Thin pyramidal cones in nematic liquid crystals.

The present study investigates the arrangement of hollow pyramidal cone shells and their interactions with degenerate planar anchoring on the inner and outer surfaces of particles within the nematic host. The shell thickness is in order of the nematic coherence length. The numerical behavior of colloids is determined by minimizing the Landau-de Gennes free energy in the presence of the Fournier surface energy and using the finite element method.

Conically degenerate anchoring effect in planar nematic-liquid-crystal shells.

We study the defect texture in symmetric and asymmetric states of a nematic-liquid-crystal shell with conic and planar degenerate surface anchorings on the inner and outer spherical boundaries, respectively. To achieve the equilibrium nematic orientation, we numerically minimize the Landau-de Gennes free energy by employing surface potentials on the shell walls. The symmetric nematic shells energetically have stable configurations independent of thickness.

Modifying Nobili-Durand surface energy for conically degenerate anchorings at the interface of liquid crystal colloids.

We propose a surface energy for conically degenerate anchorings of uniaxial liquid crystal mesogens by modifying tensorial Nobili-Durand surface energy that is usually employed for fixed anchoring orientations with preferred polar angles. By minimizing Landau-de Gennes free energy and the proposed surface energy, we obtain the equilibrium director configuration around a spherical colloid in the uniform nematic liquid crystal. Our calculations show that the proposed surface energy can cause boojum or/and Saturn-ring defect textures depending on the equilibrium conic angle.

Confined nematic liquid crystal between two spherical boundaries with planar anchoring.

Nematic shells of liquid crystals have been provided in microscales. Defect structures in the shells are very essential in the electro-optical applications of such colloidal objects. We have numerically minimized the free energy of symmetric and asymmetric spherical shells of the nematic liquid crystal.