CiteULike: weeks's dyn-het

Spatial cooperativity in soft glassy flows

J Goyon — 2008-07-03T06:17:56-00:00

Nature, Vol. 454, No. 7200. (2008), pp. 84-87.

Amorphous glassy materials of diverse nature—concentrated emulsions, granular materials, pastes, molecular glasses—display complex flow properties, intermediate between solid and liquid, which are at the root of their use in many applications1, 2, 3. A general feature of such systems, well documented yet not really understood, is the strongly nonlinear nature of the flow rule relating stresses and strain rates4, 5. Here we use a microfluidic velocimetry technique to characterize the flow of thin layers of concentrated emulsions, confined in gaps of different thicknesses by surfaces of different roughnesses. We find evidence for finite-size effects in the flow behaviour and the absence of an intrinsic local flow rule. In contrast to the classical nonlinearities of the rheological behaviour of amorphous materials, we show that a rather simple non-local flow rule can account for all the velocity profiles. This non-locality of the dynamics is quantified by a length, characteristic of cooperativity within the flow at these scales, that is unobservable in the liquid state (lower emulsion concentrations) and that increases with concentration in the jammed state. Beyond its practical importance for applications involving thin layers (for example, coatings), these non-locality and cooperativity effects have parallels in the behaviour of other glassy, jammed and granular systems, suggesting a possible fundamental universality.

Reversible plastic events in amorphous materials

Micah Lundberg — 2008-06-08T22:17:30-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 77, No. 4. (2008)

For crystalline materials, the microscopic origin of plasticity is well understood in terms of the dynamics of topological defects. For amorphous materials, the underlying structural disorder prevents such a description. Therefore identifying and characterizing the microscopic plastic events in amorphous materials remains an important challenge. We show direct evidence for the coexistence of reversible and irreversible plastic events (T1 events) at the microscopic scale in both experiments and simulations of two-dimensional foam. In the simulations, we also demonstrate a link between the reversibility of T1 events and pathways in the potential energy landscape of the system.

Following microscopic motion in a two-dimensional glass-forming binary fluid

Matthew Downton — 2008-06-25T18:22:01-00:00

Journal of Physics: Condensed Matter, Vol. 20, No. 24. (2008), 244127.

The dynamics of a binary mixture of large and small discs is studied at temperatures approaching the glass transition using an analysis based on the topology of the Voronoi polygon surrounding each atom. At higher temperatures we find that the dynamics is dominated by fluid-like motion that involves particles entering and exiting the nearest neighbour shells of nearby particles. As the temperature is lowered, the rate of topological moves decreases and motion becomes localized to regions of mixed pentagons and heptagons. In addition we find that in the low temperature state particles may translate significant distances without undergoing changes in their nearest neighbour shell. These results have implications for dynamical heterogeneities in glass-forming liquids.

Heterogeneities in granular dynamics

A Mehta — 2008-06-10T18:54:14-00:00

Proceedings of the National Academy of Sciences (9 June 2008), pp. 8244-8249.

The absence of Brownian motion in granular media is a source of much complexity, including the prevalence of heterogeneity, whether static or dynamic, within a given system. Such strong heterogeneities can exist as a function of depth in a box of grains; this is the system we study here. First, we present results from three-dimensional, cooperative and stochastic Monte Carlo shaking simulations of spheres on heterogeneous density fluctuations. Next, we juxtapose these with results obtained from a theoretical model of a column of grains under gravity; frustration via competing local fields is included in our model, whereas the effect of gravity is to slow down the dynamics of successively deeper layers. The combined conclusions suggest that the dynamics of a real granular column can be divided into different phases--ballistic, logarithmic, activated, and glassy--as a function of depth. The nature of the ground states and their retrieval (under zero-temperature dynamics) is analyzed; the glassy phase shows clear evidence of its intrinsic ("crystalline") states, which lie below a band of approximately degenerate ground states. In the other three phases, by contrast, the system jams into a state chosen randomly from this upper band of metastable states. 10.1073/pnas.0711733105

Energy Landscape, Antiplasticization, and Polydispersity Induced Crossover of Heterogeneity in Supercooled Polydisperse Liquids

Sneha Abraham — 2008-05-05T20:40:53-00:00

Physical Review Letters, Vol. 100, No. 16. (2008)

Polydispersity is found to have a significant effect on the potential energy landscape; the average inherent structure energy decreases with polydispersity. Increasing polydispersity at a fixed volume fraction decreases the glass transition temperature and the fragility of glass formation analogous to the antiplasticization seen in some polymeric melts. An interesting temperature dependent crossover of heterogeneity with polydispersity is observed at low temperature due to the faster buildup of dynamic heterogeneity at lower polydispersity.

Atomic Mobility and Strain Localization in Amorphous Metals

Francesco Delogu — 2008-04-14T23:18:41-00:00

Physical Review Letters, Vol. 100, No. 7. (2008)

Molecular dynamics simulations are employed to investigate the atomic mobility in Ni50Zr50 amorphous alloys under both static conditions and shearing. Diffusion occurs under static conditions via cooperative stringlike motion involving atoms with large volumes. Atomic mobility is instead governed by rearrangements localized in shear transformation zones (STZs) under shearing. Local atomic volume plays in both cases a key role, the atomic ensembles involved in diffusion and STZ activity being strongly correlated.

Structure and dynamics of colloidal depletion gels: Coincidence of transitions and heterogeneity

Clare Dibble — 2008-06-19T22:57:38-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 74, No. 4. (2006)

Transitions in structural heterogeneity of colloidal depletion gels formed through short-range attractive interactions are correlated with their dynamical arrest. The system is a density and refractive index matched suspension of 0.20 volume fraction poly(methyl methacyrlate) colloids with the nonadsorbing depletant polystyrene added at a size ratio of depletant to colloid of 0.043. As the strength of the short-range attractive interaction is increased, clusters become increasingly structurally heterogeneous, as characterized by number-density fluctuations, and dynamically immobilized, as characterized by the single-particle mean-squared displacement. The number of free colloids in the suspension also progressively declines. As an immobile cluster to gel transition is traversed, structural heterogeneity abruptly decreases. Simultaneously, the mean single-particle dynamics saturates at a localization length on the order of the short-range attractive potential range. Both immobile cluster and gel regimes show dynamical heterogeneity. Non-Gaussian distributions of single particle displacements reveal enhanced populations of dynamical trajectories localized on two different length scales. Similar dependencies of number density fluctuations, free particle number, and dynamical length scales on the order of the range of short-range attraction suggests a collective structural origin of dynamic heterogeneity in colloidal gels.

Shear-Induced Changes in Two-Dimensional Foam

Abd — 2008-04-26T22:15:30-00:00

Physical Review Letters, Vol. 82, No. 12. (22 March 1999), 2610.

The effects of shear strain on a two-dimensional foam, comprising a monolayer of bubbles bridging from a soap solution to a cover glass, have been studied. For initially disordered foam, m2, the second central moment of the distribution of bubble coordination numbers, fell under strain, indicating ordering. The reduction in m2 is proportional to its initial value. Further, the accompanying bubblelevel changes occur in clusters, some of which are large. Comparisons are drawn with recent studies.

Signatures of Glass Formation in a Fluidized Bed of Hard Spheres

Daniel Goldman — 2008-01-23T18:42:00-00:00

Physical Review Letters, Vol. 96, No. 14. (2006), pp. 145702-145702.

We demonstrate that a fluidized bed of hard spheres during defluidization displays properties associated with formation of a glass. The final state is rate dependent, and as this state is approached, the bed exhibits heterogeneity with increasing time and length scales. The formation of a glass results in the arrest of macroscopic particle motion and thus the loss of fluidization. Microscopic motion persists in this state, but the bed can be jammed by application of a small increase in flow rate. Thus a fluidized bed can serve as a test system for studies of glass formation and jamming.

Dynamical Heterogeneity and Jamming in Glass-Forming Liquids

N Lacevic — 2008-03-28T00:05:41-00:00

J. Phys. Chem. B, Vol. 108, No. 51. (23 December 2004), pp. 19623-19633.

Abstract: The relationship between spatially heterogeneous dynamics (SHD) and jamming is studied in a glass-forming binary Lennard-Jones system via molecular dynamics simulations. It has been suggested [Phys. Rev. Lett. 2001, 86, 111]1 that the probability distribution of interparticle forces P(F) develops a peak at the glass transition temperature Tg and that the large force inhomogeneities, responsible for structural arrest in granular materials, are related to dynamical heterogeneities in supercooled liquids that form glasses. It has been further suggested that "force chains" present in granular materials may exist in supercooled liquids and may provide an order parameter for the glass transition. Our goal is to investigate the extent to which the forces experienced by particles in a glass-forming liquid are related to SHD and compare these forces to those observed in granular materials and other glass-forming systems. Our results are summarized as follows. We calculate P(F) for positive (repulsive) instantaneous forces and find no peak in P(F) at any temperature in our system, even below Tg. We also find that particles that have been localized for a long time are less likely to experience high relative force and that mobile particles experience higher relative forces at shorter time scales, indicating a correlation between pairwise forces and particle mobility. We construct force chains based on the magnitude of pairwise positive instantaneous forces. We find that force chains constructed in this manner are composed of both localized and mobile particles; therefore there is no one-to-one correspondence between force chains as defined here and locally mobile or immobile regions of the liquid. We also find that force chains do not play the same role as force chains in granular materials but may indicate a difference in the evolution of the local environment of particles with different mobility. We also discuss a possible relationship between force chains found here and the development of stringlike motion found in this and other glass-forming liquids [Phys. Rev. Lett. 1998, 80, 2338; J. Chem. Phys. 2004, 120, 4415].2,3

On the relationship between structure and dynamics in a supercooled liquid

Asaph Widmer-Cooper — 2008-02-15T14:48:10-00:00

Journal of Physics: Condensed Matter, Vol. 17, No. 49. (2005), pp. S4025-S4034.

We present the dynamic propensity distribution as an explicit measure of the degree to which the dynamics in a liquid over the time scale of structural relaxation is determined by the initial configuration. We then examine, for a binary mixture of soft discs in two dimensions, the correlation between the spatial distribution of propensity and that of two local measures of configuration structure: the local composition and local free volume. While the small particles dominate the high propensity population, we find no strong correlation between either the local composition or the local free volume and the propensity. It is argued that this is a generic failure of purely local structural measures to capture the inherently non-local character of collective behaviour.

Correlation between Dynamic Heterogeneity and Medium-Range Order in Two-Dimensional Glass-Forming Liquids

Takeshi Kawasaki — 2007-12-07T05:03:46-00:00

Physical Review Letters, Vol. 99, No. 21. (2007), pp. 215701-215701.

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.

Correlated orientational and translational motions in supercooled liquids

Sarika Bhattacharyya — 2007-11-28T00:55:12-00:00

The Journal of Chemical Physics, Vol. 117, No. 6. (2002), pp. 2741-2746.

We have carried out NPT molecular dynamics simulations of isolated ellipsoids in a glass forming binary mixture to gain insight into the nature of orientational relaxation (OR) in a viscous liquid. At high pressures when the liquid is highly viscous, the OR is found to occur mainly via correlated hopping, sometimes involving participation of several neighboring atoms, placed in a ring like tunnel. In the glassy state, hopping is found to be accompanied by larger fluctuations in the total energy and the volume of the system. Both orientational and translational hopping are found to be gated, restricted primarily by the entropic bottlenecks, with the orientational motion becoming increasingly slower than the translation as the pressure is increased. Orientational relaxation is found to occur with a wide distribution of decay times.

Reorientation and translation of individual dye molecules in a polymer matrix

A Schob — 2007-11-28T00:34:21-00:00

European Polymer Journal, Vol. 40, No. 5. (May 2004), pp. 1019-1026.

The orientational and translational motion of individual dye molecules embedded in a polymer matrix is studied in the temperature regime above the glass transition. The rotational diffusion close to the glass transition is heterogeneous on the single molecule level and few sudden changes in the reorientational speed of single molecules are found. The exchange between these reorientational speeds is found to be one order of magnitude slower than the reorientational time constant of the molecules. Translational motion can be clearly identified at about 1.2 Tg. However, the translational diffusion shows no signs of heterogeneity on the timescale of our experiments, from which we conclude, that the timescale of the exchange process between microenvironments has become too fast or that no heterogeneity exists at the temperatures above 1.2 Tg.

Heterogeneity at the glass transition: what do we know?

Hans Sillescu — 2007-11-28T00:27:28-00:00

Journal of Non-Crystalline Solids, Vol. 307-310 (September 2002), pp. 16-23.

We critically discuss the information that can be obtained from experiments with respect to the existence, the life time, and the length scale of dynamical heterogeneity in glass-forming liquids. The ability to select a dynamically distinguishable subensemble and observe its return to the full equilibrium ensemble is illustrated by examples from multi-dimensional NMR. We also discuss non-resonant hole burning spectroscopy as an example for which two separate time scales are involved.

Direct observation of molecular cooperativity near the glass transition

E Vidalrussell — 2007-11-28T00:22:47-00:00

Nature, Vol. 408, No. 6813. (7 December 2000), pp. 695-698.

The increasingly sluggish response of a supercooled liquid as it nears its glass transition1 (for example, refrigerated honey) is prototypical of glassy dynamics found in proteins, neural networks and superconductors. The notion that molecules rearrange cooperatively has long been postulated2 to explain diverging relaxation times and broadened (non-exponential) response functions near the glass transition. Recently, cooperativity was observed and analysed in colloid glasses3 and in simulations of binary liquids well above the glass transition4. But nanometre-scale studies of cooperativity at the molecular glass transition are lacking5. Important issues to be resolved include the precise form of the cooperativity and its length scale6, and whether the broadened response is intrinsic to individual cooperative regions, or arises only from heterogeneity7, 8, 9 in an ensemble of such regions. Here we describe direct observations of molecular cooperativity near the glass transition in polyvinylacetate (PVAc), using nanometre-scale probing of dielectric fluctuations. Molecular clusters switched spontaneously among two to four distinct configurations, producing random telegraph noise. Our analysis of these noise signals and their power spectra reveals that individual clusters exhibit transient dynamical heterogeneity and non-exponential kinetics.

Spatially heterogeneous dynamics in liquids: insights from simulation

Sharon Glotzer — 2007-11-28T00:15:59-00:00

Journal of Non-Crystalline Solids, Vol. 274, No. 1-3. (September 2000), pp. 342-355.

In this paper, review of recent theoretical and simulation work on dynamical heterogeneity and correlated particle motion in glass-forming liquids and polymers is presented. Evidence for increasing mobility fluctuations in these systems with decreasing temperature, and the relationship between dynamical heterogeneity and decoupling of diffusion and structural relaxation is described. The relationship between dynamical heterogeneity, string-like collective motion, the clustering of strings, and mode-coupling theory is briefly discussed.

Heterogeneity at the glass transition: a review

Hans Sillescu — 2007-11-28T00:10:01-00:00

Journal of Non-Crystalline Solids, Vol. 243, No. 2-3. (February 1999), pp. 81-108.

Theoretical concepts and experimental evidence of heterogeneity in glass-forming liquids and polymers are reviewed. The main purpose is to provide an introduction to theoretical developments and recent experiments which have led to rapidly increasing knowledge. Realizing that there is no consensus in regard to the various scenarios of the glass transition starting from rather different assumptions we try to give a balanced overview although we also compare and interrelate some of the approaches. The experimental part describes recent nuclear magnetic resonance, dielectric, and optical experiments from which dynamically distinguishable subensembles can be selected thus proving the existence of a well defined dynamical heterogeneity.

Enhanced diffusion upon approaching the kinetic glass transition

Cliff Liu — 2007-11-27T16:18:47-00:00

Physical Review E, Vol. 53, No. 1. (January 1996), pp. 799-802.

The apparent failure of the Stokes-Einstein law in strongly supercooled liquids has provoked recent experimental and theoretical studies. In an attempt to explain this phenomenon; we study the diffusion in a dynamically disordered continuum in which small; compact regions of greater diffusivity appear and disappear in time. Within the confines of the model; we show that a systematic increase in the ratio of the diffusivity of fluidized domains to the background diffusivity appears to be the single most important factor in explaining the deviation from the Stokes relation. © 1996 The American Physical Society.

Translational and reorientational heterogeneity in the glass-forming liquid $Ca_0.4K_0.6(NO_3)_1.4$

Mauro Ribeiro — 2007-11-26T19:14:32-00:00

Phys. Chem. Chem. Phys., Vol. 6 (2004), pp. 771-774.

Molecular dynamics (MD) simulations were performed in order to reveal dynamical heterogeneity in the glass-forming liquid Ca0.4K0.6(NO3)1.4(CKN). A polarizable model for the nitrate anion has been used in a 10.0 ns simulation of 996 ions at 450 K, which is close to the previously estimated glass transition temperature for this model (Tg380 K). Mobile and immobile ions within 500.0 ps time windows were identified, and short-range spatial correlations between them were analysed. Mobile ions are strongly correlated, but they are much less correlated with immobile ones. In the case of the NO3– species, the sub-ensemble of translationally mobile ions also results in a rapidly decaying reorientational correlation function. Thus, if one probes spatial heterogeneity of rotational degrees of freedom in CKN, one will be also probing spatial heterogeneity of translational degrees of freedom, and vice-versa. By using a reorientation analogous of the van Hove correlation function, small angle rotational diffusion in the dynamics of mobile anions, and large angular jumps in the dynamics of immobile ones were observed.

On the mechanism of reorientational and structural relaxation in supercooled liquids: The role of border dynamics and cooperativity

Joohyun Kim — 2007-06-26T21:45:18-00:00

The Journal of Chemical Physics, Vol. 121, No. 9. (2004), pp. 4237-4245.

Molecular dynamics simulation and analysis based upon the many-body potential energy landscape (PEL) are employed to characterize single molecule reorientation and structural relaxation, and their interrelation, in deeply supercooled liquid CS2. The rotational mechanism changes from small-step Debye diffusion to sudden large angle reorientation (SLAR) as the temperature falls below the mode-coupling temperature Tc. The onset of SLAR is explained in terms of the PEL; it is an essential feature of low-T rotational dynamics, along with the related phenomena of dynamic heterogeneity and the bifurcation of slow and fast relaxation processes. A long trajectory in which the system is initially trapped in a low energy local minimum, and eventually escapes, is followed in detail, both on the PEL and in real space. During the trapped period, "return" dynamics occurs, always leading back to the trap. Structural relaxation is identified with irreversible escape to a new trap. These processes lead to weak and strong SLAR, respectively; strong SLAR is a clear signal of structural relaxation. Return dynamics involves small groups of two to four molecules, while a string-like structure composed of all the active groups participates in the escape. It is proposed that, rather than simple, nearly instantaneous, one-dimensional barrier crossings, relaxation involves activation of the system to the complex, multidimensional region on the borders of the basins of attraction of the minima for an extended period. ©2004 American Institute of Physics.

Probe particles alter dynamic heterogeneities in simple supercooled systems

Ronen Zangi — 2007-06-25T01:40:09-00:00

The Journal of Chemical Physics, Vol. 126, No. 10. (2007), pp. 104501-104501.

The authors present results from molecular dynamics simulations on the effect of smooth and rough probes on the dynamics of a supercooled Lennard-Jones (LJ) mixture. The probe diameter was systematically varied from one to seven times the diameter of the large particles of the LJ mixture. Mean square displacements show that in the presence of a large smooth probe the supercooled liquid speeds up, while in the presence of a large rough probe, the supercooled liquid slows down. Non-Gaussian parameters indicate that with both smooth and rough probes, the heterogeneity of the supercooled system increases. From the analysis of local Debye-Waller factors, it is evident that the change in the dynamics of the LJ system is heterogeneous, with the largest perturbations close to the probes. Large smooth and rough probes appear to set up heterogeneities in these supercooled systems that would otherwise not occur, and these heterogeneities persist for long times. ©2007 American Institute of Physics

Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation function

N Lacevic — 2007-11-20T22:24:15-00:00

J. Chem. Phys., Vol. 119 (8 October 2003), pp. 7372-7387.

Relaxation in supercooled liquids above their glass transition and below the onset temperature of "slow" dynamics involves the correlated motion of neighboring particles. This correlated motion results in the appearance of spatially heterogeneous dynamics or "dynamical heterogeneity." Traditional two-point time-dependent density correlation functions, while providing information about the transient "caging" of particles on cooling, are unable to provide sufficiently detailed information about correlated motion and dynamical heterogeneity. Here, we study a four-point, time-dependent density correlation function g4(r,t) and corresponding "structure factor" S4(q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times, and so are sensitive to dynamical heterogeneity. We study g4(r,t) and S4(q,t) via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above. We find that the correlations between particles measured by g4(r,t) and S4(q,t) become increasingly pronounced on cooling. The corresponding dynamical correlation length xi4(t) extracted from the small-q behavior of S4(q,t) provides an estimate of the range of correlated particle motion. We find that xi4(t) has a maximum as a function of time t, and that the value of the maximum of xi4(t) increases steadily from less than one particle diameter to a value exceeding nine particle diameters in the temperature range approaching the mode coupling temperature from above. At the maximum, xi4(t) and the alpha relaxation time taualpha are related by a power law. We also examine the individual contributions to g4(r,t), S4(q,t), and xi4(t), as well as the corresponding order parameter Q(t) and generalized susceptibility chi4(t), arising from the self and distinct contributions to Q(t). These contributions elucidate key differences between domains of localized and delocalized particles.

Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in water

Marco Mazza — 2007-10-16T14:47:04-00:00

Physical Review E, Vol. 76, No. 3. (2007), pp. 031203-031203.

We study the Stokes-Einstein (SE) and the Stokes-Einstein-Debye (SED) relations, Dt=kBT/6R and Dr=kBT/8R3, where Dt and Dr are the translational and rotational diffusivity, respectively, T is the temperature, the viscosity, kB the Boltzmann constant, and R the “molecular” radius. Our results are based on molecular dynamics simulations of the extended simple point charge model of water. We find that both the SE and SED relations break down at low temperature. To explore the relationship between these breakdowns and dynamical heterogeneities (DHs), we also calculate the SE and SED relations for subsets of the 7% “fastest” and 7% “slowest” molecules. We find that the SE and SED relations break down in both subsets, and that the breakdowns occur on all scales of mobility. Thus these breakdowns appear to be generalized phenomena, in contrast with a view where only the most mobile molecules are the origin of the breakdown of the SE and SED relations, embedded in an inactive background where these relations hold. At low temperature, the SE and SED relations in both subsets of molecules are replaced with “fractional” SE and SED relations, Dt~(/T)−t and Dr~(/T)−r, where t0.84(<1) and r0.75(<1). We also find that there is a decoupling between rotational and translational motion, and that this decoupling occurs in both the fastest and slowest subsets of molecules. Further, we find that, the decoupling increases upon cooling, but that the probability of a molecule being classified as both translationally and rotationally fastest also increases. To study the effect of time scale for SE and SED breakdown and decoupling, we introduce a time-dependent version of the SE and SED relations, and a time-dependent function that measures the extent of decoupling. Our results suggest that both the decoupling and SE and SED breakdowns originate at a time scale corresponding to the end of the cage regime, when diffusion starts. This is also the time scale when the DHs are more relevant. Our work also demonstrates that selecting DHs on the basis of translational or rotational motion more strongly biases the calculation of diffusion constants than other dynamical properties such as relaxation times.

Relation between Rotational and Translational Dynamic Heterogeneities in Water

Marco Mazza — 2007-06-26T00:38:18-00:00

Physical Review Letters, Vol. 96, No. 5. (2006), pp. 057803-057803.

We use molecular dynamics simulations to probe the rotational dynamics of the extended simple point charge model of water for a range of temperatures down to 200 K, 6 K above the mode coupling temperature. We find that rotational dynamics is spatially heterogeneous; i.e., there are clusters of molecules that rotate significantly more than the average for a given time interval, and we study the size and the temporal behavior of these clusters. We find that the position of a rotational heterogeneity is strongly correlated with the position of a translational heterogeneity, and that the fraction of molecules belonging to both kinds of heterogeneities increases with decreasing temperature. We further find that although the two types of heterogeneities are not identical, they are related to the same physical picture.

Time and length scales in supercooled liquids

Ludovic Berthier — 2007-10-30T13:27:13-00:00

Physical Review E, Vol. 69, No. 2. (2004), pp. 020201-020201.

We numerically obtain a quantitative demonstration that development of spatial correlations of mobility as temperature is lowered is responsible for the "decoupling" of transport properties of supercooled liquids. This result further demonstrates the necessity of a spatial description of the glass formation and therefore seriously challenges a number of popular alternative theoretical descriptions.

Entropic barriers, activated hopping, and the glass transition in colloidal suspensions

Kenneth Schweizer — 2007-10-29T19:56:08-00:00

The Journal of Chemical Physics, Vol. 119, No. 2. (2003), pp. 1181-1196.

A microscopic kinetic description of single-particle transient localization and activated transport in glassy fluids is developed which combines elements of idealized mode-coupling theory, density functional theory, and activated rate theory. Thermal fluctuations are included via a random force which destroys the idealized glass transition and restores ergodicity through activated barrier hopping. The approach is predictive, containing no adjustable parameters or postulated underlying dynamic or thermodynamic divergences. Detailed application to hard-sphere colloidal suspensions reveals good agreement with experiment for the location of the kinetic glass transition volume fraction, the dynamic incoherent scattering relaxation time, apparent localization length, and length scale of maximum nongaussian behavior. Multiple connections are predicted between thermodynamics, short-time dynamics in the nearly localized state, and long-time relaxation by entropic barrier crossing. A critical comparison of the fluid volume fraction dependence of the hopping time with fit formulas which contain ideal divergences has been performed. Application of the derivative Stickel analysis suggests that the fit functions do not provide an accurate description over a wide range of volume fractions. Generalization to treat the kinetic vitrification of more complex colloidal and nanoparticle suspensions, and thermal glass-forming liquids, is possible. ©2003 American Institute of Physics.

Activated Hopping, Barrier Fluctuations, and Heterogeneity in Glassy Suspensions and Liquids

KS Schweizer — 2007-10-29T19:53:08-00:00

J. Phys. Chem. B, Vol. 108, No. 51. (23 December 2004), pp. 19729-19741.

Abstract: Our entropic barrier hopping theory of glassy hard sphere colloidal suspensions is extended to include heterogeneity within a simple trap model framework. The origin of local domains, their size, and the corresponding static barrier fluctuations are attributed to mesoscopic density fluctuations of an amplitude controlled by the bulk compressibility. Based on typical values of the density fluctuation correlation length in dense liquids, the domain size on which correlated hopping occurs is estimated to be 3-4 particle or molecular diameters. Consequences of barrier fluctuations include an increased average relaxation time, faster diffusion, stretched exponential relaxation, diffusion-viscosity decoupling, and a fractional Stokes-Einstein relation. The common origin of the fluctuation effects is the heterogeneity-induced component of the barrier. For colloidal suspensions in the typically studied volume fraction regime the barrier fluctuations have modest consequences, but significantly larger effects are predicted in the putative glassy regime. A statistical dynamical analysis of domain lifetime suggests that for suspensions the relaxation time of mesoscopic collective density fluctuations is at least as long as the single particle hopping time. A general, model-independent analysis of the single molecule incoherent dynamic structure factor for suspensions and thermal liquids has also been performed in the long time and intermediate wavevector regime. The coupling of single particle density and longitudinal stress fluctuations results in a wavevector-dependent apparent diffusion constant and a dynamic correlation length scale which is strongly temperature dependent and directly related to the translation-rotation decoupling factor. This dynamic length is estimated to be 10 times larger than a molecular diameter for tris-naphthyl benzene near the glass transition temperature but shrinks to a molecular size above the crossover temperature that signals the emergence of collective barriers.

Activated hopping and dynamical fluctuation effects in hard sphere suspensions and fluids

Erica Saltzman — 2007-10-29T19:49:58-00:00

The Journal of Chemical Physics, Vol. 125, No. 4. (2006), pp. 044509-044509.

Single particle Brownian dynamics simulation methods are employed to establish the full trajectory level predictions of our nonlinear stochastic Langevin equation theory of activated hopping dynamics in glassy hard sphere suspensions and fluids. The consequences of thermal noise driven mobility fluctuations associated with the barrier hopping process are determined for various ensemble-averaged properties and their distributions. The predicted mean square displacements show classic signatures of transient trapping and anomalous diffusion on intermediate time and length scales. A crossover to a stronger volume fraction dependence of the apparent nondiffusive exponent occurs when the entropic barrier is of order the thermal energy. The volume fraction dependences of various mean relaxation times and rates can be fitted by empirical critical power laws with parameters consistent with ideal mode-coupling theory. However, the results of our divergence-free theory are largely a consequence of activated dynamics. The experimentally measurable alpha relaxation time is found to be very similar to the theoretically defined mean reaction time for escape from the barrier-dominated regime. Various measures of decoupling have been studied. For fluid states with small or nonexistent barriers, relaxation times obey a simple log-normal distribution, while for high volume fractions the relaxation time distributions become Poissonian. The product of the self-diffusion constant and mean alpha relaxation time increases roughly as a logarithmic function of the alpha relaxation time. The cage scale incoherent dynamic structure factor exhibits nonexponential decay with a modest degree of stretching. A nearly universal collapse of the different volume fraction results occurs if time is scaled by the mean alpha relaxation time. Hence, time-volume fraction superposition holds quite well, despite the presence of stretching and volume fraction dependent decoupling associated with the stochastic barrier hopping process. The relevance of other origins of dynamic heterogeneity (e.g., mesoscopic domains), and comparison of our results with experiments, simulations, and alternative theories, is discussed. ©2006 American Institute of Physics

Non-Gaussian effects, space-time decoupling, and mobility bifurcation in glassy hard-sphere fluids and suspensions

Erica Saltzman — 2007-10-29T19:47:05-00:00

Physical Review E, Vol. 74, No. 6. (2006)

Brownian trajectory simulation methods are employed to fully establish the non-Gaussian fluctuation effects predicted by our nonlinear Langevin equation theory of single particle activated dynamics in glassy hard-sphere fluids. The consequences of stochastic mobility fluctuations associated with the space-time complexities of the transient localization and barrier hopping processes have been determined. The incoherent dynamic structure factor was computed for a range of wave vectors and becomes of an increasingly non-Gaussian form for volume fractions beyond the (naive) ideal mode coupling theory (MCT) transition. The non-Gaussian parameter (NGP) amplitude increases markedly with volume fraction and is well described by a power law in the maximum restoring force of the nonequilibrium free energy profile. The time scale associated with the NGP peak becomes much smaller than the relaxation time for systems characterized by significant entropic barriers. An alternate non-Gaussian parameter that probes the long time relaxation process displays a different shape, peak intensity, and time scale of its maximum. However, a strong correspondence between the classic and alternate NGP amplitudes is predicted which suggests a deep connection between the early and final stages of cage escape. Strong space-time decoupling emerges at high volume fractions as indicated by a nondiffusive wave vector dependence of the relaxation time and growth of the translation-relaxation decoupling parameter. Displacement distributions exhibit non-Gaussian behavior at intermediate times, evolving into a strongly bimodal form with slow and fast subpopulations at high volume fractions. Qualitative and semiquantitative comparisons of the theoretical results with colloid experiments, ideal MCT, and multiple simulation studies are presented.

An Increasing Correlation Length in Off-Equilibrium Glasses

G Parisi — 2007-10-25T17:34:08-00:00

J. Phys. Chem. B, Vol. 103, No. 20. (20 May 1999), pp. 4128-4131.

In off-equilibrium dynamics we define a dynamical correlation length that is proportional to the size of the region in which the atoms move in a correlated way. General arguments indicate that this dynamical correlation length diverges at large times in the glassy phase. Numerical simulations for binary mixtures are consistent with this prediction, at least in the time window explored in this paper.

The Relaxation Dynamics of a Supercooled Liquid Confined by Rough Walls

P Scheidler — 2007-10-25T16:59:30-00:00

J. Phys. Chem. B, Vol. 108, No. 21. (27 May 2004), pp. 6673-6686.

Abstract: We present the results of molecular dynamics computer simulations of a binary Lennard-Jones liquid confined between two parallel rough walls. These walls are realized by frozen amorphous configurations of the same liquid and therefore the structural properties of the confined fluid are identical to the ones of the bulk system. Hence, this setup allows us to study how the relaxation dynamics is affected by the pure effect of confinement, i.e., if structural changes are completely avoided. We find that the local relaxation dynamics is a strong function of z, the distance of the particles from the wall, and that close to the surface the typical relaxation times are orders of magnitude larger than the ones in the bulk. Because of the cooperative nature of the particle dynamics, the slow dynamics also affects the dynamics of the particles for large values of z. Using various empirical laws, we are able to parametrize accurately the z dependence of the generalized incoherent intermediate scattering function Fs(q,z,t) and also the spatial dependence of structural relaxation times. These laws allow us to determine various dynamical length scales and we find that their temperature dependence is compatible with an Arrhenius law. Furthermore, we find that, at low temperatures, time- and space-dependent correlation functions fulfill a generalized factorization property similar to the one predicted by mode-coupling theory for bulk systems. For thin films and/or at sufficiently low temperatures, we find that the relaxation dynamics is influenced by the two walls in a strongly nonlinear way in that the slowing down is much stronger than the one expected from the presence of only one confining wall. Finally, we study the average dynamics of all liquid particles and find that the data can be described very well by a superposition of two relaxation processes that have clearly separated time scales. Since this is in contrast with the result of our analysis of the local dynamics, we argue that a correct interpretation of experimental data can be rather difficult.

Cooperative motion and growing length scales in supercooled confined liquids

P Scheidler — 2007-10-25T16:53:13-00:00

Europhysics Letters, Vol. 59, No. 5. (2002), pp. 701-707.

Using molecular-dynamics simulations we investigate the relaxation dynamics of a supercooled liquid close to a rough as well as to a smooth wall. For the former situation the relaxation times increase strongly with decreasing distance from the wall, whereas in the second case they strongly decrease. We use this dependence to extract various dynamical length scales and show that they grow with decreasing temperature. Finally, we calculate the frequencydependent average susceptibility of such confined systems and show that they compare very well with experimental data.

Growing Spatial Correlations of Particle Displacements in a Simulated Liquid on Cooling toward the Glass Transition

Claudio Donati — 2007-09-29T13:21:10-00:00

Physical Review Letters, Vol. 82, No. 25. (21 June 1999), pp. 5064-5067.

We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show that for an equilibrium liquid this function is related to fluctuations in a bulk dynamical variable. We evaluate this function using computer simulations of an equilibrium glass-forming liquid; and show that long range spatial correlations of displacements emerge and grow on cooling toward the mode coupling critical temperature.

Stringlike Cooperative Motion in a Supercooled Liquid

Claudio Donati — 2007-05-16T20:25:15-00:00

Physical Review Letters, Vol. 80, No. 11. (16 March 1998), pp. 2338-2341.

Extensive molecular dynamics simulations are performed on a glass-forming Lennard-Jones mixture to determine the nature of the cooperative motions occurring in this model fragile liquid. We observe stringlike cooperative molecular motion (“strings”) at temperatures well above the glass transition. The mean length of the strings increases upon cooling; and the string length distribution is found to be nearly exponential.

Dynamical Heterogeneities in a Supercooled Lennard-Jones Liquid

Walter Kob — 2007-05-18T06:48:08-00:00

Physical Review Letters, Vol. 79 (13 October 1997), pp. 2827-2830.

We present the results of a molecular dynamics computer simulation study in which we investigate whether a supercooled Lennard-Jones liquid exhibits dynamical heterogeneities. We evaluate the non-Gaussian parameter for the self part of the van Hove correlation function and use it to identify “mobile” particles. We find that these particles form clusters whose sizes grow with decreasing temperature. We also find that the relaxation time of the mobile particles is significantly shorter than that of the average particle; and that this difference increases with decreasing temperature.

Self-Diffusion in Concentrated Colloid Suspensions Studied by Digital Video Microscopy of Core-Shell Tracer Particles

A Kasper — 2007-05-18T06:56:19-00:00

Langmuir, Vol. 14, No. 18. (1 September 1998), pp. 5004-5010.

Abstract: Optical video microscopy and digital image processing have been used to study the self-diffusion of colloidal particles with a hard-sphere potential. The colloid particles consist of cross-linked polymers and are dispersed in a good solvent to avoid aggregation. To investigate single particle motion in highly concentrated dispersions, a host-tracer system, consisting of two different kinds of polymer particles, has been designed: the host particles are made of poly-t-butylacrylate (with ethanedioldiacrylate as cross-linker) and have the same refractive index as the employed solvent, 4-fluorotoluene. The tracer particles have a core-shell structure with a polystyrene core (cross-linked with m-diisopropenylbenzene) and a shell consisting of cross-linked poly-t-butylacrylate to match surface properties and interaction potential to those of the "invisible" particles. The motion of the strongly scattering core-shell particles ("tracer" particles) was observed by dark-field light microscopy. From the obtained particle trajectories, mean squared displacements, van Hove autocorrelation functions, and vector-vector correlation functions were calculated, yielding a direct real-space image of the "cage effect" at = 0.52 and of the transition to a glassy state between = 0.56 and = 0.60, as expected for a hard sphere system. The extracted long-time self-diffusion coefficients Dself,long are fully consistent with a recent theoretical prediction using full many-body hydrodynamics at 0.56 and a colloid glass transition at g = 0.583. However, even at = 0.60, Dself,long seems to be still finite, possibly indicating the existence of long-time motion of colloidal particles even in the glassy state.

How Reproducible Are Dynamic Heterogeneities in a Supercooled Liquid?

Asaph Widmer-Cooper — 2007-09-28T20:46:54-00:00

Physical Review Letters, Vol. 93, No. 13. (2004), pp. 135701-135701.

The particle dynamics in a liquid exhibits a transient spatial distribution of dynamic heterogeneities. The relationship between this kinetic structure and the underlying particle configuration remains an outstanding problem. In this Letter, we present a general simulation technique for identifying the features of the dynamic heterogeneity which arise due to a specific configuration, as distinct from the random spatial variation due to the intermittent particle dynamics.

Cooperativity and spatial correlations near the glass transition: Computer simulation results for hard spheres and disks

B Doliwa — 2007-09-28T20:13:49-00:00

Physical Review E, Vol. 61, No. 6. (June 2000), pp. 6898-6908.

We examine the dynamics of hard spheres and disks at high packing fractions in two and three dimensions; modeling the simplest systems exhibiting a glass transition. As it is well known; cooperativity and dynamic heterogeneity arise as central features when approaching the glass transition from the liquid phase; so an understanding of their underlying physics is of great interest. Cooperativity implies a reduction of the effective degrees of freedom; and we demonstrate a simple way of quantification in terms of the strength and the length scale of dynamic correlations among different particles. These correlations are obtained for different dynamical quantities X i ( t ) that are constructed from single-particle displacements during some observation time t . Of particular interest is the dependence on t . Interestingly; for appropriately chosen X i ( t ) we obtain finite cooperativity in the limit t →∞.

Cage Effect, Local Anisotropies, and Dynamic Heterogeneities at the Glass Transition: A Computer Study of Hard Spheres

B Doliwa — 2007-09-28T19:59:57-00:00

Physical Review Letters, Vol. 80, No. 22. (1 June 1998), pp. 4915-4918.

Computer simulations of a hard sphere system close to the glass transition are presented. From three-time correlations; we obtain information about the single-particle dynamics on all relevant time scales; including the presence of dynamic heterogeneities. A detailed picture of the cage effect in the β regime is obtained; yielding information about shape; size; and relaxation properties of the effective cage. Pronounced anisotropic dynamics is mainly observed in the β regime.

Nonlinear rheology of a highly supercooled liquid

R Yamamoto — 2007-09-28T17:41:56-00:00

Europhysics Letters (EPL), Vol. 40, No. 1. (1997), pp. 61-66.

We numerically examine nonlinear rheology of a highly supercooled two-di men sional fluid in shear flow via molecular-dynamics simulation. The viscosity exhibits marked shear-thinning behavior when the shear rate g exceeds the inverse of the a relaxation time ta. Bond breakage events among particle pairs are found to occur collectively in clusters. The characteristic size x of such clusters grows strongly with lowering the temperature and decreases rapidly with increasing g as x [?] tb(g)1/4. Here 1/tb(g) is the bond breakage rate tending to 1/ta for gta [?] 1 and growing as g for gta [?] 1. The viscosity is of order tb(g) in glassy states.

Coarse-grained microscopic model of glass formers

Juan Garrahan — 2007-09-27T14:39:35-00:00

Proceedings of the National Academy of Sciences, Vol. 100, No. 17. (19 August 2003), pp. 9710-9714.

We introduce a coarse-grained model for atomic glass formers. Its elements are physically motivated local microscopic dynamical rules parameterized by observables. Results of the model are established and used to interpret the measured behaviors of supercooled fluids approaching glass transitions. The model predicts the presence of a crossover from hierarchical super-Arrhenius dynamics at short length scales to diffusive Arrhenius dynamics at large length scales. This prediction distinguishes our model from other theories of glass formers and can be tested by experiment. 10.1073/pnas.1233719100

Dynamics of shear-transformation zones in amorphous plasticity: Energetic constraints in a minimal theory

JS Langer — 2007-09-27T03:37:52-00:00

Physical Review E, Vol. 68, No. 6. (23 December 2003), 061507.

We use energetic considerations to deduce the form of a previously uncertain coupling term in the shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. As in the earlier versions of the STZ theory; the onset of steady deformation at a yield stress appears here as an exchange of dynamic stability between jammed and plastically deforming states. We show how an especially simple “quasilinear” version of this theory accounts qualitatively for many features of plasticity such as yielding; strain softening; and strain recovery. We also show that this minimal version of the theory fails to describe certain other phenomena; and argue that these limitations indicate needs for additional internal degrees of freedom beyond those included here.

Dynamics of viscoplastic deformation in amorphous solids

ML Falk — 2007-09-27T03:35:32-00:00

Physical Review E, Vol. 57, No. 6. (June 1998), pp. 7192-7205.

We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional; two-component noncrystalline system. These numerical simulations reveal behavior typical of metallic glasses and other viscoplastic materials; specifically; reversible elastic deformation at small applied stresses; irreversible plastic deformation at larger stresses; a stress threshold above which unbounded plastic flow occurs; and a strong dependence of the state of the system on the history of past deformations. Microscopic observations suggest that a dynamically complete description of the macroscopic state of this deforming body requires specifying; in addition to stress and strain; certain average features of a population of two-state shear transformation zones. Our introduction of these state variables into the constitutive equations for this system is an extension of earlier models of creep in metallic glasses. In the treatment presented here; we specialize to temperatures far below the glass transition and postulate that irreversible motions are governed by local entropic fluctuations in the volumes of the transformation zones. In most respects; our theory is in good quantitative agreement with the rich variety of phenomena seen in the simulations.

Dynamics of highly supercooled liquids: Heterogeneity, rheology, and diffusion

Ryoichi Yamamoto — 2007-04-23T02:29:26-00:00

Physical Review E, Vol. 58, No. 3. (1998), pp. 3515-3529.

Highly supercooled liquids with soft-core potentials are studied via molecular-dynamics simulations in two and three dimensions in quiescent and sheared conditions. We may define bonds between neighboring particle pairs unambiguously owing to the sharpness of the first peak of the pair correlation functions. Upon structural rearrangements; they break collectively in the form of clusters whose sizes grow with lowering the temperature T . The bond lifetime τ b ; which depends on T and the shear rate γ̇; is on the order of the usual structural or α relaxation time τ α in weak shear γ̇τ α ≪1; while it decreases as 1/γ̇ in strong shear γ̇τ α ≫1 due to shear-induced cage breakage. Accumulated broken bonds in a time interval (∼0.05τ b ) closely resemble the critical fluctuations of Ising spin systems. For example; their structure factor is well fitted to the Ornstein-Zernike form; which yields the correlation length ξ representing the maximum size of the clusters composed of broken bonds. We also find a dynamical scaling relation; τ b ∼ξ z ; valid for any T and γ̇ with z =4 in two dimensions and z =2 in three dimensions. The viscosity is of order τ b for any T and γ̇; so marked shear-thinning behavior emerges. The shear stress is close to a limiting stress in a wide shear region. We also examine motion of tagged particles in shear in three dimensions. The diffusion constant is found to be of order τ b -ν with ν=0.75∼0.8 for any T and γ̇; so it is much enhanced in strong shear compared with its value at zero shear. This indicates a breakdown of the Einstein-Stokes relation in accord with experiments. Some possible experiments are also proposed.

Three-Dimensional Imaging of Colloidal Glasses under Steady Shear

R Besseling — 2007-09-19T16:31:56-00:00

Physical Review Letters, Vol. 99, No. 2. (2007), pp. 028301-028301.

Using fast confocal microscopy we image the three-dimensional dynamics of particles in a yielded hard-sphere colloidal glass under steady shear. The structural relaxation, observed in regions with uniform shear, is nearly isotropic but is distinctly different from that of quiescent metastable colloidal fluids. The inverse relaxation time alpha-1" align="middle"> and diffusion constant D, as functions of the local shear rate , show marked shear thinning with alpha-1" align="middle">D0.8 over more than two decades in . In contrast, the global rheology of the system displays Herschel-Bulkley behavior. We discuss the possible role of large scale shear localization and other mechanisms in generating this difference.

Direct visualization of ageing in colloidal glasses

Rachel Courtland — 2005-08-20T23:20:53-00:00

J. Phys.: Condens. Matter, Vol. 15 (2003), pp. S359-S365.

We use confocal microscopy to directly visualize the dynamics of ageing colloidal glasses. We prepare a colloidal suspension at high density, a simple model system that shares many properties with other glasses, and initiate experiments by stirring the sample. We follow the motion of several thousand colloidal particles after the stirring and observe that their motion significantly slows as the sample ages. The ageing is both spatially and temporally heterogeneous. Furthermore, while the characteristic relaxation timescale grows with the age of the sample, nontrivial particle motions continue to occur on all timescales.

Time-resolved correlation: a new tool for studying temporally heterogeneous dynamics

Luca Cipelletti — 2005-08-22T03:28:42-00:00

J. Phys.: Condens. Matter, Vol. 15 (16 December 2003), pp. S257-S262.

We introduce a new scheme for investigating temporally heterogeneous dynamics, which is termed time-resolved correlation (TRC). TRC is applied to data obtained by diffusing wave spectroscopy probing the slow dynamics of a strongly aggregated colloidal gel. Other examples of TRC data, collected for different jammed materials in single and multiple scattering, are provided to demonstrate the wide range of applicability of this method. In all cases we find evidence that the slow dynamics results from a series of discrete steps rather than from a continuous motion, suggesting temporal heterogeneities to be a general feature of slow dynamics in jammed systems.

Three-Dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition

Eric Weeks — 2005-06-19T21:01:36-00:00

Science, Vol. 287, No. 5453. (28 January 2000), pp. 627-631.

On the Temperature Dependence of Cooperative Relaxation Properties in Glass-Forming Liquids

Gerold Adam — 2007-05-17T03:49:06-00:00

The Journal of Chemical Physics, Vol. 43, No. 1. (1965), pp. 139-146.

A molecular-kinetic theory, which explains the temperature dependence of relaxation behavior in glass-forming liquids in terms of the temperature variation of the size of the cooperatively rearranging region, is presented. The size of this cooperatively rearranging region is shown to be determined by configuration restrictions in these glass-forming liquids and is expressed in terms of their configurational entropy. The result of the theory is a relation practically coinciding with the empirical WLF equation. Application of the theory to viscosimetric experiments permits evaluation of the ratio of the kinetic glass temperature Tg (derived from usual “quasistatic” experiments) to the equilibrium second-order transition temperature T2 (indicated by either statistical-mechanical theory or extrapolations of experimental data) as well as the hindrance-free energy per molecule. These parameters have been evaluated for fifteen substances, the experimental data for which were available. Hindrance-free energies were found to be of the magnitude to be expected from consideration of molecular interaction energies. The values of Tg/T2 thus obtained for these fifteen widely differing materials were found to be nearly the same, i.e., 1.30±8.4%. Values for Tg/T2 of nearly the same magnitude were derived by Bestul and Chang from calorimetric data. ©1965 American Institute of Physics