On the origin of the ferroelectric ordering in nematic liquid crystals and the electrostatic properties of ferroelectric nematic materials

Possible molecular origin of ferroelectricity in the nematic phase is discussed in detail considering a number of models based on direct dipole-dipole interaction and electrostatic interaction between surface charge densities. A more model which combines dipole-dipole interaction and short-range orientational-translational correlations is also considered. In particular we derive a contribution to the total free energy of the long-range tail of the dipole-dipole interaction potential and show that this contribution depends on the sample shape and on the boundary conditions. As a result this shape-dependent contribution may strongly effect the transition into the ferroelectric phase depending on the actual boundary conditions maintained experimentally. We also consider two conjugated thermodynamic potentials which depend on the electric field in the medium and on the displacement field, respectively. It is shown that the actual polarization corresponds to the minimum of one of these potentials depending on the boundary conditions which may have significant experimental consequences. In the framework of the general Landau de Gennes theory, which employs both potentials, the ferroelectric properties of different nematic cells are considered including the ones with fixed applied voltage and free cells with disconnected electrodes.