(751c) Transport in Nanoporous Materials: New Models and Pitfalls in Application of Knudsen Theory

A fundamental understanding of the processes affecting fluid behavior in nanoscale confinements is crucial to numerous emerging applications in nanotechnology, materials science, membrane science, biology as well as a host of other areas. In the last two decades a vast array of new nanoporous materials such as templated periodic MCM-41 silicas, carbon nanotubes as well as various aluminophosphates and aluminosilicates have been developed, all considered to hold promise for a variety of novel applications. The infiltration of fluids into the nanopores in these materials is a common feature of most applications being investigated. For over a century the Knudsen model has been the primary tool in the chemical engineers craft for modelling the transport of fluids in porous materials used as adsorbents, catalysts and membranes. Its success has largely revolved around the correlation of the low pressure diffusivity with square root of the ratio of temperature to molecular weight, and the use of fitting parameters such as tortuosity. However, recent simulations and the availability of mesoporous and microporous materials with ideally shaped pores has raised doubts about the applicability of the Knudsen theory at industrially relevant conditions. The primary reason is the neglect of dispersive fluid solid interactions in the purely hard sphere analysis inherent to the Knudsen approach. Here we present a new statistical mechanical theory recently developed in our group, that accounts for these interactions, and demonstrate its application to a variety of literature data that have previously been (mis)interpreted using the Knudsen model. Besides applicability to mesopores, the theory provides access to the configurational regime relevant to zeolites amd micrporous carbons, hitherto empirically modelled as an activated process. We show that the diffusivity from the new approach can often be empirically correlated with the with square root of the ratio of temperature to molecular weight within limits of experimental error, which explains the apparent success of correlating data with the Knudsen model. However, the results from correlation of data with the Knudsen model are misleading and lead to unrealistically high tortuosities, often as high as 15-25, because of overestimation of the diffusivity when dispersive interactions are neglected. Such interactions reduce the travel time of molecules between diffuse reflections, thereby dissipating the momentum more rapidly and consequently reducing the diffusivity. On the other hand the new approach leads to much more realistic values of the tortuosity, in the range of 4-8. A theoretical interpretation of experimental tortuosities based on a hybrid correlated random walk-effective medium theory will be also presented, providing a comprehensive tool for transport modelling in porous materials, combining our nanopore level statistical mechanical theory with a network model. Application of the approach to actual data will be presented, including diffusion in silica particles, in a mesoporous glass as well as in a microporous DDR zeolite membrane. In the latter case the theory is shown to accurately predict the experimental variation of permeability with molecular size, including the permeability maximum due to opposing effects of molecular size on adsorption and diffusion.