Thermal renormalization of the anchoring energy of nematic liquid crystals
The temperature dependence of the anchoring energy of a nematic liquid crystal on thermal fluctuations is studied. We consider the weak anchoring case, where the interaction of a nematic molecule on the surface with the substrate is small with respect to the mean field energy due to the other nematic molecules. The analysis is performed by means of a perturbation method in which the expansion parameter is the surface interaction. The presented model is valid for any value of the scalar order parameter. We show that the renormalization of the anchoring coefficients due to thermal fluctuations is proportional to the generalized scalar order parameters. We show also that, at the lowest order in the scalar order parameter, Landau-like theories agree with our mean field approach. An expression for the thermal renormalization of the anchoring coefficients valid in the low temperature region, where the fluctuations are small, is derived. The agreement between our theoretical predictions and the experimental data obtained by other groups is fairly good over a large temperature range.