Fluids in porous media. I. A hard sponge model

Abstract

The morphology of many porous materials is spongelike. Despite the abundance of such materials, simple models which allow for a theoretical description of these materials are still lacking. Here, we propose a hard sponge model which is made by digging spherical cavities in a solid continuum. We found an analytical expression for describing the interaction potential between fluid particles and the spongelike porous matrix. The diagrammatic expansions of different correlation functions are derived as well as that of grand potential. We derived also the Ornstein-Zernike (OZ) equations for this model. In contrast to Madden-Glandt model of random porous media [W. G. Madden and E. D. Glandt, J. Stat. Phys. 51, 537 (1988)], the OZ equations for a fluid confined in our hard sponge model have some similarity to the OZ equations of a three-component fluid mixture. We show also how the replica method can be extended to study our sponge model and that the same OZ equations can be derived also from the extended replica method.

Fluids confined in porous media: An ideal gas in different matrices

“…The one-body distribution function for a particular matrix realization has exactly the same expression as that given in equation (31). Taking the average over matrix realizations, we find the following expression for the fluid density inside the matrix,…”

“…Noting that z 0 = ρ 0 for the overlapping HS matrix, we see that the density of the confined ideal gas is given by the density of the bulk ideal gas (in equilibrium with the confined one) multiplied by the probability of a fluid particle being in the void space. Substituting equation (31) into equation (14), we obtain the following result for the Helmholtz free energy,…”

“…where equations (27), (31) and z 0 = ρ 0 were used in obtaining the last equality in equation (38). The total matrix-fluid correlation is given by…”

“…In equation (31), z 1 is the density of a bulk ideal gas at the same chemical potential as the confined ideal gas (i.e., the gas in a reservoir outside the porous medium being in equilibrium with the confined ideal gas). It is easy to prove that exp −πσ 3 0 z 0 /6 is nothing else but the probability that a fluid particle is in the void space.…”

“…A large number of investigations have been devoted to Madden-Glandt model . Recently, we have proposed some sponge-like models [31,32] and a new type of templated matrix model [33]. All these models involve quenched disorders.…”