THE STRUCTURE OF THE DISTORTION FREE-ENERGY DENSITY IN NEMATICS - 2ND-ORDER ELASTICITY AND SURFACE TERMS

By means of a phenomenological approach, we demonstrate that the mixed splay-bend elastic constant K 13 in the free energy density of nematic liquid crystals must be considered zero, unless the bulk contributions of the squares of the distortion second-order derivatives are taken into account, together with the squares of the first-order derivatives times the second-order derivatives, and with the fourth powers of the first-order derivatives. Such contributions just reduce to one in the presence of-and close to-a threshold. Furthermore, the saddle-splay K 24-term instead is shown always to play an essential role, as the bulk first-order elasticity, in determining the distortion free energy of nematics with weak anchoring subjected to spatial deformations. Finally, the new surfacelike elastic constants are shown to have a nilpotent character: thus they behave as well as K 24 from the point of view of the variational calculus. © 1990 Società Italiana di Fisica.