The influence of anchoring energy on the prolate shape of tactoids in lyotropic inorganic liquid crystals

A model was constructed to describe the prolate shape of anisotropic regions, tactoids, coexisting with the isotropic phase in lyotropic inorganic liquid crystals. The elastic energy of the tactoid, the surface energy, and the interaction energy between the director field and the boundary of the tactoid were taken into account. Large-sized tactoids were shown to be prolate because of the competition between the elastic energy of the nematic phase of the tactoid and the surface energy. Small-sized tactoids were prolate because of the competition of the surface energy with the anchoring energy between the director and the boundary of the tactoid. The suggested model was applied to experimental data to determine the ratio of the elastic constants K₃/K₁ and the ratio between the anchoring energy W and the surface tension σ depending on the “time of aging” of vanadium pentoxide sols in water.