Organizing principles for dense packings of nonspherical hard particles: Not all shapes are created equal (original) (raw)
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Physical Review Letters, 2012
We show that hard spheres confined between two parallel hard plates pack denser with periodic adaptive prismatic structures which are composed of alternating prisms of spheres. The internal structure of the prisms adapts to the slit height which results in close packings for a range of plate separations, just above the distance where three intersecting square layers fit exactly between the plates. The adaptive prism phases are also observed in real-space experiments on confined sterically stabilized colloids and in Monte Carlo simulations at finite pressure.
Effect of particle size distribution on 3D packings of spherical particles
EPJ Web of Conferences
We use molecular dynamics simulations of frictionless spherical particles to investigate a class of polydisperse granular materials in which the particle size distribution is uniform in particle volumes. The particles are assembled in a box by uniaxial compaction under the action of a constant stress. Due to the absence of friction and the nature of size distribution, the generated packings have the highest packing fraction at a given size span, defined as the ratio α of the largest size to the smallest size. We find that, up to α = 5, the packing fraction is a nearly linear function of α. While the coordination number is nearly constant due to the isostatic nature of the packings, we show that the connectivity of the particles evolves with α. In particular, the proportion of particles with 4 contacts represents the largest proportion of particles mostly of small size. We argue that this particular class of particles occurs as a result of the high stability of local configurations in which a small particle is stuck by four larger particles.
Modeling the Disordered Dense Phase in the Packing of Binary Mixtures of Spheres
Journal of Colloid and Interface Science, 1998
In this case, the ordered crystalline structure is denser A new, probabilistic approach is applied to the case of dense than the fluid one (6). random packings of binary mixtures of spheres, assuming gapless Recent experiments have shown that binary mixtures of packing. The model describes correctly the dependence of the pospherical colloidal particles which interact only via simple rosity of the packing on mixture composition and size ratio for repulsive potentials form organized structures (7). Comthe disordered dense ''phase'' of the binary mixture. The volumes puter simulations have been carried out to study this entropyof the voids are calculated accurately by means of a Monte Carlo driven formation of a superlattice in a hard-sphere binary integration instead of being evaluated by kissing spheres. The remixture (8). The formation of ordered and disordered phases sults, in term of the porosity/sphere-fraction relationship, are comin binary mixtures has also been predicted using a statistical pared with those of a previous model, also based on the gapless packing approximation. ᭧ 1998 Academic Press mechanical description of powder mixtures (9). An ordered Key Words: binary mixture; sphere packing; ordered phase; disphase is stable for the following reason (10): The organized, ordered phase; gapless packing; powder; colloids.
Maximally dense packings of two-dimensional convex and concave noncircular particles
2012
The problem of packing nonoverlapping particles in d-dimensional Euclidean spaceRd has been of interest in discrete mathematics and geometry for centuries. One overarching aim is to ascertain organizing principles that govern the nature of dense packings of various shapes [1] in order to better understand many natural phenomena, including liquid, glassy, and crystalline states of matter [2–5]; heterogeneous materials [4]; crystalline polymers [6, 7]; and biological systems [8–10]; to name a few.
Dense Regular Packings of Irregular Nonconvex Particles
Physical Review Letters, 2011
We present a new numerical scheme to study systems of non-convex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, not only from a nanoparticle but also both from a computational geometry perspective. Besides determining close-packed structures for many shapes, we also discover a new denser configuration for Truncated Tetrahedra. Moreover, we consider recently synthesized nanoparticles and colloids, where we focus on the excluded volume interactions, to show the applicability of our method in the investigation of their crystal structures and phase behavior. Extensions to the presented scheme include the incorporation of soft particle-particle interactions, the study of quasicrystalline systems, and random packings.
Dense Regular Packings of Irregular Nonconvex Particles Supplemental Material
2011
In this Supplemental Material we present the main body of data we have collected using both our composite technique and literature studies for a large group of solids, particle approximates and several miscellaneous shapes. We also prove that the crystal structures we obtained for rhombicuboctahedra and rhombic enneacontrahedra achieve the densest packing. Furthermore, we present new crystal structures for enneagons, as well as the truncated tetrahedra, which achieve higher packing fractions than previously obtained, both in a centrosymmetric-dimer lattice. In addition to these crystal structures, we consider the relation between the sphericity and packing fraction and show that there is no clear dependence between the two. Finally, we give visual representations for a few of the crystal structures we obtained during our simulation studies.
Effect of particle shape on the density and microstructure of random packings
Journal of Physics: Condensed Matter, 2007
We study the random packing of non-spherical particles by computer simulation to investigate the effect of particle shape and aspect ratio on packing density and microstructure. Packings of cut spheres (a spherical segment which is symmetric about the centre of the sphere) are simulated to assess the influence of a planar face on packing properties. It turns out that cut spheres, in common with spherocylinders and spheroids, pack more efficiently as the particle's aspect ratio is perturbed slightly from unity (the aspect ratio of a sphere) to reach a maximum density at an aspect ratio of approximately 1.25. Upon increasing the aspect ratio further the cut spheres pack less efficiently, until approximately an aspect ratio of 2, where the particles are found to form a columnar phase. The amount of ordering is sensitive to simulation parameters and for very thin disks the formation of long columns becomes frustrated, resulting in a nematic phase, in marked contrast to the behavior of long thin rods which always randomly pack into entangled isotropic networks. With respect to coordination numbers it appears that cut spheres always pack with significantly fewer contacts than required for isostatic packing.
Structural Characteristics of a Small Group of Fixed Particles and the Maximum Density of a Random Packing of Hard Spheres, 2021
The definition of random packings of hard spheres, which does not assume any specific features of a short-range order, is considered. The results obtained allow (in particular) us to determine the maximum possible density of a random packing, which has no any types of explicit or hidden long-range order. New computer experiment data, which describe the statistical–geometrical properties of random packings of twodimensional (2D) and three-dimensional (3D) hard spherical particles, are presented. The behavior of a small group of randomly chosen and fixed spheres at various packing densities and the differences between the properties of this group and the main “large” ensemble (which follow, in particular, from the theoretical results obtained) are investigated. The dependences found experimentally are consistent with the proposed theoretical solution. Let an ensemble consist of N particles occupying total volume V (at packing density η = Nu/V, where u is the particle volume). The maximum possible density of a random packing of spherical particles (ηmax) is specified by the following geometric condition: the average volume of a Voronoi polyhedron in a random close packing cannot be smaller than the average excluded volume for all points of this packing.
Quantification of the heterogeneity of particle packings
Physical Review E, 2009
The microstructure of coagulated colloidal particles, for which the interparticle potential is described by the Derjaguin-Landau-Verweg-Overbeek theory, is strongly influenced by the particles' surface potential. Depending on its value, the resulting microstructures are either more "homogeneous" or more "heterogeneous," at equal volume fractions. An adequate quantification of a structure's degree of heterogeneity ͑DOH͒, however, does not yet exist. In this work, methods to quantify and thus classify the DOH of microstructures are investigated and compared. Three methods are evaluated using particle packings generated by Brownian dynamics simulations: ͑1͒ the pore size distribution, ͑2͒ the density-fluctuation method, and ͑3͒ the Voronoi volume distribution. Each method provides a scalar measure, either via a parameter in a fit function or an integral, which correlates with the heterogeneity of the microstructure and which thus allows to quantitatively capture the DOH of a granular material. An analysis of the differences in the density fluctuations between two structures additionally allows for a detailed determination of the length scale on which differences in heterogeneity are most pronounced.
Theory of Amorphous Packings of Binary Mixtures of Hard Spheres
Physical Review Letters, 2009
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical protocols can be identified with the infinite pressure limit of long lived metastable glassy states. We test this assumption against numerical and experimental data and show that the theory correctly reproduces the variation with mixture composition of structural observables, such as the total packing fraction and the partial coordination numbers.