Fluids Confined In Porous Materials

Nowadays porous materials play an important role in technological advances related to gas storage, separation, chemical sensor, molecular sieve, catalyst, purification and electric devices etc. due to their huge internal surface area and ultrafine pore size, and porous materials with different structures (characterized by porosity and pore size) could be applied in different fields, a thorough understanding of the structure of such materials and the behavior of substances confined in them is very helpful for designing porous materials endowed with specific properties.To study the fluids confined in the random porous materials, to our knowledge there are two physically important models for porous materials in the theoretical study until now. One is Madden-Glandt model and the other is Van Tassel's template model. Although the pioneering model proposed by Madden and Glandt accounts for some basic characters of porous materials, e.g., pores connectivity, pore-size dispersion, disordered matrix structure [W. G. Madden and E. D. Glandt, J. Stat. Phys. 51, 537 (1988)], the morphology of the pore space in this model does not always mimic closely that of many real porous materials. Numerically reconstructed images from experimental data show that the pore space of many porous materials is sponge-like. Despite the abundance of such materials, simple models which allow for a theoretical description of these materials are still lacking. Here, we propose a hard sponge model which is made by digging spherical cavities in a solid continuum and give the theoretical description for simple fluids confined in such sponge-like porous materials with integral equation method.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 of their importance and the numerous experimental investigations devoted to porous materials with hierarchical pore structure, there is Van Tassel's template model available for describing such materials [P. R. van Tassel, Phys. Rev. E 60, R25 (1999)]. 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. 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.We also present a more general model for describing the adsorption of a fluid in a sponge-like porous material. Our hard sponge model is built by digging spherical cavities in a continuum. In contrast to the hard-sponge model, the continuum in the general model, namely soft-sponge model, is permeable to fluid particles. The soft-sponge model can also be considered as a simplified model of our new templated matrices (for instance, the size of matrix particle goes to infinitesimal while the density goes to infinite). The permeable continuum gives a simplified description of the primitive matrix without structural details. The pore space created by the template is described explicitly by the cavities.We present all distributions of fluids confined in such different kinds of porous materials, and give the integral equations with diagrammatic expansion method, some thermodynamical properties are also derived for fluids confined in these porous materials.