A phase space approach to supercooled liquids and a universal collapse of their viscosity

Abstract

A broad fundamental understanding of the mechanisms underlying the phenomenology of supercooled liquids has remained elusive, despite decades of intense exploration. When supercooled beneath its characteristic melting temperature, a liquid sees a sharp rise in its viscosity over a narrow temperature range, eventually becoming frozen on laboratory timescales. Explaining this immense increase in viscosity is one of the principle goals of condensed matter physicists. To that end, numerous theoretical frameworks have been proposed, which explain and reproduce the temperature dependence of the viscosity of supercooled liquids. Each of these frameworks appears only applicable to specific classes of glassformers, and each possesses a number of variable parameters. Here, we describe a classical framework for explaining the dynamical behavior of supercooled liquids based on statistical mechanical considerations, and possessing only a single variable parameter. This parameter varies weakly from liquid to liquid. Furthermore, as predicted by this new classical theory and its earlier quantum counterpart, we find with the aid of a small dimensionless constant that varies in size from ∼0.05 to 0.12, a universal (16 decades) collapse of the viscosity data as a function of temperature. The collapse appears in all known types of glass-forming supercooled liquids (silicates, metallic alloys, organic systems, chalcogenide, sugars, and water).