Role of electrostatics in the texture of islands in free standing ferroelectric liquid crystal films

Curved textures of ferroelectric smectic C* liquid crystals produce space charge when they involve divergence of the spontaneous polarization field. Impurity ions can partially screen this space charge, reducing long range interactions to local ones. Through studies of the textures of islands on very thin free-standing smectic films, we see evidence of this effect, in which materials with a large spontaneous polarization have static structures described by a large effective bend elastic constant. To address this issue, we calculated the electrostatic free energy of a free standing film of ferroelectric liquid crystal, showing how the screened coulomb interaction contributes a term to the effective bend elastic constant, in the static long wavelength limit. We report experiments which support the main features of this model.