Dynamical Heterogeneity in a Highly Supercooled Liquid under a Sheared Situation

TL;DR

This study uses molecular dynamics simulations to analyze how steady shear flow affects dynamical heterogeneity in supercooled liquids, revealing that shear suppresses heterogeneity and that certain properties scale with shear rate.

Contribution

It extends the understanding of dynamical heterogeneity by quantifying its behavior under shear using four-point correlation functions and identifying scaling laws.

Findings

All three quantities decrease with increasing shear rate.

Scaling laws: $\xi_4 o ext{shear rate}^{-0.08}$, $\chi_4 o ext{shear rate}^{-0.26}$, $ au_ ext{hetero} o ext{shear rate}^{-0.88}$.

Heterogeneity properties at $ au_ ext{alpha}$ scale similarly to equilibrium.

Abstract

In the present study, we performed molecular-dynamics simulations and investigated dynamical heterogeneity in a supercooled liquid under a steady shear flow. Dynamical heterogeneity can be characterized by three quantities: the correlation length $\xi_4(t)$, the intensity $\chi_4(t)$, and the lifetime $\tau_\text{hetero}(t)$. We quantified all three quantities by means of the correlation functions of the particle dynamics, i.e., the four-point correlation functions, which are extended to the sheared condition. Here, to define the local dynamics, we used two time intervals $t=\tau_\alpha$ and $\tau_{\text{ngp}}$; $\tau_\alpha$ 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. We discovered that all three quantities ($\xi_4(t)$, $\chi_4(t)$, and $\tau_\text{hetero}(t)$) decrease as the shear rate $\dot{\gamma}$ of the steady shear flow increases. For the time interval $t=\tau_\alpha$, the scalings $\xi_4(\tau_\alpha) \sim \dot{\gamma}^{-0.08}$, $\chi_4(\tau_\alpha) \sim \dot{\gamma}^{-0.26}$, and $\tau_\text{hetero}(\tau_\alpha) \sim \dot{\gamma}^{-0.88}$ were obtained. The steady shear flow suppresses the heterogeneous structure as well as the lifetime of the dynamical heterogeneity. In addition, our results demonstrated that the $\alpha$-relaxation time $\tau_\alpha$ dependences of three quantities coincide with those at equilibrium. This means that all three quantities of the dynamical heterogeneity can be mapped onto those in the equilibrium state through $\tau_\alpha$.