Methodology to construct large realizations of perfectly hyperuniform disordered packings

Jaeuk Kim and Salvatore Torquato
Phys. Rev. E 99, 052141 – Published 31 May 2019
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Abstract

Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space Rd. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a “bounded-cell” condition, hard particles of general shape are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size are perfectly hyperuniform in the infinite-sample-size limit, regardless of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R2 and R3. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that packings that have identical tessellations can either be nonhyperuniform or hyperuniform by simply tuning local characteristics. It is noteworthy that our computationally designed hyperuniform two-phase systems can easily be fabricated via state-of-the-art methods, such as 2D photolithographic and 3D printing technologies. In addition, the tunability of our methodology offers a route for the discovery of novel disordered hyperuniform two-phase materials.

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  • Received 31 January 2019
  • Revised 26 April 2019

DOI:https://doi.org/10.1103/PhysRevE.99.052141

©2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Statistical Physics & Thermodynamics

Authors & Affiliations

Jaeuk Kim1 and Salvatore Torquato1,2,3,4,*

  • 1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 2Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
  • 3Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
  • 4Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA

  • *torquato@princeton.edu

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Issue

Vol. 99, Iss. 5 — May 2019

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