The Theoretical Study On The Liquid Crystal State Of The Spindle In The Microdroplet

Based on Landau-de Gennes theory,the distribution of liquid crystal(LC)molecules in a kind of spindle-shaped LC droplets(tactoids)was investigated by using relaxation iteration method.The variations of the polar angle and twist angle of LC molecules in spindle structure within different conditions were mainly studied.Numerical process verified the existence of the virtual boojum structure and predicted a novel twisted bipolar structure.Firstly,within partly elastic anisotropy(k22≠k11≈k33,where k11,k22,and k33 are defined as splay,twist and bend elastic constants,respectively),when the volume of spindle system was large enough(the long semi-axis r1=20μm)and the ratio between long semi-axis and the minor semi-axis was small(r1/r2≤1.50,r2 was defined as the length of minor semi-axis),a new twisted bipolar state appeared in the system induced by spontaneous distortion phenomenon.The results show that the twist angle and the polar angle gradually disappeared with the decrease of spindle volume and the virtual boojum configuration occurred during the decreasing process of polar angle.Secondly,when the system was under elastic anisotropy(k11≠k22≠k33),and the volume was decreased to a certain size(r1=14.6μm),a new twisted structure appeared in the system.Compared splay-bend elasticity anisotropy(k11>k33)with splay-bend elasticity isotropy(k11≈k33),results showed that polar angle was easier to bend and to align along the surface.