Fluids in porous media. II. A new model of templated matrices

With the help of different templates, experimental techniques allow now for synthesizing a variety of porous materials with hierarchical pore structure, i.e., pores with multiple characteristic sizes. Despite their importance and the numerous experimental investigations devoted to porous materials with hierarchical pore structure, there are still few theoretical approaches available for describing such materials. We propose a new templated matrix model here. A primitive matrix is first prepared by quenching an equilibrium one-component fluid then the templated matrix is obtained by digging some cavities in the primitive matrix. The pore-space architecture of this model is similar to that of Van Tassel's model [Phys. Rev. E 60, R25 (1999)]. We derived the diagrammatic expansions of various distribution functions and free energy as well as the Ornstein-Zernike equations. The new model we propose here possesses several attractive features. First, in some cases, the description of structure of the templated matrix can be considerably simplified which is determined exactly and entirely analytically. Moreover, many closed analytical results can be obtained for an ideal gas adsorbed in a simple case of our model while none of such results can be obtained from Van Tassel's model under the similar conditions.