ABSTRACT
In this chapter, we discuss the role of the quadrupolar interaction in nematic liquid crystal samples in the shape of a slab, limiting the study to planar deformations. We show that this interaction gives rise to a bulk energy density that, in the elastic approximation, depends linearly on the second spatial derivative and quadratically on the first spatial derivative of the nematic orientation. This bulk energy density can be separated in a surface-like term, which gives rise only to a surface contribution, plus a term having the usual form. Both terms depend on the first derivative of the tilt angle and are proportional to the square of the electrical quadrupolar density. The bulk term quadratic in the first derivative of the tilt angle renormalizes the usual elastic energy density connected to the short range forces. The surface-like term is proportional to the first derivative of the tilt angle. It recalls the splay-bend elastic term, although the tilt angle dependence is more complicated. The energy density in the surface layers, where the quadrupolar interaction is incomplete, is also evaluated. The solution of the variational problem by means of a simple version of the density functional theory is presented.
