Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA.
J Phys Chem B. 2011 Dec 8;115(48):13989-93. doi: 10.1021/jp205128g. Epub 2011 Oct 4.
To explore the interaction between topological defects and curvature in materials with orientational order, we perform Monte Carlo studies of the two-dimensional XY model on the surface of curved substrates. Each curved surface is patterned with a random lattice constructed via random sequential absorption, and an XY spin is positioned at each lattice site. Spins lie in the plane locally tangent to the surface and interact with neighbors defined via a distance cutoff. We demonstrate that the relative phase associated with vortices is significant in curved geometries and plays a role in microstructural evolution. We also observe that any nonuniform curvature, e.g., on the surface of a torus, induces spontaneous segregation of positive and negative vortices and promotes the formation of deeply metastable defect microstructures. Though qualitative in nature, these observations provide novel insights into the patterning of topological defects in curved geometries and suggest that the Kosterlitz-Thouless transition may be altered in geometries with nonuniform curvature.
为了探索具有取向序的材料中拓扑缺陷与曲率之间的相互作用，我们在弯曲基底表面上进行了二维 XY 模型的蒙特卡罗研究。每个弯曲表面都通过随机顺序吸收形成了一个随机晶格图案，并且在每个晶格点上都放置了一个 XY 自旋。自旋位于局部切平面上，并且通过距离截止与邻居相互作用。我们证明，与涡旋相关的相对相位在弯曲几何中非常显著，并在微观结构演化中发挥作用。我们还观察到，任何非均匀曲率，例如在环面的表面上，都会引起正和负涡旋的自发分离，并促进深度亚稳态缺陷微结构的形成。尽管这些观察结果具有定性性质，但它们为弯曲几何中的拓扑缺陷模式提供了新的见解，并表明在具有非均匀曲率的几何形状中，Kosterlitz-Thouless 转变可能会发生变化。
