Nonequilibrium viscosity of glass

Since glass is a nonequilibrium material, its properties depend on both composition and thermal history. While most prior studies have focused on equilibrium liquid viscosity, an accurate description of nonequilibrium viscosity is essential for understanding the low temperature dynamics of glass. Departure from equilibrium occurs as a glass-forming system is cooled through the glass transition range. The glass transition involves a continuous breakdown of ergodicity as the system gradually becomes trapped in a subset of the available configurational phase space. At very low temperatures a glass is perfectly nonergodic (or "isostructural"), and the viscosity is described well by an Arrhenius form. However, the behavior of viscosity during the glass transition range itself is not yet understood. In this paper, we address the problem of glass viscosity using the enthalpy landscape model of Mauro and Loucks [Phys. Rev. B 76, 174202 (2007)] for selenium, an elemental glass former. To study a wide range of thermal histories, we compute nonequilibrium viscosity with cooling rates from 10^-12 to 10 ¹² K/s. Based on these detailed landscape calculations, we propose a simplified phenomenological model capturing the essential physics of glass viscosity. The phenomenological model incorporates an ergodicity parameter that accounts for the continuous breakdown of ergodicity at the glass transition. We show a direct relationship between the nonequilibrium viscosity parameters and the fragility of the supercooled liquid. The nonequilibrium viscosity model is validated against experimental measurements of Corning EAGLE XG™ glass. The measurements are performed using a specially designed beam-bending apparatus capable of accurate nonequilibrium viscosity measurements up to 10¹⁶ Pa s. Using a common set of parameters, the phenomenological model provides an accurate description of EAGLE XG™ viscosity over the full range of measured temperatures and fictive temperatures.