Mesoporous membranes with pore sizes in the range 2-50 nm provide an energy efficient alternative for separation of mixtures such as CO2 from stack effluents and volatile organic compounds (VOC) from air. Transport mechanisms such as capillary condensation, Knudsen diffusion and surface adsorption help in enrichment of a more condensable component based on the bulk mixture thermodynamics, surface chemistry and geometry of the mesopores. Despite the progress in synthesis techniques, design of better mesoporous materials for targeted separations is still a challenge due to the absence of clear design rules. Modeling techniques can be used to quantify the relevant transport processes and determine the correlations between mesopore properties and separation performance. Continuum modeling requires predetermined transport models while molecular simulations are computationally too intensive for realistic membrane processes.
Dynamic mean field theory (DMFT), a coarse-grained lattice based theory, was employed to model nonequilibrium transport in mesoporous membranes. DMFT was used to model permporometry, an experimental technique for pore size distribution measurement. It involves light gas permeation in presence of condensable vapor under near equilibrium conditions. Detailed study of transport revealed a maximum of light gas flux in the layer adjacent to the strongly adsorbed surface layer of heavy component. A highly nonequilibrium process of VOC recovery, which involves passing a mixture of light gas and condensable vapor through the mesopores under significant pressure gradient, was also modeled. Nonequilibrium steady states with capillary condensation confined to high pressure feed/inlet side (partial capillary condensation) of the mesopores were found. The conditions required for existence of these states were then investigated in single component systems. Equilibrium adsorption/desorption behavior of silica monoliths with disordered porous structure was studied using mean field theory. Dual control volume grand canonical molecular dynamics (DCV-GCMD), a combination of grand canonical Monte Carlo and molecular dynamics, was used to evaluate DMFT and study single component systems under confinement. Investigation of experimentally predicted phenomenon of enhanced flux of pure component in the presence of condensed fluid in the pore with DCV-GCMD revealed an increased surface density in the vapor region of pores with partial capillary condensation.