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

Abstract

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.

Combining Flash DSC, DSC and broadband dielectric spectroscopy to determine fragility

“…In the literature [7,41], log(C) values are obtained correlating calorimetric dynamic spectroscopy measurements (AC-Chip calorimetry, HCS, MT-DSC, 3x method…) with DSC and F-DSC data. These values are dispersed from values close to 0.3 [42]-1.5 [1,43]. In this idea, few studies compare systematically DSC and F-DSC glass transition temperature dependencies of cooling rate with BDS structural relaxation temperature dependence for a set of samples.…”

Cooling Rate Dependent Glass Transition in Thin Polymer Films and in Bulk

“…The one-to-one connection between the cooling rate dependent T g and the rate of spontaneous fluctuations has been demonstrated by several studies in the past for bulk glass formers [31,95,117]. In particular, as a result of the intimate link between the molecular mobility and the glass transition, the cooling rate dependence of the T g can also be described by the VFT equation:…”

“…This conclusion marks a sharp difference with the behaviour normally observed in bulk glass formers, where, as commented in Sect. 13.2, the two aspects of glassy dynamics have been shown to be fully related [31,59,95,103,117].…”

“…This considering that, from a conceptual point of view, the two aspects of glassy dynamics are different (linear versus non-linear dynamics). In comparison to bulk glass formers, where a one-to-one relation between them has been established [31,59,95,103,117], that of thin polymer films and, in general, confined glass formers constitutes an intriguing example of the failure of such univocal relation. According to the previous arguments a suitable framework to describe the thermal glass transition in thin polymer films must account for factors beyond the rate of spontaneous fluctuations.…”

“…13.2), it has been remarked how the behaviour of bulk glass-forming liquids in terms of the out-of-equilibrium dynamics, that is, the thermal glass transition and physical aging can be completely described considering the temperature dependence of the rate of spontaneous fluctuations [31,59,95,103,117]. In view of the results of the current study, it is natural to formulate the following question: can this connection be applied to polymer thin films and, in general, glasses under nanoscale confinement too?…”