Effect of Composition Changes on the Structural Relaxation of a Binary Mixture

TL;DR

This paper uses mode-coupling theory to analyze how mixing different-sized hard spheres affects the glass transition, revealing two distinct effects depending on size disparity, including glass stabilization and liquid plasticization.

Contribution

It provides a theoretical analysis of the impact of composition changes on the structural relaxation in binary mixtures, predicting different dynamical scenarios based on size ratios.

Findings

Small size disparity slightly extends the glass regime.

Large size disparity leads to liquid stabilization due to mixing.

Mixing decreases elastic moduli and increases Debye-Waller factors at the transition.

Abstract

Within the mode-coupling theory for idealized glass transitions, we study the evolution of structural relaxation in binary mixtures of hard spheres with size ratios $\delta$ of the two components varying between 0.5 and 1.0. We find two scenarios for the glassy dynamics. For small size disparity, the mixing yields a slight extension of the glass regime. For larger size disparity, a plasticization effect is obtained, leading to a stabilization of the liquid due to mixing. For all $\delta$, a decrease of the elastic moduli at the transition due to mixing is predicted. A stiffening of the glass structure is found as is reflected by the increase of the Debye-Waller factors at the transition points. The critical amplitudes for density fluctuations at small and intermediate wave vectors decrease upon mixing, and thus the universal formulas for the relaxation near the plateau values describe a slowing down of the dynamics upon mixing for the first step of the two-step relaxation scenario. The results explain the qualitative features of mixing effects reported by Williams and van Megen [Phys. Rev. E \textbf{64}, 041502 (2001)] for dynamical light-scattering measurements on binary mixtures of hard-sphere-like colloids with size ratio $\delta=0.6$.