Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media

Abstract

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform heterogeneous two-phase media, which include composites, porous media, foams, cellular solids, colloidal suspensions and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances ${\sigma }_{{}_V}^2(R)$ and the associated hyperuniformity order metrics ${\overline{B}}_V$. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we focus on a certain class of two-dimensional periodic cellular networks, periodic and disordered/irregular packings, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have a minimal value of ${\overline{B}}_V$ across all volume fractions. On the other hand, among all packings considered, the triangular-lattice packings have the smallest values of ${\overline{B}}_V$ for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing has the minimal order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems by inverse design procedures.

arXiv comment13 pages, 8 Figures, and 4 tables

References in corpus (33)

• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Hyperuniform States of Matter
• Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem
• Hyperuniformity in point patterns and two-phase random heterogeneous media
• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Random Sequential Addition of Hard Spheres in High Euclidean Dimensions
• Hyperuniformity and its Generalizations
• How a well-adapted immune system is organized
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• Diagnosing hyperuniformity in two-dimensional disordered jammed-packings of soft spheres
• Hydrodynamics of Random-Organizing Hyperuniform Fluids
• Designing Disordered Hyperuniform Two-Phase Materials with Novel Physical Properties
• Transport, Geometrical and Topological Properties of Stealthy Disordered Hyperuniform Two-Phase Systems
• Hyperuniformity of Quasicrystals
• Random Scalar Fields and Hyperuniformity
• Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
• Point processes and stochastic displacement fields
• Disordered Hyperuniform Heterogeneous Materials
• The Perfect Glass Paradigm: Disordered Hyperuniform Glasses Down to Absolute Zero
• Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
• Generalized stealthy hyperuniform processes : maximal rigidity and the bounded holes conjecture
• Optimizing Hyperuniformity in Self-Assembled Bidisperse Emulsions
• Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications
• Characterization of maximally random jammed sphere packings: Voronoi correlation functions
• Cloaking the Underlying Long-Range Order of Randomly Perturbed Lattices
• Hyperuniformity with no fine tuning in sheared sedimenting suspensions
• Hidden Multiscale Order in the Primes
• New Tessellation-Based Procedure to Design Perfectly Hyperuniform Disordered Dispersions for Materials Discovery
• Hyperuniform point sets on the sphere: deterministic constructions
• Rigidity and tolerance for perturbed lattices
• High-dimensional generalizations of the kagome and diamond crystals and the decorrelation principle for periodic sphere packings
• Scaling of diffraction intensities near the origin: Some rigorous results

Cited by in corpus (9)

• Local Order Metrics for Two-Phase Media Across Length Scales
• Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability
• Extraordinary Optical and Transport Properties of Disordered Stealthy Hyperuniform Two-Phase Media
• Microstructural and Transport Characteristics of Triply Periodic Bicontinuous Materials
• Hyperuniformity scaling of maximally random jammed packings of two-dimensional binary disks
• Characterizing the Hyperuniformity of Disordered Network Metamaterials
• Percolation of systems having hyperuniformity or giant number-fluctuations
• Hyperuniformity in Ashkin-Teller model
• Predictive Formulas for Scattering Mean Free Path for General Disordered Dielectric Media Beyond the Long-Wavelength Regime