Effect of mixing and spatial dimension on the glass transition

TL;DR

This paper investigates how mixing composition and spatial dimension affect the glass transition in binary hard disc and sphere systems using mode coupling theory, deriving a new expression for transition line slopes.

Contribution

It introduces a general expression for the slope of the glass transition line and applies it to predict properties of binary mixtures efficiently.

Findings

Glass transition diagram resembles random close packing in 2D.

Mixing extends the glass regime more in 2D than in 3D.

Small size disparities stabilize the glass phase quadratically.

Abstract

We study the influence of composition changes on the glass transition of binary hard disc and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this new method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard discs strongly resembles the random close packing diagram. Compared to 3D from previous studies, the extension of the glass regime due to mixing is much more pronounced in 2D where plasticization only sets in at larger size disparities. For small size disparities we find a stabilization of the glass phase quadratic in the deviation of the size disparity from unity.