Equilibrium and non-equilibrium fluctuations in a glass-forming liquid

Glass-forming liquids display strong fluctuations -- dynamical heterogeneities -- near their glass transition. By numerically simulating a binary Weeks-Chandler-Andersen liquid and varying both temperature and timescale, we investigate the probability distributions of two kinds of local fluctuations in the non-equilibrium (aging) regime and in the equilibrium regime; and find them to be very similar in the two regimes and across temperatures. We also observe that, when appropriately rescaled, the integrated dynamic susceptibility is very weakly dependent on temperature and very similar in both regimes.Comment: v1: 5 pages, 4 figures v2: 5 pages, 4 figures. Now includes results at three temperatures, two of them above T_{MCT} and one below T_{MCT}; and more extensive discussion of connections to experiment

Molecular dynamics simulations of the Johari-Goldstein relaxation in a molecular liquid

Molecular dynamics simulations (mds) were carried out to investigate the reorientational motion of a rigid (fixed bond length), asymmetric diatomic molecule in the liquid and glassy states. In the latter the molecule reorients via large-angle jumps, which we identify with the Johari-Goldstein (JG) dynamics. This relaxation process has a broad distribution of relaxation times, and at least deeply in the glass state, the mobility of a given molecule remains fixed over time; that is, there is no dynamic exchange among molecules. Interestingly, the JG relaxation time for a molecule does not depend on the local density, although the non-ergodicity factor is weakly correlated with the packing efficiency of neighboring molecules. In the liquid state the frequency of the JG process increases significantly, eventually subsuming the slower alpha-relaxation. This evolution of the JG-motion into structural relaxation underlies the correlation of many properties of the JG- and alpha-dynamics.Comment: 12 pages, 6 figure

Origin of the slow dynamics and the aging of a soft glass

We study by light microscopy a soft glass consisting of a compact arrangement of polydisperse elastic spheres. We show that its slow and non-stationary dynamics results from the unavoidable small fluctuations of temperature, which induce intermittent local mechanical shear in the sample, because of thermal expansion and contraction. Temperature-induced shear provokes both reversible and irreversible rearrangements whose amplitude decreases with time, leading to an exponential slowing down of the dynamics with sample age.Comment: published in PRL 97, 238301, 200

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

We use time-resolved X-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 non-monotonic dependence on scattering vector $q$, in stark contrast with recent experiments on strongly attractive colloidal gels [Duri and Cipelletti, \textit{Europhys. Lett.} \textbf{76}, 972 (2006)]. We propose a simple scaling argument for the $q$-dependence of fluctuations in glassy systems that rationalizes these findings.Comment: Final version published in PR

Binary mixture of hard disks as a model glass former: Caging and uncaging

I have proposed a measure for the cage effect in glass forming systems. A binary mixture of hard disks is numerically studied as a model glass former. A network is constructed on the basis of the colliding pairs of disks. A rigidity matrix is formed from the isostatic (rigid) sub--network, corresponding to a cage. The determinant of the matrix changes its sign when an uncaging event occurs. Time evolution of the number of the uncaging events is determined numerically. I have found that there is a gap in the uncaging timescales between the cages involving different numbers of disks. Caging of one disk by two neighboring disks sustains for a longer time as compared with other cages involving more than one disk. This gap causes two--step relaxation of this system

1/d1/d Expansion for kk-Core Percolation

The physics of $k$-core percolation pertains to those systems whose constituents require a minimum number of $k$ connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from orientational ordering in solid ortho-para ${\rm H}_2$ mixtures to the onset of rigidity in bar-joint networks to dynamical arrest in glass-forming liquids. Unlike ordinary ($k=1$) and biconnected ($k=2$) percolation, the mean field $k\ge3$-core percolation transition is both continuous and discontinuous, i.e. there is a jump in the order parameter accompanied with a diverging length scale. To determine whether or not this hybrid transition survives in finite dimensions, we present a $1/d$ expansion for $k$-core percolation on the $d$-dimensional hypercubic lattice. We show that to order $1/d^3$ the singularity in the order parameter and in the susceptibility occur at the same value of the occupation probability. This result suggests that the unusual hybrid nature of the mean field $k$-core transition survives in high dimensions.Comment: 47 pages, 26 figures, revtex

Length scale dependence of dynamical heterogeneity in a colloidal fractal gel

We use time-resolved dynamic light scattering to investigate the slow dynamics of a colloidal gel. The final decay of the average intensity autocorrelation function is well described by $g\_2(q,\tau)-1 \sim \exp[-(\tau/\tau\_\mathrm{f})^p]$, with $\tau\_\mathrm{f} \sim q^{-1}$ and $p$ decreasing from 1.5 to 1 with increasing $q$. We show that the dynamics is not due to a continuous ballistic process, as proposed in previous works, but rather to rare, intermittent rearrangements. We quantify the dynamical fluctuations resulting from intermittency by means of the variance $\chi(\tau,q)$ of the instantaneous autocorrelation function, the analogous of the dynamical susceptibility $\chi\_4$ studied in glass formers. The amplitude of $\chi$ is found to grow linearly with $q$. We propose a simple --yet general-- model of intermittent dynamics that accounts for the $q$ dependence of both the average correlation functions and $\chi$.Comment: Revised and improved, to appear in Europhys. Let

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

We introduce a new dynamic light scattering method, termed photon correlation imaging, which enables us to resolve the dynamics of soft matter in space and time. We demonstrate photon correlation imaging by investigating the slow dynamics of a quasi two-dimensional coarsening foam made of highly packed, deformable bubbles and a rigid gel network formed by dilute, attractive colloidal particles. We find the dynamics of both systems to be determined by intermittent rearrangement events. For the foam, the rearrangements extend over a few bubbles, but a small dynamical correlation is observed up to macroscopic length scales. For the gel, dynamical correlations extend up to the system size. These results indicate that dynamical correlations can be extremely long-ranged in jammed systems and point to the key role of mechanical properties in determining their nature.Comment: Published version (Phys. Rev. Lett. 102, 085702 (2009)) The Dynamical Activity Mapsprovided as Supplementary Online Material are also available on http://w3.lcvn.univ-montp2.fr/~lucacip/dam/movies.ht

α\alpha-Scale Decoupling of the Mechanical Relaxation and Diverging Shear Wave Propagation Lengthscale in Triphenylphosphite

We have performed depolarized Impulsive Stimulated Scattering experiments to observe shear acoustic phonons in supercooled triphenylphosphite (TPP) from $\sim$10 - 500 MHz. These measurements, in tandem with previously performed longitudinal and shear measurements, permit further analyses of the relaxation dynamics of TPP within the framework of the mode coupling theory (MCT). Our results provide evidence of $\alpha$ coupling between the shear and longitudinal degrees of freedom up to a decoupling temperature $T_c$ = 231 K. A lower bound length scale of shear wave propagation in liquids verified the exponent predicted by theory in the vicinity of the decoupling temperature