Surface-induced nematic order variation: Intrinsic anchoring and subsurface director deformations

The nematic orientation close to a solid substrate is investigated by means of a Landau--de Gennes phenomenological model. We show that a spatial variation of the scalar order parameter induces a subsurface variation of the average molecular orientation and an intrinsic contribution to the anchoring when the splay and bend elastic constants are different from the twist elastic constant. A quasi-splay-bend elastic constant is deduced by comparing the surface term proportional to the first derivative of the tilt angle with the one proposed long ago by Nehring and Saupe [J. Chem. Phys. 54, 337 (1971); 56, 5527 (1972)]. The effective anchoring being a combination of the external contribution originating from the interaction with the substrate and the intrinsic anchoring energy resulting from the spatial variation of the scalar order parameter is analyzed. Matching elastic and magnetic effects on a nematic slab, the corresponding effective extrapolation lengths are estimated.