Two-dimensional matter: order, curvature and defects

高斯曲率 曲率 拓扑缺陷 软物质 基态 环面 材料科学 凝聚态物理 位错 化学物理 各向异性 粒子(生态学) 物理 几何学 化学 胶体 光学 量子力学 数学 海洋学 地质学 哲学 等离子体 物理化学 语言学
作者
Mark J. Bowick,Luca Giomi
出处
期刊:Advances in Physics [Taylor & Francis]
卷期号:58 (5): 449-563 被引量:326
标识
DOI:10.1080/00018730903043166
摘要

Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology dictates certain broad features of the defect structure of the ground state but curvature-driven energetics controls the detailed structured of ordered phases. Among the surprises are the appearance in the ground state of structures that would normally be thermal excitations and thus prohibited at zero temperature. Examples include excess dislocations in the form of grain boundary scars for spherical crystals above a minimal system size, dislocation unbinding for toroidal hexatics, interstitial fractionalization in spherical crystals and the appearance of well-separated disclinations for toroidal crystals. Much of the analysis leads to universal predictions that do not depend on the details of the microscopic interactions that lead to order in the first place. These predictions are subject to test by the many experimental soft and hard matter systems that lead to curved ordered structures such as colloidal particles self-assembling on droplets of one liquid in a second liquid. The defects themselves may be functionalized to create ligands with directional bonding. Thus nano to meso scale superatoms may be designed with specific valency for use in building supermolecules and novel bulk materials. Parameters such as particle number, geometrical aspect ratios and anisotropy of elastic moduli permit the tuning of the precise architecture of the superatoms and associated supermolecules. Thus the field has tremendous potential from both a fundamental and materials science/supramolecular chemistry viewpoint.
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