Analysis & Simulation of Dynamics in Supercooled Liquids

The nature of supercooled liquids and the glass transition has been debated by many scientists. Several theories have been put forth to describe the remarkable properties of this out-of-equilibrium material. Each of these theories makes specific predictions as to how the scaling of various transport properties in supercooled materials should behave. Given access to a large pool of high-quality supercooled liquid data we seek to compare these theories to one another. Moreover, we explore properties of a pair of models which are the basis for one particularly attractive theory - Chandler-Garrahan theory - and discuss the models' behavior in space-time and possible implications to the behavior of experimental supercooled liquids./nHere we investigate the nature of dynamics in supercooled liquids using a two pronged approach. First we analyze the transport properties found in experiments and simulations of supercooled liquids. Then, we analyze simulation trajectories for lattice models which reproduce many of the interesting properties of supercooled liquids. In doing so, we illuminate several glass universalities, common properties of a wide variety of glass formers./nBy analyzing relaxation time and viscosity data for over 50 data sets and 1200 points, we find that relaxation time can be collapsed onto a single, parabolic curve. This collapse supports a theory of universal glass behavior based on facilitated models proposed by David Chandler and Juan Garrahan in 2003. We then show that the parabolic fit parameters for any particular liquid are a material property: they converge fast and are capable of predicting behavior in regions beyond the included data sets. We compare this property to other popular fitting schemes such as the Vogel-Fulcher, double exponential, and fractional exponential forms and conclude that these three forms result in parameters which are non predictive and therefore not material properties. Additionally, we examine the role of attractive forces in liquids by comparing simulations of a Lennard-Jones mixture, which contains both attractions and repulsions, with that of a Weeks-Chandler-Andersen mixture, which only retains repulsive forces. We show that within the framework of the parabolic collapse, these two liquids behave identically. This suggests that attractive forces do not play a key role in glassy dynamics. Rather, repulsive forces - as has been shown in dense liquids - play the largest contributing role in jamming systems into glassy states. We further investigate the predicted fragile-to-strong crossover in glass formers and find no compelling evidence for the crossover in bulk materials at this time./nAdditionally, we study ensembles of trajectories for a specific class of kinetically constrained models which reproduce the dynamic heterogeneity found in real glass formers. The one dimensional models we consider are the Fredrickson-Andersen (FA) model and the east model. These two models have been shown to behave as supercooled liquids reproducing properties such as the breakdown of the Stokes-Einstein equation relating diffusion constants and relaxation times. We use transition path sampling in the s-ensemble to bias the system into low activity regions. It has been previously shown that the FA model goes through a first-order dynamical phase transition in trajectory space. We extend this to include a slightly softened FA model, which we believe to be more representative of atomistic systems. We have determined that this first order coexistence line ends in a critical point where the surface tension between active and inactive trajectories in space-time disappears. Beyond this region as the softened FA model becomes unconstrained, the transition disappears and no phase transition is detected. Beyond simulations, these results were verified by analytical methods. This verification was achieved by mapping of soft FA model onto a model which undergoes a quantum phase transition. Beyond the FA model, we consider the softened east model. Unlike the FA model, however, the east model relaxes hierarchically and has a particular directionality. Many of the same conclusions - such as the appearance of a non-trivial critical point in space time - appear in the east model. Moreover, many of the same analytical tools can be used to determine the symmetry line that separates the active and inactive phases. However, the exact mapping of the critical point location is unknown and the location of the critical point is determined numerically. We also investigate how the inactive phase created by applying a dynamical field relaxes to the active state under no external field and find that the process appears barrierless./nLastly, we propose current and ongoing work which seeks to understand how to numerically quantify the degree to which a system is dynamically facilitated by looking at multipoint correlation functions of endured kinks. We contrast this method with previously suggested methods based on locating avalanches by testing both methods on kinetically constrained models such as the east and FA models.

Advisor: Chandler, David