Molecular-statistical approach to the description of tilted smectic phases

We have investigated the origin of spontaneous polar ordering in smectic liquid crystals in the framework of molecular-statistical approach. The polar order parameter is introduced as p = P/(rho mu), where P is the polarization, mu is the molecular transverse electric dipole and. is the concentration of molecules. We have shown that piezoelectric spontaneous polarization should generally be related to the bent shape of molecules (even for the molecules which are not normally considered as bent-shaped), while both chirality and polarization appear due to the presence of the electric dipole in the direction perpendicular to the plane of molecular bend. The molecular origin of the flexoelectric effect in tilted smectic phases and the influence of the dipole-dipole interaction on the polar order parameter is also studied. The principal result of the paper is elaboration of a self-consistent mean theory for the description of polarization in Sm-C* and Sm-C*(A) phases.