本文根据双轴向列相液晶弹性能公式，利用变分原理, 得到指向矢在空间所满足的微分方程, 对于六种不同的边界易取向轴和外场方向，推导出指向矢Fredericks转变的外场阈值。结果表明此六种情形下的外场阈值与双轴向列相液晶六个简单形变的弹性系数有关。
关键词：双轴向列相液晶, Fredericks转变, 弹性系数
Abstract：Considering a biaxial nematic liquid crystal confined between two parallel plates with strong anchoring boundary conditions. Applying an external field, the directors of biaxial nematics will be align along the easy axes in the boundary respectively at low strength external field. Yet, when the strength of external field increases and exceeds a critical value, the directors near the centre of liquid crystal bulk will rotate towards the external field. It is called the Fredericks transition where the director vary only along the vertical axis and remain unchanged in the surface plane, so it is also called uniform distortion .
According to the expression of Saupe’s elastic energy for biaxial nematics, and by using variation principle, differential equations of directors are obtained. For six types of orientations of easy axes and external field, the corresponding threshold fields of Fredericks transitions are obtained. The results show that these six threshold fields depend on six elastic constants for simple distortions in biaxial nematics.
Keywords: biaxial nematic liquid crystal, the Fredericks transition, elastic constants...