Stressfluctuations in glass-forming liquids

A model for the transverse shear stress in isothermal incompressible supercooled liquids was derived. The model shows damped transverse soundwaves and anisotropic long ranged long lived stress correlations in the solid-like state and exhibits anisotropic shear stress correlations in the liquid state. The conservation of mass and momentum are used within the Zwanzig-Mori projection operator formalism to decompose the shear stress tensor. The appearing memory kernel contains the full complexity of the problem. Based on the Zwanzig-Mori approach, the arising memory kernel is approximated using Maxwell's model for viscoelasticity with a single relaxation time. Within this approximation two characteristic scales could be identified the correlation length and the relaxation time. The correlation length characterizing the spatial extend of the solid-like region and grows proportionally to the relaxation time. In the elastic long time limit both the correlation length and the relaxation time diverge. The transverse shear stress tensor is the linear response to small amplitude oscillatory shear strain. The computed spectra depend on the wavevector direction even in the limit of vanishing wavevectors and show a damped resonance at the frequency of the transverse soundwave. The model can be rephrased in terms of generalized hydrodynamic equations. For overdamped dynamics, addressing colloidal dispersions, the spectra show an arresting peak in the loss modulus dependent on the wavevector direction.publishe