ELASTIC ENERGIES AND DIRECTOR FIELDS IN LIQUID CRYSTAL DROPLETS, I. CYLINDRICAL SYMMETRY

Abstract

The nature of point defects in nematic liquid crystals has been studied by placing droplets on a water substrate and viewing these between crossed polarizers. Three configurations are observed. These configurations are accounted for by minimizing the Frank elastic energies with suitable boundary conditions. The second order nonlinear simultaneous partial differential equations that describe systems with cylindrical symmetry are solved by relaxation methods using computer facilities. The importance of the cancellation of several contributions to the splay (divergence) is emphasized.