Maher Charles Emmett, Torquato Salvatore
Princeton University, Department of Chemistry, New Jersey 08544, USA.
Princeton University, Princeton University, Princeton University, Princeton University, Department of Chemistry, Princeton, New Jersey 08544, USA; Department of Physics, Princeton, New Jersey 08544, USA; Princeton Institute for the Science and Technology of Materials, Princeton, New Jersey 08544, USA; and Program in Applied and Computational Mathematics, Princeton, New Jersey 08544, USA.
Phys Rev E. 2024 Dec;110(6-1):064605. doi: 10.1103/PhysRevE.110.064605.
Jammed (mechanically rigid) polydisperse circular-disk packings in two dimensions (2D) are popular models for structural glass formers. Maximally random jammed (MRJ) states, which are the most disordered packings subject to strict jamming, have been shown to be hyperuniform. The characterization of the hyperuniformity of MRJ circular-disk packings has covered only a very small part of the possible parameter space for the disk-size distributions. Hyperuniform heterogeneous media are those that anomalously suppress large-scale volume-fraction fluctuations compared to those in typical disordered systems, i.e., their spectral densities χ[over ̃]{{V}}(k) tend to zero as the wavenumber k≡|k| tends to zero and are often described by the power-law χ[over ̃]{{V}}(k)∼k^{α} as k→0 where α is the so-called hyperuniformity scaling exponent. In this work, we generate and characterize the structure of strictly jammed binary circular-disk packings with a size ratio β=D_{L}/D_{S}, where D_{L} and D_{S} are the large and small disk diameters, respectively, and the molar ratio of the two disk sizes is 1:1. In particular, by characterizing the rattler fraction ϕ_{R}, the fraction of configurations in an ensemble with fixed β that are isostatic, and the n-fold orientational order metrics ψ_{n} of ensembles of packings with a wide range of size ratios β, we show that size ratios 1.2≲β≲2.0 produce maximally random jammed (MRJ)-like states, which we show are the most disordered strictly jammed packings according to several criteria. Using the large-R scaling of the volume fraction variance σ_{{V}}^{2}(R) associated with a spherical sampling window of radius R, we extract the hyperuniformity scaling exponent α from these packings, and find the function α(β) is maximized at β=1.4 (with α=0.450±0.002) within the range 1.2≤β≤2.0. Just outside of this range of β values, α(β) begins to decrease more quickly, and far outside of this range the packings are nonhyperuniform, i.e., α=0. Moreover, we compute the spectral density χ[over ̃]{_{V}}(k) and use it to characterize the structure of the binary circular-disk packings across length scales and then use it to determine the time-dependent diffusion spreadability of these MRJ-like packings. The results from this work can be used to inform the experimental design of disordered hyperuniform thin-film materials with tunable degrees of orientational and translational disorder.
二维（2D）中紧密堆积（机械刚性）的多分散圆盘堆积是结构玻璃形成体的常用模型。最大随机紧密堆积（MRJ）状态是在严格紧密堆积条件下最无序的堆积，已被证明具有超均匀性。MRJ圆盘堆积的超均匀性特征仅涵盖了圆盘尺寸分布可能参数空间的很小一部分。超均匀非均匀介质是指与典型无序系统相比异常抑制大规模体积分数波动的介质，即它们的谱密度χ̃_{V}(k)在波数k≡|k|趋于零时趋于零，并且在k→0时通常由幂律χ̃_{V}(k)∼k^{α}描述，其中α是所谓的超均匀性标度指数。在这项工作中，我们生成并表征了尺寸比β = D_{L}/D_{S}的严格紧密堆积的二元圆盘堆积结构，其中D_{L}和D_{S}分别是大圆盘和小圆盘的直径，且两种圆盘尺寸的摩尔比为1:1。特别地，通过表征摇晃粒子分数ϕ_{R}、固定β的系综中静定构型的分数以及具有广泛尺寸比β的堆积系综的n重取向序度量ψ_{n}，我们表明尺寸比1.2≲β≲2.0会产生类似最大随机紧密堆积（MRJ）的状态，我们证明根据几个标准，这些状态是最无序的严格紧密堆积。使用与半径为R的球形采样窗口相关的体积分数方差σ_{V}^{2}(R)的大R标度，我们从这些堆积中提取超均匀性标度指数α，并发现函数α(β)在1.2≤β≤2.0范围内于β = 1.4时达到最大值（α = 0.450±0.002）。就在这个β值范围之外，α(β)开始更快地下降，并且在这个范围之外很远时，堆积是非超均匀的，即α = 0。此外，我们计算谱密度χ̃_{V}(k)，并用它来表征二元圆盘堆积在不同长度尺度上的结构，然后用它来确定这些类似MRJ堆积的时间相关扩散扩展性。这项工作的结果可用于指导具有可调取向和平移无序度的无序超均匀薄膜材料的实验设计。
