Estelle Pitard

Dynamical first-order phase transition in kinetically constrained models of glasses.

We show that the dynamics of kinetically constrained models of glass formers takes place at a first-order coexistence line between active and inactive dynamical phases. We prove this by computing the large-deviation functions of suitable space-time observables, such as the number of configuration changes in a trajectory. We present analytic results for dynamic facilitated models in a mean-field approximation, and numerical results for the Fredrickson-Andersen model, the East model, and constrained lattice gases, in various dimensions. This dynamical first-order transition is generic in kinetically constrained models, and we expect it to be present in systems with fully jammed states.

First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories

We investigate the dynamics of kinetically constrained models of glass formers by analysing the statistics of trajectories of the dynamics, or histories, using large deviation function methods. We show that, in general, these models exhibit a first-order dynamical transition between active and inactive dynamical phases. We argue that the dynamical heterogeneities displayed by these systems are a manifestation of dynamical first-order phase coexistence. In particular, we calculate dynamical large deviation functions, both analytically and numerically, for the Fredrickson–Andersen model, the East model, and constrained lattice gas models. We also show how large deviation functions can be obtained from a Landau-like theory for dynamical fluctuations. We discuss possibilities for similar dynamical phase-coexistence behaviour in other systems with heterogeneous dynamics.

Universal non-diffusive slow dynamics in aging soft matter

We use conventional and multispeckle dynamic light scattering to investigate the dynamics of a wide variety of jammed soft materials, including colloidal gels, concentrated emulsions, and concentrated surfactant phases. For all systems, the dynamic structure factor f(q,t) exhibits a two-step decay. The initial decay is due to the thermally activated diffusive motion of the scatterers, as indicated by the q(-2) dependence of the characteristic relaxation time, where q is the scattering vector. However, due to the constrained motion of the scatterers in jammed systems. the dynamics are arrested and the initial decay terminates in a plateau. Surprisingly, we find that a final, ultraslow decay leads to the complete relaxation of f(q,t), indicative of rearrangements on length scales as large as several microns or tens of microns. Remarkably, for all systems the same very peculiar form is found for the final relaxation of the dynamic structure factor: f(q,t) approximately exp[-(t/tau s)p], with p approximately equal to 1.5 and tau s approximately q(-1), thus suggesting the generality of this behavior. Additionally, for all samples the final relaxation slows down with age. although the aging behavior is found to be sample dependent. We propose that the unusual ultraslow dynamics are due to the relaxation of internal stresses, built into the sample at the jamming transition, and present simple scaling arguments that support this hypothesis.

Investigation of q-dependent dynamical heterogeneity in a colloidal gel by x-ray photon correlation spectroscopy.

We use time-resolved x-ray photon correlation spectroscopy to investigate the slow dynamics of colloidal gels made of moderately attractive carbon black particles. We show that the slow dynamics is temporally heterogeneous and quantify its fluctuations by measuring the variance chi of the instantaneous intensity correlation function. The amplitude of dynamical fluctuations has a nonmonotonic dependence on scattering vector q, in stark contrast with recent experiments on strongly attractive colloidal gels [Duri and Cipelletti, Europhys. Lett. 76, 972 (2006)]. We propose a simple scaling argument for the q-dependence of fluctuations in glassy systems that rationalizes these findings.

Dynamic transition in an atomic glass former: A molecular-dynamics evidence

We find that a Lennard-Jones mixture displays a dynamic phase transition between an active regime and an inactive one. By means of molecular dynamics simulations and of a finite-size study, we show that the spacetime dynamics in the supercooled regime coincides with a dynamic first-order transition point.

Glassy behavior of a homopolymer from molecular dynamics simulations

We study at- and out-of-equilibrium dynamics of a single homopolymer chain at low temperature using molecular dynamics. The main quantities of interest are the average root mean square displacement of the monomers below the theta point, and the structure factor, as a function of time. The observation of these quantities show a close resemblance to those measured in structural glasses and suggest that the polymer chain in its low temperature phase is in a glassy phase, with its dynamics dominated by traps. In equilibrium, at low temperature, we observe the trapping of the monomers and a slowing down of the overall motion of the polymer as well as nonexponential relaxation of the structure factor. Out of equilibrium, at low temperatures, we compute the two-time quantities and observe breaking of ergodicity in a range of waiting times, with the onset of aging.

Out-of-equilibrium dynamics of a fractal model gel

Using molecular dynamics computer simulations we investigate the dynamics of a gel. We start from a fractal structure generated by the diffusion limited cluster aggregation-deflection algorithm, onto which we then impose an interaction potential consisting of a short-range attraction as well as a long-range repulsion. After relaxing the system at zero temperature, we let it evolve at a fixed finite temperature. Depending on the temperature T we find different scenarios for the dynamics. For T approximately > 0.2 the fractal structure is unstable and breaks up into small clusters which relax to equilibrium. For T approximately < 0.2 the structure is stable and the dynamics slows down with increasing waiting time. At intermediate and low T the mean squared displacement scales as t(2/3) and we discuss several mechanisms for this anomalous time dependence. For intermediate T, the self-intermediate scattering function is given by a compressed exponential at small wave vectors and by a stretched exponential at large wave vectors. In contrast, for low T it is a stretched exponential for all wave vectors. This behavior can be traced back to a subtle interplay between elastic rearrangements, fluctuations of chainlike filaments, and heterogeneity.

Large deviations and heterogeneities in a driven kinetically constrained model

Kinetically Constrained Models (KCMs) have been widely studied in the context of glassy dynamics, focusing on the influence of dynamical constraints on the slowing-down of the dynamics of a macroscopic system. In these models, it has been shown using the thermodynamic formalism for histories, that there is a coexistence between an active and an inactive phase. This coexistence can be described by a first-order transition, and a related discontinuity in the derivative of the large-deviation function for the activity. We show that adding a driving field to a KCM model does not destroy this first-order transition for the activity. Moreover, a singularity is also found in the large-deviation function of the current at large fields. We relate for the first time this property to microscopic structures, in particular the heterogeneous, intermittent dynamics of the particles, transient shear-banding and blocking walls. We describe both the shear-thinning and the shear-thickening regimes, and find that the behaviour of the current is well reproduced by a simple model.

DYNAMICAL HETEROGENEITIES IN A TWO-DIMENSIONAL DRIVEN GLASSY MODEL: CURRENT FLUCTUATIONS AND FINITE SIZE EFFECTS

In this article, we demonstrate that in a transport model of particles with kinetic constraints, long-lived spatial structures are responsible for the blocking dynamics and the decrease of the current at strong driving field. Coexistence between mobile and blocked regions can be anticipated by a first-order transition in the large deviation function for the current. By a study of the system under confinement, we are able to study finite-size effects and extract a typical length between mobile regions.

Spatial correlations in the relaxation of the Kob-Andersen model

We describe spatio-temporal correlations and heterogeneities in a kinetically constrained glassy model, the Kob-Andersen model. The kinetic constraints of the model alone induce the existence of dynamic correlation lengths, that increase as the density ρ increases, in a way compatible with a double-exponential law. We characterize in detail the trapping time correlation length, the cooperativity length, and the distribution of persistent clusters of particles. This last quantity is related to the typical size of blocked clusters that slow down the dynamics for a given density.