Flexoelectricity and piezoelectricity: the reason for the rich variety of phases in antiferroelectric smectic liquid crystals.

The free energy of antiferroelectric smectic liquid crystals which takes into account polar order explicitly is presented. Steric, van der Waals, piezoelectric, and flexoelectric interactions to the nearest layers, and dipolar electrostatic interactions to the nearest and to the next-nearest layers, induce indirect tilt interactions with chiral and achiral properties, which extend to the third- and to the fourth-nearest layers. Although the strength of microscopic interactions changes monotonically with decreasing temperature, the effective interlayer interactions change nonmonotonically and give rise to a nonmonotonic change of the modulation period through various phases. Increased chirality changes the phase sequence.