Session B47: Focus Session: Jamming, Glass Transition, and Gelation in Colloids and Soft Matter Systems

Geometrical analysis of suspension flows near jamming

The viscosity of suspensions was computed early on by Einstein and Batchelor in the dilute regime. At high density however, their rheology remains mystifying. As the packing fraction increases, steric hindrance becomes dominant and particles move under stress in a more and more coordinated way. Eventually, the viscosity diverges as the suspension jams into an amorphous solid. Such a jamming transition is reminiscent of critical points: the rheology displays scaling and a diverging length scale. Jamming bear similarities with the glass transition where steric hindrance is enhanced under cooling, and where the dynamics is also observed to become more and more collective as it slows down. In all these examples, understanding the nature of the collective dynamics and the associated rheology remains a challenge. Recent progress has been made however on a related problem, the unjamming transition where a solid made of repulsive soft particles is isotropically decompressed toward vanishing pressure. In this situation various properties of the amorphous solid, such as elasticity, transport or force propagation, display scaling with the distance to threshold. Theoretically these observations can be shown to stem from the presence of soft modes in the vibrational spectrum, a result that can be extended to thermal colloidal glasses as well. Here we focus on particles driven by shear at zero temperature. We show that if hydrodynamical interactions are neglected an analogy can be made between the rheology of such a suspension and the elasticity of simple networks, building a link between the jamming and the unjamming transition. This analogy enables us to unify in a common framework key aspects of the elasticity of amorphous solids with the rheology of dense suspensions, and to relate features of the latter to the geometry of configurations visited under flow.   

Finite Size Effects at the Jamming Transition

Packings of spheres at zero temperature and shear stress exhibit a jamming/unjamming transition as a function of density. For spheres that repel when they overlap and do not otherwise interact, packings are jammed with a nonzero static shear modulus when the density, $\phi$, exceeds a critical density, $\phi_c$. This jamming transition displays characteristics of both first and second order phase transitions with, for example, a discontinuous jump in the coordination number (average number of interacting neighbors per particle) and a power-law increase in the shear modulus. In addition, multiple length scales have been identified that diverge as $\phi$ decreases towards $\phi_c$, emphasizing the second order nature of the transition. The existence of diverging length scales suggests that quantities such as the coordination number and shear modulus should exhibit finite size scaling as $\phi_c$ is approached, but until now this has not been observed. We report the first measurements of finite size scaling at the jamming transition of soft frictionless repulsive spheres and explore the implications of these results on our current understanding of the jamming transition.   

Stability of jammed systems to generalized boundary deformations

At zero temperature and applied stress, amorphous packings of repulsive spheres exhibit a jamming transition to rigidity. As pointed out by Torquato and Stillinger, some of these ``collectively jammed'' configurations may not be stable with respect to boundary deformations, while others, ``strictly jammed,'' may be stable with respect to any change of the boundaries. We explore this by considering systems with periodic boundary conditions at packing fractions above the jamming transition as comprising the basis of an infinite square (or cubic) lattice. The displacement fields of particles corresponding to normal modes of vibration are generally not consistent with the periodic boundary conditions used to construct the basis packing. Therefore, by studying the vibrational modes we determine the linear response to boundary deformations that do not respect the periodicity of the initial system. Hence, we are able to explore the stability of packings with respect to a large class of boundary deformations. We discover that some configurations have modes with negative energies, indicating instability. We report the effects of system size and packing fraction upon the probability that a collectively jammed packing is also stable with respect to boundary deformations.   

Vestige of $T = 0$ jamming transition at finite temperature in 3D

When a random packing of spheres at T = 0 is compressed to the jamming transition, the system becomes rigid and the first peak of the pair-correlation function, $g(r)$, diverges [1]. We study the manifestation of this signature and the associated particle dynamics when the temperature, $T$, is no longer negligible. To this end, we employ a three-dimensional packing of monodisperse, micron-size, colloids made from n-isopropyl acrylimide (NIPAM). NIPAM particles change size and hence the packing fraction of the system in response to environmental temperature. Thus by changing sample temperature we can probe all packing fractions of interest using a single sample. These particles are compressible so the system can reach packing fractions and configurations inaccessible to hard colloids. We observe a vestige of the T = 0 divergence as a maximum in the first peak of $g(r)$ versus packing fraction coincident with dynamical arrest of the particles. The general features in 3D are in agreement with a previous study in a two-dimensional bi-disperse NIPAM system [2]. We report the dependence of $g(r)$ and particle motion on packing fraction.\\\ [1] C. S. O'Hern, et al., Phys. Rev. E 68, 011306 (2003). [2] Z. Zhang, N. Xu, et al., Nature 459, 230 (2009).   

Localization model for relaxation in glass-forming materials

As a material approaches its glass transition, its structural relaxation time $\tau $ rapidly increases as its particles become localized. A model relating this relaxation time increase to an experimentally accessible measure of localization (e.g. the Debye-Waller factor $\langle u^2\rangle )$ would have a fundamental impact on our understanding of glass formation and would be practically useful in the design of new materials. After examining such a relationship proposed by Leporini and coworkers and finding it to be inadequate, we develop an activated transport model that accurately describes relaxation data from a variety of simulated and experimental glass-forming materials. This model naturally extends the Hall-Wolynes and free volume models relating $\tau $ to $\langle u^2\rangle $ (or free volume). The model parameters are physically meaningful and reflect the anharmonicity and anisotropy of particle localization. The Vogel-Fulcher-Tamman relation also describes relaxation in the simulated and experimental glass-forming materials we considered, and by exploring consistency between these two relations we gain new insight into the characteristic temperatures of glass formation in terms of the extent of particle localization.   

Lattice Model of Dynamic Heterogeneity in Glassy Systems

Free volume in a fluid provides space for molecular motion; this creates local mobility and avoids ``kinetic jamming'' as the sample is rapidly cooled towards its glass transition. This physical picture has recently garnered significant interest in the polymer materials realm, where free volume is suspected to be the key factor in suppressing the glass transition of a polymer thin film near its exposed surfaces. We have developed a simple kinetic model that describes how free volume is transported in a near-glassy liquid. Model simulation results reveal that spatial fluctuations of free volume grow large near the glass transition, and this gives rise to hallmark glassy characteristics such as dynamic heterogeneity, intermittency and, ultimately, kinetic arrest. We will also discuss the response of glassy and molten states to perturbations, as a probe for characterising fluctuations near the glass transition.   

Building a Colloidal Proxy for Binary Metallic Glasses

Current experimental techniques for determining the atomic structure of metallic glasses and testing structural theories such as the efficient cluster packing model are limited to diffraction and scattering. These techniques give only average structural information that could result from many different unique structures. Simulations of metallic glasses, on the other hand, give the exact structure of every atom in the system, but are limited by computing power to a few thousand atoms which are equilibrated over a few nanoseconds. This leads to uncertainties in the reliability of reproducing real metallic glass structures. To overcome these deficiencies, we have created a proxy experimental system that can be treated much like a simulation. We have synthesized suspensions of larger, colloidal scale particles (2-3um in diameter) to build pseudo binary metallic glasses. Using confocal microscopy imaging techniques, we determine the three dimensional position of hundreds of thousands of individual particles (atoms), and calculate structural information such as the radial distribution function, Voronoi volume, and partial coordination numbers. We compare these results to both theoretical calculations and experimental results of real metallic glasses. The focus here will be on a building a proxy for the CuZr binary system.   

Contact processes in crowded environments

Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. To begin to answer the question of what happens to this system at higher densities, we investigate a conserved-particle-number contact process with a three-body interaction as opposed to the usual two-body interaction. In particular, one active (diffusing) particle collides with two inactive (non-diffusing) particles such that they can become active. In mean-field, this system exhibits a continuous absorbing phase transition belonging to conserved directed percolation universality class. Simulations on 2D lattices support our result. In contrast, the three-body interaction with two active particles colliding and activating one inactive particle exhibits a first-order transition. Inspired by kinetically-constrained models of the glass transition, we investigate the ``caging effect'' at even higher particle densities to look for a second dynamical phase transition back to an inactive phase. While mean-field calculations demonstrate a continuous transition, 2D lattice simulations show a hint of a first-order transition, suggesting a possible fluctuation-driven transition due to the highly localized geometric constraint.   

Experiments on Rearrangements and Forces in 2D Emulsion Hopper Flow

We did experiments with a quasi-two-dimensional binary emulsion flowing through a hopper. Our samples are oil-in-water emulsion confined between two close-spaced parallel plates, so that the droplets are deformed into pancake shapes. In this system, there is only viscous friction and no static friction between droplets. The hopper flow induces a high rate of rearrangement events allowing us to understand how stresses and forces change during the process. By imaging the droplets during flow, we observed T1 events, which are topological changes when droplets exchange neighbors. Simultaneously, we measured forces between the droplets using a technique we have developed and studied the evolution of forces between droplets during rearrangements.   

The Role of Solvent-Solute Interactions on The Behavior of Low Molecular Mass Organo-Gelators

Low molecular mass organo-gelators (LMOGs) are a class of small molecules that can self-assemble in organic solvents to form three-dimensional fibrillar networks. This has a profound effect on the viscoelastic properties of the solution causing physical gelation. These gels have uses in a range of industries including cosmetics, foodstuffs, plastics, petroleum and pharmaceuticals. A fundamental question in this field is: What makes a good LMOG? This talk will discuss the relationships between the viscoelastic properties and thermodynamic phase behavior of LMOG/solvent solutions. The regular solution model was used to fit the liquidus line and sol/gel transition temperature vs. concentration in different solvents to determine LMOG-solvent interaction parameters ($\chi $ = A/T). This parameter A was found to scale with the solubility parameter of the solvent, especially for non-polar solvents. This demonstrates that gelation is strongly linked to LMOG solubility and indicates that the bulk thermodynamic parameters of the LMOG (solubility parameter and melting temperature) are useful to predict the solution behavior of LMOGs.   

Effects of penalty function type on the history-penalized metabasin escape algorithm for supercooled liquids

The history-penalized metabasin escape algorithm provides an autonomous transition state pathway for a trapped system to escape from deep metastable energy minima and larger basins of attraction. The effects of penalty function type on the efficiency of the algorithm are demonstrated by sampling portions of the potential energy surface of a binary Lennard-Jones liquid close to the glass transition temperature. Our results indicate that optimal penalty functions prefer both large 3N+1 dimensional volumes and the ability to force the system over a large range. The Gaussian, which until now has served as the standard penalty function used for activation, serves as the benchmark against other representative penalty function types. Analysis shows that the triangle function results in four fold improvements in efficiency over the Gaussian, thereby furthering the reach of simulation into timescale regimes largely inaccessible to molecular dynamics.   

Nonlinear effective medium theory of disordered spring networks

Disordered soft materials, such as fibrous networks in biological contexts exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks of simple Hookian elements with disordered spring constant. We develop a mean-field approach to calculate the differential elastic bulk modulus for the macroscopic network response of such networks under large isotropic deformations. We find that the nonlinear mechanics depends only weakly on the lattice geometry and is governed by the average network connectivity. In particular, the nonlinear response is controlled by the isostatic connectivity, which depends strongly on the applied strain. Our predictions for the strain dependence of the isostatic point as well as the strain-dependent differential bulk modulus agree well with numerical results in both two and three dimensions. In addition, by using a mapping between the disordered network and a regular network with random forces, we calculate the non-affine fluctuations of the deformation field and compare it to the numerical results. Finally, we discuss the limitations and implications of the developed theory.