S. Stallinga et G. Vertogen, SOLUTION OF THE OLDANO-BARBERO PARADOX, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(2), 1996, pp. 1692-1700
The appearance of the splay-bend elastic constant K-13 in the theory o
f elasticity of nematic liquid crystals causes a serious problem. This
problem is known as the Oldano-Barbero paradox. The approaches of Bar
bero et al., Faetti, and Pergamenshchik for solving this paradox are a
nalyzed in view of two starting points of the continuum theory. The an
alysis clearly shows the imperfections of their treatments. In order t
o remedy these imperfections a proposal is made to eliminate the parad
ox in accordance with the assumptions of the continuum theory. The sol
ution requires a modification of the surface free energy density, name
ly, the derivatives of the director field normal to the surface must b
e excluded.