Reconciling calorimetric and kinetic fragilities of glass-forming liquids

The liquid fragility index (m_vis) describes the rate of viscosity change of a glass-forming liquid with temperature at the glass transition temperature (T_g), which is very important for understanding liquid dynamics and the glass transition itself. Fragility can be directly determined using viscosity measurements. However, due to various technical complications with determining viscosity, alternative methods to obtain fragility are needed. One simple method is based on measurement of the calorimetric fragility index (m_DSC), i.e., the changing rate of fictive temperature (T_f) with heating (cooling) rate in a small T_f range around T_g. The crucial question is how m_DSC is quantitatively related to m_vis. Here, we establish this relation by performing both dynamic and calorimetric measurements on some selected glass compositions covering a wide range of liquid fragilities. The results show that m_DSC deviates systematically from m_vis. The deviation is attributed to the Arrhenian approximation of the log(1/q_c) ~ T_g/T_f relationship in the glass transition range. We have developed an empirical model to quantify the deviation, by which m_vis can be well predicted from m_DSC across a large range of fragilities. Combined with the high-T viscosity limit (10^–2.93 Pa·s), we are able to obtain the entire viscosity curve of a glass-forming liquid by only performing DSC measurements.