Vitrification in a wide cooling rate range: the relations between cooling rate, relaxation time, transition width, and fragility.

The cooling rate dependence of the thermal glass transition of polystyrene (PS) is measured in a range between 0.2 K/min (0.003 K/s) and 4000 K/s using conventional differential scanning calorimetry (DSC) and Fast Scanning Calorimetry (Flash DSC 1). The cooling rate dependence of the thermal glass transition can be described in an analogy to the frequency dependence of the dynamic glass transition. The relation between cooling rate, β(c), and frequency, ω, is usually described by the Frenkel-Kobeko-Reiner-(FKR) hypothesis β(c)/ω = C, where C is a constant. We have introduced a new property to describe the kinetics of the vitrification process; the vitrification function, κ. This function is the ratio between the width of the thermal and dynamic glass transition. The validity of the FKR hypothesis is analyzed by two independent methods, the analysis of the activation diagram using the Vogel-Fulcher-Tammann-Hesse equation and the analysis of the temperature dependence of the transition width. We derived a relation for the FKR-constant, which indicates the validity range of the FKR hypotheses. This hypothesis is valid if the logarithmic width of the vitrified and the non-vitrified relaxation spectrum is temperature invariant. This condition is fulfilled for polystyrene in the measured cooling rate range. Furthermore we discuss the relation between the vitrification function, the transition width, the FKR constant, and the fragility.