MODEL OF THE GLASS-TRANSITION

This paper examines the three well-known empiricisms that accompany th e glass transition of fragile glass-forming liquids: the unusual therm odynamic behavior of supercooled liquids that is usually called the Ka uzmann paradox, the temperature dependence of the relaxation time as e mbodied in the Vogel-Fulcher law, and the time-domain relaxation law u sually known as the Kohlrausch-Williams-Watts relaxation function. Mut ually consistent descriptions of all three phenomena are presented. Th e Kauzmann paradox can be explained by recognizing that the ground sta tes of both the liquid and the crystal, and also the dominant excitati ons of these two ground states, are similar in many ways. This implies that the two phases have similar thermodynamics at low T. The Vogel-F ulcher law results from the assumption that localized regions of the l iquid must be excited above a certain threshold enthalpy before they c an relax; as the temperature falls, this threshold enthalpy becomes le ss accessible and the apparent activation enthalpy to affect relaxatio n increases. The resulting model is also consistent with the Montroll- Schlesinger-Bendler description of Kohlrausch-Williams-Watts relaxatio n, which explains the third empiricism. (C) 1995 American Institute of Physics.