Chapter 17 - Nonequilibrium Viscosity and the Glass Transition

Abstract

The glass transition involves a continuous freezing of a supercooled liquid into the glassy state. The glass transition is not a thermodynamic phase transition; rather, it is a kinetic transition with thermodynamic consequences as the configurational degrees of freedom in the liquid become frozen. Since glass is a nonequilibrium material, its properties depend on thermal history. Traditionally, the thermal history dependence of glass properties is described using an order parameter known as the fictive temperature. The nonequilibrium viscosity of glass is a function of its composition, temperature, and fictive temperature. Under normal cooling conditions, the viscosity of glass is many orders of magnitude lower than that of the corresponding supercooled liquid. During an isothermal heat treatment, the nonequilibrium viscosity of glass relaxes upward until reaching the metastable supercooled liquid state. The temperature and fictive temperature dependence of nonequilibrium viscosity are described by the Mauro-Allan-Potuzak (MAP) equation. The scaling of glass viscosity is largely determined by the viscosity of its parent supercooled liquid, in particular the values of glass transition temperature and fragility. As fragility increases, the glass transition become sharper and the nonequilibrium viscosity curve becomes steeper. The composition dependence of glass transition temperature and fragility can be determined using temperature-dependent constraint theory. The glass transition temperature is governed by the number of rigid constraints per atom in the transition region. The fragility is governed by the rate at which topological degrees of freedom are lost upon cooling through the glass transition.