física, A.P. 14-0149, Lima 14, Peru

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Phys. Rev. E 71, 041502 – Published 8 April, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.041502

Abstract

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.

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Phys. Rev. E 71, 041502– Published 8 April, 2005
  • Received 5 December 2004

© 2005 American Physical Society

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