Fluids confined in quenched disordered porous media: Thermodynamics and dynamics

We have developed a theory to calculate structural correlations, thermodynamic properties, and dynamics of a fluid confined within a random porous medium (matrix). Our study demonstrates that the quenched-disorder averaged excess free energy, arising due to the random potential fields of the matrix, can be organized to yield one- and two-body potentials for fluid particles. Averaging over disorder reduces the system to an effective one-component fluid system in which particles experience a one-body (external) potential and interact via an effective pair potential. The effective pair potential is a sum of the bare potential (the one present in the pure fluid) and the matrix-induced potential. The resulting partition function exclusively involves fluid variables. We derive equations for fluid-fluid and fluid-matrix correlation functions, as well as for the free energy, pressure, and chemical potential of the fluid. We utilize the results of pair correlation functions to determine the number of particles in a cooperatively reorganizing cluster (CRC) in which localized particles form "long-lived" nonchemical bonds with the central particle. For a relaxation event to occur, these bonds must reorganize irreversibly, and the energy involved in these processes represents the effective activation energy of relaxation. Our theory is applied to a model system of hard spheres, and we report results for the effective pair potential, correlation functions, thermodynamic properties, and dynamics. The effective pair potential is found to be attractive at the contact point and develops a repulsive peak before decaying to zero. Results for pair correlation functions, structure factor, and relaxation time are compared with simulation results for several fluid densities at two matrix densities. In all cases, a very good agreement has been found.