Zhang G, Stillinger F H, Torquato S
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
J Chem Phys. 2016 Dec 28;145(24):244109. doi: 10.1063/1.4972862.
Disordered hyperuniform many-particle systems have attracted considerable recent attention, since they behave like crystals in the manner in which they suppress large-scale density fluctuations, and yet also resemble statistically isotropic liquids and glasses with no Bragg peaks. One important class of such systems is the classical ground states of "stealthy potentials." The degree of order of such ground states depends on a tuning parameter χ. Previous studies have shown that these ground-state point configurations can be counterintuitively disordered, infinitely degenerate, and endowed with novel physical properties (e.g., negative thermal expansion behavior). In this paper, we focus on the disordered regime (0 < χ < 1/2) in which there is no long-range order and control the degree of short-range order. We map these stealthy disordered hyperuniform point configurations to two-phase media by circumscribing each point with a possibly overlapping sphere of a common radius a: the "particle" and "void" phases are taken to be the space interior and exterior to the spheres, respectively. The hyperuniformity of such two-phase media depends on the sphere sizes: While it was previously analytically proven that the resulting two-phase media maintain hyperuniformity if spheres do not overlap, here we show numerically that they lose hyperuniformity whenever the spheres overlap. We study certain transport properties of these systems, including the effective diffusion coefficient of point particles diffusing in the void phase as well as static and time-dependent characteristics associated with diffusion-controlled reactions. Besides these effective transport properties, we also investigate several related structural properties, including pore-size functions, quantizer error, an order metric, and percolation thresholds. We show that these transport, geometrical, and topological properties of our two-phase media derived from decorated stealthy ground states are distinctly different from those of equilibrium hard-sphere systems and spatially uncorrelated overlapping spheres. As the extent of short-range order increases, stealthy disordered two-phase media can attain nearly maximal effective diffusion coefficients over a broad range of volume fractions while also maintaining isotropy, and therefore may have practical applications in situations where ease of transport is desirable. We also show that the percolation threshold and the order metric are positively correlated with each other, while both of them are negatively correlated with the quantizer error. In the highly disordered regime (χ → 0), stealthy point-particle configurations are weakly perturbed ideal gases. Nevertheless, reactants of diffusion-controlled reactions decay much faster in our two-phase media than in equilibrium hard-sphere systems of similar degrees of order, and hence indicate that the formation of large holes is strongly suppressed in the former systems.
无序超均匀多粒子系统最近引起了相当大的关注，因为它们在抑制大规模密度涨落的方式上表现得像晶体，但同时又类似于没有布拉格峰的统计各向同性液体和玻璃。这类系统的一个重要类别是“隐身势”的经典基态。这种基态的有序程度取决于一个调谐参数χ。先前的研究表明，这些基态点构型可能会违反直觉地无序、具有无限简并性，并具有新颖的物理性质（例如负热膨胀行为）。在本文中，我们关注无序区域（0 < χ < 1/2），其中不存在长程序，并控制短程序的程度。我们通过用半径为a的可能重叠的球体包围每个点，将这些隐身无序超均匀点构型映射到两相介质：“粒子”相和“空穴”相分别被视为球体内部和外部的空间。这种两相介质的超均匀性取决于球体大小：虽然先前已通过解析证明，如果球体不重叠，所得的两相介质将保持超均匀性，但我们在此通过数值表明，只要球体重叠，它们就会失去超均匀性。我们研究了这些系统的某些传输性质，包括点粒子在空穴相中扩散的有效扩散系数以及与扩散控制反应相关的静态和时间相关特性。除了这些有效的传输性质外，我们还研究了几个相关的结构性质，包括孔径函数、量化误差、有序度量和渗流阈值。我们表明，我们从装饰隐身基态导出的两相介质的这些传输、几何和拓扑性质与平衡硬球系统和空间不相关的重叠球体的性质明显不同。随着短程序程度的增加，隐身无序两相介质在很宽的体积分数范围内可以达到几乎最大的有效扩散系数，同时还保持各向同性，因此在需要易于传输的情况下可能具有实际应用。我们还表明，渗流阈值和有序度量彼此正相关，而它们两者都与量化误差负相关。在高度无序区域（χ → 0），隐身点粒子构型是受到弱扰动的理想气体。然而，扩散控制反应的反应物在我们的两相介质中的衰减比在具有相似有序程度的平衡硬球系统中快得多，因此表明在前一种系统中，大孔洞的形成受到强烈抑制。
