Molecular statistical theory for inhomogeneous nematic liquid crystals with boundary conditions

Abstract

We start with a multipole expansion of the London‐van der Waals dispersion forces between elongated cylindrically symmetric molecules as a model for the two‐particle interaction. This potential is rotationally invariant and anisotropic due to both the orientation and the position of two molecules. In the next step we define a self‐consistent description of orientational ordering. If a nematogenic substance is bounded by two parallel plates, a preferred direction of equilibrium orientation is induced depending on the alignment of the molecules next to the surface of the plates. The alignment near the plates will effect the degree of order throughout the whole sample thickness via the two‐particle interaction. For the two cases of parallel and perpendicular alignment to the walls, we describe the resulting inhomogeneous phase by locally‐variable‐order parameters and investigate the temperature dependence for several sample thicknesses. It is found that the ordering induced by alignment parallel to the walls is much weaker than in the case of alignment perpendicular to the walls. This behavior corresponds to the ratio of transverse to longitudinal correlation length in nematic liquid crystals. The ratio of the correlation lengths derived from the present interaction model is found to be in excellent agreement with the ratio of the elastic constants: k₃₃/(1/2)(k₁₁+k₂₂) determined from experiments.