Using the replica trick we derive a formalism to describe the structure and the thermodynamic properties of a binary liquid in equilibrium with a porous medium. We present the replica Ornstein-Zernike equations for the general case of a k-component liquid inside a porous matrix; besides the usual liquid-state closure relations, we consider in particular the optimized random phase approximation (ORPA) restricting ourselves at present to hard-core potentials exclusively. We present furthermore several thermodynamic relations: the Gibbs-Duhem equation, the compressibility, and the virial equation. Within the framework of the ORPA (mean spherical approximation), closed expressions for the perturbation contribution to the free energy and the chemical potentials can be presented. Finally, we offer suggestions for numerical implementations.

• Received 20 January 2000

DOI:https://doi.org/10.1103/PhysRevE.61.5330