Ornstein-Zernike equations and simulation results for hard-sphere fluids adsorbed in porous media

In this paper we solve the replica Ornstein-Zernike (ROZ) equations in the hypernetted-chain (HNC), Percus-Yevick (PY), and reference Percus-Yevick (RPY) approximations for partly quenched systems. The ROZ equations, which apply to the general class of partly quenched systems, are here applied to a class of models for porous media. These models involve two species of particles: an annealed or equilibrated species, which is used to model the fluid phase, and a quenched or frozen species, whose excluded-volume interactions constitute the matrix in which the fluid is adsorbed. We study two models for the quenched species of particles: a hard-sphere matrix, for which the fluid-fluid, matrix-matrix, and matrix-fluid sphere diameters ${\mathrm{\sigma }}_{11}$, ${\mathrm{\sigma }}_{00}$, and ${\mathrm{\sigma }}_{01}$ are additive, and a matrix of randomly overlapping particles (which still interact with the fluid particle as hard spheres) that gives a ‘‘random’’ matrix with interconnected pore structure. For the random-matrix case we study a ratio ${\mathrm{\sigma }}_{01}$/${\mathrm{\sigma }}_{11}$ of 2.5, which is a demanding one for the theories. The HNC and RPY results represent significant improvements over the PY result when compared with the Monte Carlo simulations we have generated for this study, with the HNC result yielding the best results overall among those studied. A phenomenological percolating-fluid approximation is also found to be of comparable accuracy to the HNC results over a significant range of matrix and fluid densities. In the hard-sphere matrix case, the RPY is the best of the theories that we have considered.