Generalized localization model of relaxation in glass-forming liquids

Abstract

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 τ. Determining how these two phenomena relate is key to understanding glass formation. Leporini and coworkers have recently argued that τ universally depends on a localization length-scale <u2> (the Debye-Waller factor) in a way that depends only upon the value of <u2> at the glass transition. Here we find that this ‘universal’ model does not accurately describe τ 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 τ to <u2> in all systems considered. This new relationship is based on a consideration of the 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.

Cage rattling does not correlate with the local geometry in molecular liquids

“…Recently, extensive molecular-dynamics (MD) simulations evidencing the universal correlation between the structural relaxation time τ α and u 2 were reported in polymeric systems [52][53][54], binary atomic mixtures [55], colloidal gels [56] and antiplasticized polymers [41] and compared with the experimental data concerning several glassformers in a wide fragility range (20 ≤ m ≤ 191) [52,55,57,59]. One major finding was that states with equal ST-MSD u 2 have equal relaxation times τ α too.…”

“…the volume and the asphericity of the Voronoi polyhedron (VP) surrounding a tagged particle. VP asphericity has been analyzed also in water [74][75][76], small molecules [77], hard spheres [78] and polymers [41,45,79,80]. For a VP with V v volume and A v surface the asphericity is defined as:…”

“…Despite the huge range of time scales older [34] and recent theoretical [35][36][37][38][39][40][41] studies addressed the rattling process in the cage to understand the structural relaxation -the escape process -gaining support from numerical [8, 15, 41-59, 61? , 62] and experimental works on glassforming liquids [41,63,64] and glasses [38,[65][66][67][68][69][70].…”

Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials

“…DebyeWaller measurements (9, 10), based on neutron, X-ray, or other scattering measurements, emphasize another type of free volume that is associated with the volume explored by particles as they rattle about their mean positions in a condensed material. This type of free-volume modeling has also been refined to take into account the shape of these "rattle" volumes (11,12).Another family of glass-formation models emphasizes the emergent elasticity in glassy materials (13). These approaches build on the idea that the solid-like nature of glasses is one of their most conspicuous, and perhaps defining, properties.…”

“…DebyeWaller measurements (9,10), based on neutron, X-ray, or other scattering measurements, emphasize another type of free volume that is associated with the volume explored by particles as they rattle about their mean positions in a condensed material. This type of free-volume modeling has also been refined to take into account the shape of these "rattle" volumes (11,12).…”