On the validity of the elastic model for the nematic surface anchoring energy

The intrinsic uniform and non-uniform contributions to the anisotropic part of the surface energy are considered. Our analysis shows that the uniform part can be separated into an intrinsic and an extrinsic term. The first one is due to the nematic-nematic interaction only, whereas the second one is due to the nematic-substrate interaction. They are found to be of the same order of magnitude (approximate to 1 erg cm(2)). The non-uniform part takes its origin from the spatial variation of the elastic constants. By means of a semi-microscopic model it is shown that, in the framework of perfect nematic order, the extrapolation length of the elastic origin is microscopic. On the contrary, if the spatial variation of the scalar order parameter is taken into account, simple calculations indicate that the extrapolation length is of the order of the coherence length in the nematic phase.