(165a) A Theory of Self-Diffusion for Fluids Confined in Mesoporous Materials

The self-diffusion coefficient characterizes the random translational motion of molecules under conditions of macroscopic equilibrium. In the case of confined (inhomogeneous) fluids it is a quantity that possesses rich information regarding the local density distribution in the system. Experimental measurements of self-diffusivity are averaged over length scales that exceed the size of typical inhomogeneities. Thus it is of great interest to have an analytical theory that can predict local self-diffusivities and understand how they relate to experimentally measured self-diffusivities.

Lattice based density functional theories have been successfully used to explain the behavior of confined fluids with relatively low computational effort and these have recently been extended to the case of dynamics (P. A. Monson, J. Chem. Phys., 128, 084701 (2008)). The resulting dynamic mean field theory (DMFT) can be viewed as a mean field approximation to Kawasaki dynamics Monte Carlo simulations. From DMFT we have derived an analytical expression for the local self-diffusivity and show how it can be used to determine the overall self-diffusivity of the system. We apply the theory to some idealized pore geometries (slit pores, ink-bottles), estimating self-diffusivities for a range of activities (pressures) at a given temperature. In addition we study a slit pore with surface heterogeneities to show how contributions from high-density regions that are created by such heterogeneities affect the trend in self-diffusivities. In order to test our theory we estimate self-diffusion coefficients using Kawasaki Dynamics Monte Carlo simulations. We find that the neglect of correlations in the mean-field approximation does not alter the qualitative behavior of the trend in self-diffusivity vs. activity. These preliminary results from DMFT for self-diffusion suggest that this will be a powerful approach to understanding experimental self-diffusion data for fluids in porous materials.