Generalized localization model of relaxation in glass-forming liquids

Glassy solidification is characterized by two essential phenomena: localization of the solidifying material's constituent particles and a precipitous increase in its structural relaxation time tau. Determining how these two phenomena relate is key to understanding glass formation. Leporini and coworkers have recently argued that tau universally depends on a localization length-scale < u(2)> (the Debye-Waller factor) in a way that depends only upon the value of < u(2)> at the glass transition. Here we find that this 'universal' model does not accurately describe tau in several simulated and experimental glass-forming materials. We develop a new localization model of solidification, building upon the classical Hall-Wolynes and free volume models of glass formation, that accurately relates tau to < u(2)> in all systems considered. This new relationship is based on a consideration of the anisotropic nature of particle localization. The model also indicates the presence of a particle delocalization transition at high temperatures associated with the onset of glass formation.