Nematic Order in Spherical Geometries
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Nematic Liquid crystals (NLC) are rod like molecules that in the absence of external influences arrange themselves parallel to each other and hence tend to point in a given direction. The average orientation of these molecules is given by the director n, which is essentially a bi-directional vector which quantifies the orientation of the molecules in a given region of the sample. When NLCs are confined to a curved surface, the geometrical constraints imposed by the surface causes a distortion in the molecular orientation. In certain regions, the molecular orientation is such that the director cannot be defined. Such regions are called topological defects. Theory had predicted that the ground state of NLCs confined to a spherical surface has four defects located at the vertices of a tetrahedron. The tetrahedral defect structure is of great interest in material science because defects in NLCs are regions that can be functionalized to serve as bonds that could pave the way for making macroatoms with tetrahedral bonding properties similar to sp3 hybridized atoms like Carbon. By using ultrathin shells of NLCs, we show that the tetrahedral structure is indeed what we observe experimentally, verifying the theory for the first time. However, this tetrahedral structure coexists with other structures consisting of two or three defects. We also study these defect structures.