Space-resolved stress correlations and viscoelastic moduli for polydisperse systems: the faces of the stress noise

TL;DR

This paper advances the understanding of space-resolved viscoelasticity in polydisperse liquids by deriving new relations for stress correlations and moduli, applicable to long-time stress relaxation regimes.

Contribution

It introduces a generalized compressibility equation for polydisperse systems and a novel method to compute wavevector-dependent transverse moduli without non-stationary assumptions.

Findings

Derived a generalized compressibility equation for polydisperse liquids.

Established a new relation for wavevector-dependent transverse modulus.

Clarified the connection between stress noise and relaxation moduli.

Abstract

Several advances in the theory of space-resolved viscoelasticity of liquids and other amorphous systems are discussed in the present paper. In particular, considering long-time regimes of stress relaxation in liquids we obtain the generalized compressibility equation valid for systems with mass polydispersity, and derive a new relation allowing to calculate the wavevector-dependent equilibrium transverse modulus in terms of the generalized structure factors. Turning to the basic relations between the spatially-resolved relaxation moduli and the spatio-temporal correlation functions of the stress tensor, we provide their new derivation based on a conceptually simple argument that does not involve consideration of non-stationary processes. We also elucidate the relationship between the stress noise associated with the classical Newtonian dynamics and the reduced deviatoric stress coming from the Zwanzig-Mori projection operator formalism. The general relations between the stress noise and the tensor of relaxation moduli are discussed as well.