ELASTIC-CONSTANTS IN THE INTERFACIAL LAYER AT THE NEMATIC-LIQUID-CRYSTAL VAPOR INTERFACE

Close to the interface between a nematic liquid crystal (NLC) and anot her medium, the elastic constants become functions of distance z from the interface and of angle theta between the director n and the unit v ector k orthogonal to the interface. Furthermore, due to the breaking of the translation symmetry at the interface, a lot of new subsurface elastic contributions can appear. In a previous paper we investigated these subsurface anomalies by using a simple molecular model based on induced-dipole-induced-dipole interactions and by making numerical cal culations in the special case of a planar director distortion. In this way, only the numerical values of some effective subsurface elastic c onstants that characterise planar director distortions could be obtain ed. In this paper we make a more complete analytical calculation of al l the subsurface elastic constants by using a microscopic model and a more general theoretical procedure. The microscopic interaction energy is written in a general form that allows us to investigate different kinds of intermolecular interactions (induced dipole-induced dipole, q uadrupole-quadrupole and so on). Both the x-dependence and the theta-d ependence of the subsurface elastic constants are obtained in a closed analytical form. In the special case of induced-dipole-induced-dipole interactions and for planar director distortions, our analytical resu lts are shown to agree with the previous numerical results. The import ant macroscopic effect of these elastic subsurface anomalies is discus sed.