Spatial correlations in the dynamics of glassforming liquids: experimental determination of their temperature dependence

Nonlinear response theory for Markov processes: simple models for glassy relaxation

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature T_{0} determined by the value of the asymmetry. In a narrow temperature range around T_{0}, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than T_{0}), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times is considered. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.

Influence of confinement on dynamical heterogeneities in dense colloidal samples

We study a dense colloidal suspension confined between two quasiparallel glass plates as a model system for a supercooled liquid in confined geometries. We directly observe the three-dimensional Brownian motion of the colloidal particles using laser scanning confocal microscopy. The particles form dense layers along the walls, but crystallization is avoided as we use a mixture of two particle sizes. A normally liquidlike sample, when confined, exhibits slower diffusive motion. Particle rearrangements are spatially heterogeneous, and the shapes of the rearranging regions are strongly influenced by the layering. These rearranging regions become more planar upon confinement. The wall-induced layers and changing character of the spatially heterogeneous dynamics appear strongly connected to the confinement-induced glassiness.

Relaxation process and dynamical heterogeneities in chemical gels: critical behavior of self-overlap and its fluctuation

We study the dynamical behavior in chemical gelation, as the gelation threshold is approached from the sol phase. On the basis of the heterogeneous diffusion due to the cluster size distribution, as expected by the percolation theory, we predict the long time decay of the self-overlap as a power law in time t(-3/2). Moreover, under the hypothesis that the cluster diffusion coefficient decreases in size as a power law, s(-x), the fluctuation of the self-overlap, χ(4)(t), exhibits growth at short time as t((3-τ)/x), where τ is the cluster size distribution critical exponent. At longer times, χ(4)(t) decays as t(-3/2) while, at intermediate times, it reaches a maximum at time t*, which scales as s*(x), where s* is the size of the critical cluster. Finally, the value of the maximum χ(4)(t*) scales as the mean cluster size. The theoretical predictions are in agreement with molecular dynamic calculations in a model system, where spherical monomers are bonded by a finite extendable nonlinear elastic (FENE) potential.

Comparing dynamic correlation lengths from an approximation to the four-point dynamic susceptibility and from the picosecond vibrational dynamics

Recently an alternative approach to the determination of dynamic correlation lengths ξ for supercooled liquids, based on the properties of the slow (picosecond) vibrational dynamics, was carried out [Hong, Novikov, and Sokolov, Phys. Rev. E 83, 061508 (2011)]. Although these vibrational measurements are typically conducted well below the glass transition temperature, the liquid is frozen at T(g), whereby structural correlations, density variations, etc., manifested at low temperatures as spatial fluctuations of local elastic constants, can be related to a dynamic heterogeneity length scale for the liquid state. We compare ξ from this method to values calculated using an approximation to the four-point dynamic susceptibility. For 26 different materials we find good correlation between the two measures; moreover, the pressure dependences are consistent within the large experimental error. However, ξ from Boson peak measurements above T(g) have a different, and unrealistic, temperature dependence.

Third harmonics nonlinear susceptibility in supercooled liquids: a comparison to the box model

The box model, originally introduced to account for the nonresonant hole burning (NHB) dielectric experiments in supercooled liquids, is compared to the measurements of the third harmonics P(3) of the polarisation, reported recently in glycerol, close to the glass transition temperature T(g) [C. Crauste-Thibierge, C. Brun, F. Ladieu, D. L'Hôte, G. Biroli, and J.-P. Bouchaud, Phys. Rev. Lett. 104, 165703 (2010)]. In this model, each box is a distinct dynamical relaxing entity (hereafter called dynamical heterogeneity (DH)) which follows a Debye dynamics with its own relaxation time τ(dh). When it is submitted to a strong electric field, the model posits that a temperature increase δT(dh), depending on τ(dh), arises due to the dissipation of the electrical power. Each DH has thus its own temperature increase, on top of the temperature increase of the phonon bath δT(ph). Contrary to the "fast" hole burning experiments where δT(ph) is usually neglected, the P(3) measurements are, from a thermal point of view, fully in a stationary regime, which means that δT(ph) can no longer be neglected a priori. This is why the version of the box model that we study here takes δT(ph) into account, which implies that the δT(dh) of the DHs are all coupled together. The value of P(3), including both the "intrinsic" contribution of each DH as well as the "spurious" one coming from δT(ph), is computed within this box model and compared to the P(3) measurements for glycerol, in the same range of frequencies and temperatures T. Qualitatively, we find that this version of the box model shares with experiments some nontrivial features, e.g., the existence of a peak at finite frequency in the modulus of P(3) as well as its order of magnitude. Quantitatively, however, some experimental features are not accounted for by this model. We show that these differences between the model and the experiments do not come from δT(ph) but from the "intrinsic" contribution of the DHs. Finally, we show that the interferences between the 3ω response of the various DHs are the most important issue leading to the discrepancies between the box model prediction and the experiments. We argue that this could explain why the box model is quite successful to account for some kinds of nonlinear experiments (such as NHB) performed close to T(g), even if it does not completely account for all of them (such as the P(3) measurements). This conclusion is supported by an analytical argument which helps understanding how a "space-free" model as the box model is able to account for some of the experimental nonlinear features.

Experimental evidence for interplay of dynamic heterogeneity and finite-size effect in glassy polymers

Despite two decades of extensive research, direct experimental evidence of a dynamical length scale determining the glass transition of confined polymers has yet to emerge. Using a recently established experimental technique of interface micro-rheology we provide evidence of finite-size effect truncating the growth of a quantity proportional to a dynamical length scale in confined glassy polymers, on cooling towards the glass transition temperature. We show how the interplay of variation of polymer film thickness and this temperature-dependent growing dynamical length scale determines the glass transition temperature, which in our case of 2-3 nm thick films, is reduced significantly as compared to their bulk values.

Dynamical heterogeneity in a highly supercooled liquid: consistent calculations of correlation length, intensity, and lifetime

We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length ξ(4), intensity χ(4), and lifetime τ(hetero). We evaluated all three quantities consistently from a single order parameter. In a previous study [H. Mizuno and R. Yamamoto, Phys. Rev. E 82, 030501(R) (2010)], we examined the lifetime τ(hetero)(t) in two time intervals t = τ(α) and τ(ngp), where τ(α) is the α-relaxation time and τ(ngp) is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime τ(hetero)(t), we evaluated the correlation length ξ(4)(t) and the intensity χ({4)(t) from the same order parameter used for the lifetime τ(hetero)(t). We found that as the temperature decreases, the lifetime τ(hetero)(t) grows dramatically, whereas the correlation length ξ(4)(t) and the intensity χ(4)(t) increase slowly compared to τ(hetero)(t) or plateaus. Furthermore, we investigated the lifetime τ(hetero)(t) in more detail. We examined the time-interval dependence of the lifetime τ(hetero)(t) and found that as the time interval t increases, τ(hetero)(t) monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which τ(hetero)(t) plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.

On the mechanism of the highly viscous flow

The asymmetry model for the highly viscous flow postulates thermally activated jumps from a practically undistorted ground state to strongly distorted, but stable structures, with a pronounced Eshelby backstress from the distorted surroundings. The viscosity is ascribed to those stable distorted structures which do not jump back, but relax by the relaxation of the surrounding viscoelastic matrix. It is shown that this mechanism implies a description in terms of the shear compliance, with a viscosity which can be calculated from the cutoff of the retardation spectrum. Consistency requires that this cutoff lies close to the Maxwell time. The improved asymmetry model compares well with experiment.

Dynamic heterogeneities, boson peak, and activation volume in glass-forming liquids

There are various arguments and models connecting the characteristic length associated with the boson peak vibrations ξ to the length scale of dynamical heterogeneity L(het). ξ is usually defined as the ratio of the transverse sound velocity to the boson peak frequency. Here we present pressure, temperature, and molecular weight dependencies of ξ, estimated using light scattering, in a few molecular and polymeric glass formers. These dependencies are compared with respective dependencies of the activation volume ΔV(#) in the same materials. Good agreement is found for the pressure and molecular weight dependencies of ξ and ΔV(#) measured at the glass transition temperature T(g). These results provide more evidence for a possible relationship between the sensitivity of structural relaxation to density (activation volume) and the heterogeneity volume. However, contrary to the expectations for L(het), ξ does not decrease with temperature above T(g) in most of the studied materials. The temperature dependence of ξ is compared to that of L(het) in glycerol and orthoterphenyl (OTP) estimated from literature data. The analysis shows a clear difference in the behavior of ξ(T) and ΔV(#)(T) at temperatures above T(g), although ΔV(#)(T)(1/3) and L(het)(T) have similar temperature dependence. Possible reasons for the observed difference are discussed.

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.

Dynamic heterogeneity in a glass forming fluid: susceptibility, structure factor, and correlation length

We investigate the growth of dynamic heterogeneity in a glassy hard-sphere mixture for volume fractions up to and including the mode-coupling transition. We use an 80,000 particle system to test a new procedure to evaluate a dynamic correlation length ξ(t): we determine the ensemble independent dynamic susceptibility χ(4)(t) and use it to facilitate evaluation of ξ(t) from the small wave vector behavior of the four-point structure factor. We analyze relations between the α relaxation time τ(α), χ(4)(τ(α)), and ξ(τ(α)). We find that mode-coupling-like power laws provide a reasonable description of the data over a restricted range of volume fractions, but the power laws' exponents differ from those predicted by the inhomogeneous mode-coupling theory. We find ξ(τ(α))~ln(τ(α)) over the full range of volume fractions studied, which is consistent with an Adam-Gibbs-type relation.

Single-exponential activation behavior behind the super-Arrhenius relaxations in glass-forming liquids

The reported relaxation time for several typical glass-forming liquids was analyzed by using a kinetic model for liquids which invoked a new kind of atomic cooperativity--thermodynamic cooperativity. The broadly studied 'cooperative length' was recognized as the kinetic cooperativity. Both cooperativities were conveniently quantified from the measured relaxation data. A single-exponential activation behavior was uncovered behind the super-Arrhenius relaxations for the liquids investigated. Hence the mesostructure of these liquids and the atomic mechanism of the glass transition became clearer.

Subdiffusion and intermittent dynamic fluctuations in the aging regime of concentrated hard spheres

We study the nonequilibrium aging dynamics in a system of quasihard spheres at large density by means of computer simulations. We find that, after a sudden quench to large density, the relaxation time initially increases exponentially with the age of the system. After a surprisingly large crossover time, the system enters the asymptotic aging regime characterized by a nearly linear increase in the relaxation time with age. In this aging regime, single-particle motion is strongly non-fickian, with a mean-squared displacement increasing subdiffusively, associated with broad non-gaussian tails in the distribution of particle displacements. We find that the system ages through temporally intermittent relaxation events, and a detailed finite-size analysis of these collective dynamic fluctuations reveals that these events are not spanning the entire system, but remain spatially localized.

Connection between slow and fast dynamics of molecular liquids around the glass transition

The mean-square displacement (MSD) was measured by neutron scattering at various temperatures and pressures for a number of molecular glass-forming liquids. The MSD is invariant along the glass-transition line at the pressure studied, thus establishing an "intrinsic" Lindemann criterion for any given liquid. A one-to-one connection between the MSD's temperature dependence and the liquid's fragility is found when the MSD is evaluated on a time scale of ∼4 ns , but does not hold when the MSD is evaluated at shorter times. The findings are discussed in terms of the elastic model and the role of relaxations, and the correlations between slow and fast dynamics are addressed.

Analysis of dynamic heterogeneity in a glass former from the spatial correlations of mobility

The growth of characteristic length scales associated with dynamic heterogeneity in glass-forming liquids is investigated in an extensive computational study of a four-point, time-dependent structure factor defined from spatial correlations of mobility, for a model liquid for system sizes extending up to 351 232 particles, in constant-energy and constant-temperature ensembles. Our estimates for dynamic correlation lengths and susceptibilities are consistent with previous results from finite size scaling. We find scaling exponents that are inconsistent with predictions from inhomogeneous mode coupling theory and a recent simulation confirmation of these predictions.

Plasticity and dynamical heterogeneity in driven glassy materials

Many amorphous glassy materials exhibit complex spatio-temporal mechanical response and rheology, characterized by an intermittent stress strain response and a fluctuating velocity profile. Under quasistatic and athermal deformation protocols this heterogeneous plastic flow was shown to be composed of plastic events of various sizes, ranging from local quadrupolar plastic rearrangements to system spanning shear bands. In this paper, through numerical study of a 2D Lennard-Jones amorphous solid, we generalize the study of the heterogeneous dynamics of glassy materials to the finite shear rate (gamma not equal to 0) and temperature case (T not equal to 0). In practice, we choose an effectively athermal limit (T approximately 0) and focus on the influence of shear rate on the rheology of the glass. In line with previous works we find that the model Lennard-Jones glass follows the rheological behavior of a yield stress fluid with a Herschel-Bulkley response of the form, sigma = sigmaY + c1gamma(beta). The global mechanical response obtained through the use of Molecular Dynamics is shown to converge in the limit gamma --> 0 to the quasistatic limit obtained with an energy minimization protocol. The detailed analysis of the plastic deformation at different shear rates shows that the glass follows different flow regimes. At sufficiently low shear rates the mechanical response reaches a shear-rate-independent regime that exhibits all the characteristics of the quasistatic response (finite-size effects, cascades of plastic rearrangements, yield stress, ...). At intermediate shear rates the rheological properties are determined by the externally applied shear rate and the response deviates from the quasistatic limit. Finally at higher shear the system reaches a shear-rate-independent homogeneous regime. The existence of these three regimes is also confirmed by the detailed analysis of the atomic motion. The computation of the four-point correlation function shows that the transition from the shear-rate-dominated to the quasistatic regime is accompanied by the growth of a dynamical cooperativity length scale xi that is shown to diverge with shear rate as xi is proportional to gamma(-nu), with nu approximately 0.2 -0.3. This scaling is compared with the prediction of a simple model that assumes the diffusive propagation of plastic events.

Alpha-relaxation dynamics of orientanionally disordered mixed crystals composed of Cl-adamantane and CN-adamantane

The alpha-relaxation dynamics of 1-cyano-adamantane (CNA) and its mixtures with 1-chloro-adamantane (ClA) has been studied by means of broadband dielectric spectroscopy. The existence of orientationally disordered (OD) face centered cubic mixed crystals (ClA(1-X)CNA(X)) for 0.5 < or = X < or = 1 has been put in evidence by thermodynamics and structural analyses. In addition to the OD phase of CNA, mixed crystals with compositions higher than the equimolar one exhibit a freezing of the orientational degrees of freedom into a glassy state, which involves also a strong increase of the antiferroelectric order at temperatures higher than the dielectric glass transition temperature. This experimental evidence is revealed by a stairlike effect in the variation of the Kirkwood factor with the temperature as a consequence of a twin effect in the dielectric strength without any anomaly in the temperature-density curves. The characteristic relaxation times are analyzed as a function of temperature and mole fraction. By setting a common temporal origin ("isochronal origin") at tau(T(g)) = 100 s for each mole fraction, it emerges that the substitution of ClA molecules by those of CNA (diminution of X) gives rise to a slow down in the dynamics, despite that the molecular volume of ClA molecules are smaller than those of CNA. This fact goes along and is accompanied by a diminution of the lattice packing with the decrease of composition. It is also shown that the heterogeneities produced by the concentration fluctuations due to the chemical disorder are the main contribution to the non-exponential character of the alpha-relaxation peaks.

Evidence of growing spatial correlations at the glass transition from nonlinear response experiments

The ac nonlinear dielectric response chi3(omega,T) of glycerol was measured close to its glass transition temperature T(g) to investigate the prediction that supercooled liquids respond in an increasingly nonlinear way as the dynamics slows down (as spin glasses do). We find that chi3(omega,T) indeed displays several nontrivial features. It is peaked as a function of the frequency omega and obeys scaling as a function of omega tau(T), with tau(T) the relaxation time of the liquid. The height of the peak, proportional to the number of dynamically correlated molecules N(corr)(T), increases as the system becomes glassy, and chi3 decays as a power law of omega over several decades beyond the peak. These findings confirm the collective nature of the glassy dynamics and provide the first direct estimate of the T dependence of N(corr).

Temperature dependence of the characteristic length scale for glassy dynamics: combination of dielectric and specific heat spectroscopy

The temperature dependence of characteristic length scales associated to the glass transition such as the cooperativity length scale introduced by Adam and Gibbs [cooperative rearranging region (CRR)] or the dynamic heterogeneity as estimated from the four point correlation function chi4, is at the center of large interests. Broadband dielectric spectroscopy and temperature modulated differential scanning calorimetry allow to study the CRR size temperature dependence in the temperature range of ergodicity loss for glass-forming liquids, starting from the onset of cooperativity in the crossover region down to the glass transition temperature. Furthermore, the correlation between these two techniques allows to explore a large frequency range (from 1 mHz to 10 MHz). The goal of this work is to follow the cooperativity evolution along the Arrhenius plot for two different polymeric systems: poly(ethylene 1,4-cyclohexylenedimethylene terephthalate glycol) and poly(bisphenol A carbonate).

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) .

Scaling of the glassy dynamics of soft repulsive particles: a mode-coupling approach

We combine the hypernetted chain approximation of liquid state theory with the mode-coupling theory of the glass transition to analyze the structure and dynamics of soft spheres interacting via harmonic repulsion. We determine the locus of the fluid-glass dynamic transition in a temperature--volume fraction phase diagram. The zero-temperature (hard-sphere) glass transition influences the dynamics at finite temperatures in its vicinity. This directly implies a form of dynamic scaling for both the average relaxation time and dynamic susceptibilities quantifying dynamic heterogeneity. We discuss several qualitative disagreements between theory and existing simulations at equilibrium. Our theoretical results are, however, very similar to numerical results for the driven athermal dynamics of repulsive spheres, suggesting that "mean-field" mode-coupling approaches might be good starting points to describe these nonequilibrium dynamics.

Scaling the dynamics of orientationally disordered mixed crystals

The evolution of the primary relaxation time of orientationally disordered (OD) mixed crystals [(CH(3))(2)C(CH(2)OH)(2)](1-X)[(CH(3))C(CH(2)OH)(3)](X), with 0 < X < or = 0.5, on approaching the glass temperature (T(g)) is discussed. The application of the distortion-sensitive, derivative-based procedure revealed a limited adequacy of the Vogel-Fulcher-Tammann parametrization and a superiority of the critical-like description tau proportional to (T - T(C))(-phi(') ), phi(') = 9-11.5, and T(C) approximately T(g) - 10 K. Basing on these results as well as that of Drozd-Rzoska et al. [J. Chem. Phys. 129, 184509 (2008)] the question arises whether such behavior may be suggested as the optimal universal pattern for dynamics in vitrifying OD crystals (plastic crystals). The obtained behavior is in fair agreement with the dynamic scaling model (DSM) [R. H. Colby, Phys. Rev. E 61, 1783 (2000)], originally proposed for vitrifying molecular liquids and polymers. The application of DSM made it possible to estimate the size of the cooperatively rearranging regions ("heterogeneities") in OD phases near T(g).

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.

Ideal glass transition in a simple two-dimensional lattice model

We present a simple lattice model showing a glassy behavior. R matrix analysis predicts critical termination of the supercooled fluid branch at density rho(g)=0.1717. This prediction is confirmed by dynamical numerical simulations, showing power-law divergences of relaxation time tau1/2, as well as the four-susceptibility chi4 peak's location and height exactly at the predicted density. The power-law divergence of chi4 continues up to chi4 as high as 10(4). Finite-size scaling study reveals the divergence of the correlation length accompanying the transition.

Glass transition of dense fluids of hard and compressible spheres

We use computer simulations to study the glass transition of dense fluids made of polydisperse repulsive spheres. For hard particles, we vary the volume fraction, phi , and use compressible particles to explore finite temperatures, T>0 . In the hard sphere limit, our dynamic data show evidence of an avoided mode-coupling singularity near phi(MCT) is approximately 0.592; they are consistent with a divergence of equilibrium relaxation times occurring at phi(0) is approximately 0.635, but they leave open the existence of a finite temperature singularity for compressible spheres at volume fraction phi>phi(0). Using direct measurements and a scaling procedure, we estimate the equilibrium equation of state for the hard sphere metastable fluid up to phi(0), where pressure remains finite, suggesting that phi(0) corresponds to an ideal glass transition. We use nonequilibrium protocols to explore glassy states above phi(0) and establish the existence of multiple equations of state for the unequilibrated glass of hard spheres, all diverging at different densities in the range phi in [0.642, 0.664]. Glassiness thus results in the existence of a continuum of densities where jamming transitions can occur.

Shear thinning in deeply supercooled melts

We compute, on a molecular basis, the viscosity of a deeply supercooled liquid at high shear rates. The viscosity is shown to decrease at growing shear rates, owing to an increase in the structural relaxation rate as caused by the shear. The onset of this non-Newtonian behavior is predicted to occur universally at a shear rate significantly lower than the typical structural relaxation rate, by approximately two orders of magnitude. This results from a large size—up to several hundred atoms—of the cooperative rearrangements responsible for mass transport in supercooled liquids and the smallness of individual molecular displacements during the cooperative rearrangements. We predict that the liquid will break down at shear rates such that the viscosity drops by approximately a factor of 30 below its Newtonian value. These phenomena are predicted to be independent of the liquid's fragility. In contrast, the degree of nonexponentiality and violation of the Stokes–Einstein law, which are more prominent in fragile substances, will be suppressed by shear. The present results are in agreement with existing measurements of shear thinning in silicate melts.

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) .

Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition

We use dynamic light scattering and computer simulations to study equilibrium dynamics and dynamic heterogeneity in concentrated suspensions of colloidal hard spheres. Our study covers an unprecedented density range and spans seven decades in structural relaxation time, tau(alpha0, including equilibrium measurements above phi(c), the location of the glass transition deduced from fitting our data to mode-coupling theory. Instead of falling out of equilibrium, the system remains ergodic above phi(c) and enters a new dynamical regime where tau(alpha) increases with a functional form that was not anticipated by previous experiments, while the amplitude of dynamic heterogeneity grows slower than a power law with tau(alpha), as found in molecular glass formers close to the glass transition.

Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging

We introduce a new dynamic light scattering method, termed photon correlation imaging, which enables us to resolve the dynamics of soft matter in space and time. We demonstrate photon correlation imaging by investigating the slow dynamics of a quasi-two-dimensional coarsening foam made of highly packed, deformable bubbles and a rigid gel network formed by dilute, attractive colloidal particles. We find the dynamics of both systems to be determined by intermittent rearrangement events. For the foam, the rearrangements extend over a few bubbles, but a small dynamical correlation is observed up to macroscopic length scales. For the gel, dynamical correlations extend up to the system size. These results indicate that dynamical correlations can be extremely long-ranged in jammed systems and point to the key role of mechanical properties in determining their nature.

Growing length and time scales in glass-forming liquids

The glass transition, whereby liquids transform into amorphous solids at low temperatures, is a subject of intense research despite decades of investigation. Explaining the enormous increase in relaxation times of a liquid upon supercooling is essential for understanding the glass transition. Although many theories, such as the Adam-Gibbs theory, have sought to relate growing relaxation times to length scales associated with spatial correlations in liquid structure or motion of molecules, the role of length scales in glassy dynamics is not well established. Recent studies of spatially correlated rearrangements of molecules leading to structural relaxation, termed "spatially heterogeneous dynamics," provide fresh impetus in this direction. A powerful approach to extract length scales in critical phenomena is finite-size scaling, wherein a system is studied for sizes traversing the length scales of interest. We perform finite-size scaling for a realistic glass-former, using computer simulations, to evaluate the length scale associated with spatially heterogeneous dynamics, which grows as temperature decreases. However, relaxation times that also grow with decreasing temperature do not exhibit standard finite-size scaling with this length. We show that relaxation times are instead determined, for all studied system sizes and temperatures, by configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with theoretical expectations based on spin-glass models that configurational entropy is not relevant at temperatures substantially above the critical temperature of mode-coupling theory. Our results provide new insights into the dynamics of glass-forming liquids and pose serious challenges to existing theoretical descriptions.

Direct-space investigation of the ultraslow ballistic dynamics of a soft glass

We use light microscopy to investigate the aging dynamics of a glass made of closely packed soft spheres, following a rapid transition from a fluid to a solidlike state. By measuring time-resolved, coarse-grained displacement fields, we identify two classes of dynamical events, corresponding to reversible and irreversible rearrangements, respectively. The reversible events are due to the small, experimentally unavoidable fluctuations of the temperature imposed to the sample, leading to transient thermal expansions and contractions that cause shear deformations. The irreversible events are plastic rearrangements, induced by the repeated shear cycles. We show that the displacement due to the irreversible rearrangements grows linearly with time, both on average and at a local level. The velocity associated with this ballistic motion decreases exponentially with sample age, accounting for the observed slowing down of the dynamics. The displacement field due to the irreversible rearrangements has a vortexlike structure and is spatially correlated over surprisingly long distances.

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.