Replica Ornstein-Zernike self-consistent theory for mixtures in random pores

Abstract

We present a self-consistent integral equation theory for a binary liquid in equilibrium with a disordered medium, based on the formalism of the replica Ornstein-Zernike (ROZ) equations. Specifically, we derive direct formulas for the chemical potentials and the zero-separation theorems (the latter provide a connection between the chemical potentials and the fluid cavity distribution functions). Next we solve a modified-Verlet closure to ROZ equations, which has built-in parameters that can be adjusted to satisfy the zero-separation theorems. The degree of thermodynamic consistency of the theory is also kept under control. We model the binary fluid in random pores as a symmetrical binary mixture of nonadditive hard spheres in a disordered hard-sphere matrix and consider two different values of the nonadditivity parameter and of the quenched matrix packing fraction, at different mixture concentrations. We compare the theoretical structural properties as obtained through the present approach with Percus-Yevick and Martinov-Sarkisov integral equation theories, and assess both structural and thermodynamic properties by performing canonical standard and biased grand canonical Monte Carlo simulations. Our theory appears superior to the other integral equation schemes here examined and provides reliable estimates of the chemical potentials. This feature should be useful in studying the fluid phase behavior of model adsorbates in random pores in general.