Linear terms in the spatial derivatives of the director in the elastic energy density for nematic liquid crystals

We show that for materials having the nematic symmetry the spontaneous splay and the splay-bend elastic constants can be considered to be identically zero, The analysis is performed by assuming that in the bulk, the ground state of the nematic phase is the undistorted one, In this framework it is possible to build an elastic theory for nematic materials without the spontaneous splay and the splay-bend elastic constants. Our results follow from the hypothesis that in the bulk the energy density of a uniform nematic is independent of the average molecular orientation. Close to a surface, where the free energy density is expected to depend also on the orientation of the nematic director, we show that it is possible to define "effective" spontaneous splay and splay-bend elastic constants due to the reduced symmetry of the nematic liquid crystal in the surface layer and to the possible presence of "surface fields". Our analysis agrees with the one recently presented by Yokoyama. (C) 1998 Published by Elsevier Science B.V.