Fluids in random porous media: Scaled particle theory

Abstract

The scaled particle theory (SPT) is applied to describe thermodynamic properties of a hard sphere (HS) fluid in random porous media. To this purpose, we extended the SPT2 approach, which has been developed previously. The analytical expressions for the chemical potential of an HS fluid in HS and overlapping hard sphere (OPH) matrices, sponge matrix, and hard convex body (HCB) matrix are obtained and analyzed. A series of new approximations for SPT2 are proposed. The grand canonical Monte Carlo (GGMC) simulations are performed to verify an accuracy of the SPT2 approach combined with the new approximations. A possibility of mapping between thermodynamic properties of an HS fluid in random porous media of different types is discussed. It is shown that thermodynamic properties of a fluid in the different matrices tend to be equal if the probe particle porosities and the specific surface pore areas of considered matrices are identical. The obtained results for an HS fluid in random porous media as reference systems are used to extend the van der Waals equation of state to the case of a simple fluid in random porous media. It is observed that a decrease of matrix porosity leads to lowering of the critical temperature and the critical density of a confined fluid, while an increase of a size of matrix particles causes an increase of these critical parameters.

Generalization of the van der Waals Equation

“…The generalization of the results obtained in [15,16] to non-spherical molecules in porous media [17,18] allowed us to generalize the van der Waals equation [17] to anisotropic fluids in porous media. The investigations of the gas-liquid-nematic phase equilibria in the framework of the generalized van der Waals equation show a rich variety of phase behaviors that depends on the molecular shape, value of attractive intermolecular interactions, and porosity of porous media.…”

“…We note that, here and below, we use conventional notations [15][16][17][18], where the index "1" is used to denote a fluid component, the index "0" denotes matrix particles, while, for the scaled particles, the index "s" is used.…”

“…The multiplier 1/p 0 (α s , λ s ) appears due to an excluded volume occupied by matrix particles. The probability p 0 (α s , λ s ) is directly related to two different types of porosity introduced by us in [15][16][17][18]. The first one corresponds to the geometrical porosity…”

“…In accordance with the ansatz of the SPT theory [13][14][15][16][17][18], w(λ s , α s ) can be presented in the form…”

“…After the integration of relation (19) over ρ 1 , one obtains the expressions for the chemical potential and for the pressure in the SPT2 approximation [15][16][17]:…”