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

Abstract

We discuss several advances in the theory of space-resolved stress correlations and viscoelastic relaxation moduli for liquids and other amorphous systems. Our study focuses on three aspects: (i) For a given wavevector <i>q̲</i> the <i>q̲</i>-dependent longitudinal (parallel to <i>q̲</i>) and transverse (perpendicular to <i>q̲</i>) viscoelastic moduli of a fluid relax to equilibrium values in the long time limit <i>t</i> → ∞. We derive relations for the <i>q̲</i>-dependent equilibrium moduli in terms of generalized structure factors, which are valid for systems with mass polydispersity. (ii) We revisit an earlier derivation of the relation between the <i>q̲</i>-dependent tensors of viscoelastic relaxation moduli (<i>E</i>) and stress correlations (<i>C</i>), which employed the concept of the "stress noise", but was also hinged on consideration of non-stationary flows. The new derivation of the <i>C</i>-<i>E</i> relation presented here is based on a conceptually simple argument avoiding non-stationary processes. (iii) We discuss the relevance of the mass current field for the <i>q̲</i>-dependent viscoelastic relaxation moduli and the general relations between these moduli and correlation functions of the stress noise.