(496f) Effective Medium Theory-Based Modelling of Transport in Disordered Nanoporous Membranes

A fundamental understanding of the processes affecting fluid transport in nanoscale confinements is crucial to numerous emerging applications in nanotechnology, including those involving membrane separations. The Knudsen model has been our primary tool for modelling the transport of fluids in confinement; however, it has not been unequivocally validated for nanoscale pores due to the inability to make measurements at this scale. Its weakness is generally masked by the use of correlations which invoke tortuosity as a fitting parameter, while also overlooking complexities associated with structural heterogeneity. Indeed, theoretical and simulation-based results, as well as recent literature experimental data, show the Knudsen model to substantially overpredict the diffusivity in nanoscale pores.

In modelling transport in membranes it is common to consider only a single representative pore size in the support and in the membrane layers, thereby overlooking the role of structural heterogeneity in these layers. Experiments have been performed in our laboratory in which the transport in the support and the composite membrane are independently investigated for several gases, and it is shown that the use of a single representative pore size in the support is misleading. This leads to tortuosities that are dependent on the gas, and vary with temperature and operating conditions. A new effective medium theory (EMT) approach for modelling the transport in the support and membrane layers is developed, which utilizes the entire pore size distribution (PSD), and shown to adequately interpret our experimental data. The technique is free from the fitting parameter of tortuosity, but which can now be theoretically predicted, and demonstrates the importance of considering the entire PSD and network effects in the pore structure of the support. Our EMT results show that for macroporous networks different tortuosities are obtained in the Knudsen and viscous regimes, due to the different dependence on pore size. It is also found that the Knudsen model fails when applied to the mesoporous membrane layer when the modal pore diameter is below about 10 nm. On the other hand our novel transport theory considering the fluid-solid interaction and the adsorption field in the pore proves successful, when combined with the effective medium theory for such layers.

Our results clearly demonstrate that it is critical to independently investigate the resistances of the various layers, carefully decoupling these, for interpreting membrane transport data. Correct interpretation, free from artefacts, is only obtained when the full PSD and network connectivity effects are separately considered in each layer, such as by EMT, and when the effect of fluid-solid interaction on transport is considered in nanoscale pores smaller than about 10 nm in diameter.