Description of the fragile behavior of glass-forming liquids with the use of experimentally accessible parameters

The temperature dependence of viscosity of glass-forming liquids near the glass transition temperature Tg (at which viscosity η = 1012 Pa s) is given by the fragility index m = d log 10 η d ( T g / T ) T = T g , which is unique for each material. Therefore, m should not depend on the type of the model functions used to describe the viscous behavior. Using this condition, we modified the three-fitting-parameter viscosity equations, i.e., Vogel–Fulcher–Tammann (VFT) and Avramov equations, into one-fitting parameter equations. Both modified equations contain the glass transition temperature Tg and fragility index m as material constants, allowing a direct comparison of the modified equations. Experimental viscosity data are required over a wide temperature range to determine the three-fitting parameters of the VFT and Avramov equations, restricting their applicability. However, the modified equations developed here provide a convenient method of modeling the temperature dependence of viscosity by using the experimentally accessible parameters Tg and m. The modified one-fitting parameter equations were used to analyze viscous behavior of a number of oxide and organic glass-forming liquids. Based on this analysis, it was concluded that the modified Avramov equation describes the experimental data better than the modified VFT equation. Taking into account that the modified VFT equation predicts infinite viscosity at a finite temperature T0, while the modified Avramov equation predicts a continuous increase in viscosity with a decrease in temperature down to the absolute zero, the obtained results may indicate that the oxide and organic super-cooled liquids do not experience dynamic divergence when they are cooled below the glass transition temperature. Strong physical interpretations are developed for all of the parameters used in present equations to model the temperature dependence of viscosity, giving an important improvement over earlier phenomenological models.