On relaxation nature of glass transition in amorphous materials

Abstract

A short review on relaxation theories of glass transition is presented. The main attention is paid to modern aspects of the glass transition equation qτg = C, suggested by Bartenev in 1951 (q – cooling rate of the melt, τg – structural relaxation time at the glass transition temperature Tg). This equation represents a criterion of structural relaxation at transition from liquid to glass at T = Tg (analogous to the condition of mechanical relaxation ωτ = 1, where the maximum of mechanical loss is observed). The empirical parameter С = δTg has the meaning of temperature range δTg that characterizes the liquid-glass transition. Different approaches of δTg calculation are reviewed. In the framework of the model of delocalized atoms a modified kinetic criterion of glass transition is proposed (q/Tg)τg = Cg, where Cg ≅ 7·10−3 is a practically universal dimensionless constant. It depends on fraction of fluctuation volume fg, which is frozen at the glass transition temperature Cg = fg/ln(1/fg). The value of fg is approximately constant fg ≅ 0.025. At Tg the process of atom delocalization, i.e. its displacement from the equilibrium position, is frozen. In silicate glasses atom delocalization is reduced to critical displacement of bridge oxygen atom in Si-O-Si bridge necessary to switch a valence bond according to Muller and Nemilov.An equation is derived for the temperature dependence of viscosity of glass-forming liquids in the wide temperature range, including the liquid-glass transition and the region of higher temperatures. Notion of (bridge) atom delocalization is developed, which is related to necessity of local low activation deformation of structural network for realization of elementary act of viscous flow – activated switch of a valence (bridge) bond. Without atom delocalization (“trigger mechanism”) a switch of the valence bond is impossible and, consequently, the viscous flow. Thus the freezing of atom delocalization process at low temperatures, around Tg, leads to the cease of the viscous flow and transition of a melt to a glassy state. This occurs when the energy of disordered lattice thermal vibrations averaged to one atom becomes equal or less than the energy of atom delocalization.The Bartenev equation for cooling rate dependence of glass transition temperature Tg = Tg(q) is discussed. The value of fg calculated from the data on the Tg(q) dependence coincides with result of the fg calculation using the data on viscosity near the glass transition. Derivation of the Bartenev equation with the account of temperature dependence of activation energy of glass transition process is considered. The obtained generalized relation describes the Tg(q) dependence in a wider interval of the cooling rate compared Bartenev equation. Experimental data related to standard cooling rate q = 3K/min were used in this work.