Dynamical heterogeneity in a highly supercooled liquid under a sheared situation

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 ξ₄(t), the intensity χ₄(t), and the lifetime τ_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_ngp; τ_α is the α-relaxation time, and τ_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 (ξ₄(t), χ₄(t), and τ_hetero(t)) decrease as the shear rate dot{γ } of the steady shear flow increases. For the time interval t = τ_α, the scalings ξ _4(τ _α ) ∼ dot{γ }^{-0.08}, χ _4(τ _α ) ∼ dot{γ }^{-0.26}, and τ _hetero(τ _α ) ∼ dot{γ }^{-0.88} were obtained. The steady shear flow suppresses the heterogeneous structure as well as the lifetime of the dynamical heterogeneity. In addition, we demonstrated that all three quantities in the sheared non-equilibrium state can be mapped onto those in the equilibrium state through the α-relaxation time τ_α. This finding means that the same relation between τ_α and three quantities holds in both the equilibrium state and the sheared non-equilibrium state and therefore proposes that the dynamical heterogeneity can play a similar role in the drastic change of τ_α due to not only the temperature but also the shear rate.