Effect of Electric Fields on the Director Field and Shape of Nematic Tactoids

Tactoids are spindle-shaped droplets of a uniaxial nematic phase suspended in the co-existing isotropic phase. Recent experiments on tactoids of chitin nanocrystals in water show that electrical fields can very strongly elongate tactoids even though the difference between the dielectric properties of the isotropic and nematic phases differ only very subtly. We explain this by extending the Ocean-Frank elastic model of Kaznacheev et al. for bipolar tactoids to partially bipolar tactoids, where the degree of bipolarness of the director field is free to adjust itself to optimize the sum of the elastic, surface, and Coulomb free energies of the drops. By means of a combination of a scaling analysis and a numerical study, we study the elongation and director field of the tactoids as a function of their size and the strength of the electric field, and how these depend on the surface tension and anchoring strength, the various elastic constants, and the electric susceptibility anisotropy. We find that if the director field is bipolar, tactoids cannot elongate more strongly tactoids with a uniform director field unless the director field is somehow fixed in the field-free configuration. Presuming this to be the case, we find reasonable agreement with experimental data.