On relative merits of the criteria of glass formation and effects of ultraviscous liquid properties

A liquid is said to become glass when cooled to a temperature T infinitesimally below the temperature Tl → g. According to the glass-formation criteria, either, (I) τs = CI/qc at Tl → g, or, (II) (dτs/dT) ≅ CII/qc, or, (III) (τs/T) ≅ CIII/qc, where τs is taken as equal to τα, the relaxation time of the α-process, qc is the cooling rate, and CI = 16.67 K, CII ≅ 1, and CIII ≅ 1. Criterion I is generally used in glass phenomenology, criterion II was related to the effective enthalpy of activation in the Tl → g range and recommended over criterion I, and criterion III was used for discussing the pressure dependence of Tl → g. We investigate their merits by comparing formally the criteria-based τs at Tl → g in an ideal case against τα at T = Tl → g, and discuss the effects of using the glass-liquid transition temperature, Tg → l, the fictive temperature, Tf, and the midpoint temperature of the Cp-T plots as alternatives to Tl → g. The three criteria yield basically different results. Moreover, Tl → g differs from the kinetic freezing temperature of the α-relaxation process, and CI varies with both qc and the material. We suggest that contributions from several properties of ultraviscous liquids affect the shape of the Cp-T scans from which Tl → g is determined. The findings have consequences for interpretations in which τs is used as τα.