Statistical Mechanical Models of Adsorption and Diffusion of Fluids in Crystalline Nanoporous Materials

Statistical mechanical analytical theories are developed to model adsorption and diffusion of single component and binary fluids in crystalline nanoporous materials. The theory provides insight into the molecular level mechanisms governing the behavior of adsorbed molecules. The theory predicts diffusivities, adsorption isotherms, and heats of adsorption as functions of temperature, pressure, and composition. Molecular dynamics simulations have identified localized adsorption sites within the adsorbent lattice. In this work, a lattice model of adsorption is developed using an extension of the Quasi-Chemical Approximation Theory. The theory demonstrates that competing entropic and energetic effects dictate the placement of molecules within the lattice sites. The lattice theory is completely general and predictive in nature, and requires very few parameters to characterize the system. A lattice model of diffusion is developed. The theory yields a self-diffusion coefficient, which is a function of (i) temperature, (ii) adsorbate density, (iii) adsorbate size, (iv) the adsorbate-adsorbate energetic interaction, and (v) the adsorbate-pore energetic interaction. The theory incorporates no fitting parameters and is generalizable to nanoporous materials with three-dimensional porous networks (e.g. Zeolite Y) and one-dimensional porous networks (e.g. AlPO4-5). The analytical theory is tested with molecular dynamics simulations. Comparisons are presented between the results predicted by the theory and simulations. The agreements and discrepancies between the two approaches are discussed. The theory requires only a minute on a desktop PC to generate the results as against hours of parallel supercomputer time required by the simulations. This thesis presents an analytical molecular level theory that can be integrated into macroscopic process level simulators to (i) investigate new adsorbents, (ii) generate thermodynamic properties and transport properties in the adsorbed phase, and (iii) establish the principles of adsorption and diffusion in the macroscopic level using fundamentals of molecular physics and statistical mechanics