A thermodynamic description of the hysteresis in specific-heat curves in glass transitions

Abstract

By refining the definition of thermodynamic equilibrium and state variables (thermodynamic coordinate, TC) for solids, it is determined that the state of a glass substance transforms into an equilibrium state after it is solidified. In contrast, the state of a glass substance during the glass transition is a nonequilibrium state. The specific-heat (C) versus temperature (T) curve exhibits hysteresis, which is traditionally believed to invalidate thermodynamic methods. However, the glass transition slowly occurs in a manner such that structural change is decoupled with the fast process of thermal relaxation of phonons, which enables us to describe the hysteresis by thermodynamic methods. The hysteresis is caused by the structural relaxation and the time of relaxation is determined by the energy barrier, which depends solely on the current value of TCs. Therefore, the state in hysteresis can be described by the information of the current structure alone: history-dependent response functions are unnecessary. On the basis of these conclusions, the behavior of the C-T curve with changing heating/cooling rate γ is simulated. The main features of the hysteresis, the shift of C to higher temperatures with increasing γ, the hump structure, and the memory effect are well reproduced from a structure-dependent energy barrier. In view of the structural dependence of the energy barrier, it is not surprising to observe deviations from the Arrhenius law. However, only the terms that are higher than linear in T are observed in Arrhenius plot as the deviation. An important finding of this study is that the apparent energy barrier obtained using the Arrhenius plot significantly overestimates the real value. The extraordinarily large values of the pre-exponential factor of the relaxation time can also be understood on this basis.