Molecular dynamics studies of heterogeneous dynamics and dynamic crossover in supercooled atomic liquids

Roles of bond orientational ordering in glass transition and crystallization

It is widely believed that crystallization in three dimensions is primarily controlled by positional ordering, and not by bond orientational ordering. In other words, bond orientational ordering is usually considered to be merely a consequence of positional ordering and thus has often been ignored. This one-order-parameter (density) description may be reasonable when we consider an equilibrium liquid-solid transition, but may not be enough to describe a metastable state and the kinetics of the transition. Here we propose that bond orientational ordering can play a key role in (i) crystallization, (ii) the ordering to quasi-crystal and (iii) vitrification, which occurs under rather weak frustration against crystallization. In a metastable supercooled state before crystallization, a system generally tends to have bond orientational order at least locally as a result of a constraint of dense packing. For a system interacting with hard-core repulsions, the constraint is intrinsically of geometrical origin and thus the basic physics is the same as nematic ordering of rod-like particles upon densification. Furthermore, positional ordering is easily destroyed even by weak frustration such as polydispersity and anisotropic interactions which favour a symmetry not consistent with that of the equilibrium crystal. Thus we may say that vitrification can be achieved by disturbing and prohibiting long-range positional ordering. Even in such a situation, bond orientational ordering still survives, accompanying its critical-like fluctuations, which are the origin of dynamic heterogeneity for this case. This scenario naturally explains both the absence of positional order and the development of bond orientational order upon cooling in a supercooled state. Although our argument is speculative in nature, we emphasize that this physical picture can coherently explain crystallization, vitrification, quasi-crystallization and their relationship in a natural manner. For a strongly frustrated system, even bond orientational order can be destroyed. Even in such a case there may still appear a structural signature of dense packing, which is linked to slow dynamics.

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.

Structural signature of slow dynamics and dynamic heterogeneity in two-dimensional colloidal liquids: glassy structural order

Glassy states are formed if crystallization is avoided upon cooling or increasing density. However, the physical factors controlling the ease of vitrification and the nature of glass transition remain elusive. Among various glass-forming systems, colloidal liquids are one of the most ideal glass-forming systems because of the simplicity and controllability of the interactions. We use numerical simulations of two-dimensional polydisperse and binary hard discs to tackle both of these longstanding questions. For polydisperse systems, we systematically control the polydispersity, which can be regarded as the strength of frustration effects on crystallization. We reveal that crystal-like hexatic order grows in size and lifetime with an increase in the colloid volume fraction or with a decrease in polydispersity (or frustration). We stress that hexatic ordering in hard disc systems is a direct consequence of dense packing and a manifestation of low configurational entropy. Our study suggests an intriguing scenario that the strength of frustration controls both the ease of vitrification and the nature of the glass transition. Vitrification may be a process of hidden crystal-like ordering under frustration for this system. This may provide not only a physical basis for glass formation, but also an answer to another longstanding question on the structure of amorphous materials: 'order in disorder' may be an intrinsic feature of a glassy state of many materials. For binary mixtures, on the other hand, the relevant structural feature linked to slow dynamics is not hexatic order, but an amorphous structure of low structural entropy. These results suggest that slow dynamics is associated with bond orientational order linked to the crystal for a weakly frustrated system, whereas to amorphous structures of low configurational entropy for a strongly frustrated system. This suggests an intrinsic link between structure and dynamics in glass-forming materials: slow dynamics is linked to structuring ('glassy ordering') towards low configurational entropy. We discuss the nature of 'glassy order' responsible for slow dynamics.

Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture

We examine a length scale that characterizes the spatial extent of heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the mode-coupling volume fraction ϕ(c). First, we characterize the system's dynamics. Then, we utilize a method [Phys. Rev. Lett. 105, 217801 (2010)] to extract and analyze the ensemble-independent dynamic susceptibility χ(4)(t) and the dynamic correlation length ξ(t) for a range of times between the β and α relaxation times. We find that in this time range the dynamic correlation length follows a volume fraction-independent master curve ξ(t)~ln(t). For longer times, ξ(t) departs from this master curve and remains constant up to the largest time at which we can determine the length accurately. In addition to the previously established correlation τ(α)~exp[ξ(τ(α))] between the α relaxation time, τ(α), and the dynamic correlation length at this time, ξ(τ(α)), we also find a similar correlation for the diffusion coefficient D~exp[ξ(τ(α))(θ)] with θ≈0.6. We discuss the relevance of these findings for different theories of the glass transition.

Viscosity, shear waves, and atomic-level stress-stress correlations

The Green-Kubo equation relates the macroscopic stress-stress correlation function to a liquid's viscosity. The concept of the atomic-level stresses allows the macroscopic stress-stress correlation function in the equation to be expressed in terms of the space-time correlations among the atomic-level stresses. Molecular dynamics studies show surprisingly long spatial extension of stress-stress correlations and also longitudinal and transverse waves propagating in liquids over ranges which could exceed the system size. The results reveal that the range of propagation of shear waves corresponds to the range of distances relevant for viscosity. Thus our results show that viscosity is a fundamentally nonlocal quantity. We also show that the periodic boundary conditions play a nontrivial role in molecular dynamics simulations, effectively masking the long-range nature of viscosity.

Glass transition of the monodisperse Gaussian core model

We numerically investigate the dynamical properties of the one-component Gaussian core model in supercooled states. We find that nucleation is increasingly suppressed with increasing density. The system concomitantly exhibits glassy, slow dynamics characterized by the two-step stretched exponential relaxation of the density correlation and a drastic increase of the relaxation time. We also find a weaker violation of the Stokes-Einstein relation and a smaller non-Gaussian parameter than in typical model glass formers, implying weaker dynamic heterogeneities. Additionally, the agreement of the simulation data with the prediction of mode-coupling theory is exceptionally good, indicating that the nature of the slow dynamics of this ultrasoft particle fluid is mean-field-like. This fact may be understood as a consequence of the long-range nature of the interaction.

Structural origin of dynamic heterogeneity in three-dimensional colloidal glass formers and its link to crystal nucleation

The physical understanding of glass transition remains a major challenge of physics and materials science. Among various glass-forming liquids, a colloidal liquid interacting with hard-core repulsion is now regarded as one of the most ideal model systems. Here we study the structure and dynamics of three-dimensional polydisperse colloidal liquids by Brownian dynamics simulations. We reveal that medium-range crystalline bond orientational order of the hexagonal close packed structure grows in size and lifetime with increasing packing fraction. We show that dynamic heterogeneity may be a direct consequence of this transient structural ordering, which suggests its origin is thermodynamic rather than kinetic. We also reveal that nucleation of crystals preferentially occurs in regions of high medium-range order, reflecting the low crystal-liquid interfacial energy there. These findings may shed new light not only on the fundamental nature of the glass transition, but also the mechanism of crystal nucleation.

Probing a critical length scale at the glass transition

We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size, which is typical of critical phenomena. Our approach is to introduce an external, static perturbation to extract the structural information from the system's response. In particular, we consider the transformation behavior of the local minima of the underlying potential energy landscape (inherent structures), under a static deformation. The finite-size scaling analysis of our numerical results indicate that the correlation length diverges at a temperature Tc, below the temperatures where the system can be equilibrated. Our numerical results are consistent with random first order theory, which predicts such a divergence with a critical exponent ν=2/3 at the Kauzmann temperature, where the extrapolated configurational entropy vanishes.

Diverging length scale of the inhomogeneous mode-coupling theory: a numerical investigation

Biroli 's extension of the standard mode-coupling theory to inhomogeneous equilibrium states [G. Biroli, J. P. Bouchaud, K. Miyazaki, and D. R. Reichman, Phys. Rev. Lett. 97, 195701 (2006)] allowed them to identify a characteristic length scale that diverges upon approaching the mode-coupling transition. We present a numerical investigation of this length scale. To this end we derive and numerically solve equations of motion for coefficients in the small q expansion of the dynamic susceptibility chiq(k;t) that describes the change of the system's dynamics due to an external inhomogeneous potential. We study the dependence of the characteristic length scale on time, wave vector, and on the distance from the mode-coupling transition. We verify scaling predictions of Biroli In addition, we find that the numerical value of the diverging length scale qualitatively agrees with lengths obtained from four-point correlation functions. We show that the diverging length scale has very weak k dependence, which contrasts with very strong k dependence of the q-->0 limit of the susceptibility, chiq=0(k;t) . Finally, we compare the diverging length obtained from the small q expansion to that resulting from an isotropic approximation applied to the equation of motion for the dynamic susceptibility chiq(k;t) .

Second-order dynamic transition in a p=2 spin-glass model

We consider the dynamics of a disordered p -spin model with p=2 , analyzing the dynamics within Ruelle's thermodynamic formalism, We use an indicator of the dynamical activity to construct the relevant dynamical Gibbs ensemble. We prove that the dynamics in the low-temperature (spin-glass) phase of the model take place at a second-order phase transition between dynamically active and inactive trajectories. We also show that the same behavior is found in a related model of a three-dimensional ferromagnet.

Molecular random tilings as glasses

We have recently shown that p-terphenyl-3,5,3',5'-tetracarboxylic acid adsorbed on graphite self-assembles into a two-dimensional rhombus random tiling. This tiling is close to ideal, displaying long-range correlations punctuated by sparse localized tiling defects. In this article we explore the analogy between dynamic arrest in this type of random tilings and that of structural glasses. We show that the structural relaxation of these systems is via the propagation-reaction of tiling defects, giving rise to dynamic heterogeneity. We study the scaling properties of the dynamics and discuss connections with kinetically constrained models of glasses.

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) .

Three-point susceptibilities chi(n) (k;t) and chi(n)s (k;t): mode-coupling approximation

Recently, it was argued that a three-point susceptibility equal to the density derivative of the intermediate scattering function, chi{n}(k;t)=dF(k;t)dn , enters into an expression for the divergent part of an integrated four-point dynamic density correlation function of a colloidal suspension [Berthier, J. Chem. Phys. 126, 184503 (2007)]. We show that, within the mode-coupling theory, the equation of motion for chi{n}(k;t) is essentially identical as the equation of motion for the q-->0 limit of the three-point susceptibility chi{q}(k;t) introduced by Biroli [Phys. Rev. Lett. 97, 195701 (2006)]. We present a numerical solution of the equation of motion for chi{n}(k;t) . We also derive and numerically solve an equation of motion for the density derivative of the self-intermediate scattering function, chi_{n};{s}(k;t)=dF;{s}(k;t)dn . We contrast the wave vector dependence of chi{n}(k;t) and chi{n};{s}(k;t) .

Scaling analysis of dynamic heterogeneity in a supercooled Lennard-Jones liquid

We have performed molecular dynamics computer simulations of a dense Lennard-Jones liquid mixture to study dynamic heterogeneity from normal liquid temperatures down to a supercooled temperature 15% above the previously identified mode-coupling temperature Tc of the model. A temperature-dependent correlation length associated with the correlation function of mobility fluctuations is calculated. The results are used to test two sets of scaling hypotheses for the dynamic heterogeneity. The results are in close agreement with the inhomogeneous mode-coupling theory of Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)] for both the alpha and beta relaxation regimes. Comparison with results for kinetically constrained models suggest that the Lennard-Jones mixture studied is more similar to models of fragile liquids than models of very strong liquids.

Subdiffusive motion in kinetically constrained models

We discuss a kinetically constrained model in which real-valued local densities fluctuate in time, as introduced recently by Bertin, Bouchaud, and Lequeux. We show how the phenomenology of this model can be reproduced by an effective theory of mobility excitations propagating in a disordered environment. Both excitations and probe particles have subdiffusive motion, characterized by different exponents and operating on different time scales. We derive these exponents, showing that they depend continuously on one of the parameters of the model.

Divergent four-point dynamic density correlation function of a glassy suspension

We use a recently derived diagrammatic formulation of the dynamics of interacting Brownian particles [G. Szamel, J. Chem. Phys. 127, 084515 (2007)10.1063/1.2759487] to study a four-point dynamic density correlation function. We resum a class of diagrams which separate into two disconnected components upon cutting a single propagator. The resulting formula for the four-point correlation function can be expressed in terms of three-point functions closely related to the three-point susceptibility introduced by Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)10.1103/PhysRevLett.97.195701] and the standard two-point correlation function. The four-point function has a structure very similar to that proposed by Berthier and collaborators [Science 310, 1797 (2005)10.1126/science.1120714; J. Chem. Phys. 126, 184503 (2007)10.1063/1.2721554]. It exhibits a small wave vector divergence at the mode-coupling transition.

Universal link between the boson peak and transverse phonons in glass

The physical properties of a topologically disordered amorphous material (glass), such as heat capacity and thermal conductivity, are markedly different from those of its ordered crystalline counterpart. The understanding of these phenomena is a notoriously complex problem. One of the universal features of disordered glasses is the 'boson peak', which is observed in neutron and Raman scattering experiments. The boson peak is typically ascribed to an excess density of vibrational states. Here, we study the nature of the boson peak, using numerical simulations of several glass-forming systems. We discovered evidence suggestive of the equality of the boson peak frequency to the Ioffe-Regel limit for 'transverse' phonons, above which transverse phonons no longer propagate. Our results indicate a possibility that the origin of the boson peak is transverse vibrational modes associated with defective soft structures in the disordered state. Furthermore, we suggest a possible link between slow structural relaxation and fast boson peak dynamics in glass-forming systems.

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.

Study of spatial correlations in a supercooled molecular system

Spatial heterogeneities have been investigated in a supercooled system composed of diatomic molecules with an associated dipole moment by using the molecular dynamics simulation technique. Pair distribution functions of molecules with different mobilities have been evaluated, and it has been found that molecules belonging to the same dynamic domain are spatially correlated. Molecules with extremely large mobilities form larger clusters than those resulting from random statistics. These clusters are stringlike shaped. The mean cluster size displays a maximum at times between the ballistic and the diffusive regime, approximately at the end of the beta-relaxation zone. The value of this maximum increases upon cooling the system. An analogous profile has been observed for the characteristic cluster length when plotted against time. Agreement with Adam-Gibbs predictions has been encountered when considering these clusters as the basic dynamic units of the theory. For the extremely slow molecules, a cluster distribution has also been encountered. These clusters are smaller than the ones composed by fast molecules; they do not have a quasilinear geometry and no maximum is observed for their mean cluster size.

Negative differential mobility of weakly driven particles in models of glass formers

We study the response of probe particles to weak constant driving in kinetically constrained models of glassy systems, and show that the probe's response can be nonmonotonic and give rise to negative differential mobility: increasing the applied force can reduce the probe's drift velocity in the force direction. Other significant nonlinear effects are also demonstrated, such as the enhancement with increasing force of the probe's fluctuations away from the average path, a phenomenon known in other contexts as giant diffusivity. We show that these results can be explained analytically by a continuous-time random walk approximation where there is decoupling between persistence and exchange times for local displacements of the probe. This decoupling is due to dynamic heterogeneity in the glassy system, which also leads to bimodal distributions of probe particle displacements. We discuss the relevance of our results to experiments.

Decoupling of exchange and persistence times in atomistic models of glass formers

With molecular dynamics simulations of a fluid mixture of classical particles interacting with pairwise additive Weeks-Chandler-Andersen potentials, we consider the time series of particle displacements and thereby determine the distributions for local persistence times and local exchange times. These basic characterizations of glassy dynamics are studied over a range of supercooled conditions and were shown to have behaviors, most notably decoupling, similar to those found in kinetically constrained lattice models of structural glasses. Implications are noted.

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.

Glassiness of Thermotropic Liquid Crystals across the Isotropic−Nematic Transition

The orientational dynamics of thermotropic liquid crystals across the isotropic-nematic phase transition have traditionally been investigated at long times or low frequencies using frequency domain measurements. The situation has now changed significantly with the recent report of a series of interesting transient optical Kerr effect (OKE) experiments that probed orientational relaxation of a number of calamitic liquid crystals (which consist of rod-like molecules) directly in the time domain, over a wide time window ranging from subpicoseconds to tens of microseconds. The most intriguing revelation is that the decay of the OKE signal at short to intermediate times (from a few tens of picoseconds to several hundred nanoseconds) follows multiple temporal power laws. Another remarkable feature that has emerged from these OKE measurements is the similarity in the orientational relaxation behavior between the isotropic phase of calamitic liquid crystals near the isotropic-nematic transition and supercooled molecular liquids, notwithstanding their largely different macroscopic states. In this article, we present an overview of the understanding that has emerged from recent computational and theoretical studies of calamitic liquid crystals across the isotropic-nematic transition. Topics discussed include (a) single-particle as well as collective orientational dynamics at a short-to-intermediate time window, (b) heterogeneous dynamics in orientational degrees of freedom diagnosed by a non-Gaussian parameter, (c) fragility, and (d) temperature-dependent exploration of underlying energy landscapes as calamitic liquid crystals settle into increasingly ordered mesophases upon cooling from the high-temperature isotropic phase. A comparison of our results with those of supercooled molecular liquids reveals an array of analogous features in these two important classes of soft matter systems. We further find that the onset of growth of the orientational order in the parent nematic phase induces translational order, resulting in smectic-like layers in the potential energy minima of calamitic systems if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. We discuss implications of this startling observation. We also discuss recent results on the orientational dynamics of discotic liquid crystals that are found to be rather similar to those of calamitic liquid crystals.

Connecting microscopic simulations with kinetically constrained models of glasses

Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some "mobility" field. The identity of this "mobility" field has remained elusive due to the lack of coarse-graining procedures to obtain these models from a more microscopic point of view. Here we exhibit a scheme to map the dynamics of a two-dimensional soft disk glass former onto a kinetically constrained spin model, providing an attempt at bridging these two approaches.

Equilibrium density of states and thermodynamic properties of a model glass former

This paper presents an analysis of the thermodynamics of a model glass former. We have performed equilibrium sampling of a popular binary Lennard-Jones model, employing parallel tempering Monte Carlo to cover the crystalline, amorphous, and liquid regions of configuration space. Disconnectivity graphs are used to visualize the potential energy landscape in the vicinity of a crystalline geometry and in an amorphous region of configuration space. The crystalline global minimum is separated from the bulk of the minima by a large potential energy gap, leading to broken ergodicity in conventional simulations. Our sampling reveals crystalline global minima that are lower in potential energy than some of the previous candidates. We present equilibrium thermodynamic properties based on parallel tempering simulations, including heat capacities and free energy profiles, which depend explicitly on the crystal structure. We also report equilibrium melting temperatures.

Spontaneous and induced dynamic fluctuations in glass formers. I. General results and dependence on ensemble and dynamics

We study theoretically and numerically a family of multipoint dynamic susceptibilities that quantify the strength and characteristic length scales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments (fluctuation-dissipation relations and symmetries of relevant dynamical field theories) to relate the sensitivity of averaged two-time correlators to temperature and density to spontaneous fluctuations of the local dynamics. Our theoretical results are then compared to molecular dynamics simulations of the Newtonian, Brownian, and Monte Carlo dynamics of two representative glass-forming liquids, a fragile binary Lennard-Jones mixture, and a model for the strong glass-former silica. We justify in detail the claim made by Berthier et al. [Science 310, 1797 (2005)] that the temperature dependence of correlation functions allows one to extract useful information on dynamic length scales in glassy systems. We also discuss some subtle issues associated with the choice of microscopic dynamics and of statistical ensemble through conserved quantities, which are found to play an important role in determining dynamic correlations.

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations

We study in detail the predictions of various theoretical approaches, in particular, mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wave vector dependence of multipoint correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multipoint correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular, explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multipoint correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.

Revisiting the slow dynamics of a silica melt using Monte Carlo simulations

We implement a standard Monte Carlo algorithm to study the slow, equilibrium dynamics of a silica melt in a wide temperature regime, from 6100K down to 2750K . We find that the average dynamical behavior of the system is in quantitative agreement with results obtained from molecular dynamics simulations, at least in the long-time regime corresponding to the alpha -relaxation. By contrast, the strong thermal vibrations related to the boson peak present at short times in molecular dynamics are efficiently suppressed by the Monte Carlo algorithm. This allows us to reconsider silica dynamics in the context of mode-coupling theory, because several shortcomings of the theory were previously attributed to thermal vibrations. A mode-coupling theory analysis of our data is qualitatively correct, but quantitative tests of the theory fail, raising doubts about the very existence of an avoided singularity in this system. We discuss the emergence of dynamic heterogeneity and report detailed measurements of a decoupling between translational diffusion and structural relaxation, and of a growing four-point dynamic susceptibility. Dynamic heterogeneity appears to be less pronounced than in more fragile glass-forming models, but not of a qualitatively different nature.

The laboratory glass transition

The phenomenology of the laboratory glass transition is examined in the enthalpy landscape framework. It is shown that a generic description of the glassy state based on partitioning of the phase space caused by the finiteness of the time of observation explains all universal features of glass transition. Using this description of glass, which is referred to as the extrinsically constrained liquid, expressions are derived for properties of glass and for property changes at the laboratory glass transition. A model enthalpy landscape is used to illustrate the basic concepts of this description. Additional new consequences of this description, such as the role of complexity in glass transition and the zero residual entropy of a glass, are discussed.

Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy materials

In a recent article [M. Merolle et al., Proc. Natl. Acad. Sci. U.S.A. 102, 10837 (2005)], it was argued that dynamic heterogeneity in d-dimensional glass formers is a manifestation of an order-disorder phenomenon in the d+1 dimensions of space time. By considering a dynamical analog of the free energy, evidence was found for phase coexistence between active and inactive regions of space time, and it was suggested that this phenomenon underlies the glass transition. Here we develop these ideas further by investigating in detail the one-dimensional Fredrickson-Andersen (FA) model, in which the active and inactive phases originate in the reducibility of the dynamics. We illustrate the phase coexistence by considering the distributions of mesoscopic space-time observables. We show how the analogy with phase coexistence can be strengthened by breaking microscopic reversibility in the FA model, leading to a nonequilibrium theory in the directed percolation universality class.

Lengthscale dependence of dynamic four-point susceptibilities in glass formers

Dynamical four-point susceptibilities measure the extent of spatial correlations in the dynamics of glass forming systems. We show how these susceptibilities depend on the lengthscales that necessarily form part of their definition. The behavior of these susceptibilities is estimated by means of an analysis in terms of renewal processes within the context of dynamic facilitation. The analytic results are confirmed by numerical simulations of an atomistic model glass former, and of two kinetically constrained models. Hence we argue that the scenario predicted by the dynamic facilitation approach is generic.

Bridge functions near the liquid-vapor coexistence curve in binary Lennard-Jones mixtures

We have carried out extensive molecular-dynamics simulation studies of binary Lennard-Jones mixtures to calculate directly the bridge function at state points lying in a very narrow single fluid phase region between the vapor-liquid and solid-liquid coexistence lines [Lamm and Hall, Fluid Phase Equilib. 182, 37 (2001); 194-197, 197 (2002)]. By varying the density close to the liquid-vapor coexistence line, significant deviations are observed at intermediate distances between the simulated bridge function and two widely used approximate closures in the integral equation theory of liquids, viz. the hybrid mean spherical approximation and the Duh-Henderson closures. The overall qualitative agreement remains the same with small variation in temperature that brings the system closer to either the liquid-vapor or liquid-solid coexistence curve. We also report a comparison of the direct and indirect correlation functions obtained from our simulation studies as well as from the integral equation theory of liquids. Our results emphasize the need for developing new closures applicable to binary fluid mixtures over a wide range of thermodynamic parameters.

Hybrid Monte Carlo simulation of a glass-forming binary mixture

We propose a different, hybrid Monte Carlo algorithm that combines configurational bias particle swaps with parallel tempering. We use this algorithm to simulate a standard model of a glass-forming binary mixture above and below the so-called mode-coupling temperature T(MCT). We find that an ansatz that was used previously to extrapolate thermodynamic quantities to temperatures below T(MCT) breaks down in the vicinity of the mode-coupling temperature. We also find that the Adam-Gibbs relations D(alpha)exp(-a/TS(c)) and tau(alpha)exp(b/TS(c)), which connect the diffusion coefficient D and the relaxation time tau with the configurational entropy S(c), are valid for all temperatures for which the configurational and vibrational contributions to the free energy decouple.

Time scale for the onset of Fickian diffusion in supercooled liquids

We propose a quantitative measure of a time scale on which Fickian diffusion sets in for supercooled liquids, and we use Brownian dynamics computer simulations to determine the temperature dependence of this onset time in a Lennard-Jones binary mixture. The time for the onset of Fickian diffusion ranges between 6.5 and 31 times the relaxation time (the relaxation time is the characteristic relaxation time of the incoherent intermediate scattering function). The onset time increases faster with decreasing temperature than the relaxation time. Mean-squared displacement at the onset time increases with decreasing temperature.

Dynamical heterogeneity close to the jamming transition in a sheared granular material

The dynamics of a bidimensional dense granular packing under cyclic shear is experimentally investigated close to the jamming transition. Measurement of multipoint correlation functions are produced. The self-intermediate scattering function, displaying slower than exponential relaxation, suggests dynamic heterogeneity. Further analysis of four point correlation functions reveal that the grain relaxations are strongly correlated and spatially heterogeneous, especially at the time scale of the collective rearrangements. Finally, a dynamical correlation length is extracted from a spatiotemporal pattern of mobility. Our experimental results open the way to a systematic study of dynamic correlation functions in granular materials.