Structure and dynamics of glass formers: predictability at large length scales

Correlating structural order with structural rearrangement in dusty plasma liquids: can structural rearrangement be predicted by static structural information?

Whether the static microstructural order information is strongly correlated with the subsequent structural rearrangement (SR) and their predicting power for SR are investigated experimentally in the quenched dusty plasma liquid with microheterogeneities. The poor local structural order is found to be a good alarm to identify the soft spot and predict the short term SR. For the site with good structural order, the persistent time for sustaining the structural memory until SR has a large mean value but a broad distribution. The deviation of the local structural order from that averaged over nearest neighbors serves as a good second alarm to further sort out the short time SR sites. It has the similar sorting power to that using the temporal fluctuation of the local structural order over a small time interval.

Using mutual information to measure order in model glass formers

Whether or not there is growing static order accompanying the dynamical heterogeneity and increasing relaxation times seen in glassy systems is a matter of dispute. An obstacle to resolving this issue is that the order is expected to be amorphous and so not amenable to simple order parameters. We use mutual information to provide a general measurement of order that is sensitive to multiparticle correlations. We apply this to two glass-forming systems (two-dimensional binary mixtures of hard disks with different size ratios to give varying amounts of hexatic order) and show that there is little growth of amorphous order in the system without crystalline order. In both cases we measure the dynamical length with a four-point correlation function and find that it increases significantly faster than the static lengths in the system as density is increased. We further show that we can recover the known scaling of the dynamic correlation length in a kinetically constrained model, the two-vacancy-assisted-hopping triangular lattice gas.

The physics of the colloidal glass transition

As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.

Random pinning in glassy spin models with plaquette interactions

We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk relaxation to localization in a single state. At low temperatures, both models exhibit scaling behavior. We discuss the growing length and time scales associated with amorphous order, and the fraction of pinned spins required to localize the system in a single state. These results, obtained for finite dimensional interacting models, provide a theoretical scenario for the effect of random pinning that differs qualitatively from previous approaches based either on mean-field, mode-coupling, or renormalization group treatments.

Correlation between dynamical heterogeneities, structure and potential-energy distribution in a 2D amorphous solid

We investigate the collective properties of particles in a 2D experimental system which consists of a bi-disperse mixture of colloidal particles confined at an air/water interface. We find a direct correlation between structure and dynamical heterogeneities in this system: particles belonging to locally ordered structures have lower potential energy and are slower than other particles. In a more general way we show that particles with high potential energy are dominating the dynamics especially in the α-relaxation regime.

Field theory of fluctuations in glasses

We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium arguments, we eliminate time from the description and we completely characterize fluctuations in the beta regime. We identify different sources of fluctuations and show that the most relevant ones are associated to variations of "self-induced disorder" in the initial condition of the dynamics. It follows that heterogeneites can be described through a cubic field theory with an effective random field term. The phenomenon of perturbative dimensional reduction ensues, well known in random field problems, which implies an upper critical dimension of the theory equal to 8. We apply our theory to finite size scaling for mean-field systems and we test its prediction against numerical simulations.

Spatial correlation of the dynamic propensity of a glass-forming liquid

We present computer simulation results on the dynamic propensity (as defined by Widmer-Cooper et al 2004 Phys. Rev. Lett. 93 135701) in a Kob-Andersen binary Lennard-Jones liquid system consisting of 8788 particles. We compute the spatial correlation function for the dynamic propensity as a function of both the reduced temperature T, and the time scale on which the particle displacements are measured. For T ≤ 0.6, we find that non-zero correlations occur at the largest length scale accessible in our system. We also show that a cluster-size analysis of particles with extremal values of the dynamic propensity, as well as 3D visualizations, reveal spatially correlated regions that approach the size of our system as T decreases, consistently with the behavior of the spatial correlation function. Next, we define and examine the 'coordination propensity', the isoconfigurational average of the coordination number of the minority B particles around the majority A particles. We show that a significant correlation exists between the spatial fluctuations of the dynamic and coordination propensities. In addition, we find non-zero correlations of the coordination propensity occurring at the largest length scale accessible in our system for all T in the range 0.466 < T < 1.0. We discuss the implications of these results for understanding the length scales of dynamical heterogeneity in glass-forming liquids.

Glass transition of two-dimensional binary soft-disk mixtures with large size ratios

We simulate binary soft-disk systems in two dimensions and investigate how the dynamics slow as the area fraction is increased toward the glass transition. The "fragility" quantifies how sensitively the relaxation time scale depends on the area fraction, and the fragility strongly depends on the composition of the mixture. We confirm prior results for mixtures of particles with similar sizes, where the ability to form small crystalline regions correlates with fragility. However, for mixtures with particle size ratios above 1.4, we find that the fragility is not correlated with structural ordering, but rather with the spatial distribution of large particles. The large particles have slower motion than the small particles and act as confining "walls" which slow the motion of nearby small particles. The rearrangement of these confining structures governs the lifetime of dynamical heterogeneity, that is, how long local regions exhibit anomalously fast or slow behavior. The strength of the confinement effect is correlated with the fragility and also influences the aging behavior of glassy systems.

Spatiotemporal hierarchy of relaxation events, dynamical heterogeneities, and structural reorganization in a supercooled liquid

We identify the pattern of microscopic dynamical relaxation for a two-dimensional glass-forming liquid. On short time scales, bursts of irreversible particle motion, called cage jumps, aggregate into clusters. On larger time scales, clusters aggregate both spatially and temporally into avalanches. This propagation of mobility takes place along the soft regions of the systems, which have been identified by computing isoconfigurational Debye-Waller maps. Our results characterize the way in which dynamical heterogeneity evolves in moderately supercooled liquids and reveal that it is astonishingly similar to the one found for dense glassy granular media.

From coupled elementary units to the complexity of the glass transition

Supercooled liquids display fascinating properties upon cooling such as the emergence of dynamic length scales. Different models strongly vary with respect to the choice of the elementary subsystems as well as their mutual coupling. Here we show via computer simulations of a glass former that both ingredients can be identified via analysis of finite-size effects within the continuous-time random walk framework. The subsystems already contain complete information about thermodynamics and diffusivity, whereas the coupling determines structural relaxation and the emergence of dynamic length scales.

Local elasticity map and plasticity in a model Lennard-Jones glass

In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

Dynamics and energy landscape in a tetrahedral network glass-former: direct comparison with models of fragile liquids

We report molecular dynamics simulations for a new model of tetrahedral network glass-former, based on short-range spherical potentials. Despite the simplicity of the forcefield employed, our model reproduces some essential physical properties of silica, an archetypal network-forming material. Structural and dynamical properties, including dynamic heterogeneities and the nature of local rearrangements, are investigated in detail and a direct comparison with models of close-packed, fragile glass-formers is performed. The outcome of this comparison is rationalized in terms of the properties of the potential energy surface, focusing on the unstable modes of the stationary points. Our results indicate that the weak degree of dynamic heterogeneity observed in network glass-formers may be attributed to an excess of localized unstable modes, associated with elementary dynamical events such as bond breaking and reformation. In contrast, the more fragile Lennard-Jones mixtures are characterized by a larger fraction of extended unstable modes, which lead to a more cooperative and heterogeneous dynamics.

Anisotropic spatially heterogeneous dynamics on the alpha and beta relaxation time scales studied via a four-point correlation function

We examine the anisotropy of a four-point correlation function G4(k[over ],r[over ];t) and its associated structure factor S4(k[over ],q[over ];t) calculated using Brownian dynamics computer simulations of a model glass forming system. These correlation functions measure the spatial correlations of the relaxation of different particles. We examine the time and temperature dependences of the anisotropy in both functions. We find that the anisotropy is strongest at nearest-neighbor distances at time scales corresponding to the peak of the non-Gaussian parameter alpha_{2}(t)=3deltar;{4}(t)/[5deltar;{2}(t);{2}]-1 but is still pronounced around the alpha relaxation time. We find that the structure factor S4(k[over ],q[over ];t) is anisotropic even for the lowest wave vector accessible in our simulation, suggesting that our system (and other systems commonly used in computer simulations) may be too small to extract the q[over ]-->0 limit of the structure factor. We find that the determination of a dynamic correlation length from S4(k[over ],q[over ];t) is influenced by the anisotropy. We extract an effective anisotropic dynamic correlation length from the small q behavior of S4(k[over ],q[over ];t) .

Intermittent and spatially heterogeneous single-particle dynamics close to colloidal gelation

Dynamical heterogeneities exist ubiquitously in materials near a dynamical arrest transition, such as glass formation or gelation. Among the readily discernible features of heterogeneous dynamics is a non-Gaussian exponential component in the distribution of the constituent particle displacements that is not understood at the single-particle level. We present an experimental study of particle dynamics and self-van Hove functions G_{s}(r,t) in a colloid-polymer system approaching gelation. We show experimental evidence, in the special case of a gelation transition, for exponentially distributed times for anomalously large displacements, and confirm that an exponential tail in G_{s} arises from rare events with associated Poisson statistics. We focus on the role of the anomalous large displacements and analyze their time scales, relating them to other time scales typically used to describe structural relaxation in gels and glasses: the time to cage breakup and the time for re-emergence of Fickian behavior at long times. Furthermore, we search for a structural origin of the dynamical heterogeneity. Various quantities characterizing local structure are examined. We found evidence of a strong correlation between local structure and local dynamics, in contrast to what has been found in supercooled liquids.

Glass transitions in one-, two-, three-, and four-dimensional binary Lennard-Jones systems

We investigate the calorimetric liquid-glass transition by performing simulations of a binary Lennard-Jones mixture in one through four dimensions. Starting at a high temperature, the systems are cooled to T = 0 and heated back to the ergodic liquid state at constant rates. Glass transitions are observed in two, three and four dimensions as a hysteresis between the cooling and heating curves. This hysteresis appears in the energy and pressure diagrams, and the scanning rate dependence of the area and height of the hysteresis can be described using power laws. The one-dimensional system does not experience a glass transition but its specific heat curve resembles the shape of the D≥2 results in the supercooled liquid regime above the glass transition. As D increases, the radial distribution functions reflect reduced geometric constraints. Nearest neighbor distances become smaller with increasing D due to interactions between nearest and next-nearest neighbors. Simulation data for the glasses are compared with crystal and melting data obtained with a Lennard-Jones system with only one type of particle and we find that with increasing D crystallization becomes increasingly more difficult.

Tracking heterogeneous dynamics during the alpha relaxation of a simple glass former

We study the relaxation process in a simple glass former--the Kob-Andersen lattice gas model. We show that, for this model, structural relaxation is due to slow percolation of regions of cooperatively moving particles, which leads to heterogeneous dynamics of the system. We find that the size distribution of these regions is given by a power law and that their formation is encoded in the initial structure of the particles, with the memory of initial configuration increasingly retained with increasing density.

Exploring the potential energy landscape of glass-forming systems: from inherent structures via metabasins to macroscopic transport

In this review a systematic analysis of the potential energy landscape (PEL) of glass-forming systems is presented. Starting from the thermodynamics, the route towards the dynamics is elucidated. A key step in this endeavor is the concept of metabasins. The relevant energy scales of the PEL can be characterized. Based on the simulation results for some glass-forming systems one can formulate a relevant model system (ideal Gaussian glass-former) which can be treated analytically. The macroscopic transport can be related to the microscopic hopping processes, using either the strong relation between energy (thermodynamics) and waiting times (dynamics) or, alternatively, the concepts of the continuous-time random walk. The relation to the geometric properties of the PEL is stressed. The emergence of length scales within the PEL approach as well as the nature of finite-size effects is discussed. Furthermore, the PEL view is compared to other approaches describing the glass transition.

Dynamical heterogeneity in a glass-forming ideal gas

We conduct a numerical study of the dynamical behavior of a system of three-dimensional "crosses," particles that consist of three mutually perpendicular line segments of length sigma rigidly joined at their midpoints. In an earlier study [W. van Ketel, Phys. Rev. Lett. 94, 135703 (2005)] we showed that this model has the structural properties of an ideal gas, yet the dynamical properties of a strong glass former. In the present paper we report an extensive study of the dynamical heterogeneities that appear in this system in the regime where glassy behavior sets in. On the one hand, we find that the propensity of a particle to diffuse is determined by the structure of its local environment. The local density around mobile particles is significantly less than the average density, but there is little clustering of mobile particles, and the clusters observed tend to be small. On the other hand, dynamical susceptibility results indicate that a large dynamical length scale develops even at moderate densities. This suggests that propensity and other mobility measures are an incomplete measure of the dynamical length scales in this system.

Correlation between dynamic heterogeneity and medium-range order in two-dimensional glass-forming liquids

A glassy state of matter results if crystallization is avoided upon cooling or increasing density. However, the physical factors controlling the ease of vitrification and nature of the glass transition remain elusive. Using numerical simulations of polydisperse hard disks, we find a direct relation between medium-range crystalline ordering and the slow dynamics which characterizes the glass transition. This suggests an intriguing scenario that the strength of frustration controls both the ease of vitrification and nature of the glass transition. Vitrification may be a process of hidden crystalline ordering under frustration, at least in our system.