Fragility of supercooled liquids from differential scanning calorimetry traces: theory and experiment

Starting from the Debye model for frequency-dependent specific heat and the Vogel-Fulcher-Tammann (VFT) model for its relaxation time, an analytic expression is presented for the heat capacity versus temperature trace for differential scanning calorimetry (DSC) of glass transitions, suggesting a novel definition of the glass transition temperature based on a dimensionless criterion. An explicit expression is presented for the transition temperature as a function of the VFT parameters and the cooling rate, and for the slope as a function of fragility. Also a generalization of the results to non-VFT and non-Debye relaxation is given. Two unique ways are proposed to tackle the inverse problem, i.e., to extract the fragility from an experimental DSC trace. Good agreement is found between theoretically predicted DSC traces and experimental DSC traces for glycerol for different cooling rates.