New Theoretical Proofs for the Existence of the Three-Dimensional Solution of the K₁₃ Elastic Problem in Nematics

Abstract

The variation of bulk elastic terms of a divergent type in the energy of nematics and cholesterics is performed by direct tensor calculations. The molecular surface field of a completely free uniaxial nematic is obtained. The K ₁₃ elastic contribution is compared to that obtained earlier (Mol. Cryst. Liq. Cryst., 148, 197 (1987)). The kind of the surface molecular field is checked by appropriate calculations and discussed relative to the anchoring of the liquid crystal.

Key Words:

• K₁₃ elastic problem
• 3-D variation