Session W13: Focus Session: Jamming II

Avalanches and di?usion in model bubble rafts near jamming

Energy dissipation distributions and particle displacement statistics are studied in the mean field version of Durian's bubble model. A two dimensional (2D) bi-disperse mixture is simulated at various strain rates, $\dot{\gamma}$, and packing ratios, $\phi$, above the close packing limit, $\phi_c$. Well above $\phi_c$, and at sufficiently low $\dot{\gamma}$, the system responds in a highly intermittent way, reminiscent of other dynamically critical systems with a power law distribution of energy dissipation. As one increases $\dot{\gamma}$ at fixed $\phi$ or tunes $\phi\rightarrow \phi_c$ at fixed $\dot{\gamma}$, the intermittent behavior vanishes. Displacement distributions are non-Fickian at short times but cross to a Fickian regime at a universal strain, $\Delta\gamma_*$, independent of $\dot{\gamma}$ and $\phi$. Despite the profound differences in short-time dynamics, at intermediate $\Delta\gamma$ the systems surprisingly exhibit qualitatively similar spatial patterns of deformation, with lines of slip extending across large fractions of the simulation cell. The results raise new questions about the nature of quasistatic shear near $\phi_c$ and should have important consequences for various kinds of jammed systems.   

Observing rearrangements in a 2D emulsion flowing through a hopper

Jamming in granular flow through a hopper has been well studied, and structures such as arches have been found in simulations both with and without friction, and in experiments with friction. To study if jamming can happen in other frictionless systems, we pump dense emulsions (oil in water) through a glass hopper. The oil droplets experience a viscous friction but do not have static friction acting between touching droplets, in contrast to granular particles. For easy imaging, we squeeze the droplets into quasi two-dimensional disks by injecting the emulsion into a thin chamber made from two parallel glass plates. Movies of the flow are taken from the top by a microscope. Due to the narrowing confinement in the hopper, droplets are forced to rearrange, and we observe topological changes such as T1 events. At the same time, the interdroplet forces are measured from the deformation of the droplets. By varying the hopper gap width and angle, we study how the constriction affects the particles' motions, and how this relates to the interdroplet forces.   

How do hard, regular tetrahedra pack?

We simulate a system of hard tetrahedra using Monte Carlo simulations and determine the density-pressure equation of state by compressing an initially disordered fluid. Depending on the speed of the compression, the system either jams or spontaneously orders to a quasicrystal. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is 0.8503. We show that the system is able to achieve such high densities by the local ordering of tetrahedra into certain favorable motifs, forming larger structures that pack efficiently in both jammed and ordered structures. Jamming and crystallization are preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed pentagonal pyramids that form a percolating network at the transition. Our results demonstrate how particle shape and entropy may be exploited to achieve highly complex structures. [1] A. Haji-Akbari, M. Engel et al., Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra, Nature, in press (2009).   

Minimal Energy Polymer Packings

We examine the structure and dynamics of collapsed polymers using a variety of simulation and theoretical techniques. For flexible chains of N ``sticky'' tangent hard spheres, at small N, the ground states are the same as for the nonpolymeric case (NPC) [1], while at large N the ground states are crystallites with close-packed cores. The polymeric nature of the packings gives rise to distinguishable ground-state structures whose multiplicity relative to the NPC grows rapidly with N. We explicitly enumerate the polymer packings for small N and study the most likely packings for large N. We explore the extent to which the packing types and probabilities change with several important properties of the polymer, including the softness of the interaction potential, bending stiffness, bond length, and heterogeneity of the monomers. Typically, small variations of these properties break the degeneracy of NPC ground states, while large variations produce qualitatively different ground-state packings. We also characterize the slow dynamics of transitions between low-energy states at finite temperature. \\[4pt] [1] N. Arkus, V. N. Manoharan, and M. P. Brenner, PRL, 103, 118303 (2009).   

The Packing and Jamming of Real Polymer Chains

Jamming make a hope to unifying theme for granular materials, glasses and threshold behavior in materials. Here we experimentally prepared a real polymer (polystyrene, PS) with various packing density which was described by inter-segment distances (\textbf{\textit{r}}) detected by NMR. We cold-pressed PS powder at 20 $^{\circ}$C (with shearing) and then released the pressure. We found that a transparent pellet with high modulus was formed. PS is usually manufactured by a hot-melting process at 180 $^{\circ}$C. The rigidity and transparency of our cold-pressed pellet and its accuracy of the form are testimony that the PS powder once flowed under cold compression to take the shape of its container. This shear-induced melting is exactly what is expected within the jamming picture. By measuring r and the applied pressure $\sigma $ under which the polymer chain starts to flow, we drew a schematic jamming phase diagram. The \textbf{\textit{$\sigma $}}\textbf{-}\textbf{\textit{r}} curve for a real polymer is convex at \textbf{\textit{r}} $<$ 0.5 nm, while it becomes concave as r is larger than 1 nm. It is the van der Waals attraction that acts as a confining pressure on segments, and makes the \textbf{\textit{$\sigma $}}\textbf{-}\textbf{\textit{r}} curve convex on the very short scales.   

Frictionless Packings of Rod-like Granular Materials

Piles of large aspect ratio granular materials are known to form solid plugs significantly more rigid than piles of ordinary sand or rice. We create random, jammed packings of spherocylinders --- cylinders with hemispherical endcaps --- using energy minimization techniques. The packing fraction at high aspect ratios agrees with a mean-field model that scales as the inverse of excluded volume, implying that that contact number is constant even for very long, thin particles. This is confirmed by a direct analysis of the average contact number at large aspect ratios. The structure of the jammed state can be investigated through the dynamical matrix of elastic modes. In contrast with other work on ellipsoids, our packings show low energy translational modes and higher energy rotational modes, which we explain as resulting due to the absence of particle curvature.   

Jamming in Granular Polymers and Frictional Granular Assemblies

Jamming has attracted growing attention as a possible unifying theme for granular materials, glasses and threshold behaviour in materials. Recent results for frictionless granular systems suggest that jamming is a second order phase transition with critical properties. A question of paramount importance is whether this behaviour is universal to more complex systems. To address this issue we have simulated the compression of granular polymers and frictional granular monomers. The jamming density of the granular polymers decreases with increasing chain length due to formation of loops or voids, in agreement with recent experiments [1,2]. For frictional granular monomers the jamming density is depressed relative to a frictionless system, and we observe the formation of voids in the packing, which does not occur in the frictionless case. We discuss our results in terms of the fragile jamming phase recently studied in compression experiments [3]. [1] L.-N. Zou et al, Science, 326 (5951), 408 (2009). [2] C. J. Olson Reichhardt and L. M. Lopatina, Science, 326 (5951), 374 (2009). [3] M. Bandi, M. Rivera, F. Kakzia, and R. Ecke, submitted.   

How does jamming and glassy behavior depend on particle shape?

We present extensive computational studies of glassy and jamming behavior in particulate systems composed of anisotropic particles in two and three dimensions. We focus on two classes of anisotropic particle shapes, convex (ellipsoidal) and concave (dimer) particles, which display contrasting structural and mechanical properties even at the same aspect ratio. For example, static packings of convex ellipsoidal particles are hypostatic with fewer contacts than necessary for mechanical stability from naive counting of degrees of freedom, and possess anomalously small static shear moduli. In contrast, packings of dimers are isostatic, where the number of contacts matches the number of degrees of freedom. Does hypostaticity affect the low-temperature glassy dynamics? To investigate this question, we will study stress and structural relaxation times and the linear and nonlinear response to applied shear strain in jammed and glassy systems composed of dimers and ellipsoids.   

Large-Scale Structures in Dense Granular Flows through a Vertical Channel

We have used NMR/MRI techniques to probe the dense, gravity-driven flow of a dry granular medium (400$~\mu$m diameter seeds) through a 10$~$ mm diameter vertical channel with rough walls. The flow rate, controlled by a variable-diameter outlet restriction many channel diameters downstream from the measurement region, is macroscopically steady and continuous for all flow rates used. Averaged over long times, the flow is plug-like in the channel center with a shear band near the wall a few particles wide. However, the NMR measurements reveal short-lived structures in the flow with size scales comparable to the channel diameter. At low mean flow speeds ($<3~$cm/s) transient jamming events appear randomly in space and time; these events appear key to determining the average flow profile and speed. It does not appear that the flow would be correctly explained by a local constitutive relation in this regime, due to the large spatial scale of the transient events. At higher flow speeds an organized density wave appears, traveling upward opposite the mean flow direction.   

Avalanches Near the Onset of Jamming

As the jamming transition is approached from the liquid-like side, experiments and simulations demonstrate that a random assembly of particles exhibits avalanche-like behaviour in response to a probe particle being dragged through it. To better understand this response, we construct a lattice model with active and inactive particles occupying some fraction of the lattice, with each site being occupied by at most one particle. Only the active particles can hop to empty neighboring sites and can activate $k$ neighboring inactive particles at some rate $\lambda_k$. Also, active particles can become inactive at some rate $\gamma$. When $lambda_{k\geq 2}=0 $, this model is closely related to the conserved lattice gas model which is thought to belong to the universality class of absorbing phase transitions with a conserved field, i.e. conserved stochastic sandpile models. To mimic the approach towards jamming, an increasingly more crowded environment, we study this model for $\lambda_{k\geq 1}>0$ and search for a new universality class as $\lambda_{k=1}$ approaches zero.   

Jamming in Vertical Channels

We experimentally study jamming of cylindrical grains in a vertical channel. The grains have a low aspect-ratio (height/diameter $<$ 1) so their shape is like antacid tablets or poker chips. They are allowed to fall through a vertical channel with a square cross section. The channel width is greater than the diameter of a grain and constant throughout the length of the channel with no obstructions or constrictions. It is observed that grains sometimes jam in this apparatus. In a jam, grains form a stable structure from one side of the channel to the other with nothing beneath them. Jams may be strong enough to support additional grains above. The probability of a jam occurring is a function of the grain height and diameter. We will present experimental measurements of the jamming probability in this system and discuss the relationship of these results to other experiments and theories.   

Confinement of Colloidal Suspensions in a Cylindrical Geometry

We study colloidal suspensions confined within a tapered glass microcapillary to model the glass transition in confined cylindrical geometries. We observe the particle dynamics using high speed three-dimensional confocal microscopy. The microcapillary is only slightly tapered, providing a range of local volumes for a single colloidal sample. Confinement of the samples slows down particle motion and induces glassy behavior. Additionally, the particles layer against the capillary walls, and these layers appear to have a secondary effect on particle mobility; particles within a layer move even slower, in addition to the primary slowness caused by the confinement. We observe that within each region, the component of mobility perpendicular to the confining boundaries varies radially while the parallel component does not.