The coupling between polarization and tilt in homologous series of ferroelectric liquid crystals

At temperatures well below the vicinity of the transition to the ferroelectric phase the coupling between the spontaneous polarization of the SmC* phase with the director tilt angle exhibits nonlinear behaviour. In a generalized Landau model of ferroelectric liquid crystals this is theoretically described by two terms in the free enthalpy density expansion: (i) the chiral bilinear or piezoelectric coupling term and (ii) the achiral biquadratic coupling term, which describes the transversal quadrupolar ordering. We have investigated two homologous series of ferroelectric liquid crystals of varying phase sequence with respect to piezoelectric and quadrupolar coupling. It is shown that the linear coupling increases with increasing molecular length, while nonlinear contributions decrease. Effects of varying phase sequences N*-TGBA*-SmA*-SmC* versus N*-SmC* are discussed