Characteristic temperatures of liquid–glass transition

We treat liquid-to-glass transition as a sequence of self-similar “smeared” ideal transitions emerging at characteristic temperatures T0,Tg and Tc. The characteristic temperatures (Vogel–Fulcher T0, calorimetric Tg and crossover Tc temperatures) are discussed through the Vogel–Fulcher–Tamman equation. It is shown that their ratio is the measure of the degree of fragility mg observed near Tg. Besides the known equation Tg/T0=(1−m1/mg)−1, with adjustable parameter m1=16±2, the equation Tc/Tg=(1+m2/mg)/(1−m2/mg) with m2=7±1, are shown to be in accord with experiment. Based on the continuous curvature of the primary relaxation time scale, related to mg, the equation involving all the characteristic temperatures is introduced and the upper and the lower estimates for the calorimetrically established characteristic temperature Tg are found. Predictions are given for characteristic temperatures Tc and fragilities mc for a number of glass-forming liquids