在向列相液晶中悬浮的球形微粒周围可能存在两种类型的缺陷: 土星环结构和偶极子结构。文章通过计算它们的自由能, 研究了向列相液晶中两种类型缺陷的稳定性。计算结果表明: 当k24＜k 1-12lnR1r()c时, 土星环缺陷是稳定的, 并且和球形微粒的半径无关, 其中R1是液晶分子的长度, k和k24是弹性常数, rc是向错线核心的半径; 当k24＞k 1-12lnR1r()c时, 对于半径较小的球形微粒土星环缺陷比较稳定, 但是对于较大的球形微粒偶极子缺陷比较稳定。进而可得, 通过增加粒子半径、鞍形展曲弹性常数k24或者减小弹性常数k的方法可以实现土星环缺陷向偶极子缺陷的转变。

The stability of Saturn-ring and dipole defects in nematic liquid crystals is studied. Two structures are possible around microspheres suspended in nematic liquid crystals: a Saturn-ring and a dipole, which are investigated by calculating their Frank free energy. As a result, if k24＜k 1-12lnR1r()c, the Saturn-ring is the preferred configuration which does not depend on the particle size, where R1is the length of liquid crystal molecule, kand k24are the elastic constants, and rcis the radius of the disclination line core. If k24＞k 1-12lnR1r()c, for small particles the Saturn-ring defect is more stable, and contrarily for large particles the dipole defect is more stable. The results demonstrate that a transition from the Saturn-ring defect to the dipole defect is induced either by increasing the particle size, the saddle-splay elastic constant k24or by decreasing k.