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

TL;DR

This paper investigates how the self diffusion coefficients in a dense binary mixture depend on the mass ratio of the particles, revealing a generalized scaling relation and reentrant behavior near the transition.

Contribution

It introduces a mode coupling theory-based model to analyze the dependence of diffusion on mass ratio, including nonlinear effects and reentrant dynamics near the ENE transition.

Findings

A general scaling relation $D_2 \\sim D_1^a$ with a non-universal exponent a.

Reentrant behavior of diffusion coefficients near the ergodicity-nonergodicity transition.

Agreement of the theoretical results with simulation data.

Abstract

We calculate the self diffusion coefficients $D_S$ for the species $s=1,2$ of a mixture, and show that a general scaling relation $D_2{\sim}D_1^a$ with a non universal exponent $a$ holds. The generalized diffusion coefficients, dependent on the mass ratio $\kappa=m_2/m_1$ of the constituent particles of the mixture, are computed using a proper formulation of the self-consistent mode coupling theory(MCT). The present model for the dense mixture includes nonlocal and nonlinear effects within the adiabatic approximation of fast decay of momentum fluctuations compared to the density fluctuations. The dependence of the slow dynamics near the characteristic ergodicity-nonergodicity (ENE) transition of the MCT on $\kappa$ is also studied and a reentrant behavior of of $D_1$ with respect to $D_2$, in agreement with simulations is obtained.