On the elastic properties of ferroelectric Sc∗ liquid crystals

On the basis of the symmetry consideration of the Sc∗ phase, a generalized elastic free energy of ferroelectric Sc∗ liquid crystals is presented to account for the layer compression or dilatation and the layer distortion as well as c director deformation. The present elastic free energy is expressed in terms of three vectors, i.e. the c director and the wave vector and the spontaneous polarization vector. According to the present Sc∗ model with C 2 symmetry, it is shown that there may exist 17 non-chiral, 4 chiral terms and 14 flexoelectric terms in the Sc∗ phase. A few practical applications are also presented to elucidate some interesting elastic properties of Sc∗ (or Sc) in simplifed geometries.