Application of an extended Tool–Narayanaswamy–Moynihan model: Part 1. Description of vitrification and complex heat capacity measured by temperature-modulated DSC

Abstract

Complex heat capacity in equilibrium can be considered as a compliance in the scheme of linear response. Nevertheless, often the Tool–Narayanaswamy–Moynihan (TNM) or the Kovacs–Aklonis–Hutchinson–Ramos (KAHR) models are used to describe complex as well as total heat capacity in the glass transition region. This is attractive because the TNM–KAHR models take into account the dependence of the relaxation time on temperature as well as fictive temperature and are able to handle non-equilibrium situations. A TNM-model extended by a non-Arrhenius temperature dependence of the relaxation time is applied to describe results from temperature-modulated DSC (TMDSC) measurements. The temperature dependence of the relaxation time, as introduced in the model, is independently determined by a VFTH-fit to heat capacity spectroscopic data in a wide frequency range. Finally, only the stretched exponential factor β and the non-linearity parameter x of the TNM-model must be adjusted to describe the measured curves reasonable well. The model is capable to describe all features of the heat capacities measured in TMDSC scan experiments in the glass transition region of polystyrene. This includes the curve shape, the frequency dependence of T g( ω), the cooling rate dependence of T g( q 0) and possible interference between vitrification and dynamic glass transition. For the complex heat capacity in equilibrium, above vitrification, no influence of fictive temperature on the relaxation time was observed. Consequently, it can be considered as an equilibrium quantity.