Microscopic origin of ferroelectricity in chiral smectic C* liquid crystals and ordering of 'ferroelectric fishes' proposed by de Gennes

The qualitative microscopic mechanism of ferroelectric ordering in smectic C* liquid crystals originally proposed by de Gennes and others is analysed in detail using the molecular-statistical approach. The general expression is obtained for the spontaneous polarisation of the smectic C* phase composed of chiral and polar molecules of the C2 symmetry. The polarisation is shown to be determined by molecular chirality, molecular transverse dipole and the non-polar biaxial order parameter which does not vanish in the non-chiral smectic C phase. A particular molecular model is considered in which molecular chirality and molecular biaxiality are determined by the pair of off-centre transverse molecular dipoles. In the context of this model the spontaneous polarisation is evaluated both analytically and numerically.