Mechanical Responses and Stress Fluctuations of a Supercooled Liquid in a Sheared Non-Equilibrium State

TL;DR

This study uses molecular dynamics simulations to explore how supercooled liquids respond mechanically and fluctuate under steady shear flow, revealing isotropic behaviors, anisotropies, and limitations of the effective temperature concept.

Contribution

The paper introduces a simple two-mode Maxwell model capturing key non-equilibrium responses and highlights the anisotropic effects and limitations of effective temperature in sheared supercooled liquids.

Findings

Supercooled liquids show isotropic responses even under strong shear.

A two-mode Maxwell model effectively describes the storage and loss moduli.

Effective temperature varies between components, indicating oversimplification.

Abstract

A steady shear flow can drive supercooled liquids into a non-equilibrium state. Using molecular dynamics simulations under steady shear flow superimposed with oscillatory shear strain for a probe, non-equilibrium mechanical responses are studied for a model supercooled liquid composed of binary soft spheres. We found that even in the strongly sheared situation, the supercooled liquid exhibits surprisingly isotropic responses to oscillating shear strains applied in three different components of the strain tensor. Based on this isotropic feature, we successfully constructed a simple two-mode Maxwell model that can capture the key features of the storage and loss moduli, even for highly non-equilibrium state. Furthermore, we examined the correlation functions of the shear stress fluctuations, which also exhibit isotropic relaxation behaviors in the sheared non-equilibrium situation. In contrast to the isotropic features, the supercooled liquid additionally demonstrates anisotropies in both its responses and its correlations to the shear stress fluctuations. Using the constitutive equation (a two-mode Maxwell model), we demonstrated that the anisotropic responses are caused by the coupling between the oscillating strain and the driving shear flow. We measured the magnitude of this violation in terms of the effective temperature. It was demonstrated that the effective temperature is notably different between different components, which indicates that a simple scalar mapping, such as the concept of an effective temperature, oversimplifies the true nature of supercooled liquids under shear flow. An understanding of the mechanism of isotropies and anisotropies in the responses and fluctuations will lead to a better appreciation of these violations of the FDT, as well as certain consequent modifications to the concept of an effective temperature.