Long-range stress correlations in viscoelastic and glass-forming fluids

Abstract

A simple and rigorous approach to obtain stress correlations in viscoelastic liquids (including supercooled liquid and equilibrium amorphous systems) is proposed. The long-range dynamical correlations of local shear stress are calculated and analyzed in 2-dimensional space. It is established how the long-range character of the stress correlations gradually emerges as the relevant dynamical correlation length l grows in time. The correlation range l is defined by momentum propagation due to acoustic waves and vorticity diffusion which are the basic mechanisms for transmission of shear stress perturbations. We obtain the general expression defining the time- and distance-dependent stress correlation tensor in terms of material functions (generalized relaxation moduli). The effect of liquid compressibility is quantitatively analyzed; it is shown to be important at large distances and/or short times. The revealed long-range stress correlation effect is shown to be dynamical in nature and unconnected with static structural correlations in liquids (correlation length ξ). Our approach is based on the assumption that ξ is small enough as reflected in weak wave-number dependencies of the generalized relaxation moduli. We provide a simple physical picture connecting the elucidated long-range fluctuation effect with anisotropic correlations of the (transient) inherent stress field, and discuss its implications.

Relaxation dynamics in supercooled oligomer liquids: From shear-stress fluctuations to shear modulus and structural correlations

“…We are thus driven to conclude that spatial correlations of local stress and of local structure (including local rigidity) in the studied amorphous systems are likely to be long-range (in addition to being persistent in time). Two main possibilities can be anticipated: (i) that the relevant structural correlation length ξ s (characterizing the amorphous inherent structure) is finite, but is larger than (or comparable with) the system size, ξ s L ∼ 20; (ii) that ξ s is practically infinite and stress correlations follow a power-law decay with the distance r. The latter scenario is in harmony with recent theoretical results revealing long-range correlations of the shear stress frozen in the inherent structure showing a universal decay law, 1/r D (here D is the space dimension) 13,36,37 . Interestingly, a large dynamical correlation length is also hinted at by a difference of the long-time behavior of the relaxation modulus G(t) for the two systems (cf.…”

“…More precisely, it is a canonical affine transformation in the phase space that must be applied at t = 0. 6,13 The relaxation function G(t) is closely related to the shear stress correlation function…”

“…The stress correlation function C(t) is connected to G(t) via the stress-fluctuation equation 6,13,14 (relating the relaxation modulus in the linear response regime with fluctuations of the shear stress):…”

Emergent solidity of amorphous materials as a consequence of mechanical self-organisation

“…The emergence of long-range stress correlations in amorphous solids has also been discussed as a consequence of the ideal liquid-to-glass transition where the relaxation time τ diverges, by mode-coupling theories 9,10,37 , mean-field replica approaches 17 and the fluctuation-dissipation theorem 38 . However, it is argued that the long-range character of stress correlations is established through momentum propagation/conservation 9,10,38 , which is therefore dynamical in nature, distinct from the above static approach for the correlations [4][5][6][7] . The relevance of these meanfield predictions in experimental glasses [10][11][12][13][14] and the relations between these dynamical approaches and the above-mentioned static ones remain to be examined.…”

Stress correlation function and linear response of Brownian particles

“…As refs. [5][6][7]29] contain the pertinent results including the overdamped limit which is considered here, this discussion shall not be repeated.…”