Session N22: Focus Session: Jamming I

Discontinuous jamming transition in driven foam

Aqueous foam (gas bubbles with liquid walls) is a surprising substance. Every molecule in foam is in a fluid state, either liquid or gas. Yet, the entire foam holds its shape as a solid would. In fact, when subjected to an applied strain at a slow enough strain rate, the initial response of the foam is the same as an elastic solid. On the other hand, under sufficiently large stress or strain, the foam can flow in a fashion similar to a fluid. This is similar to plastic flow that occurs in many ``molecular'' solids. In this talk, we will focus on experimental studies of the transition from solid behavior to flowing behavior, with an emphasis on to what degree this ``jamming'' transition is analogous to a ``real'' phase transition. We will focus on recent results using a model, two-dimensional foam: bubble rafts. Bubble rafts are a single layer of bubbles on the surface of water. By focusing on a two-dimensional system, it is relatively easy to track individual bubbles and gain insight into the connection between bubble dynamics (the mesoscopic scale) and the response of the entire foam (macroscopic scale). We will focus on recent measurements of a \textit{discontinuous } transition from solid to fluid like behavior in the bubble raft.   

Dynamical heterogeneity at the jamming transition

We investigate the dynamics of a variety of soft materials close to the jamming transition, including strongly attractive colloidal gels, concentrated surfactant phases, and charged platelets (Laponite). By using novel time- and space-resolved light scattering techniques, we show that, quite generally, the dynamics of these systems are strongly hetergogeneous both in time and space, suggesting that they relax through discrete rearrangement events. Surprisingly, we find that each event affects a volume much larger that the size of the system's constituent (particles or clusters). This finding is in stark contrast with simulations and experiments on supercooled fluids, where spatial correlations of the dynamics extend over a few particles at most.   

A Statistical Ensemble for Soft Granular Matter

Work on packings of soft spheres (PRE \textbf{68}, 011306 (2003)) has shown the existence of a Jamming transition and has highlighted the need for a general statistical framework to describe granular packings. This work presents an extension of the formalism proposed by Edwards (Physica A \textbf{157}, 1080 (1989)) to packings of soft particles. We base our analysis on a height formalism developed in two dimensions (PRL \textbf{88}, 115505 (2002)) to extract a topological invariant $\Gamma$, the trace of the global stress tensor, which is conserved under internal rearrangements of the system. Upon assuming a flat measure in $\Gamma$-space, we can derive a canonical distribution of the local $\Gamma$-values in a grain packing. We then check the predictions of this ensemble against distributions of mechanically stable packings of frictionless disks obtained from computer simulations. Work supported by NSF-DMR 0549762.   

Some Packings Are More Equal Than Others

Computer simulations of packings of frictionless and frictional monodisperse spheres are discussed in the context of the jamming transition. Power-law scalings in several quantities characterising the packings are identified with distance from the jamming transition point, over several orders of magnitude in the particle friction coefficient. It is also noted that the `critical' values of the coordination number and packing fraction scale with the friction coefficient. How friction modifies the structural and dynamical properties of the packings are also discussed.   

Isostatic Frictional Packings: Topology and Response Functions

Frictionless disks and spheres are known to spontaneously organize into isostatic contact networks with minimal coordination number under common loadings such as gravity or compression. The isostatic character of such networks has been associated with the force-chain character and constitutive properties of the macroscopic assembly. However, for non-spherical or frictional grains, the conditions for an isostatic network are no longer spontaneously satisfied, most notably due to the indeterminacy associated with frictional contacts. Here I show the existence of a general isostatic limit of frictional packings of general shape grains similar to the case of frictionless disks. I discuss the consequences for force response functions and relationship to experiments showing the onset of network failure at low coordination numbers.   

Growing length scale for dynamical heterogeneity in an air-driven granular system near jamming

Anomalous behaviour known as ``spatially heterogeneous dynamics'' (SHD) has been observed in supercooled liquids, dense colloids, and, more recently, in confined granular packings. Dynamics in these systems may be governed by proximity to a generic ``jamming transition,'' beyond which rearrangements cease and the viscosity diverges. However, the universality of this jamming hypothesis has not yet been tested in terms of variation in the hallmark dynamical heterogeneities as a function of control parameter. Here, we report measurement of SHD in systems of air-driven granular beads, as a simultaneous function of both density and effective temperature. On approach to jamming, the dynamics are found to become progressively slower and more heterogeneous. The measured dynamical time and length scales appear to diverge, and can be modeled both by mode-coupling theory and by the Vogel Tammann-Fulcher (VFT) equation, in quantitative analogy with glass-forming liquids. The Vogel temperature arising from the VFT fit, which corresponds to an ideal glass transition temperature in liquids, coincides with point-J, the volume fraction corresponding to a random close-packed structure. Our findings provide a significant step forward in the quest for a unified theory of ``jamming'' in disparate systems.   

Jamming with attractive interactions

We numerically study the effects of cohesion on granular solids using a minimal model relevant to various experimental settings. The inclusion of a small amount of attraction between contacting grains is shown to significantly alter even the qualitative features of both the attainable mechanically stable packings and their material response. The structure of the jammed packings formed using energy minimization techniques varies from dilute and heterogeneous gel-like states with large void spaces to dense and homogeneous packings reminiscent of the random close packed state. The mechanical response exhibits stability under tension and a much greater sensitivity to plastic events produced by non-affine grain motion. In elastic regions the values of the moduli depend on geometric features of the packing.   

Shear-Induced crystallization in jammed systems

Simulations are used to address the effects of oscillating shear strain on jammed systems composed of spherical particles. The simulations show that shear oscillations with amplitudes of more than a few percent lead to substantial crystallization of the system. To ensure that the conclusions are independent of the simulation methodology, a range of simulations are carried out that use both molecular dynamics and athermal dynamics methods, soft and hard potentials, potentials with and without attractive forces, and systems with and without surrounding walls. The extent of crystallization is monitored primarily by the Q6 order parameter, but also in some simulations by the potential energy and the radial distribution function, and by direct visual inspection. A mechanism is proposed for shear-induced crystallization of jammed systems, based on fold catastrophes of the free energy landscape.   

Heterogeneity of the structural relaxation of jammed state in particle-filled elastomers

The Payne effect is a low-strain hysteretic softening in particle-filled elastomers which we recognize as part of jamming physics [1-2]. We find that in particle-filled elastomers aging at a fixed oscillatory strain $\gamma _{a}$ produces a spectral hole in the loss modulus vs strain spectrum which is localized near the aging strain [3]. Sequential aging at two strains reveals that when $\gamma _{a1}>\gamma _{a2}$ the resulting dynamic spectra appear to be a combination of that aged at $\gamma _{a1 }$and $\gamma _{a2}$; whereas for $\gamma _{a1}<\gamma _{a2}$, the resulting dynamic spectra only reflect the characteristic hole burning of the second strain after holding at $\gamma _{a2}$. This remarkable behavior of particle-filled elastomers suggests that structural relaxations in jammed state are heterogeneous and aging at a fixed strain $\gamma_{a}$ only affects part of the relaxation spectra. \newline \newline [1] \textit{Phys. Rev. E}, \textbf{2005}, 72 (3), 031406; \newline [2] \textit{Phys. Rev. Lett.}, \textbf{2005}, 95, 075703; \newline [3] \textit{Europhys. Lett.}, \textbf{2006}, 76(2) 278.