Theory and simulation of adsorption in a templated porous material: Hard sphere systems

Abstract

An emerging strategy for controlling porosity in disordered materials is to employ a removable template during synthesis. We present here a theoretical description of adsorption in a templated porous material modeled as a collection of particles formed by an equilibrium quench of a binary mixture of matrix and template particles and subsequent removal of the template component. We show, using the replica method, that an adsorbed phase in the templated material is just the s=0 limit of a special s+2 component replica system. We present a set of Ornstein–Zernike equations relating the correlation functions of the matrix, template, and adsorbate components, solve these equations for the case of hard sphere interactions within the Percus–Yevick closure, and evaluate the system thermodynamics via the compressibility route. We also present a grand canonical Monte Carlo simulation of this model system and find good agreement between theory and simulation. We show that for systems of constant matrix+template volume fraction, templating always enhances adsorption and this enhancement is most pronounced when the template/matrix ratio is low and/or the template size is small.

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

“…It can be easily checked that equation (42) gives the same result as equation (37). The direct fluid-fluid correlation function is given by…”

“…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.…”

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

“…Now, with the purpose of providing a sensible approximation for the fluid-fluid direct correlation under confinement required within the formalism, we have resorted to a ROZ equation with an HNC closure for a templated matrix 5,16 (ROZ-HNC). This approach furnishes fluid-fluid correlations averaged over matrix disorder, and these will be seen to represent a better approximation for our adsorbed fluid than the corresponding bulk counterparts.…”

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

“…Thereafter, numerous studies were carried out exploring the replica OZ approach for both fluid and matrix represented with atomic liquid models [10][11][12][13][14][15][16][17][18][19][20][21][22][23] (see also recent reviews in [29,30]). In particular, the questions of the thermodynamics of a quenched-annealed system were thoroughly addressed [11][12][13][14].…”