Investigating the validity of the Bosanquet equation for predicting the self-diffusivities of fluids inside nanotubes using equilibrium molecular dynamics simulations

Abstract

The self-diffusion of fluids in nanotubes generally consists of both molecule–molecule and molecule–wall interactions, which can be quantitatively described by the Knudsen mechanism and the molecular mechanism, respectively. Combining these two effects, the Bosanquet equation is generally used to predict the self-diffusivities of molecules in one-dimensional nanopores. In this work, equilibrium molecular dynamics simulations were employed to investigate the validity of the equation in predicting the self-diffusivities of fluids inside carbon, boron nitride, and silicon carbide nanotubes with diameters from ∼1.0 to 4.3 nm. Our results indicate that although the Bosanquet equation can predict the self-diffusivities of H2, Ar, CH4, CO2, C2H6, and C3H8 in carbon nanotubes in the same order of magnitude, the accuracy of these predictions is generally rather poor. At high and moderate loadings, the large deviation mainly results from the limited accuracy of the simplistic free path model, which tends to neglect the intermolecular forces of fluid molecules. However, at low loadings, the failure of the Bosanquet equation can be traced to the failure of the Knudsen model, which largely underestimates the diffusivity in nanotubes due to the smoothness of the tube wall. Furthermore, the Bosanquet equation fails to predict the self-diffusivities of H2O in confinement since the presence of hydrogen bonding violates the mean free path theory. It is suggested that further modification of this extrapolation should take into account the intermolecular forces of fluid molecules as well as the smoothness of the tube wall.