Department of Chemistry, Department of Physics, Princeton Center for Theoretical Science, 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. 2018 Jul 14;149(2):020901. doi: 10.1063/1.5036657.
Packing problems have been a source of fascination for millennia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals, and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable, and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.
包装问题一直是千百年来人们关注的焦点，对其的研究产生了跨越众多学科的丰富文献。对硬粒子堆积模型的研究为理解物质凝聚相的结构和体性质提供了基本的认识，包括低温状态（例如，分子和胶体液体、晶体和玻璃）、多相多相异质介质、颗粒介质和生物系统。最密集的堆积在纯数学中非常有趣，包括离散几何和数论。本文综述了有关各向同性空间维度中硬粒子堆积的平衡、亚稳和非平衡堆积的相关理论和计算文献。对于被堵塞的堆积，重点将放在“几何结构”方法上，该方法提供了一种强大而统一的手段，通过堵塞类别和“顺序”图来定量地描述单个堆积。它包含了极端堵塞状态，包括最密集的堆积、最大随机堵塞状态和最低密度堵塞结构。还调查了相同球体、具有尺寸分布的球体和非球体颗粒的堆积。本文最后确定了未来研究的挑战和未解决的问题。
