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A. G. Kalugin, D. V. Pavlov

Author affiliations
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics,
1 Leninskiye Gory, Moscow, 119991, Russia. 
E-mail: kalugin@mech.math.msu.su

Abstract
The problem of equilibrium of a planar oriented plane layer of a nematic liquid crystal is considered. It is shown that nontrivial periodical solutions for the director disturbance exist if divergent (splay-bend) terms in the Frank energy are taken into account. This solution has a wave vector, which is perpendicular to the initial director orientation. The correlations connecting the magnitude of the coefficient for divergent terms with wave number, layer thickness, and other parameters of the media are obtained. This formula and some well-known experimental data are used for Frank splay-bend constant estimation.

Keywords: splay-bend constant, nematic liquid crystals, surface elastic constant