Hyperuniformity scaling of maximally random jammed packings of two-dimensional binary disks

Abstract

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 ${\tilde{\chi }}_{{}_V}(\mathbf{k})$ tend to 0 as the wavenumber $k\equiv |\mathbf{k}|$ tends to 0 and are described by the power-law ${\tilde{\chi }}_{{}_V}(\mathbf{k})\sim k^{\alpha }$ as $k\to 0$ where $\alpha$ is the hyperuniformity scaling exponent. In this work, we generate and characterize the structure of strictly jammed binary circular-disk packings with disk-size ratio $\beta$ and a molar ratio of 1:1. By characterizing the rattler fraction, the fraction of isostatic configurations in an ensemble with fixed $\beta$, and the $n$-fold orientational order metrics of ensembles of packings with a wide range of $\beta$, we show that size ratios $1.2\lesssim \beta \lesssim 2.0$ produce MRJ-like states, which we show are the most disordered packings according to several criteria. Using the large-length-scale scaling of the volume fraction variance, we extract $\alpha$ from these packings, and find the function $\alpha (\beta )$ is maximized at $\beta$ = 1.4 (with $\alpha =0.450\pm 0.002$) within the range $1.2\le \beta \le 2.0$, and decreases rapidly outside of this range. The results from this work can inform the experimental design of disordered hyperuniform thin-film materials with tunable degrees of orientational and translational disorder. (abridged)

arXiv comment13 pages, 8 figures

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