Nonlinear Phenomena in Complex Systems, 2016, Vol.19, No.1, pp.95-101

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2016, Vol.19, No.1, pp.95-101

Stable States of Ferroelectric Smectic C^∗ Liquid Crystal Confined between Patterned Surfaces
Aleksey A. Kudreyko, Nail G. Migranov and Dana N. Migranova

In this study we consider equilibrium states in a monolayered sample of ferroelectric smectic C^∗ confined between two differently patterned substrates with strong anchoring under the applied electric field. By using the continuum theory for a "bookshelf" aligned sample of ferroelectric liquid crystal, we obtain elliptic sine-Gordon equation. It is shown that due to the patterned structure of the substrates, competing boundary conditions in the thin film generate a specific alignment of liquid crystals, which can be controlled by the electric field. This theoretical finding is described as a system with harmonically coupled atoms with an external potential within the framework of the Frenkel-Kontorova model.

Key words: surface-stabilized ferroelectric liquid crystal, thin films, elliptic sine-Gordon equation, Frenkel-Kontorova model

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