Three-dimensional construction of hyperuniform, nonhyperuniform, and antihyperuniform disordered heterogeneous materials and their transport properties via spectral density functions

Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. The spectral density function χ V(k), which can be obtained experimentally from scattering data, enables accurate determination of various transport and wave propagation characteristics, including the time-dependent diffusion spreadability S(t) and effective dynamic dielectric constant ϵe for electromagnetic wave propagation. Moreover, χ V(k) determines rigorous upper bounds on the fluid permeability K. Given the importance of χ V(k), we present here an efficient Fourier-space based computational framework to construct three-dimensional (3D) statistically isotropic two-phase heterogeneous materials corresponding to targeted spectral density functions. In particular, we employ a variety of analytical functional forms for χ V(k) that satisfy all known necessary conditions to construct disordered stealthy hyperuniform, standard hyperuniform, nonhyperuniform, and antihyperuniform two-phase heterogeneous material systems at varying phase volume fractions. We show that by tuning the correlations in the system across length scales via the targeted functions, one can generate a rich spectrum of distinct structures within each of the above classes of materials. Importantly, we present the first realization of antihyperuniform two-phase heterogeneous materials in 3D, which are characterized by autocovariance function χV(r) with a power-law tail, resulting in microstructures that contain clusters of dramatically different sizes and morphologies. We also determine the diffusion spreadability S(t) and estimate the fluid permeability K associated with all of the constructed materials directly from the corresponding spectral densities. Although it is well established that the long-time asymptotic scaling behavior of S(t) only depends on the functional form of χ V(k), with the stealthy hyperuniform and antihyperuniform media, respectively, achieving the most and least efficient transport, we find that varying the length-scale parameter within each class of χ V(k) functions can also lead to orders of magnitude variation of S(t) at intermediate and long time scales. Moreover, we find that increasing the solid volume fraction φ1 and correlation length a in the constructed media generally leads to a decrease in the dimensionless fluid permeability K/a2, while the antihyperuniform media possess the largest K/a2 among the four classes of materials with the same φ1 and a. These results indicate the feasibility of employing parameterized spectral densities for designing composites with targeted transport properties.