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

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

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

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

Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities

The aim of this paper is to discuss some basic notions regarding generic glass forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction we discuss the so called `glass transition' in which super-cooled amorphous state is formed, accompanied with a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length-scales we show that (i) the system remains ergodic at all temperatures. (ii) the number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N. (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N, showing that the graph of configurations has the `small world' property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0Comment: 10 pages, 9 figures, submitted to PR

Aging in a Colloidal Glass in Creep Flow: Time-Stress Superposition

In this work, we study ageing behavior of aqueous laponite suspension, a model soft glassy material, in creep. We observe that viscoelastic behavior is time dependent and is strongly influenced by the deformation field; the effect is known to arise due to ageing and rejuvenation. We show that irrespective of strength of deformation field (shear stress) and age, when imposed time-scale is normalized with dominating relaxation mode of the system, universal ageing behavior is obtained demonstrating time-stress superposition; the phenomena that may be generic in variety of soft materials.Comment: 10 pages, 4 figure

Non-equilibrium thermodynamics. IV: Generalization of Maxwell, Claussius-Clapeyron and Response Functions Relations, and the Prigogine-Defay Ratio for Systems in Internal Equilibrium

We follow the consequences of internal equilibrium in non-equilibrium systems that has been introduced recently [Phys. Rev. E 81, 051130 (2010)] to obtain the generalization of Maxwell's relation and the Clausius-Clapeyron relation that are normally given for equilibrium systems. The use of Jacobians allow for a more compact way to address the generalized Maxwell relations; the latter are available for any number of internal variables. The Clausius-Clapeyron relation in the subspace of observables show not only the non-equilibrium modification but also the modification due to internal variables that play a dominant role in glasses. Real systems do not directly turn into glasses (GL) that are frozen structures from the supercooled liquid state L; there is an intermediate state (gL) where the internal variables are not frozen. Thus, there is no single glass transition. A system possess several kinds of glass transitions, some conventional (L \rightarrow gL; gL\rightarrow GL) in which the state change continuously and the transition mimics a continuous or second order transition, and some apparent (L\rightarrow gL; L\rightarrow GL) in which the free energies are discontinuous so that the transition appears as a zeroth order transition, as discussed in the text. We evaluate the Prigogine-Defay ratio {\Pi} in the subspace of the observables at these transitions. We find that it is normally different from 1, except at the conventional transition L\rightarrow gL, where {\Pi}=1 regardless of the number of internal variables.Comment: 42 pages, 3 figures, citations correcte

Solidity of viscous liquids. V. Long-wavelength dominance of the dynamics

This paper is the fifth in a series exploring the physical consequences of the solidity of glass-forming liquids. Paper IV proposed a model where the density field is described by a time-dependent Ginzburg-Landau equation of the nonconserved type with rates in $k$ space of the form $\Gamma_0+Dk^2$. The model assumes that $D\gg\Gamma_0a^2$ where $a$ is the average intermolecular distance; this inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) to a good approximation may be taken to be ultralocal. In the present paper we argue that this is the simplest model consistent with the following three experimental facts: 1) Viscous liquids approaching the glass transition do not develop long-range order; 2) The glass has lower compressibility than the liquid; 3) The alpha process involves several decades of relaxation times shorter than the mean relaxation time. The paper proceeds to list six further experimental facts characterizing equilibrium viscous liquid dynamics and shows that these are readily understood in terms of the model; some are direct consequences, others are quite natural when viewed in light of the model

Confinement effects on glass forming liquids probed by DMA

Many molecular glass forming liquids show a shift of the glass transition T-g to lower temperatures when the liquid is confined into mesoporous host matrices. Two contrary explanations for this effect are given in literature: First, confinement induced acceleration of the dynamics of the molecules leads to an effective downshift of T-g increasing with decreasing pore size. Second, due to thermal mismatch between the liquid and the surrounding host matrix, negative pressure develops inside the pores with decreasing temperature, which also shifts T-g to lower temperatures. Here we present dynamic mechanical analysis measurements of the glass forming liquid salol in Vycor and Gelsil with pore sizes of d=2.6, 5.0 and 7.5 nm. The dynamic complex elastic susceptibility data can be consistently described with the assumption of two relaxation processes inside the pores: A surface induced slowed down relaxation due to interaction with rough pore interfaces and a second relaxation within the core of the pores. This core relaxation time is reduced with decreasing pore size d, leading to a downshift of T-g proportional to 1/d in perfect agreement with recent differential scanning calorimetry (DSC) measurements. Thermal expansion measurements of empty and salol filled mesoporous samples revealed that the contribution of negative pressure to the downshift of T-g is small (<30%) and the main effect is due to the suppression of dynamically correlated regions of size xi when the pore size xi approaches