On thek13-Dependent Energy Term in Nematic Liquid Crystals

Abstract

The difficulties arising from the inclusion of term k ₁₃ (div n div n) in the expression of the free energy density are discussed. It is shown that they are related to the fact that in this term second order spatial derivatives n_i,jk of the nematic director n appear. Each term containing a second order derivative would give a distorted configuration of the director field. The global effect is zero in the bulk, owing to the divergence structure of the term, but different from zero near to the boundaries.