Session K8: Focus Session: Jamming in Glasses, Grains and Gels II

Mechanisms of Reversible Shear Thickening in Concentrated Colloidal Dispersions

Experimental studies on model systems of colloidal and nanoparticles dispersions of spherical, elliptical and plate-like particles, where both rheology and mictrostructure are measured, are summarized and compared to illustrate the salient features of reversible shear thickening in well-defined model systems. Reversible shear thickening is shown to be stress-controlled and a connection between the transition from ``continuous'' to ``discontinuous'' shear thickening and underlying thermodynamic phase transitions (liquid-crystal, and liquid- nematic) is demonstrated. Theoretical models based on particle micromechanics which include lubrication hydrodynamics are shown to successfully predict the onset of reversible shear thickening. Small angle neutron scattering and light scattering measurements indicate the formation of ``hydroclusters'' as the source of the increased viscous dissipation and validate the micromechanical modeling. A comparison is made between reversible shear thickening and jamming in concentrated colloidal and nanoparticles dispersions under shear and extensional flows.   

Nature of Strain-Induced Nonlinearity in Filled Rubbers

We present evidence suggesting the existence of an analogy between dynamic strain-induced nonlinearity in modulus of filled rubbers and physics of the glass transition of glass-forming materials and the jamming transition of vibrated granular materials. This analogy stems from the fact that shear strain in dynamic measurements introduce fluctuations in fillers that can be described by an ``effective temperature.'' The nonlinearity in modulus of filled rubbers simply reflects a de-jamming transition of fillers in rubber matrices. Filled rubbers with respect to strain therefore display many unusual phenomena, including the asymmetric kinetics, crossover effects, and the glass-like transitions. In addition, the jamming transition in filled rubbers also behaves as an isoenergetic thermodynamic transition. This evidence suggests that although jamming is kinetic, it may also be thermodynamic in nature. The coexistence of kinetic and thermodynamic descriptors of the jamming transition is analogous to observations of thermoreversible gels. Based on those results, we propose a unified phase diagram for jamming transitions. The significance of the new jamming phase diagram is that it has incorporated variables that are all derivable from Hamiltonians and may facilitate crucial comparisons between theories and experiments. [1]. C. G. Robertson and Xr. Wang, Phys. Rev. Lett. 95, 075703, 2005. [2]. Xr. Wang and C. G. Robertson, Phys. Rev. E 72, 031406, 2005.   

Transition rates in the Lennard-Jones binary mixture

The slow relaxation in glass forming liquids approaching the glass transition is often described by the Vogel-Fulcher-Tammann (VFT) equation which predicts a diverging viscosity at a non-zero temperature. The origin of this anomalously slow relaxation is an outstanding problem. Recent work (PRE 70, 060501(R) (2004)) shows that a system will obey the VFT equation near a critical point if the transition rates between different macrostates have an asymmetric form: energy lowering rates depend only on the entropy change and energy raising rates depend only on the energy change. Here we investigate this mechanism for glassy dynamics in the the Lennard-Jones binary mixture (LJBM); a well-known glass former. The transition rates between different inherent structures (local minima of the potential energy) are calculated using the interval-bisection method. We find that the energy lowering transition rates are not temperature-sensitive, while the energy raising ones depend on the temperature. The dynamics in the IS energy space is however, non Markovian. We discuss these findings in light of the proposed mechanism for glassy relaxation characterized by a VFT form.   

Pushing on colloids: How a gel can stress a glass

We employ a novel technique to for the application of external mechanical and osmotic stress on dense suspensions of colloidal particles. Thermally expandable NIPA hydrogels are used to confine a sediment of colloidal particles. By allowing the gel to expand up to ten times it's initial volume, we dramatically compress the sediment. Using laser scanning confocal microscopy, we directly measure the effects of increased stress on the properties of a colloidal hard sphere suspensions. We observe the appearance of heterogeneities as the particles are pushed together. We will present results on the analysis of the local volume and dynamical properties of these heterogeneities and postulate their equivalence to characteristic features of analogous systems near their jamming transition.   

Microscopic dynamics of recovery in sheared concentrated depletion gels

We describe x-ray photon correlation spectroscopy and diffusing wave spectroscopy investigations of concentrated depletion gels formed from nanoscale silica colloids in solutions of nonabsorbing polymer. The experiments track the changing microscopic dynamics as these jammed, nonergodic systems recover following the cessation of large shear. The two techniques provide a quantitatively coherent picture of the dynamics as ballistic or convective motion of colloidal clusters whose internal motion is arrested. While the evolution of the dynamics possesses features characteristic of nonergodic soft solids, including a characteristic relaxation time that grows linearly with the time since cessation of shear, comparison with the behavior of quenched supercooled liquids indicates the dynamics are not directly related to traditional aging and rejuvenation phenomena in glasses.   

Local Disturbances of Binary Colloidal Glass Systems

We look at local disturbances in colloidal systems as they approach the glass transition. A colloidal system is a fluid filled with microscopic particles which can serve as a model for the atoms of a glass. When the concentration of these particles becomes sufficiently large the particles can no longer move. This is the point which we refer to as the glass transition. We study systems at concentrations just below the glass transition by ``pulling'' a magnetic bead through the sample using an external magnetic field. In our samples there are particles of two distinct sizes that have been dyed such that they fluoresce at different wavelengths. This allows the microscope to differentiate between the two sizes and gives us the ability to isolate and analyze their respective motions independently. From this we examine the motion of the surrounding colloids as the magnetic bead is pulled through the sample, and characterize the behavior as the glass transition is approached.   

Polymer Statics and Dynamics in Confined Geometries

Current work on biological systems and glass forming polymers (JCP 106, 6176 (1997)) has led to an interest in the study of single polymer systems. The main questions concern relaxation phenomena and the shape adopted by single polymers under hard and soft boundaries. Little is known about the possibility of inducing a glass transition through pure dimensional confinement. We are concerned with whether or not there is a critical value of the confining length scale. Both structure and relaxation can be described using scaling arguments and tested with Monte Carlo simulations using the bond-fluctuation algorithm (Macromolecules 21,2819 (1988)), which uses a lattice representation of the polymer chain with excluded volume effects. We look at the effects of confinement on a \textit{single polymer chain} by measuring quantities such as the magnitude end-to-end vector, the radius of gyration, and single monomer motion (JACS 124, 20 (2004)). A primary question is whether the self-avoidance constraint manifests itself in a manner similar to kinetically constrained models of the glass transition. Understanding how these quantities change with various confining geometries will lead to a deeper understanding of biological structures and glass formation. Work supported by NSF-DMR 0403997.   

Nonlinear behavior of a driven probe in a colloidal suspension near the Glass Transition.

By applying a force to isolated microscopic magnetic particles embedded in a PMMA colloidal suspension a nonlinear relationship between the applied force and the measured velocity was measured with the assistance of a confocal microscope.~ Over short time scales it is possible to observe a threshold force, below which no apparent motion is detected.~ The value of this threshold force is highly dependent upon the concentration of the sample.~ At stronger forces, the velocity of a driven magnetic particle displays a power law dependence upon the applied force.~ In particular, the behavior becomes increasingly nonlinear as the concentration is raised toward the colloidal glass transition point. This behavior was consistent across numerous samples with different concentrations and a varying size ratio of PMMA to magnetic particle.   

Yielding in concentrated emulsions

We studied the non linear rheological response of two kinds of soft glassy materials: direct concentrated emulsions with and without a short range interparticle attraction induced by adding surfactant. Using high frequency ultrasonic velocimetry, the velocity profiles in a Couette cell are recorded simultaneously to the global rheological data during start up experiments. Under applied shear rate in the vicinity of the yielding transition, the gel ie the adhesive emulsion separates into a liquid state sheared rapidly at a rate higher than a substantial critical shear rate and a static solid region. The static region disappears at high shear rate. On the contrary, the glass ie the non adhesive emulsions flows homogeneously. Below the yield stress the emulsions remains solid like whereas above it becomes liquid like. Under applied shear rate no coexisting states between a liquid like phase and a solid like phase are evidenced. Our data point out that ``glass'' and ``gel'' flow differently in the vicinity of the yielding transition suggesting that the involved mechanisms are not universal.   

Numerical studies of two-dimensional $k$-core percolation

The disconnected-connected phase transition in {\em uncorrelated} percolation has long been known to exhibit a continuous phase transition. Is this property retained when {\em correlations} between occupied sites are incorporated into percolation? An example of such a model is $k$-core percolation. In $k$-core percolation a constraint is introduced where a site can remain occupied only if it has at least $k$ occupied neighbors; otherwise it is removed from the lattice. The mean field $k$-core transition is random first-order (or hybrid). What then is the nature of the $k$-core transition in finite-dimensions? We show numerical evidence for a hybrid transition in two-dimensions for a variant of $k$-core where there is an additional constraint of pseudo-force-balance. Using finite-size scaling analysis we demonstrate that there is a jump in the usual order parameter at the transition along with, not one, but two, diverging correlation length exponents, neither of which scale as $1/2$ (or $1$). This model may have some implications for the jamming transition.   

Generic rugged landscapes under strain and the possibility of rejuvenation in glasses

A strain-dependent random landscape model shows that many aspects of the mechanical response of disordered materials are universal, and arise from the rugged nature of the energy landscape. Simulations with this model demonstrate that states produced by mechanical deformation will generally be distinct from the states traversed during thermal aging. This behavior is a generic consequence of a rugged energy landscape, and is independent of any specific microstructure of the material. Thus, mechanical deformation does not literally ``rejuvenate'' a material, although the states produced by mechanical deformation may in some ways resemble less aged systems.   

The frequency distribution of mechanically stable packings

We generate mechanically stable packings of soft particles in 2D using an algorithm in which we successively grow or shrink purely repulsive grains and minimize the total energy at each step until particles are just at contact and at rest. We focus on small systems of up to $20$ particles, and thus we are able to enumerate nearly all of the possible mechanically stable packings. Complete enumeration allows us to factorize the probability distribution, $P(\phi)$, for obtaining a mechanically stable state at packing fraction $\phi$ into algorithm-dependent and independent contributions, $\beta(\phi)$ and $\rho(\phi)$. $\rho(\phi)$ is the probability density to obtain a distinct mechanically stable packing at $\phi$, while $\beta(\phi)$ is the frequency with which each distinct state occurs. We found several remarkable features of the frequency distribution. For example, the frequency averaged over bins of width $d\phi$ grows exponentially with increasing packing fraction. In addition, distinct mechanically stable packings within $d\phi$ can occur with frequencies that differ by orders of magnitude. We also add thermal fluctuations to these stable configurations to understand the relationship between the frequency and shape of the potential landscape near the stable configurations.   

Collision Times and Stress Distributions in Mono and Polydisperse Granular Flows

We investigate, using simulations, collision times and stress distributions in two and three-dimensional steady-state granular matter in jammed versus diffuse flows. We find that the level of order or disorder in the grains dictates values of collision time power-laws. This observation is consistent in both two and three dimensions. We compare our simulations to experimental results.