通过对经典向列相液晶自由能密度表达式的深入分析, 添加了一项代表液晶缺陷自由能的表面项. 利用$\phi $映射方法和拓扑流理论研究了集中在缺陷处的自由能密度的 表达式. 结果显示, 缺陷自身的自由能密度是以$\frac{1}{2}k\pi $为单位拓扑量子化的, 且拓扑量子数由Hopf指数和Brouwer度决定. 进一步给出了一些不同向错强度下缺陷附近的液晶分子的分布构形.

Through the investigation to the classical expressions of free energy density of nematic liquid crystal, a surface term was added to represent the free energy of defects in liquid crystals. By means of $\phi $-mapping method and topological current theory, the new expression of free energy density which was concentrated on the defects was studied. It is shown that the free energy density concentrated on the defects is topologically quantized in the unit of $\frac{1}{2}k\pi $, and the topological quantum numbers are determined by Hopf index and Brouwer degree. The configurations of molecules of liquid crystal around the different disclination strengths of defects are also given in this paper.