On the validity of the Rapini-Papoular surface anchoring energy form in nematic liquid crystals

Recent reports have claimed that the simple Rapini-Papoular form for the anchoring energy of nematic liquid crystals is not correct for large distortions. We show that, taking into account the dielectric energy associated with the flexoelectric effect, a reanalysis of the data is consistent with the Rapini-Papoular form. The consideration of flexoelectricity is necessary in most practical cases where the Debye screening length of the material compares to (or is larger than) the surface anchoring energy extrapolation length. Close to the nematic-isotropic transition, another dielectric effect, related to the order-electricity, must also be considered. This effect can justify the functional form proposed in order to interpret the experimental data giving the surface torque vs. tilt angle near the nematic isotropic transition.