Manifestations of Dynamical Facilitation in Glassy Materials

By characterizing the dynamics of idealized lattice models with a tunable kinetic constraint, we explore the different ways in which dynamical facilitation manifests itself within the local dynamics of glassy materials. Dynamical facilitation is characterized both by a mobility transfer function, the propensity for highly-mobile regions to arise near regions that were previously mobile, and by a facilitation volume, the effect of an initial dynamical event on subsequent dynamics within a region surrounding it. Sustained bursts of dynamical activity -- avalanches -- are shown to occur in kinetically constrained models, but, contrary to recent claims, we find that the decreasing spatiotemporal extent of avalanches with increased supercooling previously observed in granular experiments does not imply diminishing facilitation. Viewed within the context of existing simulation and experimental evidence, our findings show that dynamical facilitation plays a significant role in the dynamics of systems investigated over the range of state points accessible to molecular simulations and granular experiments.Comment: 10 pages, 5 figure

How Do Quasicrystals Grow?

Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal `nucleus' to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral clusters by the growing quasicrystal. Our results demonstrate how local atomic interactions give rise to the long-range aperiodicity of quasicrystals.Comment: 4 pages, 4 figures. Figures and text have been updated to the final version of the articl

Liquid-Solid Transitions with Applications to Self-Assembly.

We study the thermodynamic and kinetic pathways by which liquids transform into solids, and their relation to the metastable states that commonly arise in self-assembly applications. As a case study in the formation of ordered metastable solids, we investigate the atomistic mechanism by which quasicrystals form. We show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal "nucleus" to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In a related study, we propose a two-part mechanism for forming 3d dodecagonal quasicrystals by self-assembly. Our mechanism involves (1) attaching small mobile particles to the surface of spherical particles to encourage icosahedral packing and (2) allowing a subset of particles to deviate from the ideal spherical shape, to discourage close-packing. In addition to studying metastable ordered solids, we investigate the phenomenology and mechanism of the glass transition. We report measurements of spatially heterogeneous dynamics in a system of air-driven granular beads approaching a jamming transition, and show that the dynamics in our granular system are quantitatively indistinguishable from those for a supercooled liquid approaching a glass transition. In a second study of the glass transition, we use transition path sampling to study the structure, statistics and dynamics of localized excitations for several model glass formers. We show that the excitations are sparse and localized, and their size is temperature-independent. We show that their equilibrium concentration is proportional to exp[-Ja(1/T-1/To)], where "Ja" is the energy scale for irreversible particle displacements of length "a," and "To" is an onset temperature. We show that excitation dynamics is facilitated by the presence of other excitations, causing dynamics to slow in a hierarchical way as temperature is lowered. To supplement our studies of liquid-solid transitions, we introduce a shape matching framework for characterizing structural transitions in systems with complex particle shapes or morphologies. We provide an overview of shape matching methods, explore a particular class of metrics known as "harmonic descriptors," and show that shape matching methods can be applied to a wide range of nanoscale and microscale assembly applications.Ph.D.Chemical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78931/1/askeys_1.pd

A Tale of Two Tilings

What do you get when you cross a crystal with a quasicrystal? The surprising answer stretches from Fibonacci to Kepler, who nearly 400 years ago showed how the ancient tiles of Archimedes form periodic patterns.Comment: 3 pages, 1 figur

Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase

We present results of molecular simulations that predict the phases formed by the self-assembly of model nanospheres functionalized with a single polymer "tether", including double gyroid, perforated lamella and crystalline bilayer phases. We show that microphase separation of the immiscible tethers and nanospheres causes confinement of the nanoparticles, which promotes local icosahedral packing that stabilizes the gyroid and perforated lamella phases. We present a new metric for determining the local arrangement of particles based on spherical harmonic "fingerprints", which we use to quantify the extent of icosahedral ordering.Comment: 8 pages, 4 figure

Excitations are localized and relaxation is hierarchical in glass-forming liquids

For several atomistic models of glass formers, at conditions below their glassy dynamics onset temperatures, ${T_\mathrm{o}}$, we use importance sampling of trajectory space to study the structure, statistics and dynamics of excitations responsible for structural relaxation. Excitations are detected in terms of persistent particle displacements of length $a$. At supercooled conditions, for $a$ of the order of or smaller than a particle diameter, we find that excitations are associated with correlated particle motions that are sparse and localized, occupying a volume with an average radius that is temperature independent and no larger than a few particle diameters. We show that the statistics and dynamics of these excitations are facilitated and hierarchical. Excitation energy scales grow logarithmically with $a$. Excitations at one point in space facilitate the birth and death of excitations at neighboring locations, and space-time excitation structures are microcosms of heterogeneous dynamics at larger scales. This nature of dynamics becomes increasingly dominant as temperature $T$ is lowered. We show that slowing of dynamics upon decreasing temperature below $T_\mathrm{o}$ is the result of a decreasing concentration of excitations and concomitant growing hierarchical length scales, and further that the structural relaxation time $\tau$ follows the parabolic law, $\log(\tau / \tau_\mathrm{o}) = J^2(1/T - 1/T_\mathrm{o})^2$, for $T<T_\mathrm{o}$, where $J$, $\tau_\mathrm{o}$ and $T_\mathrm{o}$ can be predicted quantitatively from dynamics at short time scales. Particle motion is facilitated and directional, and we show this becomes more apparent with decreasing $T$. We show that stringlike motion is a natural consequence of facilitated, hierarchical dynamics.Comment: 15 pages, 6 figures, + links to movies; To appear in Phys. Rev.