Numerical investigation of surface distortion and order parameter variation in nematics

We analyse the variations of the director n and of the scalar order parameter S of a nematic liquid crystal in contact with a surface which imposes a sinusoidal boundary distortion. The amplitude A of the surface profile and the corresponding wavelength lambda vary in ranges compatible with the elastic regime Aq < 1, where q = 2 pi/lambda is the surface wave vector. The analysis is carried out by means of a Landau expansion of the free energy where both n and S gradients are taken into account. We obtain an evident coupling between S and n in a nematic surface layer of thickness xi(S) of the order of a few hundred Angstroms. Moreover S can vanish close to the surface if the distortion imposed by the boundary conditions is strong enough. The numerical approach presented in this paper is based on the finite element method.