Flexoelectric polarization in the biaxial nematic phase

The dipole flexoelectric (FE) polarization in liquid crystals is derived in the thermodynamic limit at small distortions and small density. General microscopic expressions for the FE coefficients are obtained in the case of the uniaxial and biaxial nematic phases composed of C_2v molecules. The expressions involve the one-particle distribution function and the potential energy of two-body short-range interactions. In the case of the biaxial nematic phase, six basic deformations produce FE polarization but there are only five independent FE coefficients.