Invariance of Structure in an Aging Colloidal Glass

We study concentrated colloidal suspensions, a model system which has a glass transition. The non-equilibrium nature of the glassy state is most clearly highlighted by aging -- the dependence of the system's properties on the time elapsed since vitrification. Fast laser scanning confocal microscopy allows us to image a colloidal glass and track the particles in three dimensions. We analyze the static structure in terms of tetrahedral packing. We find that while the aging of the suspension clearly affects its dynamics, none of the geometrical quantities associated with tetrahedra change with age.Comment: Submitted to the proceedings of "The 3rd International Workshop on Complex Systems" in Sendai, Japa

Self-Organized Criticality Below The Glass Transition

We obtain evidence that the dynamics of glassy systems below the glass transition is characterized by self-organized criticality. Using molecular dynamics simulations of a model glass-former we identify clusters of cooperatively jumping particles. We find string-like clusters whose size is power-law distributed not only close to T_c but for ALL temperatures below T_c, indicating self-organized criticality which we interpret as a freezing in of critical behavior.Comment: 4 pages, 3 figure

Forced motion of a probe particle near the colloidal glass transition

We use confocal microscopy to study the motion of a magnetic bead in a dense colloidal suspension, near the colloidal glass transition volume fraction $\phi_g$. For dense liquid-like samples near $\phi_g$, below a threshold force the magnetic bead exhibits only localized caged motion. Above this force, the bead is pulled with a fluctuating velocity. The relationship between force and velocity becomes increasingly nonlinear as $\phi_g$ is approached. The threshold force and nonlinear drag force vary strongly with the volume fraction, while the velocity fluctuations do not change near the transition.Comment: 7 pages, 4 figures revised version, accepted for publication in Europhysics Letter

Correlations of Structure and Dynamics in an Aging Colloidal Glass

We study concentrated colloidal suspensions, a model system which has a glass transition. Samples in the glassy state show aging, in that the motion of the colloidal particles slows as the sample ages from an initial state. We study the relationship between the static structure and the slowing dynamics, using confocal microscopy to follow the three-dimensional motion of the particles. The structure is quantified by considering tetrahedra formed by quadruplets of neighboring particles. We find that while the sample clearly slows down during aging, the static properties as measured by tetrahedral quantities do not vary. However, a weak correlation between tetrahedron shape and mobility is observed, suggesting that the structure facilitates the motion responsible for the sample aging.Comment: Submitted to Solid State Communication

Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics

We explore the existence of time reparametrization symmetry in p-spin models. Using the Martin-Siggia-Rose generating functional, we analytically probe the long-time dynamics. We perform a renormalization group analysis where we systematically integrate over short timescale fluctuations. We find three families of stable fixed points and study the symmetry of those fixed points with respect to time reparametrizations. One of those families is composed entirely of symmetric fixed points, which are associated with the low temperature dynamics. The other two families are composed entirely of non-symmetric fixed points. One of these two non-symmetric families corresponds to the high temperature dynamics. Time reparametrization symmetry is a continuous symmetry that is spontaneously broken in the glass state and we argue that this gives rise to the presence of Goldstone modes. We expect the Goldstone modes to determine the properties of fluctuations in the glass state, in particular predicting the presence of dynamical heterogeneity.Comment: v2: Extensively modified to discuss both high temperature (non-symmetric) and low temperature (symmetric) renormalization group fixed points. Now 16 pages with 1 figure. v1: 13 page

Aging in Dense Colloids as Diffusion in the Logarithm of Time

The far-from-equilibrium dynamics of glassy systems share important phenomenological traits. A transition is generally observed from a time-homogeneous dynamical regime to an aging regime where physical changes occur intermittently and, on average, at a decreasing rate. It has been suggested that a global change of the independent time variable to its logarithm may render the aging dynamics homogeneous: for colloids, this entails diffusion but on a logarithmic time scale. Our novel analysis of experimental colloid data confirms that the mean square displacement grows linearly in time at low densities and shows that it grows linearly in the logarithm of time at high densities. Correspondingly, pairs of particles initially in close contact survive as pairs with a probability which decays exponentially in either time or its logarithm. The form of the Probability Density Function of the displacements shows that long-ranged spatial correlations are very long-lived in dense colloids. A phenomenological stochastic model is then introduced which relies on the growth and collapse of strongly correlated clusters ("dynamic heterogeneity"), and which reproduces the full spectrum of observed colloidal behaviors depending on the form assumed for the probability that a cluster collapses during a Monte Carlo update. In the limit where large clusters dominate, the collapse rate is ~1/t, implying a homogeneous, log-Poissonian process that qualitatively reproduces the experimental results for dense colloids. Finally an analytical toy-model is discussed to elucidate the strong dependence of the simulation results on the integrability (or lack thereof) of the cluster collapse probability function.Comment: 6 pages, extensively revised, final version; for related work, see http://www.physics.emory.edu/faculty/boettcher/ or http://www.fysik.sdu.dk/staff/staff-vip/pas-personal.htm

Direct visualization of aging in colloidal glasses

We use confocal microscopy to directly visualize the dynamics of aging colloidal glasses. We prepare a colloidal suspension at high density, a simple model system which 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 aging is both spatially and temporally heterogeneous. Furthermore, while the characteristic relaxation time scale grows with the age of the sample, nontrivial particle motions continue to occur on all time scales.Comment: submitted to proceedings for Liquid Matter Conference 200

Particle dynamics in colloidal suspensions above and below the glass-liquid re-entrance transition

We study colloidal particle dynamics of a model glass system using confocal and fluorescence microscopy as the sample evolves from a hard-sphere glass to a liquid with attractive interparticle interactions. The transition from hard-sphere glass to attractive liquid is induced by short-range depletion forces. The development of liquid-like structure is indicated by particle dynamics. We identify particles which exhibit substantial motional events and characterize the transition using the properties of these motional events. As samples enter the attractive liquid region, particle speed during these motional events increases by about one order of magnitude, and the particles move more cooperatively. Interestingly, colloidal particles in the attractive liquid phase do not exhibit significantly larger displacements than particles in the hard-sphere glass

Atomistic mechanism of physical ageing in glassy materials

Using molecular simulations, we identify microscopic relaxation events of individual particles in ageing structural glasses, and determine the full distribution of relaxation times. We find that the memory of the waiting time $t_w$ elapsed since the quench extends only up to the first relaxation event, while the distribution of all subsequent relaxation times (persistence times) follows a power law completely independent of history. Our results are in remarkable agreement with the well known phenomenological trap model of ageing. A continuous time random walk (CTRW) parametrized with the atomistic distributions captures the entire bulk diffusion behavior and explains the apparent scaling of the relaxation dynamics with $t_w$ during ageing, as well as observed deviations from perfect scaling.Comment: 5 pages, 5 figure

Growing dynamical length, scaling and heterogeneities in the 3d Edwards-Anderson model

We study numerically spatio-temporal fluctuations during the out-of-equilibrium relaxation of the three-dimensional Edwards-Anderson model. We focus on two issues. (1) The evolution of a growing dynamical length scale in the glassy phase of the model, and the consequent collapse of the distribution of local coarse-grained correlations measured at different pairs of times on a single function using {\it two} scaling parameters, the value of the global correlation at the measuring times and the ratio of the coarse graining length to the dynamical length scale (in the thermodynamic limit). (2) The `triangular' relation between coarse-grained local correlations at three pairs of times taken from the ordered instants $t_3 \leq t_2 \leq t_1$. Property (1) is consistent with the conjecture that the development of time-reparametrization invariance asymptotically is responsible for the main dynamic fluctuations in aging glassy systems as well as with other mechanisms proposed in the literature. Property (2), we stress, is a much stronger test of the relevance of the time-reparametrization invariance scenario.Comment: 24 pages, 12 fig