Luo Alan M, Wenk Stefan, Ilg Patrick
ETH Zürich, Department of Materials, Polymer Physics, CH-8093 Zürich, Switzerland.
ETH Zürich, Department of Materials, Polymer Physics, CH-8093 Zürich, Switzerland and School of Mathematical and Physical Sciences, University of Reading, Reading RG6 6AX, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):022502. doi: 10.1103/PhysRevE.90.022502. Epub 2014 Aug 18.
We study the orientational ordering on the surface of a sphere using Monte Carlo and Brownian dynamics simulations of rods interacting with an anisotropic potential. We restrict the orientations to the local tangent plane of the spherical surface and fix the position of each rod to be at a discrete point on the spherical surface. On the surface of a sphere, orientational ordering cannot be perfectly nematic due to the inevitable presence of defects. We find that the ground state of four +1/2 point defects is stable across a broad range of temperatures. We investigate the transition from disordered to ordered phase by decreasing the temperature and find a very smooth transition. We use fluctuations of the local directors to estimate the Frank elastic constant on the surface of a sphere and compare it to the planar case. We observe subdiffusive behavior in the mean square displacement of the defect cores and estimate their diffusion constants.
我们使用棒状粒子与各向异性势相互作用的蒙特卡罗模拟和布朗动力学模拟，研究球体表面的取向有序性。我们将取向限制在球面的局部切平面内，并将每根棒状粒子的位置固定在球面上的离散点处。在球体表面，由于不可避免地存在缺陷，取向有序不可能是完美的向列相。我们发现，四个 +1/2 点缺陷的基态在很宽的温度范围内是稳定的。我们通过降低温度来研究从无序相到有序相的转变，发现这是一个非常平滑的转变。我们利用局部指向矢的涨落来估计球体表面的弗兰克弹性常数，并将其与平面情况进行比较。我们观察到缺陷核心的均方位移呈现亚扩散行为，并估计了它们的扩散常数。
