Characterization of Void Space, Large-Scale Structure, and Transport Properties of Maximally Random Jammed Packings of Superballs

Abstract

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by $|x_1{|}^{2p}+|x_2{|}^{2p}+|x_3{|}^{2p}\le 1$, where $p>0$ is a deformation parameter indicating to what extent the shape deviates from a sphere. As $p$ increases from the sphere point ($p=1$), the superball attains cubic symmetry, and attains octahedral symmetry when $p<1$. Previous characterization of superball packings has shown that they have a maximally random jammed (MRJ) state, whose properties (e.g., packing fraction $\varphi$) vary nonanalytically as $p$ diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings. We characterize their large-scale structure by examining the small-$Q$ behavior of their structure factors and spectral densities, which indicate these packings are effectively hyperuniform. We show that the mean width $\bar{w}$ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. We also compute the complementary cumulative pore-size distribution $F(\delta )$ and find the pore sizes tend to decrease as $|1-p|$ increases. From $F(\delta )$, we estimate the fluid permeability, mean survival time, and principal diffusion relaxation time of the packings. Additionally, we compute the diffusion spreadability and find the long-time power-law scaling indicates these packings are hyperuniform. Our results can be used to help inform the design of granular materials with targeted densities and transport properties.

arXiv comment16 Pages, 17 Figures. SI: 4 Pages, 6 Figures

References in corpus (44)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Is Random Close Packing of Spheres Well Defined?
• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Mean field theory of hard sphere glasses and jamming
• Hyperuniform States of Matter
• Dense Packings of the Platonic and Archimedean Solids
• Pair Correlation Function Characteristics of Nearly Jammed Disordered and Ordered Hard-Sphere Packings
• Superdense Crystal Packings of Ellipsoids
• Approximate analytical description of the nonaffine response of amorphous solids
• Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
• Unexpected Density Fluctuations in Jammed Disordered Sphere Packings
• Hyperuniformity in point patterns and two-phase random heterogeneous media
• Phase diagram of colloidal hard superballs: from cubes via spheres to octahedra
• Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings
• Tetratic Order in the Phase Behavior of a Hard-Rectangle System
• Optimal Packings of Superballs
• Basic Understanding of Condensed Phases of Matter via Packing Models
• Phase Behavior of Colloidal Superballs: Shape Interpolation from Spheres to Cubes
• Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
• Diagnosing hyperuniformity in two-dimensional disordered jammed-packings of soft spheres
• Novel Features Arising in the Maximally Random Jammed Packings of Superballs
• Suppressed compressibility at large scale in jammed packings of size disperse spheres
• Dense Packings of Superdisks and the Role of Symmetry
• Incompressibility of polydisperse random close packed colloidal particles
• Critical slowing down and hyperuniformity on approach to jamming
• Hypostatic jammed packings of frictionless nonspherical particles
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
• Disordered Hyperuniform Heterogeneous Materials
• Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states
• Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
• Effect of Dimensionality on the Percolation Threshold of Overlapping Nonspherical Hyperparticles
• Organizing Principles for Dense Packings of Nonspherical Hard Particles: Not All Shapes Are Created Equal
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
• Structural Characterization of Many-Particle Systems on Approach to Hyperuniform States
• Characterization of maximally random jammed sphere packings: Voronoi correlation functions
• Long-Range Anomalous Decay of the Correlation in Jammed Packings
• Characterization of Maximally Random Jammed Sphere Packings. III. Transport and Electromagnetic Properties via Correlation Functions
• Characterization of Maximally Random Jammed Sphere Packings: II. Correlation Functions and Density Fluctuations
• Critical pore radius and transport properties of disordered hard- and overlapping-sphere models
• Three-step melting of hard superdisks in two dimensions
• Hard convex lens-shaped particles: Characterization of dense disordered packings
• Morphology and Kinetics of Random Sequential Adsorption of Superballs: From Hexapods to Cubes
• Kinetic Frustration Effects on Dense Two-Dimensional Packings of Convex Particles and Their Structural Characteristics

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