Scott Butler

The origin of glassy dynamics in the 2D facilitated kinetic Ising model

Monte Carlo simulation data from the two‐dimensional facilitated kinetic Ising model proposed by Fredrickson and Andersen is examined with the goal of understanding the processes responsible for the characteristic features of glassy dynamics. The spatial distribution of spin flip rates is found to be highly nonuniform with pockets of rapidly relaxing spins surrounded by kinetically locked domains. The slow relaxation of these latter domains, which gives rise to the characteristic long time tail of the linear response function, is due to the action of rare clusters of spins which are able to propagate their influence throughout the sample. An analytic expression is derived for the density of these active sites which is found to fully account for the non‐Arrhenius temperature dependence of the relaxation time in this model. The consequences of these results for both theories and experiments in structural glasses are discussed.

Factors determining crystal-liquid coexistence under shear

The interaction between an imposed shear flow and an order–disorder transition underlies a broad range of phenomena. Under the influence of shear flow, a variety of soft matter is observed to spontaneously form bands characterized by different local order—for example, thermotropic liquid crystals subjected to shear flow exhibit rich phase behaviour. The stability of order under the influence of shear flow is also fundamental to understanding frictional wear and lubrication. Although there exists a well developed theoretical approach to the influence of shear flow on continuous transitions in fluid mixtures, little is known about the underlying principles governing non-equilibrium coexistence between phases of different symmetry. Here we show, using non-equilibrium molecular dynamics simulations of a system of spherical particles, that a stationary coexistence exists between a strained crystal and the shearing liquid, and that this coexistence cannot be accounted for by invoking a non-equilibrium analogue of the chemical potential. Instead of such thermodynamic arguments, we argue that a balancing of the crystal growth rate with the rate of surface erosion by the shearing melt can account for the observed coexistence.

Glassy relaxation at surfaces: The correlation length of cooperative motion in the facilitated kinetic Ising model

A measure of cooperativity in glassy liquids is defined in terms of the kinetic correlation length of relaxation at a surface. This length and its temperature dependence is measured for the facilitated kinetic Ising model with both free and pinned surfaces. A simple power law is found to describe the relationship between the kinetic correlation length and the bulk relaxation time over four decades of data.

Simulation of the coexistence of a shearing liquid and a strained crystal

The coexistence between a strained crystal and its shearing melt is studied using nonequilibrium molecular dynamics simulations of Lennard-Jones particles. The coexistence is found to be independent of initial conditions, boundary effects, and the details of the thermostat. The nonequilibrium phase diagram is presented. The shear stress at coexistence is found to be significantly smaller than the yield stress of the crystal. It is demonstrated that there exists no physically reasonable prescription for a nonequilibrium analogue of chemical potential for the shearing liquid by which the coexistence could be attributed to an equality of chemical potentials between the two phases. We conclude that the nonequilibrium coexistence is determined by the stability of the interface.

Shear induced ordering in simulations of colloidal suspensions: Oscillatory shear and computational artefacts

We report on the nature of the shear induced order observed in nonequilibrium Brownian dynamics simulations of particles interacting via a screened Coulomb potential. Under steady shear, the nature of the ordered phase differs depending on the temperature. Below the equilibrium melting temperature, the shear induced order takes the form of hexagonally packed strings aligned along the direction of flow. Above the melting temperature, the liquid organizes itself into unstructured layers whose normal lies parallel to the shear gradient. We find a significant and anisotropic system size dependence of the ordering transition under steady shear. The critical shear rate required for ordering increases with increasing length of the simulation cell along the direction of flow. No such size dependence is found in oscillatory shears whose amplitude is less than half the cell length. Our results suggest that the order found in simulations under steady shear is an artefact of pseudo‐oscillations resulting from shearin...

The shear induced disordering transition in a colloidal crystal: Nonequilibrium Brownian dynamic simulations

The shear induced disordering transition as observed in a dilute suspension of charged colloidal particles is modeled using nonequilibrium Brownian dynamics simulations. We report both real space and reciprocal space representations of the structure and dynamics of the sequence of steady states found as the shear rate is increased. While reproducing the observed steady‐state structures at low shear rates, the simulated system was found to follow a different path to disorder with increasing shear. We find that the disordering process involves the accumulation of interstitial‐vacancy defects in the shearing crystal as the shear rate increases. The disordering transition is also shown to exhibit an anisotropic dependence on system size. These two observations are combined in a new picture of the shear induced disordering transition. In this model a nonequilibrium defect density, generated by the coupling of long‐wavelength fluctuations with the shear flow, eventually results in a collective disordering simil...