Interlayer Interactions in Smectic C* Structure

Abstract
Distortion formation mechanism of the director field (the most probable orientation of long molecular axes) of ferroelectric liquid crystals was theoretically investigated. We assumed that director distortions were formed in the perpendicular direction to the layered structure. A reason for appearance of director distortions can be a non-uniform depolarization field in the same direction. Such non-uniformity of the depolarization field can be induced by surfaces. In particular, we represent the director's azimuthal angle of each layer as the sum of the profile director function in the perpendicular direction to the substrates and a certain additive correction term, which depends on the monolayer position. The structure of ferroelectric liquid crystal in smectic C* phase in the direction perpendicular to the substrates was described by using the continuum theory. A discrete approach was applied to describe the director’s behavior in the direction perpendicular to the layered structure. It was shown that when the additive correction term is absent in the model, the free energy is equal to the free energy of the surface-stabilized ferroelectric liquid crystal. Minimization of the free energy with respect to the additive correction term leads to the iterative dependence of the additive correction term for the adjoining layers. The unknown additive correction terms for each smectic layer of the studied layered structure were calculated. The calculation results show that finite length helical structures can occur in such cells. Their appearance can be used to explain the existence of various sub-phases of ferroelectric liquid crystals.

Keywords: ferroelectric liquid crystals, Euler-Lagrange equation, depolarization field, helical structures