Relations between surface profile and free surface energy of smectic C liquid crystals

Using symmetry arguments, order parameter expansions for the free surface energy of chiral and nonchiral smectic C liquid crystals anchored at a solid plate are derived. Surface forces are sensitive to surface profiles obtained by rubbing the plate. The free surface energy can be combined with a Landau expansion for the free energy of the bulk phase. In an equilibrium configuration the sum of the surface and the bulk free energy is a minimum. The theoretical approach is useful to predict stable configurations of the smectic layer planes and the director with respect to boundaries.