A unified thermodynamic picture for the glass transition and liquid fragility

Glass transition is a reversible transition that occurs in most amorphous materials. However, the nature of glass transition remains far from being clarified. A key to understand the glass transition is to clarify what determines the glass transition temperature (T_g) and liquid fragility (m). Here the glass transition thermodynamics for 150 different glass-forming systems are studied statistically. It is found that the activation characters in the energy landscape are crucial to precisely portray the glass transition and, in particular, both the activation free energy (G*) and the activation entropy (S*) play critical roles. G* determines T_g, T_g=G*/290+25.5, while S* determines m, m=S*/RRln10+15, where R is the gas constant. Based on the Boltzmann definition of entropy, the fragility is an indication of the number of the degeneracy of the evolution paths. This explains why the nano-confined, low-dimension or high-pressured glasses exhibit stronger characteristics, which has been a puzzling phenomenon for a long time.