Characterization of Maximally Random Jammed Sphere Packings. III. Transport and Electromagnetic Properties via Correlation Functions

TL;DR

This paper investigates the physical properties of maximally random jammed sphere packings, revealing their potential for designing materials with unique electromagnetic and transport characteristics due to their disordered hyperuniform structure.

Contribution

It introduces analytical bounds and formulas for effective transport and electromagnetic properties of MRJ packings, extending understanding of their physical behavior and applications.

Findings

MRJ packings exhibit disordered hyperuniformity with unique physical properties.

Effective property formulas predict qualitative trends and guide experiments.

Disordered dielectric MRJ spheres form dissipationless, isotropic two-phase media.

Abstract

In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here, we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.