Characteristic temperatures of liquid–glass transition

Abstract

We treat liquid-to-glass transition as a sequence of self-similar “smeared” ideal transitions emerging at characteristic temperatures T 0, T g and T c . The characteristic temperatures (Vogel–Fulcher T 0, calorimetric T g and crossover T c temperatures) are discussed through the Vogel–Fulcher–Tamman equation. It is shown that their ratio is the measure of the degree of fragility m g observed near T g . Besides the known equation T g / T 0=(1− m 1/ m g ) −1, with adjustable parameter m 1=16±2, the equation T c / T g =(1+ m 2/ m g )/(1− m 2/ m g ) with m 2=7±1, are shown to be in accord with experiment. Based on the continuous curvature of the primary relaxation time scale, related to m g , the equation involving all the characteristic temperatures is introduced and the upper ( T 0T c ) and the lower ( 3 T 0T c 2 ) estimates for the calorimetrically established characteristic temperature T g are found. Predictions are given for characteristic temperatures T c and fragilities m c for a number of glass-forming liquids.