Structure and thermodynamic properties of a binary liquid in a porous matrix: The formalism

Using the replica trick we derive a formalism to describe the structure and the thermodynamic properties of a binary liquid in equilibrium with a poro us medium. We present the replica Ornstein-Zernike equations for the genera l case of a k-component liquid inside a porous matrix; besides the usual li quid-state closure relations, we consider in particular the optimized rando m phase approximation (ORPA) restricting ourselves at present to hard-core potentials exclusively. We present furthermore several thermodynamic relati ons: the Gibbs-Duhem equation, the compressibility, and the virial equation . Within the framework of the ORPA (mean spherical approximation), closed e xpressions for the perturbation contribution to the free energy and the che mical potentials can be presented. Finally, we offer suggestions for numeri cal implementations.