A new model of templated porous materials

With the help of different templates, experimental techniques allow nowadays for synthesizing a variety of porous materials with hierarchical pore structure, i.e., pores with multiple characteristic sizes. Despite of 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 in the present work. A primitive matrix is first prepared by quenching an equilibrium one-component fluid then a 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 (Ref. [33]). One attractive feature of the proposed new model is that the description of the matrix structure can be considerably simplified in some cases. In the case of a simple model, the structure of the templated matrix can be determined exactly and entirely analytically. In more general cases, we derived the diagrammatic expansions of various distribution functions of the matrix and the corresponding Ornstein-Zernike equations.