Disordered spherical bead packs are anisotropic

Investigating how tightly objects pack space is a long-standing problem, with relevance for many disciplines from discrete mathematics to the theory of glasses. Here we report on the fundamental yet so far overlooked geometric property that disordered mono-disperse spherical bead packs have significant local structural anisotropy manifest in the shape of the free space associated with each bead. Jammed disordered packings from several types of experiments and simulations reveal very similar values of the cell anisotropy, showing a linear decrease with packing fraction. Strong deviations from this trend are observed for unjammed configurations and for partially crystalline packings above 64%. These findings suggest an inherent geometrical reason why, in disordered packings, anisotropic shapes can fill space more efficiently than spheres, and have implications for packing effects in non-spherical liquid crystals, foams and structural glasses. open access editor’s choice Copyright c © EPLA, 2010 When frictional spheres of equal size are packed disorderly they can form mechanically stable “jammed” configurations which occupy a fraction of the available volume in the range between 0.55 and 0.64. However, for non-spherical particles this limiting packing fraction has a higher value: it has been recently reported that anisotropic bodies such as M&M chocolate candies pack more tightly than spheres in the disordered phase reaching packing fractions of φ≈ 0.71 for spheroids and φ≈ 0.735 for general ellipsoids [1,2]. Understanding why anisotropic shapes fill space more tightly than spheres is an open question whose answer lies in the complex geometrical properties of disordered packings. Our study comprises experimental data sets of mechanically stable “jammed” glass bead packs prepared by a fluidised bed method, FB [3], and dry acrylic beads (a)E-mail: [email protected] 1Different definitions of what constitutes the “jammed” state have been given. As a minimal common property, all “jammed” packings analysed here are “locally jammed”, i.e. each sphere is held in place by its neighbours. packs prepared by a tapping/compression method, DA [3]. Coordinates of the bead centres are extracted from 3D X-ray computed tomography images via FFT deconvolution and watershed methods [3,4], with precision better than 0.1% of the sphere diameter. Simulated bead packs of realistic frictional beads are obtained by a discrete element method, DEM [5]. Idealised packs of frictionless spheres undergoing Newtonian dynamics with no gravity are generated by the Lubachevsky-Stillinger Algorithm, LS [6]. Additional unjammed data sets are generated from the bead centre coordinates of the jammed DA data sets by random Monte Carlo moves, MC. The appendix contains details of experiments and simulations. The shape of the free space around each bead is determined by the Voronoi diagram which is a partition of space into N convex cells {Ki} with respect to a set of N points P = {ri}, here the bead centres, such that all points inside the Voronoi cell Ki are closer to ri than to any of the other points rj ∈ P with i = j, see fig. 1. Voronoi diagrams are computed with qhull [7] for all beads in the data set, taking periodic boundary conditions into account