Fréedericksz transitions in supra-μm nematic droplets

Abstract

The stability of uniaxial nematic-liquid-crystalline structures in supra-\ensuremath{\mu}m-size spherical cavities that impose a weak homeotropic anchoring is studied theoretically. The equilibrium equations are obtained with the minimization of the deformation, surface, and field contributions to the free energy and are solved numerically. The dependencies of the solutions on the ratio of elastic constants ${\mathit{K}}_{33}$/${\mathit{K}}_{11}$, ${\mathit{K}}_{24}$/${\mathit{K}}_{11}$, anchoring strength, and external field strength are discussed, and the stability diagrams with lines of structural (Fr\'eedericksz) transitions are constructed. In the region of strong anchoring and large external field strengths, a triple point, where radial, nonsingular axial, and axial structure with the line defect, is predicted. Particular attention is paid to the inversion point corresponding to the critical-field strength above which radial structure is no longer stable. Two possible methods for saddle-splay elastic constant ${\mathit{K}}_{24}$ determination are suggested.