Thermodynamics of fluids in quenched disordered matrices

Abstract

Using the replica method, we derive the thermodynamic relations for a fluid in equilibrium with a quenched porous matrix. In particular, t~e appropriate Gibbs-Duhem equation is obtained as well as the equivalence between grand canonical and canonical ensembles. The exact compressiblity and virial equations are derived. Whereas the compressibility equation remains a direct and practical way to obtain I. the adsorption isotherm, the virial equation involves terms which do not relate easily to the properties of the fluid/matrix system. This explains the inconsistency between previous theoretical predictions and computer simulation results.-,1

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

“…This case is the closest to the RHS/RC model discussed in section 5.A. In this case, the partition function for a particular matrix realization has the same expression as that given in equation (24). The grand potential averaged over matrix realizations is given by Ω = −kT ln Ξ 1 (q N0 …”

“…is the partition function of a bulk ideal gas and Ξ IG/OHSM 1 (q N0 ) is the partition function of an ideal gas in a particular realization of an overlapping hard-sponge matrix [see equation (24)]. We obtain the following expression for the thermodynamic pressure,…”

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

“…1 It is interesting to investigate the respective roles of these parameters. The possibility of a temperature mismatch has been noted in previous work [41], but an explicit assessment of its consequences has not been carried out yet.…”

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.…”