Mutual diffusion in binary Ar-Kr mixtures and empirical diffusion models

Abstract

Molecular dynamics simulations of four binary Ar-Kr mixtures are used to compute self- and mutual-diffusion coefficients. Results using mean squared displacements and using velocity correlation functions are presented. The diffusivity coefficients are also presented in the time and frequency domains where a comparatively low frequency structure is evident in some simulations. The computed diffusivities are dependent on the maximum time over which the velocity correlation functions are integrated and the time at which the Einstein relationships are evaluated. This dependence explains in part the small systematic differences between our results (20--80 ps) and earlier molecular dynamics results (4 ps) in the system Ar-Kr. We compare the computed mutual diffusion coefficients to two empirical models, Darken's model and the common force model. Darken's model is consistent with our results over the entire frequency range we resolve. At frequencies lower than about 5 ${\mathrm{ps}}^{\mathrm{\ensuremath{-}}1}$ Darken's model and the common force model converge and we cannot discriminate between them. At higher frequencies the common force model prediction is significantly different from the computed mutual diffusion coefficient. Assumptions regarding the contribution of cross correlations that are implicit in the empirical models are discussed and tested against our simulation results. The net contribution of velocity cross correlations is found to be negligible, as is often assumed in deriving Darken's model, but the individual cross-correlation terms are substantial and negative---a finding contrary to common assumptions. \textcopyright{} 1996 The American Physical Society.