“Three-dimensional construction of hyperuniform, nonhyperuniform, and antihyperuniform disordered heterogeneous materials and their transport properties via spectral density functions” Published in Physical Review E

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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 \(\tilde{\chi}_V(k)\), which can be obtained experimentally from scattering data, enables accurate determination of various transport and wave propagation characteristics, including the time-dependent diffusion spreadability \(\mathcal{S}(t)\) and effective dynamic dielectric constant \(\epsilon_e\) for electromagnetic wave propagation. Moreover, \(\tilde{\chi}_V(k)\) determines rigorous upper bounds on the fluid permeability \(k\). Given the importance of \(\tilde{\chi}_V(k)\), 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 \(\tilde{\chi}_V(k)\) 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 \(\chi_V(r)\) with a power-law tail, resulting in microstructures that contain clusters of dramatically different sizes and morphologies. We also determine the diffusion spreadability \(\mathcal{S}(t)\) 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 \(\mathcal{S}(t)\) only depends on the functional form of \(\tilde{\chi}_V(k)\), 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 \(\tilde{\chi}_V(k)\) functions can also lead to orders of magnitude variation of \(\mathcal{S}(t)\) at intermediate and long time scales. Moreover, we find that increasing the solid volume fraction \(\phi_1\) and correlation length \(a\) in the constructed media generally leads to a decrease in the dimensionless fluid permeability \(k/a^2\), while the antihyperuniform media possess the largest \(k/a^2\) among the four classes of materials with the same \(\phi_1\) and \(a\). These results indicate the feasibility of employing parameterized spectral densities for designing composites with targeted transport properties.