Surface variations of the density and scalar order parameter and the elastic constants of a uniaxial nematic phase

The elastic constants $K_{24}$ and $K_{13}$ of a spatially restricted nematic phase are found to essentially depend on behavior of the density ρ and orientational order parameter η at the surface. The cancellation of the effective constant $K_{13},$ recently revealed by Faetti and Riccardi [J. Phys. II 5, 1165 (1995)], is obtained as a particular case of a constant η and arbitrary ρ; whereas a spatial-dependent η violates this cancellation and restores a finite $K_{13}$ term.