Dynamic Glass Transition in Two Dimensions

TL;DR

This paper investigates the existence and characteristics of a structural glass transition in two-dimensional systems using mode coupling theory, revealing a transition at a specific packing fraction and comparing results with simulations and experiments.

Contribution

The study explicitly derives the d-dependence of the mode coupling memory functional and applies it to two dimensions, providing numerical solutions and comparing with simulations and experiments.

Findings

A dynamic glass transition occurs at a critical packing fraction of 0.697 in 2D.

The critical packing fraction scales with random close packing values across dimensions.

MCT results align qualitatively with simulation and experimental data.

Abstract

The question about the existence of a structural glass transition in two dimensions is studied using mode coupling theory (MCT). We determine the explicit d-dependence of the memory functional of mode coupling for one-component systems. Applied to two dimensions we solve the MCT equations numerically for monodisperse hard discs. A dynamic glass transition is found at a critical packing fraction phi_c^{d=2} = 0.697 which is above phi_c^{d=3} = 0.516 by about 35%. phi^d_c scales approximately with phi^d_{\rm rcp} the value for random close packing, at least for d=2, 3. Quantities characterizing the local, cooperative 'cage motion' do not differ much for d=2 and d=3, and we e.g. find the Lindemann criterion for the localization length at the glass transition. The final relaxation obeys the superposition principle, collapsing remarkably well onto a Kohlrausch law. The d=2 MCT results are in qualitative agreement with existing results from MC and MD simulations. The mean squared displacements measured experimentally for a quasi-two-dimensional binary system of dipolar hard spheres can be described satisfactorily by MCT for monodisperse hard discs over four decades in time provided the experimental control parameter Gamma (which measures the strength of dipolar interactions) and the packing fraction phi are properly related to each other.