Kim Jaeuk, Torquato Salvatore
Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E. 2019 May;99(5-1):052141. doi: 10.1103/PhysRevE.99.052141.
Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space R^{d}. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a "bounded-cell" condition, hard particles of general shape are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size are perfectly hyperuniform in the infinite-sample-size limit, regardless of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R^{2} and R^{3}. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that packings that have identical tessellations can either be nonhyperuniform or hyperuniform by simply tuning local characteristics. It is noteworthy that our computationally designed hyperuniform two-phase systems can easily be fabricated via state-of-the-art methods, such as 2D photolithographic and 3D printing technologies. In addition, the tunability of our methodology offers a route for the discovery of novel disordered hyperuniform two-phase materials.
无序超均匀堆积（或分散体）是一类特殊的非晶态两相材料，具有奇异的物理性质。与普通无序材料相比，此类超均匀系统的特征在于在无限长波长下体积分数涨落的反常抑制。尽管对这种非晶态物质的奇异状态的兴趣与日俱增，但一个主要障碍是由于传统数值和实验方法的实际限制，无法制备出完全超均匀的大尺寸样品。为克服这些限制，我们引入一种通用的理论方法来在(d)维欧几里得空间(\mathbb{R}^{d})中构建完全超均匀堆积。具体而言，从满足“有界单元”条件的由不相交单元对空间进行的初始通用镶嵌开始，将一般形状的硬粒子放置在每个单元内部，使得局部单元粒子堆积分数与全局堆积分数相同。我们证明，在无限样本尺寸极限下，构建的具有尺寸多分散性的堆积无论粒子形状、位置以及每个单元中的粒子数量如何，都是完全超均匀的。我们使用这种理论公式设计一种高效且可调谐的算法来生成此类堆积的极大规模实现。我们采用两种不同的初始镶嵌：Voronoi镶嵌以及球体镶嵌。从Voronoi镶嵌开始，我们表明我们的算法能够在(\mathbb{R}^{2})和(\mathbb{R}^{3})中将极大规模的非超均匀堆积显著地转变为超均匀堆积。在球体镶嵌上实施我们的理论方法，我们确立了经典的Hashin - Shtrikman多尺度涂层球体结构的超均匀性，已知其为具有最优有效传输和弹性性质的两相介质微观结构。我们工作的一个结果是严格证明了具有相同镶嵌的堆积可以通过简单调整局部特征而要么是非超均匀的要么是超均匀的。值得注意的是，我们通过计算设计的超均匀两相系统可以很容易地通过诸如二维光刻和三维打印技术等先进方法制造出来。此外，我们方法的可调谐性为发现新型无序超均匀两相材料提供了一条途径。
