A theory for the dynamics of glassy mixtures with particle size swaps

TL;DR

This paper develops a theoretical framework for understanding how particle size swaps influence the dynamics of glassy mixtures, revealing that swaps facilitate relaxation and shift the glass transition to higher densities.

Contribution

The paper introduces a novel theory incorporating particle size swaps into the mode-coupling framework for glassy dynamics, providing new insights into the glass transition behavior.

Findings

Particle size swaps accelerate density fluctuation relaxation.

The dynamic glass transition shifts to higher densities with increasing size ratio.

Transition line saturates at a diameter ratio of approximately 1.2.

Abstract

We present a theory for the dynamics of a binary mixture with particle size swaps. The theory is based on a factorization approximation similar to that employed in the mode-coupling theory of glassy dynamics. The theory shows that, in accordance with physical intuition, particle size swaps open up an additional channel for the relaxation of density fluctuations. Thus, allowing swaps speeds up the dynamics and moves the dynamic glass transition towards higher densities and/or lower temperatures. We calculate an approximate dynamic glass transition phase diagram for an equimolar binary hard sphere mixture. We find that in the presence of particle size swaps, with increasing ratio of the hard sphere diameters the dynamic glass transition line moves towards higher volume fractions, up to the ratio of the diameters approximately equal to 1.2, and then saturates. We comment on the implications of our findings for the theoretical description of the glass transition.