Three-Dimensional Construction of Hyperuniform, Nonhyperuniform and Antihyperuniform Random Media via Spectral Density Functions and Their Transport Properties

TL;DR

This paper introduces a Fourier-space computational framework to construct and analyze 3D heterogeneous materials with various hyperuniformity properties, revealing how microstructural tuning affects transport properties like diffusion and permeability.

Contribution

The study presents the first realization of 3D antihyperuniform materials and demonstrates how spectral density functions can be used to design materials with targeted transport behaviors.

Findings

Generated diverse 3D hyperuniform and nonhyperuniform structures.

First realization of 3D antihyperuniform materials with power-law autocovariance.

Varying spectral parameters significantly affects diffusion and permeability.

Abstract

Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. We present here an efficient Fourier-space based computational framework and employ a variety of analytical ${\tilde \chi}_{_V}({k})$ functions that satisfy all known necessary conditions to construct 3D disordered stealthy hyperuniform, standard hyperuniform, nonhyperuniform, and antihyperuniform two-phase heterogeneous material systems at varying phase volume fractions. We show that a rich spectrum of distinct structures within each of the above classes of materials can be generated by tuning correlations in the system across length scales. We present the first realization of antihyperuniform two-phase heterogeneous materials in 3D, which are characterized by a power-law autocovariance function $\chi_{_V}(r)$ and contain clusters of dramatically different sizes and morphologies. We also determine the diffusion spreadability ${\cal S}(t)$ and estimate the fluid permeability $k$ associated with all of the constructed materials directly from the corresponding ${\tilde \chi}_{_V}({k})$ functions. We find that varying the length-scale parameter within each class of ${\tilde \chi}_{_V}({k})$ functions can also lead to orders of magnitude variation of ${\cal S}(t)$ at intermediate and long time scales. Moreover, we find that increasing solid volume fraction $\phi_1$ and correlation length $a$ in the constructed media generally leads to a decrease in the dimensionless fluid permeability $k/a^2$. These results indicate the feasibility of employing parameterized ${\tilde \chi}_{_V}({k})$ for designing composites with targeted transport properties.