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

Improved reconstructions of random media using dilation and erosion processes

By using the most sensitive two-point correlation functions introduced to date, we reconstruct the microstructures of two-phase random media with heretofore unattained accuracy. Such media arise in a host of contexts, including porous and composite media, ecological structures, biological media, and astrophysical structures. The aforementioned correlation functions are special cases of the so-called canonical n-point correlation function H(n) and generalize the ones that have been recently employed to advance our ability to reconstruct complex microstructures [Y. Jiao, F. H. Stillinger, and S. Torquato, Proc. Natl. Acad. Sci. 106, 17634 (2009)]. The use of these generalized correlation functions is tantamount to dilating or eroding a reference phase of the target medium and incorporating the additional topological information of the modified media, thereby providing more accurate reconstructions of percolating, filamentary, and other topologically complex microstructures. We apply our methods to a multiply connected "donut" medium and a dilute distribution of "cracks" (a set of essentially zero measure), demonstrating improved accuracy in both cases with implications for higher-dimensional and biconnected two-phase systems. The high information content of the generalized two-point correlation functions suggests that it would be profitable to explore their use to characterize the structural and physical properties of not only random media, but also molecular systems, including structural glasses.

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.

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.

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.

Computer simulations of colloidal transport on a patterned magnetic substrate

We study the transport of paramagnetic colloidal particles on a patterned magnetic substrate with kinetic Monte Carlo and Brownian dynamics computer simulations. The planar substrate is decorated with point dipoles in either parallel or zigzag stripe arrangements and exposed to an additional external magnetic field that oscillates in time. For the case of parallel stripes we find that the magnitude and direction of the particle current is controlled by the tilt angle of the external magnetic field. The effect is reliably obtained in a wide range of ratios between temperature and magnetic permeability. Particle transport is achieved only when the period of oscillation of the external field is greater than a critical value. For the case of zigzag stripes a current is obtained using an oscillating external field normal to the substrate. In this case, transport is possible only in the vertex of the zigzag, giving rise to a narrow stream of particles. The magnitude and direction of the particle current are found to be controlled by a combination of the zigzag angle and the distance of the colloids from the substrate. Metropolis Monte Carlo and Brownian dynamics simulations predict results that are in good agreement with each other. Using kinetic Monte Carlo we find that at high density the particle transport is hindered by jamming.

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.

Low-temperature dynamics of water confined in a hydrophobic mesoporous material

Quasielastic neutron scattering was used to study the dynamics of three-dimensional confined water in a hydrophobic mesoporous material designated as CMK-1 in the temperature range from 250 to 170 K. We observe a crossover phenomenon at temperature T(L) . We find that T(L) of water confined in CMK-1 occurs in between previous observations of one-dimensional confined water in materials with different hydrophilicities. This provides the first evidence that besides the obvious surface effect brought about by the hydrophobic confinements, T(L) is also dependent on the dimensionality of the geometry of the confinement.

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.

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node bifurcation point in the weak-noise limit, while the final value of the deterministic solution changes discontinuously at the point. A systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method. In this formulation, the critical nature turns out to originate from the neutrality of exiting time from a saddle point. The theoretical calculation explains results of numerical simulations.

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).

The Dynamic Response Function χ T(Q,t) of Confined Supercooled Water and its Relation to the Dynamic Crossover Phenomenon

We have made a series of Quasi-Elastic Neutron Scattering (QENS) studies of supercooled water confined in 3-D and 1-D geometries, specifically, interstitial water in aged cement paste (3-D) and water confined in MCM-41-S and Double Wall Nano Tube DWNT (1-D). In addition, we also include the cases of hydration water on protein surface and other biopolymer surfaces (pseudo 2-D). By analyzing the QENS spectra using Relaxing Cage Model (RCM), we are able to extract accurately the self-intermediate scattering function of hydrogen atoms FH(Q,t), at low-Q as a function of temperature T, showing an α-relaxation process at long time. We can then construct the Dynamic Response Function χT(Q,t) = -dFH(Q,t)/dT. χT(Q,t) as a function of t at constant Q shows a single peak at the characteristic α-relaxation time 〈τ〉, the amplitude of which grows as we approach the dynamic crossover temperature TL observed before in each of these geometries. However, the peak height of χT(Q,t) decreases after passing the crossover temperature TL. We make an argument to relate the occurrence of the extremum of the peak height in χT to the existence of the dynamic crossover temperature in each of these cases.

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.

Growing static and dynamic length scales in a glass-forming liquid

We investigate the characteristic length scales associated with the glass transition phenomenon. By studying an atomic glass-forming liquid in negatively curved space, for which the local order is well identified and the amount of frustration opposing the spatial extension of this order is tunable, we provide insight into the structural origin of the main characteristics of the dynamics leading to glass formation. We find that the structural length and the correlation length characterizing the increasing heterogeneity of the dynamics grow together as temperature decreases. However, the system eventually enters a regime in which the former saturates as a result of frustration whereas dynamic correlations keep building up.

Density nonlinearities in field theories for a toy model of fluctuating nonlinear hydrodynamics of supercooled liquids

We study a zero-dimensional version of the fluctuating nonlinear hydrodynamics (FNH) of supercooled liquids originally investigated by Das and Mazenko (DM) [Shankar P. Das and Gene F. Mazenko Phys. Rev. A 34, 2265 (1986)]. The time-dependent density-like and momentum-like variables are introduced with no spatial degrees of freedom in this toy model. The structure of nonlinearities takes the similar form to the original FNH, which allows one to study in a simpler setting the issues raised recently regarding the field theoretical approaches to glass forming liquids. We study the effects of density nonlinearities on the time evolution of correlation and response functions by developing field theoretic formulations in two different ways: first by following the original prescription of DM and then by constructing a dynamical action which possesses a linear time-reversal symmetry as proposed recently. We show explicitly that, at the one-loop order of the perturbation theory, the DM-type field theory does not support a sharp ergodic-nonergodic transition, while the other admits one. The simple nature of the toy model in the DM formulation allows us to develop numerical solutions to a complete set of coupled dynamical equations for the correlation and response functions at the one-loop order.

Nonlocal nature of the viscous transport in supercooled liquids: complex fluid approach to supercooled liquids

Using molecular dynamics simulations, we show clear evidence for the nonlocal mesoscopic nature of the anomalous viscous transport in a supercooled liquid and its direct link to dynamic heterogeneity: (i) a distinct crossover from the microscopic to macroscopic viscosity at a mesoscopic length scale, which is comparable to the correlation length of dynamic heterogeneity and grows with an increase in the degree of supercooling; (ii) a strong anisotropic decay of the shear-stress autocorrelation at a finite wave number, which indicates intrinsic decoupling between the longitudinal and transverse dynamics. Our findings suggest the fundamental importance of the growing dynamic correlation in anomalous transport and shed new light on the nature of slow dynamics.

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.

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) .

Dynamic susceptibility of supercooled water and its relation to the dynamic crossover phenomenon

We study the dynamic susceptibility chi_{T}(Q,t) of deeply supercooled water by means of quasielastic neutron scattering and molecular dynamics simulations. Both techniques show an increase in the peak height of chi_{T}(Q,t) as the temperature is lowered toward the dynamic crossover temperature T_{L} . Below T_{L} , the peak height decreases steadily. We attribute this phenomenon to the change in slope of the Arrhenius plot of the translational relaxation time at T_{L} . In contrast, the peak height of the calculated four-point correlation function chi_{4}(Q,t) , directly related to the size of dynamic heterogeneity, increases toward and below T_{L} .

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.

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) .

MD simulation of concentrated polymer solutions: structural relaxation near the glass transition

We examine by molecular dynamics simulations the relaxation of polymer-solvent mixtures close to the glass transition. The simulations employ a coarse-grained model in which polymers are represented by bead-spring chains and solvent particles by monomers. The interaction parameters between polymer and solvent are adjusted such that mixing is favored. We find that the mixtures have one glass transition temperature T(g) or critical temperature T(c) of mode-coupling theory (MCT). Both T(g) and T(c) (> T(g)) decrease with increasing solvent concentration φ(S). The decrease is linear for the concentrations studied (up to φ(S) = 25%). Above T(c) we explore the structure and relaxation of the polymer-solvent mixtures on cooling. We find that, if the polymer solution is compared to the pure polymer melt at the same T, local spatial correlations on the length scale of the first peak of the static structure factor S(q) are reduced. This difference between melt and solution is largely removed when comparing the S(q) of both systems at similar distance to the respective T(c). Near T(c) we investigate dynamic correlation functions, such as the incoherent intermediate scattering function φ(q)(s)(t), mean-square displacements of the monomers and solvent particles, two non-Gaussian parameters, and the probability distribution P(ln r; t) of the logarithm of single-particle displacements. In accordance with MCT we find, for instance, that φ(q)(s)(t) obeys the time-temperature superposition principle and has α relaxation times τ(q)(s) which are compatible with a power law increase close (but not too close) to T(c). In divergence to MCT, however, the increase of τ(q)(s) depends on the wavelength q, small q values having weaker increase than large ones. This decoupling of local and large-length scale relaxation could be related to the emergence of dynamic heterogeneity at low T. In the time window of the α relaxation an analysis of P(ln r; t) reveals a double-peak structure close to T(c). The first peak corresponds to "slow" particles (monomer or solvent) which have not moved much farther than 10% of their diameter in time t, whereas the second occurs at distances of the order of the particle diameter. These "fast" particles have succeeded in leaving their nearest-neighbor cage in time t. The simulation thus demonstrates that large fluctuations in particle mobility accompany the final structural relaxation of the cold polymer solution in the vicinity of the extrapolated T(c).

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.

Fluctuation-dissipation-relation-preserving field theory of the glass transition in terms of fluctuating hydrodynamics

A field theoretical method for fluctuating hydrodynamics with preserved fluctuation-dissipation relations is reformulated. By assuming that the correlations including momentum are irrelevant in the long time region, we demonstrate that the equation obtained from the first-order perturbation is reduced to that for standard mode-coupling theory.

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.

Suppression of the rate of growth of dynamic heterogeneities and its relation to the local structure in a supercooled polydisperse liquid

The relationship between the microscopic arrangement of molecules in a supercooled liquid and its slow dynamics at low temperature near glass transition is studied by molecular dynamics simulations. A Lennard-Jones liquid with polydispersity in size and mass of constituent particles is chosen as the model system. Our studies reveal that the local structure (that varies with polydispersity) plays a crucial role both in the slowing down of dynamics and in the growth of the dynamic heterogeneities, besides determining the glass forming ability of the system. Increasing polydispersity at fixed volume fraction is found to suppress the rate of growth of dynamic correlations, as detected by the growth in the peak of the nonlinear density response function, chi4(t). The growth in dynamical correlation is manifested in a stronger than usual breakdown of Stokes-Einstein relation at lower polydispersity at low temperatures and also leads to a decrease in the fragility of the system with polydispersity. We show that the suppression of the rate of growth of the dynamic heterogeneity can be attributed to the loss of structural correlations (as measured by the structure factor and the local bond orientational order) with polydispersity. While a critical polydispersity is required to avoid crystallization, we find that a further increase in polydispersity lowers the glass forming ability.

Atomic bond fluctuations and crossover to potential-energy-landscape-influenced regime in supercooled liquid

The ideas related to potential-energy landscape and cooperativity of atomic rearrangements are widely discussed in the research field of glass transition. The crossover transition from high-temperature regime to potential-energy-landscape-influenced regime was extensively studied using the concept of inherent structure. However, the interpretation of this crossover behavior in terms of microscopic changes in real structures is still lacking. In this paper we present several observations on the crossover behavior on real structures. We compare fluctuations in the global properties (total number of bonds, total potential energy, pressure) versus fluctuations in the local properties (coordination number, atomic potential energy, local atomic pressure) by means of molecular dynamics simulations. We then show that the total and local fluctuations in the number of atomic bonds in the system depend on temperature differently above and below the temperature of crossover to the landscape-influenced regime. Similarly, the ratio between the global and local fluctuations in the potential energy and pressure changes in the vicinity of the crossover temperature, whereas the change is less distinct than in the case of the bond fluctuations. Our results indicate that local fluctuations become more correlated below the crossover temperature, most likely via the interaction through the dynamic shear elastic field.

Dynamical heterogeneity in a model for permanent gels: different behavior of dynamical susceptibilities

We present a systematic study of dynamical heterogeneity in a model for permanent gels upon approaching the gelation threshold. We find that the fluctuations of the self-intermediate scattering function are increasing functions of time, reaching a plateau whose value, at large length scales, coincides with the mean cluster size and diverges at the percolation threshold. Another measure of dynamical heterogeneities-i.e., the fluctuations of the self-overlap-displays instead a peak and decays to zero at long times. The peak, however, also scales as the mean cluster size. Arguments are given for this difference in the long-time behavior. We also find that the non-Gaussian parameter reaches a plateau in the long-time limit. The value of the plateau of the non-Gaussian parameter, which is connected to the fluctuations of diffusivity of clusters, increases with the volume fraction and remains finite at the percolation threshold.

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.