Cooling a spherical nematic shell

Abstract

Within the framework of Landau-de Gennes theory for nematic liquid crystals, we study the temperature-induced isotropic-nematic phase transition on a spherical shell. Below a critical temperature, a thin layer of nematic coating a microscopic spherical particle exhibits non-uniform textures due to the geometrical frustration. We find the exact value of critical threshold for the temperature and determine exactly the nematic textures at the transition by means of a weakly nonlinear analysis. The critical temperature is affected by the extrinsic curvature of the sphere, and the nematic alignment is consistent with the Poincaré-Hopf index theorem and experimental observations. The stability analysis of the bifurcate textures at the isotropic-nematic transition highlight that only the tetrahedral configuration is stable.

References in corpus (5)

• Two-Dimensional Matter: Order, Curvature and Defects
• Nematic textures in spherical shells
• Topological Defects in Spherical Nematics
• Dynamics of active nematic defects on the surface of a sphere
• Elastic interactions between topological defects in chiral nematic shells

Cited by in corpus (3)

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