A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system

TL;DR

This study tests the mode-coupling theory of the ideal glass transition using molecular dynamics simulations of a binary Lennard-Jones system, finding that the theory accurately predicts many features but requires some modifications for better agreement.

Contribution

It provides a quantitative comparison between mode-coupling theory predictions and simulation results, highlighting areas of agreement and proposing modifications to improve the theory.

Findings

MCT accurately estimates the critical coupling constant.

MCT predicts the wave-vector dependence of nonergodicity parameters well.

Certain modifications to MCT can improve its agreement with simulations.

Abstract

Using a molecular dynamics computer simulation we determine the temperature dependence of the partial structure factors for a binary Lennard-Jones system. These structure factors are used as input data to solve numerically the wave-vector dependent mode-coupling equations in the long time limit. Using the so determined solutions, we compare the predictions of mode-coupling theory (MCT) with the results of a previously done molecular dynamics computer simulation [Phys. Rev. E 51, 4626 (1995), ibid. 52, 4134 (1995)]. From this comparison we conclude that MCT gives a fair estimate of the critical coupling constant, a good estimate of the exponent parameter, predicts the wave-vector dependence of the various nonergodicity parameters very well, except for very large wave-vectors, and gives also a very good description of the space dependence of the various critical amplitudes. In an attempt to correct for some of the remaining discrepancies between the theory and the results of the simulation, we investigate two small (ad hoc) modifications of the theory. We find that one modification gives a worse agreement between theory and simulation, whereas the second one leads to an improved agreement.