Dipolar and Quadrupolar Ordering in Ferroelectric Liquid Crystals

(Received 22 September 1994, revised 27 February 1995, accepted 14 April 1995)

Abstract
The influence of molecular biaxiality on the ferroelectric properties of smectics C ^* is considered in detail using both phenomenological and molecular-statistical approaches. We present the generalized Landau-de Gennes theory of the ferroelectric C ^* smectics in which the free energy is expressed in terms of the spontaneous polarization, the tilt and the biaxial order parameter, which characterizes the quadrupolar ordering of the molecular short axes. From the microscopic point of view the quadrupolar ordering corresponds to the biaxial ordering of flat molecular cores in the smectic C phase. The interaction between the dipolar and quadrupolar order parameters and the tilt results in the additional temperature dependence of the spontaneous polarization, static dielectric constant and the helical pitch in the broad vicinity of the smectic A-smectic C transition point. The general density-functional theory of the ferroelectric ordering in the smectic C ^* phase is also developed taking into account both polar and nonpolar ordering of the short molecular axes. The theory enables one to obtain simple equations for the spontaneous polarization and the biaxial order parameter. These results are used to explain the strong temperature variation of the ratio of the spontaneous polarization and the tilt angle, which has been observed in some ferroelectric liquid crystals. It is also shown that the absolute value and the sign of the spontaneous polarization must be very sensitive to the orientation of the transverse electric and steric dipoles with respect to the flat molecular core.