Structures and phase transitions in polar smectic liquid crystals

A discrete phenomenological model of antiferroelectric liquid crystals is used to study the structures and phase transitions in bulk samples and thin films. An important ingredient of our investigations is minimization of the free energy with respect to the phase and modulus of the order parameter. A simple version of the free energy, which contains only the nearest-neighbor and the next-nearest-neighbor layer interactions gives a complete phase diagram with all the observed smectic-${\mathrm{C}}^{*}$ $\left(\mathrm{Sm}{C}^{*}\right)$ variant phases. In thin free-standing films, surface ordering may lead to suppression of the bulk $\mathrm{Sm}{C}_{\alpha }^{*}$ helix and to formation of planar structures. Transitions between these structures are accompanied by the $90°$ reorientation of the polarization direction. We also discuss the influence of chirality on subphase structures.