Tagged-particle dynamics in a hard-sphere system: mode-coupling theory analysis

TL;DR

This paper evaluates the accuracy of mode-coupling theory in predicting particle dynamics near the glass transition by comparing it with simulation data, identifying its strengths and limitations.

Contribution

It provides a detailed quantitative comparison between MCT predictions and simulation results for a polydisperse quasi-hard-sphere system near the glass transition, including corrections and analysis of errors.

Findings

Good agreement over a wide range of conditions after corrections.

Deviations occur at high densities and small wave vectors.

Static structure approximations significantly affect transition density predictions.

Abstract

The predictions of the mode-coupling theory of the glass transition (MCT) for the tagged-particle density-correlation functions and the mean-squared displacement curves are compared quantitatively and in detail to results from Newtonian- and Brownian-dynamics simulations of a polydisperse quasi-hard-sphere system close to the glass transition. After correcting for a 17% error in the dynamical length scale and for a smaller error in the transition density, good agreement is found over a wide range of wave numbers and up to five orders of magnitude in time. Deviations are found at the highest densities studied, and for small wave vectors and the mean-squared displacement. Possible error sources not related to MCT are discussed in detail, thereby identifying more clearly the issues arising from the MCT approximation itself. The range of applicability of MCT for the different types of short-time dynamics is established through asymptotic analyses of the relaxation curves, examining the wave-number and density-dependent characteristic parameters. Approximations made in the description of the equilibrium static structure are shown to have a remarkable effect on the predicted numerical value for the glass-transition density. Effects of small polydispersity are also investigated, and shown to be negligible.