Fluid distributions in random media: Arbitrary matrices

Abstract

The graphical theory of Madden and Glandt [J. Stat. Phys. 51, 537 (1988)] for a fluid adsorbed into a quenched medium has been extended to situations in which the distribution of the immobile species has an arbitrary form, not necessarily arising from a thermal quench. The working equations of Madden and Glandt are shown to be applicable to this general case and the approximations common in the theory of equilibrium mixtures are appropriate in this application as well. Extensions to mixtures are considered and the connection with the graphical theory of small molecules is discussed.

Description of a Polar Molecular Liquid in a Disordered Microporous Material With Activating Chemical Groups by a Replica Rism Theory

“…This is much like the replica OZ equations for atomic liquids reduce to the Madden-Glandt (MG) OZ theory [3,5] when neglecting the blocking effects [8][9][10][11][12][13][14].…”

“…Madden and Glandt (MG) [3,5] performed a cluster diagram analysis of this quenched-annealed, or partially quenched system and derived the integral equations of Ornstein-Zernike type (OZ) [31]. In physical essence, the MG-OZ equations can be viewed as treating the matrix as a single rigid supermolecule immersed in the fluid at infinite dilution [4].…”

“…Madden [5] also discussed this approach from the point of view of the MG diagram analysis and suggested the use of the Chandler-Silbey-Ladanyi (CSL) equations [36,31] to provide the interaction site theory to be proper in the diagrammatic sense. Thompson and Glandt [24] combined the polymer RISM theory (PRISM) of Schweizer and Curro [37] with the MG formalism [3,5] to describe a polymer fluid of ideal freely jointed hard sphere chains in a hard sphere matrix. Ford, Thompson, and Glandt [25] further developed the MG-PRISM as well as MG-OZ methods to obtain the thermodynamic properties of fluids confined in disordered porous solids by using the scaled particle theory (SPT) approach.…”

Application of Replica Ornstein-Zernike equations in studies of the adsorption of electrolyte mixtures in disordered matrices of charged particles

“…In the last decades, new class of theories appeared in which the disordered porous materials filled with fluid are treated as partly quenched systems in which some of the degrees of freedom are quenched and others are annealed. The systems differ from regular mixtures; the statistical-mechanical average which is needed to obtain the free energy describing the confined fluid, becomes a double ensemble average [10][11][12][13][14][15][16][17]. The thermodynamic and structural properties of these systems can be calculated using the computer simulations and/or the replica integral equation theories.…”

Adsorption of Hard Sphere Fluid in Porous Material: A Monte Carlo Simulation Approach for Pressure Calculation

“…Theoretical tools for the investigation of the properties of fluids and fluid mixtures adsorbed in disordered porous materials have been mainly adapted from the liquid-state statistical mechanics and include integral equation approach, pioneered by Madden and Glandt [13,14]. These authors have presented exact Mayer cluster expansions for the correlation functions for the case when the matrix (quenched species subsystem) is generated by a quench from an equilibrium distribution, as well as for the case of arbitrary distribution of obstacles.…”