Model of the glass transition

Abstract

This paper examines the three well-known empiricisms that accompany the glass transition of fragile glass-forming liquids: the unusual thermodynamic behavior of supercooled liquids that is usually called the Kauzmann paradox, the temperature dependence of the relaxation time as embodied in the Vogel–Fulcher law, and the time-domain relaxation law usually known as the Kohlrausch–Williams–Watts relaxation function. Mutually consistent descriptions of all three phenomena are presented. The Kauzmann paradox can be explained by recognizing that the ground states of both the liquid and the crystal, and also the dominant excitations of these two ground states, are similar in many ways. This implies that the two phases have similar thermodynamics at low T. The Vogel–Fulcher law results from the assumption that localized regions of the liquid must be excited above a certain threshold enthalpy before they can relax; as the temperature falls, this threshold enthalpy becomes less accessible and the apparent activation enthalpy to affect relaxation increases. The resulting model is also consistent with the Montroll–Schlesinger–Bendler description of Kohlrausch–Williams–Watts relaxation, which explains the third empiricism.