Signatures of dynamical heterogeneity in the structure of glassy free-energy minima

From numerical minimization of a model free-energy functional for a system of hard spheres, we show that the width of the local peaks of the time-averaged density field at a glassy free-energy minimum exhibits large spatial variation, similar to that of the "local Debye-Waller factor" in simulations of dynamical heterogeneity. Molecular dynamics simulations starting from a particle configuration generated from the density distribution at a glassy free-energy minimum show similar spatial heterogeneity in the degree of localization, implying a direct connection between dynamical heterogeneity and the structure of glassy free-energy minima.     

Aging, yielding, and shear banding in soft colloidal glasses

Soft colloidal interactions in colloidal glasses are modeled using suspensions of multiarm star polymers. Using a preshearing protocol that ensures a reproducible initial state ("rejuvenation" of the system), we report here the evolution of the flow curve from monotonically increasing to one dominated by a stress plateau, demonstrating a corresponding shear-banded state. Phenomenological understanding is provided through a scalar model that describes the free-energy landscape.     

Avalanche behavior in yield stress fluids

We show that, above a critical stress, typical yield stress fluids (gels and clay suspensions) and soft glassy materials (colloidal glasses) start flowing abruptly and subsequently accelerate, leading to avalanches that are remarkably similar to those of granular materials. Rheometrical tests reveal that this is associated with a bifurcation in rheological behavior: for small stresses, the viscosity increases in time; the material eventually stops flowing. For slightly larger stresses the viscosity decreases continuously in time; the flow accelerates. Thus the viscosity jumps discontinuously to infinity at the critical stress. We propose a simple physical model capable of reproducing these effects.     

Glassy dynamics: effective temperatures and intermittencies from a two-state model

We show the existence of intermittent dynamics in one of the simplest model of a glassy system: the two-state model, which has been used [Physica A 329 (2003) 357] to explain the origin of the violation of the fluctuation–dissipation theorem. The dynamics is analyzed through a Langevin equation for the evolution of the state of the system through its energy landscape. The results obtained concerning the violation factor and the non-Gaussian nature of the fluctuations are in good qualitative agreement with experiments measuring the effective temperature and the voltage fluctuations in gels and in polymer glasses. The method proposed can be useful to study the dynamics of other slow relaxation systems in which non-Gaussian fluctuations have been observed.     

Geometric approach to the dynamic glass transition

We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by the vanishing of the instability index of saddle points of the potential energy. Furthermore, we show that the potential energy barriers connecting local glassy minima increase with decreasing energy of the minima, and we relate this behavior to the fragility of the system. Finally, we analyze the real space structure of activated processes by studying the distribution of particle displacements for local minima connected by simple saddles.     

Multiple scaling regimes in simple aging models

We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging behavior and multiple scaling regimes for the correlation function. Both the exponents characterizing the scaling of the different relaxation times with the waiting time and those characterizing the asymptotic decay of the scaling functions are obtained analytically by invoking a "partial equilibrium" concept.     

Thermodynamic Properties of Inhomogeneous Structures in Supercooled Liquids

The weighted density-functional theory is applied to investigate the free-energy landscape of dense supercooled liquids. Metastable states intermediate to the liquid and crystal phases are found, which can be identified with the supercooled states seen in computer simulations. These states are marked by a lower degree of mass localization as compared to the highly localized state termed as "hard-sphere glass" found in earlier studies. We evaluate the free energy using the modified weighted density approximation (MWDA), as formulated by Denton and Ashcroft (1989) Phys. Rev. A , 39 , 4701. The inhomogeneous density is parametrized in terms of Gaussian profiles centered around random lattice sites. The effects of heterogeneity coming from a fluctuation of the width of these Gaussian profiles show that the free energy of the system increases with increase in the fluctuations and, finally, the metastable minima disappear with growing fluctuations.     

Equilibrium glassy phase in a polydisperse hard-sphere system

The phase diagram of a polydisperse hard-sphere system is examined by numerical minimization of a discretized form of the Ramakrishnan-Yussouff free-energy functional. Crystalline and glassy local minima of the free energy are located and the phase diagram in the density-polydispersity plane is mapped out by comparing the free energies of different local minima. The crystalline phase disappears and the glass becomes the equilibrium phase beyond a "terminal" value of the polydispersity. A crystal-to-glass transition is also observed as the density is increased at high polydispersity. The phase diagram obtained in our study is qualitatively similar to that of hard spheres in a quenched random potential.     

Experimental umbilic diabolos in random optical fields

The intensity of a random optical field consists of bright speckle spots (maxima) separated from dark areas (minima and optical vortices) by saddle points. We show that hidden in this complicated landscape are umbilic points--singular points at which the eigenvalues Lambda (+/-) of the Hessian matrix that measure the curvature of the landscape become degenerate. Although not observed previously in random optical fields, umbilic points are the most numerous of all special points, outnumbering maxima, minima, saddle points, and vortices. We show experimentally that the directions of principal curvature, the eigenvectors Psi (+/-), rotate about intensity umbilic points with positive or negative half-integer winding number, in accord with theory, and that Lambda (+) and Lambda (-) generate a double cone known as a diabolo. At optical vortices the curvature of the amplitude is singular, and we show from both theory and experiment that for this landscape Psi (+/-) rotate about vortex centers with a positive integer winding number. Diabolos can be classified as elliptic or hyperbolic, and we present initial results for the measured fractions of these two different types of umbilic diabolos.     

A Topological Glass

We propose and study a model with glassy behavior. The state space of the model is given by all triangulations of a sphere with n nodes, half of which are red and half are blue. Red nodes want to have 5 neighbors while blue ones want 7. Energies of nodes with other numbers of neighbors are supposed to be positive. The dynamics is that of flipping the diagonal of two adjacent triangles, with a temperature dependent probability. We show that this system has an approach to a steady state which is exponentially slow, and show that the stationary state is unordered. We also study the local energy landscape and show that it has the hierarchical structure known from spin glasses. Finally, we show that the evolution can be described as that of a rarefied gas with spontaneous generation of particles and annihilating collisions.     

A review of the dynamical susceptibility in different complex systems

The dynamical susceptibility has been introduced to characterize the dynamical heterogeneities in glass forming liquids. We have used it as a tool to investigate the slow dynamics of other disordered systems such as gels, granular media and spin glasses. We review here the results obtained via numerical simulations of different model systems. The comparative study of the behaviour of the dynamical susceptibility sheds some light on the significant differences in the complex slow dynamics of glasses, spin glasses, granular media, irreversible gels, and colloidal gels.     

Cooperative rearrangement regions and dynamical heterogeneities in colloidal glasses with attractive versus repulsive interactions

Water-lutidine mixtures permit the interparticle potentials of colloidal particles suspended therein to be tuned, in situ, from repulsive to attractive. We employ these systems to directly elucidate the effects of interparticle potential on glass dynamics in experimental samples composed of the same particles at the same packing fractions. Cooperative rearrangement regions (CRRs) and heterogeneous dynamics are observed in both types of glasses. Compared to repulsive glasses, the attractive glass dynamics are found to be heterogeneous over a wider range of time and length scales, and its CRRs involve more particles. Additionally, the CRRs are observed to be stringlike structures in repulsive glasses and compact structures in attractive glasses. Thus, the experiments demonstrate explicitly that glassy dynamics can depend on the sign of the interparticle interaction.     

Novel colloidal crystalline states on two-dimensional periodic substrates

We show, using numerical simulations, that a rich variety of novel colloidal crystalline states are realized on square and triangular two-dimensional periodic substrates which can be experimentally created using crossed-laser arrays. When there are more colloids than potential substrate minima, multiple colloids are trapped at each substrate minima and act as a single particle with a rotational degree of freedom, giving rise to a new type of orientational order. We call these states colloidal molecular crystals. A two-step melting can also occur in which individual colloidal molecules initially rotate, destroying the overall orientational order, followed by the onset of interwell colloidal hopping.     

Energy landscapes, supergraphs, and "folding funnels" in spin systems

Dynamical connectivity graphs, which describe dynamical transition rates between local energy minima of a system, can be displayed against the background of a disconnectivity graph which represents the energy landscape of the system. The resulting supergraph describes both dynamics and statics of the system in a unified coarse-grained sense. We give examples of the supergraphs for several two-dimensional spin and protein-related systems. We demonstrate that disordered ferromagnets have supergraphs akin to those of model proteins whereas spin glasses behave like random sequences of amino acids that fold badly.     

Disclination dipoles as the basic structural elements of dielectric glasses

We show that the experimentally observed behavior of thermal conductivity of dielectric glasses over a wide temperature range can be explained by a combination of two scattering processes: phonon scattering due to biaxial dipoles of wedge disclinations and Rayleigh type scattering. The results obtained support the cluster picture suggested earlier for glassy materials.     

Temperature Controlled Sequential Gelation in Composite Microgel Suspensions

Depending on the volume fraction and interparticle interactions, colloidal suspensions can exhibit a variety of physical states, ranging from fluids, crystals, and glasses to gels. For microgel particles made of thermoresponsive polymers, both parameters can be tuned using environmental parameters such as temperature and ionic strength, making them excellent systems to experimentally study state transitions in colloidal suspensions. Using a simple two‐step synthesis it is shown that the properties of composite microgels, with a fluorescent latex core and a responsive microgel shell, can be finely tuned. With this system the transitions between glass, liquid, and gel states for suspensions composed of a single species are explored. Finally, a suspension of two species of microgels is demonstrated, with different transition temperatures, gels in a sequential manner. Upon increasing temperature a distinct core–sheath structure is formed with a primary gel composed of the species with lowest transition temperature, which acts as a scaffold for the aggregation of the second species.     

Transport coefficients and mechanical response in hard-disk colloidal suspensions

We investigate the transport properties and mechanical response of glassy hard disks using nonlinear Langevin equation theory.We derive expressions for the elastic shear modulus and viscosity in two dimensions on the basis of thermalactivated barrier-hopping dynamics and mechanically accelerated motion.Dense hard disks exhibit phenomena such as softening elasticity,shear-thinning of viscosity,and yielding upon deformation,which are qualitatively similar to dense hard-sphere colloidal suspensions in three dimensions.These phenomena can be ascribed to stress-induced "landscape tilting".Quantitative comparisons of these phenomena between hard disks and hard spheres are presented.Interestingly,we find that the density dependence of yield stress in hard disks is much more significant than in hard spheres.Our work provides a foundation for further generalizing the nonlinear Langevin equation theory to address slow dynamics and rheological behavior in binary or polydisperse mixtures of hard or soft disks.