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

An emerging strategy for controlling porosity in disordered materials is to employ a removable template during synthesis. We present here a theoretica l description of adsorption in a templated porous material modeled as a col lection of particles formed by an equilibrium quench of a binary mixture of matrix and template particles and subsequent removal of the template compo nent. We show, using the replica method, that an adsorbed phase in the temp lated 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 correl ation functions of the matrix, template, and adsorbate components, solve th ese equations for the case of hard sphere interactions within the Percus-Ye vick closure, and evaluate the system thermodynamics via the compressibilit y route. We also present a grand canonical Monte Carlo simulation of this m odel system and find good agreement between theory and simulation. We show that for systems of constant matrix+template volume fraction, templating al ways enhances adsorption and this enhancement is most pronounced when the t emplate/matrix ratio is low and/or the template size is small. (C) 2000 Ame rican Institute of Physics. [S0021-9606(00)70405-3].