Tests of mode-coupling theory in two dimensions

TL;DR

This study tests the predictions of Mode-Coupling Theory (MCT) on the glassy dynamics of two-dimensional binary hard disk mixtures through extensive simulations, confirming several theoretical effects and accurately determining the glass transition point.

Contribution

The paper provides a comprehensive validation of MCT predictions in two-dimensional systems and precisely locates the ideal glass transition point through simulations.

Findings

Verification of four predicted mixing effects by MCT

Observation of speed-up and slowdown in dynamics depending on size disparity

Quantitative agreement with MCT predictions for the glass transition point

Abstract

We analyze the glassy dynamics of a binary mixtures of hard disks in two dimensions. Predictions of the Mode-Coupling theory(MCT) are tested with extensive Brownian dynamics simulations. Measuring the collective particle density correlation functions in the vicinity of the glass transition we verify four predicted mixing effects. For instance, for large size disparities, adding a small amount of small particles at fixed packing fraction leads to a speed up in the long time dynamics, while at small size disparity it leads to a slowing down. Qualitative features of the non-ergodicity parameters and the $\beta$-relaxation which both depend in a non-trivial way on the mixing ratio are found in the simulated correlators. Studying one system in detail we are able to determine its ideal MCT glass transition point as $\phi^c = 0.7948$ and test MCT predictions quantitatively.