NONLOCAL DESCRIPTION OF NEMATIC LIQUID-CRYSTALS

A non-local description of nematic liquid crystals is presented. By co nsidering a generic two body interaction, the total energy of a nemati c sample is formally evaluated. It is given by a generalized non-local functional. The minimization of the total energy shows that the actua l nematic tilt angle profile, characterizing the nematic director, is a solution of an integral equation that in the simplest case is of the Freedholm type. This new equation takes the place of the well known E uler-Lagrange equation used in the elastic theory of nematic liquid cr ystals. The existence of sub-surface deformations localized close to t he limiting surfaces is studied by means of this integral equation. Th e analysis has been performed for cases of strong and weak anchoring, with and without external fields. The sources of the subsurface deform ations are discussed in the framework of the usual Frank elastic theor y.