Configurational entropy approach to the kinetics of glasses

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 eta (0,T) is log eta (0,T) - B - AF(T)kT where F is the free energy and T the temperature. Contrast this to the Vogel-Fulcher law log eta (0,T) - B + A/(T - T-c). 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 transition. The new expression for eta (0,T) has no singularity at a critical temperature T-c as in the Vogel-Fulcher law and the behavior reduces to the Arrhenius form in the glass region. Our formula for eta (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 eta(omega ,T), the diffusion coefficient D(omega ,T), and the dielectric response epsilon(omega, T) are also obtained for our kinetic model and found to be consistent with stretched exponential behavior.