Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture

TL;DR

This study investigates the growth and behavior of a dynamic length scale in a glass-forming binary hard-sphere mixture, revealing a logarithmic growth pattern and correlations with relaxation times and diffusion, relevant to glass transition theories.

Contribution

It introduces a new method to analyze dynamic susceptibility and correlation length, demonstrating their growth patterns and relationships with relaxation times in glass-forming systems.

Findings

Dynamic correlation length follows xi(t) ~ ln(t) between beta and alpha relaxation times.

A correlation tau_alpha ~ exp[xi(tau_alpha)] is confirmed, linking relaxation time and length scale.

Diffusion coefficient D correlates with xi(tau_alpha) as D ~ exp[xi(tau_alpha)^0.6].

Abstract

We examine a length scale that characterizes the spatial extent of heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the mode-coupling volume fraction phi_c. First, we characterize the system's dynamics. Then, we utilize a new method [Phys. Rev. Lett. 105, 217801 (2010)] to extract and analyze the ensemble independent dynamic susceptibility chi_4(t) and the dynamic correlation length xi(t) for a range of times between the beta and alpha relaxation times. We find that in this time range the dynamic correlation length follows a volume fraction independent curve xi(t) ~ ln(t). For longer times, xi(t) departs from this curve and remains constant up to the largest time at which we can determine the length accurately. In addition to the previously established correlation tau_alpha ~ exp[xi(tau_alpha)] between the alpha relaxation time, tau_alpha, and the dynamic correlation length at this time, xi(tau_alpha), we also find a similar correlation for the diffusion coefficient D ~ exp[xi(tau_alpha)^theta] with theta approximately 0.6. We discuss the relevance of these findings for different theories of the glass transition.