Emergence of Goldstone excitations in stress correlations of glass-forming colloidal dispersions

¹ University of Konstanz - D-78457 Konstanz, Germany
² University Göttingen - D-37077 Göttingen, Germany

^(a) annette@theorie.physik.uni-goettingen.de
^(b) matthias.fuchs@uni-konstanz.de

Received: 8 January 2019
Accepted: 14 March 2019

Abstract

We compute the dynamic correlations of the nonlocal shear stress at the liquid to glass transition in colloidal dispersions. Whereas Eshelby's elastic pattern is recovered independently of the dynamics, the Goldstone modes of the colloidal glass are diffusive, , because the transverse momentum is not conserved —excluding propagating transverse sound. Precursors of both, the Goldstone modes and the long-ranged, anisotropic stress correlations, can be observed in the colloidal fluid. The slow diffusive mode dominates the dynamics in the supercooled liquid for wave numbers with a correlation length which grows like the square root of the relaxation time τ. Time- and space-dependent stress correlations are anisotropic, decaying like . These results are derived within a hydrodynamic theory, generalising Maxwell‘s model to finite wave numbers, after the dynamics has been decomposed into potentially slow modes, associated with the order parameter, and fast microscopic degrees of freedom. Alternatively, hydrodynamic equations, closed by constitutive laws, can be used to predict the linear response of stress to an applied shear flow.