THE PHENOMENOLOGICAL FUNCTIONS THAT CHARACTERIZE THE SURFACE FREE-ENERGY DENSITY OF NEMATIC LIQUID-CRYSTALS - A MICROSCOPIC ANALYSIS

In recent paper, Faetti proposed a new phenomenological expression for the surface free energy density F-s of a nematic Liquid crystal in co ntact with an isotropic substrate. F-s depends on director n, on the u nit vector k orthogonal to the interface and on their gradients at the interface. Five different terms appear in the expression of F-s. The first term is the standard anchoring energy contribution, the second a nd third terms are elastic contributions that depend on the surface ta ngential director gradients, the fourth and fifth terms are new geomet rical contributions that account for the effect of a local curvature o f the interfaces. The expression of the surface free energy density is characterized by five phenomenological functions W(n(k)), K-13(n(k)) , K-24(n(k)), A(1)(n(k)) and A(2)(n(k)) where n(k) is the scalar prod uct n . k. In this paper we give the first microscopic calculation of these new surface functions by using a simplified microscopic model of intermolecular interactions. Surface functions A(1)(n(k)), A(2)(n(k)) , and K-24(n(k)) are found to be of the same order of magnitude of th e Frank bulk elastic constants, whilst K-13(n(k)) = 0. The geometric surface functions A(1)(n(k)) and Az(nk) satisfy the simple relation A( 1)(n(k)) = -n(k)(2) A(2)(n(k)). Both the results K-13(n(k)) = 0 and A (1)(n(k)) = n(k)(2) A(2)(n(k)) are shown to be a direct consequence of the invariance with respect to the transform n --> -n of the interact ion energy between molecules.