论文标题
具有n折旋转对称性二维的颗粒的相位场晶体模型
Phase Field Crystal model for particles with n-fold rotational symmetry in two dimensions
论文作者
论文摘要
我们引入了一个相位场晶体（PFC）模型，用于在二维中具有N折旋转对称性的颗粒。我们的方法是基于一个自由能函数，该函数取决于降低的一颗粒子密度，方向的强度以及方向的方向，其中所有这些顺序参数都取决于位置。该功能的构建是使得对具有轴向对称性的颗粒（即，n = 2）H.Löwen引入的液晶模型的PFC模型[J.物理学：冷凝。 Matter 22，364105（2010）]已回收。我们讨论了功能的稳定性，并以$ 1 \ leq n \ leq 6 $进行探索阶段。除了各向同性，列，条纹和三角形顺序外，我们还观察到具有正方形，菱形，蜂窝，甚至准晶对称性的簇晶体。颗粒的n倍对称性对应于可以实现具有对称布置斑块的胶体的对称。我们解释了我们的模型中如何描述了这两者，包括排斥和有吸引力的补丁。
We introduce a Phase Field Crystal (PFC) model for particles with n-fold rotational symmetry in two dimensions. Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the orientation, and the direction of the orientation, where all these order parameters depend on the position. The functional is constructed such that for particles with axial symmetry (i. e. n = 2) the PFC model for liquid crystals as introduced by H. Löwen [J. Phys.: Condens. Matter 22, 364105 (2010)] is recovered. We discuss the stability of the functional and explore phases that occur for $1 \leq n \leq 6$. In addition to isotropic, nematic, stripe, and triangular order, we also observe cluster crystals with square, rhombic, honeycomb, and even quasicrystalline symmetry. The n-fold symmetry of the particles corresponds to the one that can be realized for colloids with symmetrically arranged patches. We explain how both, repulsive as well as attractive patches, are described in our model.
