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.

13 pages, 8 Figures, and 4 tables

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• 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