Thermodynamics and kinetics of the glass transition: A generic geometric approach

Abstract

A generic phenomenological theory of the glass transition is developed in the framework of a quasilinear formulation of the thermodynamics of irreversible processes. Starting from one of the basic principles of this science in its approximate form given by de Donder’s equation, after a change of variables the temperature dependence of the structural parameter ξ(T), the thermodynamic potentials ΔG̃(T), the thermodynamic functions and the time of molecular relaxation τ of vitrifying systems is constructed. In doing so, a new effect in the ΔG̃(T) course is observed. The analysis of the higher derivatives of the thermodynamic potential, and especially the nullification of the second derivative of the configurational specific heats ΔC̃p(T) of the vitrifying liquid defines glass transition temperature T̃g and leads directly to the basic dependence of glass transition kinetics: the Frenkel–Kobeko–Reiner equation. The conditions guaranteeing the fulfillment of this equation specify the temperature dependence of the activation energy U(T,ξ̃) for viscous flow and give a natural differentiation of glass formers into fragile and strong liquids. The effect of thermal prehistory on the temperature dependence of both thermodynamic functions and kinetic coefficients is established by an appropriate separation of de Donder’s equation.

Stress development and relaxation during crystal growth in glass-forming liquids

“…In Eq. (28), DH m is the melting enthalpy per particle, T r = T/T m and the Volmer-Turnbull equation (5) was employed. In Fig.…”

“…By this reason, we have set the Young's modulus of the ambient phase equal to the modulus of the crystal, E c = 76 GPa. There exists a variety of experimental data and general theoretical arguments indicating the existence of a considerable increase of Young's modulus of glass-forming melts with decreasing temperature near the respective temperature of vitrification, T g [6,17,[24][25][26][27][28]. The incorporation of such effects (as done, for example, in Ref.…”

The glass transition in terms of Landau’s phenomenological approach

“…This principle was first demonstrated by the achievements of the phenomenological kinetic treatment of glass transition, introduced by VolÕkenstein and Ptizyn [5], continued by Moynihan et al [6], Kovacs et al [7] (see also [8]) and then by the attempts to apply to glass transition the thermodynamics of irreversible processes (see [9,10] and literature cited in [3,8]). This second phenomenological approach is most appropriate in describing glass transition, because in its framework the change from an equilibrium (ergodic) into a non-equilibrium (non-ergodic) system, (the glass) can be overbridged.…”

“…This second phenomenological approach is most appropriate in describing glass transition, because in its framework the change from an equilibrium (ergodic) into a non-equilibrium (non-ergodic) system, (the glass) can be overbridged. In a recent series of publications [8,10,11] we tried to unite both phenomenological approaches in order to develop a generic thermodynamics and kinetics of vitrification.…”

“…In the framework of this approximation, the G(T)-dependence of the frozen-in glass is determined as a tangent (at T = T g ) to the G(T)-curve of the undercooled metastable liquid [16][17][18]. However, the main efforts here are directed upon applying LandauÕs method to the real course of the thermodynamic functions and coefficients in the glass-transition region, as this is known from experiment and from above mentioned general generic description of the kinetics of vitrification [8,10].…”