Thermodynamic Origin of the Vitreous Transition

The vitreous transition is characterized by a freezing of atomic degrees of freedom at a temperature T_g depending on the heating and cooling rates. A kinetic origin is generally attributed to this phenomenon instead of a thermodynamic one which we develop here. Completed homogeneous nucleation laws reflecting the energy saving due to Fermi energy equalization of nascent crystals and their melt are used. They are applied to bulk metallic glasses and extended to inorganic glasses and polymers. A transition T*_g among various T_g corresponds to a crystal homogeneous nucleation temperature, leading to a preliminary formation of a cluster distribution during the relaxation time preceding the long steady-state nucleation time of crystals in small samples. The thermally-activated energy barrier ΔG*_2ls/k_BT at T*_g for homogeneous nucleation is nearly the same in all glass-forming melts and determined by similar values of viscosity and a thermally-activated diffusion barrier from melt to cluster. The glass transition T*_g is a material constant and a linear function of the energy saving associated with charge transfers from nascent clusters to the melt. The vitreous transition and the melting temperatures alone are used to predict the free-volume disappearance temperature equal to the Vogel-Fulcher-Tammann temperature of fragile glass-forming melts, in agreement with many viscosity measurements. The reversible thermodynamic vitreous transition is determined by the disappearance temperature T*_g of the fully-relaxed enthalpy H_r that is not time dependent; the observed specific heat jump at T*_g is equal to the proportionality coefficient of H_r with (T*_g - T_a) for T ≤ T*_g as expected from the enthalpy excess stored by a quenched undercooled melt at the annealing temperature T_a and relaxed towards an equilibrium vitreous state. However, the heat flux measurements found in literature over the last 50 years only gave an out-of-equilibrium T_g since the enthalpy is continuous at T*_g without visible heat jump.