Emergence of long-ranged stress correlations at the liquid to glass transition

TL;DR

This paper develops a first-principles theory explaining how long-range stress correlations emerge at the liquid to glass transition, linking microscopic dynamics to continuum elasticity and generalizing the Maxwell model.

Contribution

It introduces a first-principles theory for non-local shear stress correlations at the liquid-glass transition, highlighting the coupling to transverse momentum and proposing a generalized Maxwell model.

Findings

Long-ranged stress correlations emerge at the glass transition.

A generalized Maxwell model captures divergence of correlation length.

The theory connects stress correlations to hydrodynamic and elasto-plastic models.

Abstract

A theory for the non-local shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence of long-ranged stress correlations in glass, as expected from classical continuum elasticity. The long-ranged stress correlations can be traced to the coupling of shear stress to transverse momentum, which is ignored in the classic Maxwell model. To rescue this widely used model, we suggest a generalization in terms of a single relaxation time $\tau$ for the fast degrees of freedom only. This generalized Maxwell model implies a divergent correlation length $\xi\propto\tau$ as well as dynamic critical scaling and correctly accounts for the far-field stress correlations. It can be rephrased in terms of generalized hydrodynamic equations, which naturally couple stress and momentum and furthermore allow to connect to fluidity and elasto-plastic models.