Thermodynamics and kinetics of the glass transition: A generic geometric approach

A generic phenomenological theory of the glass transition is developed in t he framework of a quasilinear formulation of the thermodynamics of irrevers ible processes. Starting from one of the basic principles of this science i n its approximate form given by de Donder's equation, after a change of var iables the temperature dependence of the structural parameter xi(T), the th ermodynamic potentials Delta (G) over tilde(T), the thermodynamic functions and the time of molecular relaxation tau of vitrifying systems is construc ted. In doing so, a new effect in the Delta (G) over tilde(T) course is obs erved. The analysis of the higher derivatives of the thermodynamic potentia l, and especially the nullification of the second derivative of the configu rational specific heats Delta (C) over tilde(p)(T) of the vitrifying liquid defines glass transition temperature (T) over tilde(g) and leads directly to the basic dependence of glass transition kinetics: the Frenkel-Kobeko-Re iner equation. The conditions guaranteeing the fulfillment of this equation specify the temperature dependence of the activation energy U(T,<(xi)over tilde>) for viscous flow and give a natural differentiation of glass former s into fragile and strong liquids. The effect of thermal prehistory on the temperature dependence of both thermodynamic functions and kinetic coeffici ents is established by an appropriate separation of de Donder's equation. ( C) 2000 American Institute of Physics. [S0021-9606(00)51024-1].