Binary mixtures of charged colloids: a potential route to synthesize disordered hyperuniform materials

Abstract

Disordered hyperuniform materials are a new, exotic class of amorphous matter that exhibits crystal-like behavior, in the sense that volume-fraction fluctuations are suppressed at large length scales, and yet they are isotropic and do not display diffraction Bragg peaks. These materials are endowed with novel photonic, phononic, transport and mechanical properties, which are useful for a wide range of applications. Motivated by the need to fabricate large samples of disordered hyperuniform systems at the nanoscale, we study the small-wavenumber behavior of the spectral density of binary mixtures of charged colloids in suspension. The interaction between the colloids is approximated by a repulsive hard-core Yukawa potential. We find that at dimensionless temperatures below 0.05 and dimensionless inverse screening lengths below 1.0, which are experimentally accessible, the disordered systems become effectively hyperuniform. Moreover, as the temperature and inverse screening length decrease, the level of hyperuniformity increases, as quantified by the "hyperuniformity index". Our results suggest an alternative approach to synthesize large samples of effectively disordered hyperuniform materials at the nanoscale under standard laboratory conditions. In contrast with the usual route to synthesize disordered hyperuniform materials by jamming particles, this approach is free from the burden of applying high pressure to compress the systems.

Methodology to construct large realizations of perfectly hyperuniform disordered packings

“…For these reasons, it is desirable to employ alternative criteria to determine whether a system is effectively hyperuniform. A useful empirical criterion to deem a system to be hyperuniform is that the hyperuniformity metric H is less than 10 −2 or 10 −3 [3,56,61], where H is defined by…”

“…In practice, however, these methods are system-size limited due to computational cost or imperfections. For instance, the collective-coordinate optimization technique [19,20,62,63] and equilibrium plasma [7,8,56] can achieve perfect hyperuniformity, but their long-range interactions lead the computation cost to grow rapidly with system size. Random organization models [11,55] yield disordered hyperuniform packings at critical absorbing states but are limited in producing perfect hyperuniformity because of critical slowing-down phenomena [3,61].…”

Characterization of Void Space, Large-Scale Structure, and Transport Properties of Maximally Random Jammed Packings of Superballs

“…Such classes apply analogously to structure factors that approach the origin with a power-law form [14,70,71]. Moreover, a system is deemed to be "effectively hyperuniform" (i.e., that a system is, for all intents and purposes, hyperuniform) when the hyperuniformity index H, defined as [72],…”

“…where χV (Q peak ) is the largest peak of the spectral density, is less than about 10 −2 [72]. Equation ( 15) is exact in the infinite system limit, but a numerical extrapolation is required for numerical simulations due to finite system sizes.…”

Nearly hyperuniform, nonhyperuniform, and antihyperuniform density fluctuations in two-dimensional transition metal dichalcogenides with defects

“…Recently, in a seminal study, using various theoretical models, Kim and Torquato [29] demonstrated that while thermal excitation and point defects such as vacancies and interstitials destroy hyperuniformity, uncorrelated random displacements preserve hyperuniformity, but could change the class of hyperuniformity. To quantify the degree of hyperuniformity of real systems, the hyperuniformity index [29,[42][43][44]…”