Polar liquid crystals with multilayer ordering

The structures of multilayer phases of polar smectic liquid crystals have been calculated within the Landau theory of phase transitions with a two-component order parameter. Escape from frustration, which appears in polar smectics because of the competition between interaction between neighboring smectic layers and through one molecular layer, can result in the formation of six-layer antiferroelectric (SmC$^*_{\text{d6/4A}}$) or ferrielectric (SmC$^*_{\text{d6/4F}}$) structures. The SmC$^*_{\text{d6/4A}}$-phase becomes stable owing to the spatial modulation of the absolute value of the order parameter or to the interlayer interaction through two molecular layers. It has been shown that, for the formation of the SmC$^*_{\text{d6/4A}}$- and SmC$^*_{\text{d6/4F}}$-phases with a constant absolute value of the order parameter, the sign of the coefficient of the interlayer interaction through two molecular layers should be alternating. The temperature sequence of polar structures, including the recently discovered SmC$^*_{\text{d4/4F}}$- phase, has been calculated in agreement with the experimental observation.