Modeling Self-Diffusion of Simple Fluids in Nanopores

The recent frictional model of the transport of fluid mixtures in nanopores developed in this laboratory is extended here to formulate a new theory of the self diffusion of Lennard-Jones fluids in cylindrical pores by considering the problem of diffusion of identical molecules that differ only in color. The new theory is found to predict the self-diffusivity accurately over a wide range of densities and pore sizes, extending from molecularly narrow pores to large mesopores. However, deviations from the theory appear near to the critical temperature where the correlation length of the fluid diverges and when intermolecular interactions are important in molecularly narrow pores. Under such circumstances, local averaging of the fluid-fluid density to obtain a local viscosity does not adequately capture the effects of viscous friction. A new criterion is developed for determining the significance of fluid-fluid intermolecular interactions in a nanopore by considering the ratio of oscillation times of a fluid molecule in the force field of the surrounding fluid molecules and that in the force field of the pore wall. The ratio is. shown to give good predictions of the region where intermolecular interactions are important and explains the region of deviation between theory and simulation in molecularly narrow pores.