Orientational structures in nematic droplets with conical boundary conditions

Oblate nematic droplets encapsulated in a polymer specifying conical boundary conditions have been considered. Calculations by the extended Frank elastic continuum approach show that a number of various structures can be formed in such droplets under the variation of their size. Polarizing optical microscopy studies of composite film samples confirm the results of calculation and demonstrate the formation of the following orientational structures in the considered system: (i) a radial-bipolar structure with a twisted hedgehog defect and two hyperbolic boojums, (ii) an axial-bipolar structure with a circular disclination and two radial boojums, and (iii) a structure with a hedgehog defect, a hyperbolic boojum, and a radial boojum. Such a diversity of possible topologies of droplets is due to a complex balance between the energies of elasticity of the director field, disclinations, and anchoring with the surface, which is ensured by conical boundary conditions.