Crystalline particle packings on constant mean curvature (Delaunay) surfaces.
Crystalline particle packings on constant mean curvature (Delaunay) surfaces.
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恒定平均曲率 (Delaunay) 表面上的结晶颗粒堆积。
DOI：
10.1103/physreve.88.012405
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Zhenwei Yao
中科院分区：
文献类型：
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作者：
E. Bendito;M. Bowick;A. Medina;Zhenwei Yao
研究了在等平均曲率旋转表面上晶体粒子阵列的结构。这种弯曲晶体是通过在液体毛细管桥上建立电荷稳定的胶体阵列来实现的。1841年Delaunay对CMC旋转曲面进行了分类，包括2球面、圆柱体、平均曲率消失的链面（最小曲面），以及丰富但研究较少的不椭球面和节面。在三维欧几里德空间r(3)中测量距离r，我们确定了1000个点状粒子与一对排斥1/r(3)势相互作用的数值候选基态构型。我们通过确定排列在一系列德劳内表面上的粒子的平衡构型来模拟毛细管桥的拉伸，这些德劳内表面是由给定的初始表面（无论是胖圆柱体还是方圆柱体）在恒定体积下增加或减少高度获得的。在这种情况下，拉伸过程需要通过一系列复杂的德劳奈曲面，每个曲面都有不同的几何参数，包括纵横比、平均曲率和最大高斯曲率。此过程中均出现不曲状、链状和结节状。随着毛细管桥在腰部（赤道）变窄和最大（负）高斯曲率增大，基态缺陷母基从边界的位错到内部的位错，再到内部的褶皱和疤痕，然后在内部形成孤立的七倍位错。我们还验证了理论预测，即当表面包含一个积分高斯曲率超过-π/3的测地线盘时，在基态存在孤立偏差。最后，我们探索了给定Delaunay曲面的片集上的最小能量组态，并获得了与拉伸中所见一致的组态和缺陷基元。
We investigate the structure of crystalline particle arrays on constant mean curvature (CMC) surfaces of revolution. Such curved crystals have been realized physically by creating charge-stabilized colloidal arrays on liquid capillary bridges. CMC surfaces of revolution, classified by Delaunay in 1841, include the 2-sphere, the cylinder, the vanishing mean curvature catenoid (a minimal surface), and the richer and less investigated unduloid and nodoid. We determine numerically candidate ground-state configurations for 1000 pointlike particles interacting with a pairwise-repulsive 1/r(3) potential, with distance r measured in three-dimensional Euclidean space R(3). We mimic stretching of capillary bridges by determining the equilibrium configurations of particles arrayed on a sequence of Delaunay surfaces obtained by increasing or decreasing the height at constant volume starting from a given initial surface, either a fat cylinder or a square cylinder. In this case, the stretching process takes one through a complicated sequence of Delaunay surfaces, each with different geometrical parameters, including the aspect ratio, mean curvature, and maximal Gaussian curvature. Unduloids, catenoids, and nodoids all appear in this process. Defect motifs in the ground state evolve from dislocations at the boundary to dislocations in the interior to pleats and scars in the interior and then isolated sevenfold disclinations in the interior as the capillary bridge narrows at the waist (equator) and the maximal (negative) Gaussian curvature grows. We also check theoretical predictions that the isolated disclinations are present in the ground state when the surface contains a geodesic disk with integrated Gaussian curvature exceeding -π/3. Finally, we explore minimal energy configurations on sets of slices of a given Delaunay surface, and we obtain configurations and defect motifs consistent with those seen in stretching.