Flexoelectric Polarization, Interactions of Longer Range and Multilayer Structures

Flexoelectric interactions in antiferroelectric liquid crystals are a reason for effective interactions to more distant layers in systems where the polarizations in neighboring layers directly interact. In a presence of strong biquadratic coupling which favors uniplanar tilts, the system locks to commensurate structure. The commensurate period of the structure is related to the range of indirect interlayer interactions which are the strongest on average. Systems with strong interaction to nearest neighboring layers favor period one i.e. synclinic tilts for negative sign of the coefficient giving corresponding interaction and period two i.e. anticlinic tilts. As in antiferroelectric liquid crystals the effective interactions to next nearest neighboring layers always favor antiparallel tilts due to the flexoelectric effect, the period four, i.e. two times two, is stabilized when interactions to nearest layers are negligible. As interactions to third nearest neighbors favor either parallel or antiparallel tilts, structures with periods three and six layers are possible. Structures with other periods are highly unlikely to appear in antiferroelectric liquid crystals as stable states.