Dipole-dipole interactions and the origin of ferroelectric ordering in polar nematics

A molecular origin of the ferroelectric ordering in the nematic phase is considered in detail considering a model based on electrostatic interaction between permanent molecular dipoles modulated by the anisotropic molecular shape. It is shown that a contribution to the total free energy of the long-range tail of the dipole-dipole interaction potential defines the total electrostatic energy of the system which depends on the sample shape and on the boundary conditions. This contribution may strongly affect the transition into the ferroelectric phase. However, the dipole-dipole interaction itself can hardly be responsible for the ferroelectric ordering in nematic liquid crystals for any reasonable values of the molecular dipole. A more promising model which combines dipole-dipole interaction and short-range orientational-translational correlations is also considered.