Critical Reexamination of Berreman's Theory on Surface Anchoring

Abstract

We critically reexamine well-known Berreman's theory [Phys. Rev. Lett. 28, 1683 (1972)] on the anchoring of a nematic liquid crystal due to its elastic distortions induced by a sinusoidally grooved surface. We put emphasis on the effect of azimuthal distortions of the director n and the contribution of saddle-splay surface elasticity characterized by K ₂₄. We give a correct calculation of the anchoring energy and show that Berreman's theory gives a correct result only when K ₁ = K ₂ and K ₂₄ = 0, where K ₁ and K ₂ are the splay and twist elastic constants, respectively. We also present our preliminary numerical attempts to evaluate the anchoring energy of a surface with square patterns and compare the anchoring energy calculated numerically with an analytical one obtained by a direct extension of our theoretical argument on one-dimensional parallel grooves.

Keywords:

• Berreman's theory
• Frank elasticity
• nematic liquid crystal
• numerical calculation
• surface anchoring
• surface elasticity

This work is in part supported by Kakenhi (Grant-in-Aid for Scientific Research) on Priority Area “Soft Matter Physics” from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and the Sasakawa Scientific Research Grant from the Japan Science Society.