The low-density diffusion coefficient of soft-sphere fluids in nanopores: Accurate correlations from exact theory and criteria for applicability of the Knudsen model

Abstract

Molecular transport in confined spaces is of central importance to many traditional and emerging applications, such as gas separation and storage, catalytic and non-catalytic fluid–solid reactions and nanofluidics. The classical method to model the influence of solid–fluid particles collisions in transport comes from the early works of Knudsen and Smoluchowski, in which van-der-Walls interactions are neglected. While such assumption may be adequate for wide channels or high temperatures, it has been shown to lead to significant overprediction of the low-density diffusion coefficient in narrow pores at low and moderate temperatures, when compared to that obtained through molecular dynamics simulations. However, while molecular dynamics offers a much more accurate route for the calculation of diffusivities, its implementation and use is time-consuming and the Knudsen formulation remains preferred, particularly for interpretation of experimental permeation data. On the other hand, the oscillator model, developed in recent years in this laboratory, provides a straightforward method to estimate the low-density diffusivity, taking into account the dispersive forces exerted by the wall through rigorous statistical–mechanical considerations. The computational demand of the oscillator model is several orders of magnitude lower than that of a typical molecular dynamics run, though much greater than that of the simple Knudsen formulation. In order to facilitate its use, we provide several simple correlations for the fast estimation of the oscillator model-based diffusion coefficient for LJ fluids in simple geometries, as a function of the pore size and the LJ fluid–solid interaction parameters. Moreover, the parameter values for which the Knudsen equation supplies a reasonable estimation of the diffusion coefficient are presented for various degrees of accuracy.