Fluids Confined in Porous Media:  A Soft-Sponge Model

Abstract

The morphology of many porous materials is sponge-like. For describing fluid adsorption in such materials, we propose here a quite general sponge model which is built by digging spherical cavities in a continuum. In contrast to the hard-sponge model proposed recently by Zhao et al. [Zhao, S. L.; Dong, W.; Liu, Q. H. J. Chem. Phys. 2006, 125, 244703], the continuum in the present soft-sponge model is permeable to fluid particles. Although the general expression of the fluid−matrix interaction potential is not pair additive, we were able to extend some statistical-mechanics formalism of liquid state to deal with this model. We derived the diagrammatic expansions of various correlation functions and Ornstein−Zernike equations. Usually, one would not expect that the thermodynamic quantities (e.g., internal energy) of a system with a nonpair-additive interaction can be completely determined from the structural information at the two-body level. We found a remarkable result that for the soft-sponge model considered here, the internal potential energy can be determined from only two-body correlation functions. In the particular case of a soft-sponge model with nonoverlapping cavities, we show that the fluid−matrix interaction can be also described by a pair-additive potential. In this case, the Madden−Glandt formalism applies. The Ornstein−Zernike equations obtained by using the pair-additive fluid−matrix interaction potential look to be quite different from those obtained by starting with the nonpair-additive potential. We found the relationship between the two descriptions and show how the two sets of Ornstein−Zernike equations can be transformed from each other for a soft-sponge model with nonoverlapping cavities.

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

“…For Van Tassel model of templated matrices, no analytical result has been found in the case that the matrix is built from a Widom-Rowlinson mixture. The integral-equation theory based on Ornstein-Zernike equations for the matrix models considered in the present paper is now available [1,[31][32][33]37]. The application of such a theoretical approach also requires approximate closures.…”

“…Recently, Dong, Krakoviack and Zhao have proposed a soft sponge model [32]. A sketch of this model is presented in figure 4.…”

“…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.…”

Self-diffusion of ions in charged nanoporous media

“…Dynamic properties of partly-quenched systems made of charged and/or uncharged particles, represented as hard or soft spheres, have attracted lots of theoretical interest in recent years. 7,[15][16][17][18][19][20][21][22][23][24] A mode coupling theory associated with the replica Ornstein-Zernike theory allowed Krakoviack to predict a dynamic phase diagram in hard sphere systems. 15,18,20 More recently, numerical simulations were used to compute the dynamic properties of annealed particles in such systems, 21,23 which were then compared with the predictions of the mode coupling theory.…”

Effects of porous confinement on the structural properties of the Gaussian core model

“…From the theoretical point of view, the description of particle interactions in soft systems via effective potentials [20] has reached nowadays a very high level of sophistication, so that even for colloidal particles with a complex internal architecture highly reliable effective interactions can be deduced via suitable averaging procedures over the huge number of internal degrees of freedom. Finally, theoretical frameworks have been proposed to consider more realistic models for matrix representations [21][22][23][24][25][26].…”