Biaxial potential of surface-stabilized ferroelectric liquid crystals

A biaxial surface potential Φ_{s} of smectic-C^{*} surface-stabilized ferroelectric liquid crystals (SSFLCs) is introduced in this paper to explain the experimentally observed electric-field dependence of polarization P[over ̃]_{cell}(E), in particular the shape of the static hysteresis loops. Our potential consists of three independent parts. The first nonpolar part Φ_{n} describes the deviation of the prime director n (which is the most probable orientation of the long molecular axes) from the easy alignment axis R, which is located in the boundary surface plane. It is introduced in the same manner as the uniaxial Rapini potential. The second part Φ_{p} of the potential is a polar term associated with the presence of the polar axis in a FLC. The third part Φ_{m} relates to the inherent FLC biaxiality, which has not been taken into consideration previously. The Φ_{m} part takes into account the deviations of the secondary director m (which is the most probable orientation of the short molecular axes) from the normal to the boundary surface. The overall surface potential Φ_{s}, which is a sum of Φ_{n},Φ_{p}, and Φ_{m}, allows one to model the conditions when either one, two, or three minima of the SSFLC cell free energy are realized depending on the biaxiality extent. A monodomain or polydomain structure, as well as the bistability or monostability of SSFLC cells, depends on the number of free-energy minima, as confirmed experimentally. In this paper, we analyze the biaxiality impact on the FLC alignment. We also answer the question of whether the bistable or monostable structure can be formed in an SSFLC cell. Our approach is essentially based on a consideration of the biaxial surface potential, while the uniaxial surface potential cannot adequately describe the experimental observations in the FLC.