Modeling Pure Gas Permeation in Nanoporous Materials and Membranes

The low-pressure transport of simple fluids in nanopores and in disordered nanoporous networks is analyzed, using a recent oscillator model theory from the author's laboratory, considering the trajectories of molecules moving in the potential energy field of the fluid pore wall interaction. The scaling behavior of the single-pore theory is discussed, and it is shown that the Knudsen model provides an upper bound to the diffusivity scaled with the pore radius. The single-pore theory is shown to apply well to ordered materials and successfully interprets recent literature data on the variation of permeability with diffusant molecular size for a DDR zeolite membrane. A peak in permeability is seen at a pore-size-dependent molecular size because of the opposing effects of equilibrium and transport. Application to disordered pore networks is also presented on the basis of a hybrid correlated random walk effective medium theory imbedding the oscillator model at the single-pore level, and a rigorous expression for the tortuosity is derived from the theory. A rich variety of behavior is predicted for the tortuosity, which can increase or decrease with increasing extent of pore size nonuniformity as well as with changes in temperature because the diffusing species preferentially flows through more conducting pores. Weakly adsorbing gases such as helium are seen to have a higher tortuosity than more strongly adsorbing ones. The predicted values of tortuosity are shown to be in line with those obtained from the interpretation of recent experimental mesoporous membrane transport data and are in the range of 5-10 whereas those extracted using the Knudsen model are unrealistically high, in the range of 10-20.