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

Abstract

Within the model of delocalized atoms, it is shown that the parameter δTg, which enters the glasstransition equation qτg = δTg and characterizes the temperature interval in which the structure of a liquid is frozen, is determined by the fluctuation volume fraction \({f_g} = {\left( {{{\Delta {V_e}} \mathord{\left/ {\vphantom {{\Delta {V_e}} V}} \right. \kern-\nulldelimiterspace} V}} \right)_{T = {T_g}}}\) frozen at the glass-transition temperature Tg and the temperature Tg itself. The parameter δTg is estimated by data on fg and Tg. The results obtained are in agreement with the values of δTg calculated by the Williams–Landel–Ferry (WLF) equation, as well as with the product qτg—the left-hand side of the glass-transition equation (q is the cooling rate of the melt, and τg is the structural relaxation time at the glass-transition temperature). Glasses of the same class with fg ≈ const exhibit a linear correlation between δTg and Tg. It is established that the currently used methods of Bartenev and Nemilov for calculating δTg 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 = ΔVe/V can be interpreted as an internal structural parameter analogous to the parameter ξ 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).