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

## TL;DR

This paper introduces a tessellation-based method to create large, perfectly hyperuniform disordered dispersions, enabling the design of novel materials with unique physical properties and overcoming previous computational and experimental limitations.

## Contribution

A new simple construction procedure guarantees perfect hyperuniformity in large samples, transforming nonhyperuniform dispersions into hyperuniform ones and establishing their properties analytically and numerically.

## Key findings

- Method guarantees perfect hyperuniformity in large samples.
- Numerical demonstrations in 2D and 3D confirm the approach.
- Establishes hyperuniformity of Hashin-Shtrikman dispersions.

## 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.