A model for viscous liquid dynamics
Jeppe C. Dyre,
Roskilde University, Denmark
Mon, Nov. 20th 2006, 14:15
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
Glass-formation is a general property of liquids, an unavoidable process if the liquid is cooled fast enough to avoid crystallization. We first give an overview of the physical properties of highly viscous liquids, emphasizing the universal features. The most common phenomenological models are then briefly reviewed. The main focus of the talk is on a description of highly viscous liquids based on a standard time-dependent Ginzburg-Landau equation for the density dynamics, supplemented by the assumption of long-wavelength dominance of the dynamics [1]. The density field is described as a non- conserved field, a feature which reflects the "solidity" of highly viscous liquids - the property that they are more like solids that flow, than like ordinary, less-viscous liquids. The long-wavelength dominance assumption implies that one may assume an ultralocal Hamiltonian, thus simplifying the model quite a lot. We finally show how the case with just a third-order term is able to reproduce the (conjectured) generic property of viscous liquids that the high-frequency decay of the alpha (main) relaxation process varies with frequency as $\omega^{-1/2}$ [2]. Basically, this comes from a "long-time-tail mechanism, working at a range of short times." Refs: 1. J. C. Dyre, Europhys. Lett. 71, 646 (2005); Phys. Rev. E 74, 021502 (2006). 2. N. B. Olsen et al, Phys. Rev. Lett. 86, 1271 (2001).