UC Berkeley

In this thesis, we study the relaxation dynamics and phase transformations in supercooled liquids where microscopic motion dramatically slows down below an onset temperature To. To this end, we use theoretical and computational tools from statistical mechanics and compare our predictions to the available experimental and simulation data.

In the first chapter, we focus on the impact of glassy dynamics on crystallization. We develop a coarse-grained lattice model, the Arrow-Potts model, which can simulate crystallization and vitrification. The Arrow-Potts model produces phenomena observed in experiments and molecular dynamics (MD) simulations, including poly-crystalline microstructures near the melting temperature $T_m$ and ramified crystals at low temperatures. To explain these phenomena, we combine several theories that account for the nucleation and growth of crystals, e.g., the Kolmogorov-Johnson-Mehl-Avrami theory, with dynamical facilitation (DF) theory of glassy dynamics. As a result, we derive a formula that predicts the energy barrier for crystallization without fitting to simulation data.

In the last two chapters, we delve deeper into understanding relaxation dynamics at a microscopic level by studying the open questions surrounding DF theory. DF theory explains glassy dynamics by assuming the existence of spatially localized excitations, which drive motion and facilitate the formation of nearby excitations. Despite its success, open questions remain within DF theory regarding the microscopic origin of these assumptions. To this end, we develop a theory of excitations and facilitation in supercooled liquids, where we find that excitations are localized pure-shear events whose characteristics and activation energy can be explained using the theory of linear elastic solids. Furthermore, linear elasticity theory can explain how excitations facilitate new excitations via elastic interactions. By constructing a Markov state model based on elastically interacting excitations, we can reproduce key elements of glassy dynamics that agree with experimental observations and MD simulations.