The glass transition width and its dependence on fragility, nonexponentiality and nonlinearity

Abstract

This paper presents a comprehensive and critical analysis of the glass transition width (1/Tg -1/Tg’) or the reduced width (ΔTg/Tg’) observed in simulated Differential Scanning Calorimetry (DSC) heating and cooling scans. The study employs the Tool-Narayanaswamy-Moynihan model (TNM) for 24 diverse materials, encompassing inorganic glasses, organic polymers and molecular glassy systems. The analysis reveals an important novel finding. The width (or the reduced width) of the glass transition cooling scan is shown to be inversely proportional to the activation energy (h*/R), or fragility index (m), as well as the sum the non-exponentiality 𝛽 and nonlinearity 𝑥 parameters, following the relationship: 1/[(h*/R)(𝛽+𝑥)] or 1/[m(𝛽+𝑥)]. The proportionality constants depend on the specific method used to determine Tg and Tg' values. For precise determinations, the resulting estimate for the sum of (𝛽+𝑥) has an accuracy comparable to that obtained using the established peak shift method proposed by Hutchinson.