Order electricity and the nematic, smectic A, smetic C phase transitions

Smectic liquid crystal are quadrupolar oriented systems, with a spatial modulation across layers. This modulation creates an order electric antiferroelectric polarization. The associated dielectric depolarization energy, originating from long range forces, creates a new non analytic term, which must be added to the usual Landau-de Gennes expansion. This new term can physically explain the molecular tilt inside the layers and the smectic A-Nematic reentrance. The tilt appears as an intrinsic property of well ordered quadrupolar layered systems.