Using derivative plots to ascertain fragilities of glass-formers

The dynamics of materials slow as the temperature is cooled to the glass transition temperature (T_g). The rapidity at which the equilibrium dynamics slow upon cooling is known as "fragility", if evaluated at T_g. The measurement of fragility in various glassy systems is a huge body of research, with discrepancies in measured fragility values being common. This report reviews the mathematics behind determining fragility as it relates to glassy dynamics in polymers, small molecules, and inorganics. Various derivative plots are proposed that demonstrate how the fragility of a system is strongly dependent on chosen empirical constants such as T_g. This includes visualizations of how fragility changes with the value chosen for T_g or with the time constant τ_g used to define T_g, with τ_g = 100 s being a common choice. Using poly(vinyl acetate) as an example, it is demonstrated how various factors affect the measurement of fragility.