Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session B17: Focus Session: Packing of Anisotropic Particles |
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Sponsoring Units: GSNP DPOLY Chair: Rob Hoy Room: 402 |
Monday, March 3, 2014 11:15AM - 11:27AM |
B17.00001: Solving the Granular Inverse Packing Problem with Artificial Evolution Marc Miskin, Heinrich Jaeger If a collection of identical particles is poured into a container, it is obvious that different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a solution to this inverse-packing problem by framing it in the context of artificial evolution. By representing shapes as bonded spheres, we show how particles may be mutated, simulated, and selected to produce particularly dense or loose packing aggregates, both with and without friction. Moreover, we show how motifs emerge linking these shapes together. The result is a set of design rules that function as an effective solution to the inverse packing problem for given packing procedures and boundary conditions. Finally, we show that these results may be verified by experiments on 3d printed prototypes used to make packings in the real world. [Preview Abstract] |
Monday, March 3, 2014 11:27AM - 11:39AM |
B17.00002: Shape Alloys of Nanorods and Nanospheres from Self-Assembly Jaime Millan, Xingchen Ye, Michael Engel, Jun Chen, Benjamin Diroll, Sharon Glotzer, Chris Murray Mixtures of anisotropic nanocrystals promise a great diversity of superlattices and phase behaviors beyond those of single-component systems. However, obtaining a colloidal shape alloy in which two different shapes are thermodynamically co-assembled into a crystalline superlattice has remained a challenge. Here we present a joint experimental-computational investigation of two geometrically ubiquitous nanocrystalline building blocks---nanorods and nanospheres---that overcome their natural entropic tendency towards macroscopic phase separation and co-assemble into three intriguing phases over centimeter scales, including an AB2-type binary superlattice. Monte Carlo simulations reveal that although this shape alloy is entropically stable at high packing fraction, demixing is favored at experimental densities. Simulations with short-ranged attractive interactions demonstrate that the alloy is stabilized by interactions induced by ligand stabilizers and/or depletion effects. An asymmetry in the relative interaction strength between rods and spheres improves the robustness of the self-assembly process. Reference: Ye, Millan, Engel, Chen, Diroll, Glotzer, Murray, Nano Letters 13, 4980 (2013). [Preview Abstract] |
Monday, March 3, 2014 11:39AM - 11:51AM |
B17.00003: What is the Real Lewis Law? Size-Topology Correlations for Anisotropic Objects Sangwoo Kim, Muyun Cai, Sascha Hilgenfeldt Ever since its empirical formulation in 1928, Lewis`s law has intrigued scientists, postulating a linear correlation between the average in-plane area and the number of neighbors in a two-dimensional tiling. Many supporting and dissenting results have been reported in systems as diverse as foams, Voronoi tilings in glass models, and nanocrystals. A strong size-topology correlation is consistently observed, but it is often pronouncedly nonlinear. Recently, a variant of the granocentric model explained numerous cases of nonlinear correlations, but cannot account for the linear version of the law. We revisit Lewis's original work by conducting more extensive experiments on cucumber epidermis tissue. The data confirms the linear law, but also shows that the individual cells have a pronounced anisotropy, not present in systems with nonlinear correlation laws. We demonstrate how the granocentric model can be modified taking into account the cell anisotropy, and how this feature is capable of reproducing the linear Lewis law, as well as other characteristic differences in size-topology statistical quantities. The model should be generally applicable to jammed, plane-filling systems and identifies domain anisotropy as an important ingredient in their statistical description. [Preview Abstract] |
Monday, March 3, 2014 11:51AM - 12:03PM |
B17.00004: Size-Topology Correlations and Crystallization in Tilings and Packings Sascha Hilgenfeldt Empirical studies have long shown complex statistics in polygonal tilings of the plane or the corresponding packings of objects. Using a 2D variant of the granocentric model, we provide an analytical explanation for correlations of domain size and neighbor number, as well as for the relation between the widths of these two distributions characterizing the tiling or packing. The results agree with data from a large variety of living and inanimate systems [1]. This strictly local approach also gives insight into order-disorder transitions: A dramatic narrowing of the neighbor distribution indicates crystallization, for which well-defined disorder thresholds can be extracted both in systems with continuous disorder and in bidisperse systems, in very good agreement with simulation results [2].\\ \\ $[1]$ M. P. Miklius and S. Hilgenfeldt, Phys. Rev. Lett. 108, 015502 (2012).\\ $[2]$ S. Hilgenfeldt, Phil. Mag. 93, 4018 (2013). [Preview Abstract] |
Monday, March 3, 2014 12:03PM - 12:15PM |
B17.00005: Unified Theoretical Framework for Shape Entropy in Colloids Greg van Anders, N. Khalid Ahmed, Daphne Klotsa, Michael Engel, Sharon C. Glotzer Entropy has long been known to order colloidal systems ranging from dense suspensions of hard particles to dilute suspensions of spheres in the presence of smaller polymeric depletants. We present a framework for treating directional entropic forces (DEFs) in systems of colloidal shapes. By introducing an effective potential of mean force and torque we demonstrate that the microscopic origin of the entropic ordering of anisotropic shapes is the emergence of DEFs that tend to align neighboring particles. We define and compute these forces and show that, at the onset of ordering, they are on par with traditional depletion interactions, as well as and other forces contributing to assembly in nanocolloidal systems. By retaining only steric interactions, we allow the comparison of the role of shape to other forces present in experimental systems. Well-known cases involving spheres arise as the limit of ``zero shape.'' Our results apply to monodisperse systems and mixtures of hard particles of arbitrary shape and to systems of hard particles with traditional depletants. As such, we present a single theoretical framework that unifies the ordering of arbitrary shapes due to entropy alone, incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa. [Preview Abstract] |
Monday, March 3, 2014 12:15PM - 12:27PM |
B17.00006: Stress supporting structures from interlocking in random packings of granular materials Eric Brown, Shomeek Mukhopadhyay, Alice Nasto, Sulimon Sattari, David Brantley, Kevin Mitchell We present experimental results and a model for strong strain-stiffening in random packings of interlocking granular materials such as chains and staples. Measurements of stress vs. strain are made on the materials under uniaxial compression, along with x-ray tomography to observe interlocking. These packings are found to exhibit strain-stiffening and sustain stresses several orders-of-magnitude beyond those of unconfined granular materials as long as there are system-filling clusters of interlocked particles. To model this behavior, we use a mean-field theory approach. First, the conditions for system-filling clusters can be predicted by by using the area available for interlocking for a given particle shape and a random network model. This model correctly predicts, for example, the minimum chain length required to have system-filling clusters. In this strong regime, the packing stiffness can be calculated using the link stiffness, mean strain on each link, and the probability of tight links, which agrees with experiments within a factor of 2. This model explains the strength of these packings as coming from stretching the links between interlocked particles, and strain-stiffening as a result of increasing number of tightly interlocked particles with increasing strain. [Preview Abstract] |
Monday, March 3, 2014 12:27PM - 12:39PM |
B17.00007: Self-Assembly of Multi-Dimpled Spherical Particles N. Khalid Ahmed, Greg van Anders, Elizabeth R. Chen, Michael Engel, Sharon C. Glotzer Self-assembly of hard convex polyhedra has been extensively studied, demonstrating the formation of complex crystal structures. Recently synthesized multi-dimpled concave particles made of spheres have the potential for comparable complexity. Phase behavior and confinement have been studied for single-dimpled spherical cap and bowl shaped particles. Motivated by the synthesis of multi-dimpled spherical concave particles, we investigate the assembly of spherical particles with up to six dimples. We demonstrate that the assembly is controlled by competition between the spherical and the dimpled surface segments of the particle. Shrinking and swelling the inner spherical core of such particles can result in reconfigurable structures. [Preview Abstract] |
Monday, March 3, 2014 12:39PM - 12:51PM |
B17.00008: Binary mixtures of polyhedral nanoparticles: from phase separation to superstructures Mihir Khadilkar, Umang Agarwal, Fernando Escobedo Polyhedral nanoparticles have emerged as important model systems for both fundamental studies of entropic self-assembly as well as material design. The mixing of more than one shape provides a promising strategy towards achieving a greater variety of structures and properties. We explore this with the study of the phase behavior of binary mixtures of hard convex polyhedra having similar sizes but different shapes. Choosing representative particle shapes from those readily synthesizable, we find that the phase behavior of such mixtures is dependent on the interplay of mixing and packing entropy, which can give rise to miscible or phase-separated states. While expectedly many of the binary systems studied exhibit phase separation at high pressures due to the incompatible pure-component crystal structures, our study shows that the essential qualitative trends in miscibility and phase separation can be correlated to properties of the pure components, such as the relative values of the order-disorder transition pressure of each component. However, the relative size ratios and the presence of mesophases for the pure-component systems are also critical in aiding the formation of fully miscible blends of novel plastic crystalline superstructures. [Preview Abstract] |
Monday, March 3, 2014 12:51PM - 1:03PM |
B17.00009: Assembly precursors in fluids of hard polyhedra M. Eric Irrgang, Michael Engel, Sharon C. Glotzer The role of shape in entropy-driven self-assembly has recently been highlighted in computer simulations of hard anisotropic particles. A rich diversity of crystal and other solid-like phases has been demonstrated in particular for hard polyhedra. Moreover, a correlation has been observed between local structure in the fluid phase and structure of the solid-like phase[1]. Here we investigate the question of when the fluid first ``recognizes'' particle shape and anticipates a pending phase transition. We present equations of state for systems of hard polyhedra spanning the low-density fluid to high- density solid states, obtained numerically from equilibrium Monte Carlo simulations. We discuss trends in the behavior for different shapes, and show some general features common to all systems. [1] P. F. Damasceno, M. Engel, and S. C. Glotzer, Science 337, 453 (2012) [Preview Abstract] |
Monday, March 3, 2014 1:03PM - 1:15PM |
B17.00010: Complexity in surfaces of densest packings for families of polyhedra Daphne Klotsa, Elizabeth R. Chen, Michael Engel, Pablo F. Damasceno, Sharon C. Glotzer Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, colloidal matter, and biology. In all these fields, particle shape is important for structure and properties, especially upon crowding. In this talk, we explore packing as a function of shape. By combining simulations and analytic calculations, we study three 2-parameter families of hard polyhedra and report an extensive and systematic analysis of the densest known packings of more than 55,000 convex shapes. The three families have the symmetries of triangle groups (20-hedral, 8-hedral, 4-hedral) and interpolate between various symmetric solids (Platonic, Archimedean, Catalan). We find that maximum packing density surfaces reveal unexpected richness and complexity, containing as many as 130 different structures within a single family. Our results demonstrate the importance of thinking about shape not as a static property of an object, in the context of packings, but rather as but one point in a higher dimensional shape space whose neighbors in that space may have identical or markedly different packings. Finally, we propose a method to distinguish regions of packings and classify types of transitions between them. [Preview Abstract] |
Monday, March 3, 2014 1:15PM - 1:27PM |
B17.00011: Pessimal shapes for packing Yoav Kallus The question of which convex shapes leave the most empty space in their densest packing is the subject of Reinhardt's conjecture in two dimensions and Ulam's conjecture in three dimensions. Such conjectures about pessimal packing shapes have proven notoriously difficult to make progress on. I show that the regular heptagon is a local pessimum among all convex shapes, and that the 3D ball is a local pessimum among origin-symmetric shapes. Any shape sufficiently close in the space of shapes to these local pessima can be packed at a greater efficiency than they. In two dimensions and in dimensions above three, the ball is not a local pessimum, so the situation in 3D is unusual and intriguing. I will discuss what conditions conspire to make the 3D ball a local pessimum and whether we can prove that it is also a global pessimum. [Preview Abstract] |
Monday, March 3, 2014 1:27PM - 1:39PM |
B17.00012: Mean-field theory of random close packings of axisymmetric particles Lin Bo, Adrian Baule, Romain Mari, Louis Portal, Hernan Makse Finding the optimal random packing of non-spherical particles is an open problem with great significance in a broad range of scientific and engineering fields. So far, this search has been performed only empirically on a case-by-case basis, in particular, for shapes like dimers, spherocylinders and ellipsoids of revolution. Here, we present a mean-field formalism to estimate the packing density of axisymmetric non-spherical particles. We derive an analytic continuation from the sphere that provides a phase diagram predicting that, for the same coordination number, the density of monodisperse random packings follows the sequence of increasing packing fractions: spheres $<$ oblate ellipsoids $<$ prolate ellipsoids $<$ dimers $<$ spherocylinders. We find the maximal packing densities of $73.1\%$ for spherocylinders and $70.7\%$ for dimers, in good agreement with the largest densities found in simulations. Moreover, we find a packing density of $73.6\%$ for lens-shaped particles, representing the densest random packing of the axisymmetric objects studied so far. [Preview Abstract] |
Monday, March 3, 2014 1:39PM - 1:51PM |
B17.00013: The shape of jams to come: hidden geometric symmetries of jamming Peter Morse, Eric Corwin The mechanical vacuum of systems below jamming is surprisingly rich in structure. Using geometric quantities derived from the Voronoi tessellation we report on the discovery of a new phase transition preceding the mechanical jamming transition. This phase transition corresponds to the appearance of a new kind of symmetry hidden in the shape of the Voronoi cells. We characterize this symmetry by looking at properties related to the maximum inscribed sphere in each cell, moments of the volume distribution of cells, and the aspect ratios of cells. Each contains a very different signature of the jamming transition with various scaling laws. We offer several possible routes towards renormalization of this system and discuss whether a field theory could be made to explain the various phases. [Preview Abstract] |
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