Scaling behavior of self-diffusion coefficients: Dependence on the mass ratio of a binary mixture

Abstract

In the present work we demonstrate how the diffusion constants D S for a tagged particle of species s ( = 1 , 2 ) of a binary mixture depend on the mass ratio κ = m 2 / m 1 of the two constituents. This dependence has also been reported earlier from simulations of a mixture. We use here a proper formulation of the self-consistent mode-coupling theory (MCT) of a two-component system. The effects of nonlocal and nonlinear coupling of slowly decaying hydrodynamic fluctuations on the long-time dynamics of a dense mixture is calculated here. The MCT memory functions are estimated here in the adiabatic approximation which assumes for the glassy state fast decay of momentum fluctuations compared to that of the number density. Plots D 1 and D 2 obtained from evaluation of the self-consistent MCT formulas, shows that for nearly equal-sized particles, the two self-diffusion coefficients are related as D 1 ∼ D a 2 with a nonuniversal exponent a and this relation holds over a wide range of κ values. The simple MCT used here predicts an ideal ergodic-nonergodic transition from liquid to glassy state for critical packings { η c 2 , η c 1 } of the two species. For high packing of one species η 2 , at which the mixture is already in a nonergodic state, transition to an ergodic state occurs at a small η c 1 and a reenetry into the nonergodic phase can occur again at an even larger value of η c 1 , while η 2 remains same as before.