On the nature of the liquid-to-glass transition equation

Within the model of delocalized atoms, it is shown that the parameter delta T (g) , which enters the glasstransition equation q tau (g) = delta T (g) and characterizes the temperature interval in which the structure of a liquid is frozen, is determined by the fluctuation volume fraction frozen at the glass-transition temperature T (g) and the temperature T (g) itself. The parameter delta T (g) is estimated by data on f (g) and T (g) . The results obtained are in agreement with the values of delta T (g) calculated by the Williams-Landel-Ferry (WLF) equation, as well as with the product q tau (g) -the left-hand side of the glass-transition equation (q is the cooling rate of the melt, and tau (g) is the structural relaxation time at the glass-transition temperature). Glasses of the same class with f (g) ae const exhibit a linear correlation between delta T (g) and T (g) . It is established that the currently used methods of Bartenev and Nemilov for calculating delta T (g) yield overestimated values, which is associated with the assumption, made during deriving the calculation formulas, that the activation energy of the glass-transition process is constant. A generalized Bartenev equation is derived for the dependence of the glass-transition temperature on the cooling rate of the melt with regard to the temperature dependence of the activation energy of the glasstransition process. A modified version of the kinetic glass-transition criterion is proposed. A conception is developed that the fluctuation volume fraction f = Delta V (e) /V can be interpreted as an internal structural parameter analogous to the parameter xi in the Mandelstam-Leontovich theory, and a conjecture is put forward that the delocalization of an active atom-its critical displacement from the equilibrium position-can be considered as one of possible variants of excitation of a particle in the Vol'kenshtein-Ptitsyn theory. The experimental data used in the study refer to a constant cooling rate of q = 0.05 K/s (3 K/min).