Dynamical Heterogeneity in a Highly Supercooled Liquid under a Sheared Situation

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 $ξ_4(t)$, the intensity $χ_4(t)$, and the lifetime $τ_\text{hetero}(t)$. 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 $t=τ_α$ and $τ_{\text{ngp}}$; $τ_α$ is the $α$-relaxation time, and $τ_{\text{ngp}}$ is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. We discovered that all three quantities ($ξ_4(t)$, $χ_4(t)$, and $τ_\text{hetero}(t)$) decrease as the shear rate $\dotγ$ of the steady shear flow increases. For the time interval $t=τ_α$, the scalings $ξ_4(τ_α) \sim \dotγ^{-0.08}$, $χ_4(τ_α) \sim \dotγ^{-0.26}$, and $τ_\text{hetero}(τ_α) \sim \dotγ^{-0.88}$ 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 $α$-relaxation time $τ_α$ 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 $τ_α$.