Dynamic glass transition in two dimensions

Abstract

The question of 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 disks. A dynamic glass transition is found at a critical packing fraction phi(c)d=2 approximately equal 0.697 which is above phi(c)d=3 approximately equal 0.516 by about 35%. Phi(c)d scales approximately with phi(rcp)d, 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 Monte Carlo and molecular dynamics 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 disks 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.