Configurational entropy approach to the kinetics of glasses

Abstract

A kinetic theory of glasses is developed using equilibrium theory as a foundation.After establishing basic criteria for glass formation and the capability of the equilibrium entropy theory to describe the equilibrium aspects of glass formation, a minimal model for the glass kinetics is proposed.Our kinetic model is based on a trapping description of particle motion in which escapes from deep wells provide the rate-determining steps for motion.The formula derived for the zero frequency viscosity ␩ (0, T ) is log␩(0, T ) = B -AF (T )kT where F is the free energy and T the temperature.Contrast this to the Vogel-Fulcher law log ␩ (0, T ) = B + A/(T -Tc).A notable feature of our description is that even though the location of the equilibrium second-order transition in temperature-pressure space is given by the break in the entropy or volume curves the viscosity and its derivative are continuous through the transi-tion.The new expression for ␩ (0, T ) has no singularity at a critical temperature Tc as in the Vogel-Fulcher law and the behavior reduces to the Arrhenius form in the glass region.Our formula for ␩ (0, T ) is discussed in the context of the concepts of strong and fragile glasses, and the experimentally observed connection of specific heat to relaxation response in a homologous series of polydimethylsiloxane is explained.The frequency and temperature dependencies of the complex viscosity ␩ ( , T ), the diffusion coefficient D ( , T ), and the dielectric response ␧ ( , T ) are also obtained for our kinetic model and found to be consistent with stretched exponential behavior.