Dynamical heterogeneity in a highly supercooled liquid: Consistent calculations of correlation length, intensity, and lifetime

TL;DR

This study uses molecular dynamics simulations to analyze dynamical heterogeneity in supercooled liquids, revealing that lifetime increases dramatically with decreasing temperature, while correlation length and intensity grow slowly or plateau.

Contribution

It provides a consistent evaluation of correlation length, intensity, and lifetime from a single order parameter in supercooled liquids, extending previous work on heterogeneity lifetime.

Findings

Lifetime grows dramatically as temperature decreases.

Correlation length and intensity increase slowly or plateau.

Heterogeneous dynamics migrate via diffusion at large time intervals.

Abstract

We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length $\xi_4$, intensity $\chi_4$, and lifetime $\tau_{\text{hetero}}$. We evaluated all three quantities consistently from a single order parameter. In a previous study (H. Mizuno and R. Yamamoto, Phys. Rev. E {\bf 82}, 030501(R) (2010)), we examined the lifetime $\tau_{\text{hetero}}(t)$ in two time intervals $t=\tau_\alpha$ and $\tau_{\text{ngp}}$, where $\tau_\alpha$ is the $\alpha$-relaxation time and $\tau_{\text{ngp}}$ is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime $\tau_{\text{hetero}}(t)$, we evaluated the correlation length $\xi_4(t)$ and the intensity $\chi_4(t)$ from the same order parameter used for the lifetime $\tau_{\text{hetero}}(t)$. We found that as the temperature decreases, the lifetime $\tau_{\text{hetero}}(t)$ grows dramatically, whereas the correlation length $\xi_4(t)$ and the intensity $\chi_4(t)$ increase slowly compared to $\tau_{\text{hetero}}(t)$ or plateaus. Furthermore, we investigated the lifetime $\tau_{\text{hetero}}(t)$ in more detail. We examined the time-interval dependence of the lifetime $\tau_{\text{hetero}}(t)$ and found that as the time interval $t$ increases, $\tau_{\text{hetero}}(t)$ monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which $\tau_{\text{hetero}}(t)$ plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.