Glass transition temperatures of pure glass-forming liquids and binary mixtures.

The glass transition remains one of the most enduring and debated problems in condensed matter science, engaging researchers across disciplines. Two main approaches have traditionally been used to study the glass transition in pure glass formers and their mixtures: the thermodynamic approach and the dynamic (kinetic) approach. The latter focuses on the relaxation dynamics of glasses, with the key parameter being the temperature-dependent relaxation time. Despite decades of research, no physically justified relation between the relaxation time and the glass transition temperature has been established. Here, we propose a new framework for studying the glass transition that builds upon dynamic approaches and bridges them with thermodynamic concepts. We derive equations for the glass transition temperature based on relaxation parameters and demonstrate that the relaxation time at the glass transition is not constant-as is commonly assumed on the laboratory timescale-but depends on the intrinsic relaxation characteristics of the system. Extending this framework to mixtures of glass formers, we show that the Gordon-Taylor equation naturally emerges from ideal dynamic mixing rules. However, for accurate prediction of glass transition properties in mixtures, understanding deviations from ideal mixing remains crucial.