O. V. Manyuhina, M. Ben Amar
We examine theoretically the role of anchoring effects in nematic films of submicron thickness spread on liquid substrates. The competing boundary conditions and the saddle-splay elasticity may cause the periodic undulations of the director, characterising the stripe state. We conjecture four different base states for the nematic director depending on the thickness of the film and the anchoring strengths: i) planar, ii) hybrid aligned nematic (HAN), iii) twisted and iv) twist-bended. The planar and HAN base states become linearly unstable with respect to the perturbation of the wavevector in the direction orthogonal to the initial state. However, the wavelength at the bifurcation is finite only in presence of nonzero azimuthal anchoring at either of the two interfaces. The presence of azimuthal anchoring at both interfaces results in the twisted base state and the possibility of periodic distortions in mutually orthogonal directions. Our theoretical findings give insight into recent experimental observations of cyanobiphenyl liquid crystals deposited on water and glycerol [A. M. Cazabat et al., Adv. Colloid Interface Sci. 168, 29 (2011)].
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http://arxiv.org/abs/1206.4859
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