Replica Ornstein-Zernike equations and simulations of the structure of a simple fluid in disordered porous media. Application to monomolecular adsorption

A two-dimensional (2D) model for a simple fluid adsorbed in a disordered porous medium is investigated by means of the replica Ornstein-Zernike (ROZ) equations with the hypernetted chain (HNC) and Percus-Yevick (PY) approximations. In addition, Monte Carlo simulations for this model are presented. The structural properties of adsorbed monolayer resulting from the theory agree well with the computer simulation data. Also we obtain the fluid compressibility from the ROZ equations and the adsorption isotherms. Besides the hard core repulsion, a long-range interaction between the fluid species in the form of an attractive square well is included. The contribution of this long-range term is considered using a mean-field approximation. This permits us to analyze the qualitative dependence of the behavior of the critical density and temperature on the matrix parameters. We find that the critical temperature of the hard discs with a square well attraction decreases with an increasing density of the quenched component. The critical density is less sensitive to these changes.