Explicit spatial description of fluid inclusions in porous matrices in terms of an inhomogeneous integral equation

Abstract

We study the fluid inclusion of both Lennard-Jones particles and particles with competing interaction ranges -short range attractive and long range repulsive (SALR)-in a disordered porous medium constructed as a controlled pore glass in two dimensions. With the aid of a full twodimensional Ornstein-Zernike approach, complemented by a Replica Ornstein-Zernike integral equation, we explicitly obtain the spatial density distribution of the fluid adsorbed in the porous matrix and a good approximation for the average fluid-matrix correlations. The results illustrate the remarkable differences between the adsorbed Lennard-Jones (LJ) and SALR systems. In the latter instance, particles tend to aggregate in clusters which occupy pockets and bays in the porous structure, whereas the LJ fluid uniformly wets the porous walls. A comparison with Molecular Dynamics simulations shows that the two-dimensional Ornstein-Zernike approach with a Hypernetted Chain closure together with a sensible approximation for the fluid-fluid correlations can provide an accurate picture of the spatial distribution of adsorbed fluids for a given configuration of porous material.

A three dimensional integral equation approach for fluids under confinement: Argon in zeolites

“…The use of a direct correlation function corresponding to a confined fluid averaged over the porous matrix disorder improved upon the simple bulk fluid approximation, which although suitable for solvation problems, is of limited validity under conditions of tight confinement. 19 The results presented in Ref. 19 for fluids interacting via short range attractive-long range repulsive (SALR) and Lennard-Jones (LJ) potentials indicate that the combination of the 3DOZ-HNC and ROZ-HNC equations is a promising alternative to describe explicitly the spatial distribution of fluids under conditions of confinement in the nanometer regime.…”

“…19 The results presented in Ref. 19 for fluids interacting via short range attractive-long range repulsive (SALR) and Lennard-Jones (LJ) potentials indicate that the combination of the 3DOZ-HNC and ROZ-HNC equations is a promising alternative to describe explicitly the spatial distribution of fluids under conditions of confinement in the nanometer regime.…”

“…Already in the work of Beglov and Roux, 2 these authors computed the density profile of a simple fluid adsorbed into a crude model of zeolite solving the 3DOZ-HNC equation and using as an approximation for the fluid-fluid direct correlation function (dcf) that of the bulk fluid. More recently, two of the authors in collaboration with Kahl 19 revisited the approach of Beglov and Roux to describe the structure of a fluid inclusion into a model of controlled pore glass in two-dimensions. Since the model in question could be thought as a partly quenched mixture, the authors resorted to the use of the Replica Ornstein Zernike (ROZ) approach [20][21][22] in order to approximate the fluidfluid dcf.…”

“…19, we will here present the solution of the 3DOZ-HNC equation for a simple fluid, argon modeled as a one-site LJ fluid, adsorbed into three zeolite models, namely, silicalite-1 (all silica analogue of the ZSM-5 zeolite, framework type MFI), silicalite-2 (all silica analogue of the ZSM-11 zeolite, framework type MEL) and an all silica model of faujasite (framework type FAU). Both MFI and MEL zeolites are composed of 4-, 5-, and 6-membered rings linked to form a system of channels with 10-membered ring openings.…”

“…The calculation of density maps, particularly in regions where the sampling is poor due to problems of accessibility might turn into a computationally lengthy process. 19 Therefore, the development of theoretical tools capable of describing explicitly and accurately the three dimensional structure of a fluid confined in porous material is of primary interest. Already in the work of Beglov and Roux, 2 these authors computed the density profile of a simple fluid adsorbed into a crude model of zeolite solving the 3DOZ-HNC equation and using as an approximation for the fluid-fluid direct correlation function (dcf) that of the bulk fluid.…”