Effect of Glass Composition on Activation Energy of Viscosity in Glass-melting-temperature Range

Viscosity, a key property for glass processing, is a function of glass composition and temperature. Nuclear waste glasses must be formulated to obtain a desired viscosity at the melter processing temperature for each waste composition to be vitrified. Over the past decades, a large viscosity database has been accumulated at various laboratories in the US. The database, compiled at the Pacific Northwest National Laboratory, comprises over 1300 compositions with 83 components and 6800 viscosity data. We used this database to develop a mathematical model for the viscosity-composition relationship for viscosities lower than 1000 Pa·s that are important for the melting process. In this high-temperature range, the viscosity-temperature relationship has the form of an Arrhenius function, i.e., ln(η) = A + B/T, where η is the viscosity, T is the absolute temperature, A is a constant coefficient, and B is the activation energy. We obtained B for each data point and then fitted a firstor second-order model to B as a function of glass composition while A was kept constant for all glasses. Altogether, we have developed 12 versions of viscosity-composition relationships with a variety of firstand second-order coefficients. Two models, one first order and one second order, are presented in this paper. I. VISCOSITY-COMPOSITION RELATIONSHIPS Viscosity-temperature relationships are important for both glass melting and glass forming. Over the wide interval of temperatures—from the glass transition temperature to the temperature at which glass is being refined—viscosity spans 12 orders of magnitude. Many approximation functions have been suggested in the literature to model the viscosity-temperature relationship. The most popular among them are the Vogel-Fulcher-Tammann equation and the Adam-Gibbs equation, the latter of which is more versatile and allows better fitting of high-temperature data. As has been demonstrated with various viscosity databases, both for commercial and waste glasses, high-temperature viscosity is best fitted by an Arrhenius function, T B A / ) ln( + = η (1) where η is the viscosity, T is the temperature, A is a constant coefficient, and B is the activation energy. In Equation (1), both A and B are independent of temperature. Thus, for low viscosities, η < 10 Pa·s, the activation energy depends on composition only. Because the melting temperatures of glass are usually below 10 Pa·s, Equation (1) fully suffices for formulating glasses to meet melt-processing constrains with respect to glass formulation as well as mathematical modeling of glass-melting furnaces.