Structures of possible phases of achiral polar smectic liquid crystals formed by bow shaped molecules

The stare of order of achiral polar liquid crystals formed by bow shaped molecules is described by two two-dimensional order parameters, (P) over right arrow and <(xi)over right arrow>, giving the order of molecular dipoles and the tilt of the molecules, respectively. The free energy is written as an expansion in terms of both order parameters up to the sixth order and takes into account interactions between nearest neighbouring smectic layers. Three different antiferroelectric structures consistent with experimental observations are the result of the free energy minimization. An experiment to verify the suggested structures is proposed.