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 T-l -> g. According to the glass-formation criteria, either, (I) tau(s) = C-I/q(c) at T-l -> g or, (II) (d tau(s)/dT) congruent to C-II/q(c) or, (III) (tau(s)/T) congruent to C-III/q(c), where tau(s) is taken as equal to tau(alpha), the relaxation time of the alpha-process, q(c) is the cooling rate, and C-I = 16.67 K, C-II congruent to 1, and C-III congruent to 1. Criterion I is generally used in glass phenomenology, criterion II was related to the effective enthalpy of activation in the T-l -> g range and recommended over criterion I, and criterion III was used for discussing the pressure dependence of T-l -> g. We investigate their merits by comparing formally the criteria-based tau(s) at T-g -> l gin an ideal case against tau(alpha) at T = T-l -> g, and discuss the effects of using the glass-liquid transition temperature, T-g -> l, the fictive temperature, T-f, and the midpoint temperature of the C-P-T plots as alternatives to T-l -> g. The three criteria yield basically different results. Moreover, T-l -> g differs from the kinetic freezing temperature of the alpha-relaxation process, and C-I varies with both q(c) and the material. We suggest that contributions from several properties of ultraviscous liquids affect the shape of the C-P-T scans from which T-l -> g is determined. The findings have consequences for interpretations in which tau(s) is used as tau(alpha).