Session F50: Soft Glasses

Controlling disordered materials from the boundaries

We study general models of materials with frozen disorder, such as spin glasses or solids with heterogeneities, and ask how domain walls or optimal fracture surfaces can be controlled by selection of the boundary conditions on the surface of a given sample. We have developed and applied algorithms for optimal ground states that can explore all possible sets of boundary conditions (e.g., the boundary conditions for a disordered Ising model on a square lattice with sides $L$, with sizes up to $L=2048$) and thereby rapidly determine all possible paths for domain walls for certain two-dimensional models. We apply this algorithm to uncorrelated and power-law correlated disorder. While this computation has implications for the uniqueness of the ground state in disordered magnetic materials, it fits within a broader set of questions on the sensitivity of the interior of disordered material, as might be seen in the force chains in a given granular packing, when one considers all possible boundary conditions. Interior regions that are shielded by disorder from boundary effects then act as rigid sets of degrees of freedom.   

Connecting glassy dynamics to micro-scale elasticity

We report a new experimental method for exploring the connection between the dynamics and structure in colloidal glasses. Using ellipsoids of controlled size and eccentricity as passive micro-probes, we explore the rheological properties of the local environment of the colloidal glass, in particular fluctuations in the local elasticity. We do this by measuring the random fluctuations in the rotational motion of the probe ellipsoids using depolarized light scattering. This is facilitated by index matching the spherical colloidal particles that form the glass to the background fluid: the only optical contrast is provided by the ellipsoids. Decoupling the optical anisotropy from the eccentricity of the probe particles further enhances the sensitivity of the probe to rotational motion.   

Jamming and free energy landscapes for three caged soft disks

We use a Monte Carlo simulation to study jamming in a model of three soft Brownian disks with harmonic repulsive potential confined in a circular corral. For large corrals, the disks can freely rearrange where one particle passes in between the other two, but for small corrals rearrangements become rare. Rearrangement events correspond to the system crossing over the energy barrier. With low temperature and/or small corral size, the energy barrier becomes larger and the system approaches a glass transition. We calculate the Helmholtz free energy from the distribution of configurations in the system and quantify both the entropic and potential components of the free energy barrier. In a hard disk model, the free energy barrier for rearrangements is entirely entropic. By comparing the entropic component of the soft model to a model of hard disks, we model the soft disks as hard disks with a temperature-dependent effective size. We find that our results are generalizable to other soft disk potentials as well.   

Microscopic Theory of Activated Penetrant Diffusion in Liquids and Glasses

We formulate a force-level, self-consistent, nonlinear Langevin equation theory for the long-time diffusivity of a penetrant in molecular and polymeric supercooled liquids and glasses. The theory predicts that for a wide range of penetrant to matrix molecular unit size ratios (R), activated hopping is the dominant transport mechanism. The penetrant diffusivity (D) and jump distance exhibit different R-dependences in three dynamic regimes: R\textless 0.5, 0.5\textless R\textless 1, R\textgreater 1, which are physically distinguished by the nature of the matrix motion required to facilitate hopping. The penetrant diffusion constant decreases the fastest with R in the first regime where the matrix behaves as a harmonic amorphous solid. The other two regimes involve larger scale, anharmonic matrix motions. Below and above the matrix glass transition temperature, D exhibits an Arrhenius and supra-Arrhenius temperature dependence, respectively. The reduction of D associated with penetrant-matrix attractive forces has also been studied. Our a priori theoretical calculations agree reasonably well with experiments for both fast transport (e.g., gas permeation) and slow transport (e.g., barrier materials) systems, covering more than 10 orders of magnitude of variation of the diffusion constant.   

Antiferromagnetic Ising Model in Hierarchical Networks

The Ising antiferromagnet is a convenient model of glassy dynamics. It can introduce geometric frustrations and may give rise to a spin glass phase and glassy relaxation at low temperatures $[1]$. We apply the antiferromagnetic Ising model to 3 hierarchical networks which share features of both small world networks and regular lattices. Their recursive and fixed structures make them suitable for exact renormalization group analysis as well as numerical simulations. We first explore the dynamical behaviors using simulated annealing and discover an extremely slow relaxation at low temperatures. Then we employ the Wang-Landau algorithm to investigate the energy landscape and the corresponding equilibrium behaviors for different system sizes. Besides the Monte Carlo methods, renormalization group $[2]$ is used to study the equilibrium properties in the thermodynamic limit and to compare with the results from simulated annealing and Wang-Landau sampling. \\ $[1]$ C. P. Herrero, Phys. Rev. E. {\bf 77}, 04112 (2008)\\ $[2]$ V. Singh, C. T. Brunson, S. Boettcher, arXiv:1408.0669 (2014)   

Protein crowding in solution, frozen and freeze-dried states: small-angle neutron and X-ray scattering study of lysozyme/sorbitol/water systems

For effective preservation, proteins are often stored as frozen solutions or in glassy states using a freeze-drying process. However, aggregation is often observed after freeze-thaw or reconstitution of freeze-dried powder and the stability of the protein is no longer assured. In this study, small-angle neutron and X-ray scattering (SANS and SAXS) have been used to investigate changes in protein-protein interaction distances of a model protein/cryoprotectant system of lysozyme/sorbitol/water, under representative pharmaceutical processing conditions. The results demonstrate the utility of SAXS and SANS methods to monitor protein crowding at different stages of freezing and drying. The SANS measurements of solution samples showed at least one protein interaction peak corresponding to an interaction distance of $\sim$ 90 {\AA}. In the frozen state, two protein interaction peaks were observed by SANS with corresponding interaction distances at 40 {\AA} as well as 90 {\AA}. On the other hand, both SAXS and SANS data for freeze-dried samples showed three peaks, suggesting interaction distances ranging from $\sim$ 15 {\AA} to 170 {\AA}. Possible interpretations of these interaction peaks will be discussed, as well as the role of sorbitol as a cryoprotectant during the freezing and drying process.   

Typical Value of Susceptibilities in the Three Dimensional Edwards-Anderson Spin Glass Model in an External Field

We study the Edwards-Anderson model on a simple cubic lattice with a finite constant external field using a Monte Carlo simulation code, which employs graphics processing units to dramatically speedup the simulation. Conventional indicators, such as the Binder ratio and correlation length, do not show any signs of a phase transition. We also studied R12, or the ratio of spin glass susceptibilities at finite wavenumbers, and show it is quite noisy that a systematic analysis cannot come to clear conclusion. This is largely due to the fact that the susceptibilities follow a broad, fat-tailed distribution, and the average is possibly dominated by rare events. Therefore we propose to study the typical value of these parameters by taking the geometric average over different disorder realizations, and compare it with the linear average measurements. We argue that the typical value should be also studied in additional to conventional linear average value, to provide another perspective for the study of phase transition in spin glasses.   

Dimensional dependence of mobility correlations and dynamic heterogeneity in two-dimensional and three-dimensional glass forming fluids

We examine mobility correlations and heterogeneous dynamics in simulations of glass-forming two-dimensional and three-dimensional binary Lennard-Jones fluids. We compare the relationships between the dynamic correlation length $\xi_4$, the dynamics susceptibility $\chi_4$, and the alpha-relaxation time $\tau_\alpha$ by analyzing four-point structure factors $S_4(q;t)$ that are designed to investigate heterogeneous dynamics. We find that the relationships between $\xi_4$, $\chi_4$, and $\tau_\alpha$ depend strongly on dimension. Specifically, in two dimensions these relationships depend on whether the underlying dynamics is Newtonian or Brownian, but there is no dynamics dependence in three dimensions. Furthermore, in systems undergoing Newtonian dynamics $\xi_4$ grows much faster with $\tau_\alpha$ in two-dimensions than three-dimensions. Therefore, we demonstrate that dynamic heterogeneities have different properties in two and three dimensional glass forming fluids.   

Correlations of structure and dynamics in colloidal supercooled liquids

We are studying the correlations between measured quantities in colloidal samples that are in equilibrium. We track the movement of particles in systems using confocal microscopy. We see correlations between a particle's displacement during short time scales and its long term displacement. In addition, we look at correlations between a particle's displacement during different time scales and structural variables such as its voronoi volume or local volume fraction. We study how these correlations vary as the colloidal volume fraction approaches the glass transition volume fraction.   

Measurement of Stress Networks in 3D Colloidal Glasses

We measure the inhomogeneous stress fields in a 3D colloidal glass by using a confocal microscope to image a binary suspension's microstructure. Despite extensive studies of the contact forces in static systems (e.g., granular systems and emulsions), it has been difficult to measure these inhomogeneous stress fields in thermal systems. We determine these particle level Brownian stresses from all particle positions using the ``Stress Assessment from Local Structural Anisotropy'' (SALSA) method. First, we show that SALSA method accurately reports the 3D stress field of a colloidal glass at particle-level resolution using molecular dynamics simulations. Furthermore, we quantify the measured pressure statistics and examine the q-model, Edwards ensemble and other theoretical predictions. Finally, the SALSA method enables us to investigate the underlying origin of the mechanical heterogeneities by comparing stress distribution with particle configuration.   

Physical Aging in a Colloidal Glass Subjected to Concentration Jump Conditions

We have prepared a thermo-sensitive core-shell PS-PNIPAM/AA latex system and have investigated the aging dynamics of its colloidal dispersions subsequent to the temperature (or concentration)-jump perturbations using sequential creep experiments to probe the response of the system. The aging experiments were performed in the vicinity of the glass transition concentration or temperature as evidenced by the strongly varying relaxation time with decreasing temperature (or increasing concentration). The aging results from the current colloidal glass study are compared with those expected in the Kovacs' catalogue of experiments in structural recovery of glassy polymers, viz., intrinsic isotherms, asymmetry of approach and memory events [1]. We found that colloidal glass displays aging behavior and time-aging time superposition is valid here. There are similarities in aging dynamics between colloidal glasses and molecular glasses, and differences also persist. \\[4pt] [1] A.J. Kovacs, Fortschritte der Hochpolymeren-Forschung, 3, 394-507 (1963).   

Structural signatures of dynamic heterogeneities in monolayers of colloidal ellipsoids

When a liquid is supercooled towards the glass transition, its dynamics drastically slows down, whereas its static structure remains relatively unchanged. Finding a structural signature of the dynamic slowing-down is a major challenge, yet it is often too subtle to be uncovered. Here we discover the structural signatures for both translational and rotational dynamics in monolayers of colloidal ellipsoids by video-microscopy experiments and computer simulations. The correlation lengths of the dynamic slowest-moving clusters, the static glassy clusters, the static local structural entropy and the dynamic heterogeneity follow the same power-law divergence, suggesting that the kinetic slowing down is caused by a decrease in the structural entropy and an increase in the size of the glassy cluster. Ellipsoids with different aspect ratios exhibit single- or double-step glass transitions with distinct dynamic heterogeneities. These findings demonstrate that the particle shape anisotropy has important effects on the structure and dynamics of the glass. The power-law divergence of the static correlation length with exponent -1 suggests that the glass transition is likely a two-dimensional Ising-type critical phenomenon.   

Dynamics approaching the 2D colloidal glass transition

We make 2D colloidal glasses by allowing bidisperse silica particles of diameters 2.53 and 3.38 $\mu$m to settle down under gravity in a monolayer at a coverslip interface. Controlling the area fraction gives us a wide range of behaviour, from liquid-like to supercooled and glassy. We use this model glass forming system to study the dynamics on approaching the glass transition, in 2D. We measure the increasing alpha relaxation times as the area fraction is increased toward the glass transition. We measure the growth of dynamical heterogeneity on approaching the glass transition. We quantify dynamical heterogeneity through the non-Gaussian parameter and the four point susceptibility $\chi_4$. Further, we measure the probability of local cage rearrangements as a function of waiting time(time since quench), for different area fractions, and relate this to other dynamical quantities such as diffusion coefficients, dynamical heterogeneity, etc. For glassy samples, we observe the slowing down of mean square displacements with waiting time, a sign of aging.   

Dynamical heterogeneities in hard-sphere systems near random close packing

Hard-sphere systems at finite temperatures diffuse at low packing fraction, but display glassy dynamics as the packing fraction increases toward random close packing (RCP). As the system approaches RCP, structural relaxation dramatically slows down and becomes highly cooperative and heterogeneous in space and time. We quantify dynamical heterogeneities in bidisperse hard-sphere systems as a function of packing fraction near RCP using the non-Gaussian parameter $\alpha_2$ and four-point density correlation function. We show that $\alpha_2$ does not diverge, but instead reaches an upper bound $< 2$ as the packing fraction approaches RCP. We present a simple theoretical model to explain this upper limit.   

A new phase of disordered phonons modelled by random matrices

Starting from the clean harmonic crystal and \emph{not} invoking two-level systems, we propose a model for phonons in a disordered solid. In this model the strength of mass and spring constant disorder can be increased separately. Both types of disorder are modelled by random matrices that couple the degrees of freedom locally. Treated in coherent potential approximation (CPA), the speed of sound decreases with increasing disorder until it reaches zero at finite disorder strength. There, a critical transition to a strong disorder phase occurs. In this novel phase, we find the density of states at zero energy in three dimensions to be finite, leading to a linear temperature dependence of the heat capacity, as observed experimentally for vitreous systems. For any disorder strength, our model is stable, i.e.\ masses and spring constants are positive, and there are no runaway dynamics. This is ensured by using appropriate probability distributions, inspired by Wishart ensembles, for the random matrices. The CPA self-consistency equations are derived in a very accessible way using planar diagrams. The talk focuses on the model and the results.