Thermodynamic and kinetic origins of the vitreous transition

A unique vitreous transition temperature T* g has been recently determined by an extrapolation of the fully-relaxed enthalpy H r down to zero as a function of temperature. This exothermic heat is linearly decreasing with temperature and the slope dH r /dT is equal to the specific heat jump from the vitreous to the undercooled state and to the specific heat difference between crystal and melt because a freezing of atom freedom degrees in the liquid state is associated with the vitreous transition at T* g. It has been also shown that T*g is a material constant which is equal to a crystal homogeneous nucleation temperature in glass-forming melts. A volume energy saving  v has been added to the classical Gibbs free energy change H m /V m for a crystal formation in a melt where H m is the fusion heat, V m the molar volume, = (TT m)/T m and T m the melting temperature. We show here that  v is equal to the Laplace pressure change (p-p 0) as compared to the classical pressure p 0 = H m /V m acting on crystals imbedded in a melt. The model is able to strictly predict the precise values of the Vogel-Fulcher-Tamman temperature, the energy saving  v, the Laplace pressure p and the ratio T* g /T 0g of fragile liquids when the equilibrium transition temperature T* g is known.