  The statistical theory of the dipole flexoelectric (FE) polarization in
liquid crystals is used to calculate the temperature dependence of order
parameters, the elastic constants and the FE coefficients. Two systems with
polar wedge-shaped and banana-shaped molecules are investigated. In both cases
the FE coefficients are proportional to the dipole moment component parallel to
the molecule symmetry axis. The origin of the FE effect and microscopic
pictures of the distorted phases are discussed.
