Stable States of Ferroelectric Smectic C* Liquid Crystal Confined between Patterned Surfaces

Abstract

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.