Phenomenological model of supercooled liquid as a possible resolution of the Kauzmann paradox

Abstract

The diverging relaxation time in approaching hypothetical ideal glass transition is a subject of hot debate. In the current paper we demonstrate, how diverging relaxation time and turning excess entropy to zero (which is an essence of Kauzmann's paradox) can be avoided, using as an example the model molecular glassformer, propylene carbonate. For this purpose we compare its thermodynamic and dielectric relaxation properties, both known from the literature. The agreement between two sets of data can be achieved, if we suppose, that enthalpy of supercooled liquid propylene carbonate is governed by activation law, and relaxation time follows double exponential law. We propose the generalized Adam-Gibbs law to reconcile this two dependencies, and qualitatively discuss its implications.