Reconciling calorimetric and kinetic fragilities of glass-forming liquids

The liquid fragility index (mvis) describes the rate of viscosity change of a glass-forming liquid with temperature at the glass transition temperature (Tg), 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 (mDSC), i.e., the changing rate of fictive temperature (Tf) with heating (cooling) rate in a small Tf range around Tg. The crucial question is how mDSC is quantitatively related to mvis. 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 mDSC deviates systematically from mvis. The deviation is attributed to the Arrhenian approximation of the log(1/qc) ~ Tg/Tf relationship in the glass transition range. We have developed an empirical model to quantify the deviation, by which mvis can be well predicted from mDSC 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.