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 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 frag ility m(g) observed near T-g. Besides the known equation T-g/T-0 = (1 - m(l )/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 re laxation time scale, related to ill,, the equation involving all the charac teristic temperatures is introduced and the upper (root T0Tc) and the lower ((3)root T0Tc2) estimates for the calorimetrically established characteris tic temperature T-g are found. Predictions are given for characteristic tem peratures T-c and fragilities nl, for a number of glass-forming liquids. (C ) 1999 Elsevier Science B.V. All rights reserved.