Temperature Dependence of Topological Defect in the Twist-Bend Nematic Liquid Crystal Droplets Dispersed in Isotropic Fluid

We investigate the temperature dependence of topological defect in the liquid crystal droplets exhibiting nematic ($\mbox{N})$ and underlying twist-bend nematic ($\mbox{N}_{\mbox{tb}} )$ phases with a use of polarizing optical microscopy. In this study, we adopt two surface anchoring boundary conditions: 1) tangential (director $\mathbf{\hat{{n}}}$ is parallel to the droplet's surface) and 2) homeotropic ($\mathbf{\hat{{n}}}$ is perpendicular to the droplet's surface). In N phase of the studied material, the droplets with a tangential anchoring possess two point defects, boojums, of strength 1 at the poles, while the ones under a homeotropic condition show a point defect, hedgehog, of strength 1 at the center of the droplets. These defects are normal topological features in the nematic phase. As the temperature $T$ approaches the $\mbox{N}\;\mbox{-}\,\mbox{N}_{\mbox{tb}} $ transition temperature ($T_{\mbox{N-Ntb}} )$, however, the hedgehog in the droplets with a homeotropic anchoring splits into two point defects. As $T$ is lowered further, the split defects move toward the poles of the droplet and are eventually located at poles in the $\mbox{N}_{\mbox{tb}} $ phase. We ascribe the transition to the significant drop of the bend elastic constant $K_{3} $ near $T_{\mbox{N-Ntb}} $. Further experiments are in progress to verify how the intriguing features of the elastic constant in the $\mbox{N}_{\mbox{tb}} $ phase affect the director configuration and topological behavior in the droplets.