New Tessellation-Based Procedure to Design Perfectly Hyperuniform Disordered Dispersions for Materials Discovery

Abstract

Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an anomalous suppression of long-wavelength volume-fraction fluctuations, endowing them with novel physical properties. While such unusual materials have received considerable attention, a stumbling block has been an inability to create large samples that are truly hyperuniform due to current computational and experimental limitations. To overcome such barriers, we introduce a new, simple construction procedure that guarantees perfect hyperuniformity for very large sample sizes. It involves tessellating space into cells and then inserting a particle into each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We analytically prove that such dispersions are perfectly hyperuniform in the infinite-sample-size limit. Our methodology enables a remarkable mapping that converts a very large nonhyperuniform disordered dispersion into a perfectly hyperuniform one, which we numerically demonstrate in two and three dimensions. A similar analysis also establishes the hyperuniformity of the famous Hashin-Shtrikman multiscale dispersions, which possess optimal transport and elastic properties. Our hyperuniform designs can be readily fabricated using modern photolithographic and 3D printing technologies. The exploration of the enormous class of hyperuniform dispersions that can be designed and tuned by our tessellation-based methodology paves the way for accelerating the discovery of novel hyperuniform materials.

11 pages, 6 figures, 1 supplementary material, and published in Acta Materialia (with several corrections.)

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Cited by in corpus (14)

• Stone-Wales Defects Preserve Hyperuniformity in Amorphous Two-Dimensional Materials
• Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
• Cloaking the Underlying Long-Range Order of Randomly Perturbed Lattices
• Nearly hyperuniform, nonhyperuniform, and antihyperuniform density fluctuations in two-dimensional transition metal dichalcogenides with defects
• Methodology to Construct Large Realizations of Perfectly Hyperuniform Disordered Packings
• Effective Elastic Wave Characteristics of Composite Media
• Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime
• Extraordinary Optical and Transport Properties of Disordered Stealthy Hyperuniform Two-Phase Media
• Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media
• Hyperuniform Density Distributions of Brownian Particles via Designer External Potentials
• Microstructural and Transport Characteristics of Triply Periodic Bicontinuous Materials
• Characterizing the Hyperuniformity of Disordered Network Metamaterials
• Hyperuniformity of Weighted Particle Systems
• Predictive Formulas for Scattering Mean Free Path for General Disordered Dielectric Media Beyond the Long-Wavelength Regime