ANCHORING ENERGY FOR NEMATIC LIQUID-CRYSTALS - CONTRIBUTION FROM THE SPATIAL VARIATION OF THE ELASTIC-CONSTANTS

The influence of the spatial variation of the elastic constants of a n ematic liquid crystal on the detectable surface anchoring energy is an alyzed. It is shown that, in the framework of the usual elastic approa ch, the apparent surface free energy connected with the spatial variat ion of the elastic constants is proportional to the difference between the average value of the elastic constant in the surface layer and th e bulk value. The related extrapolation length is estimated to be of t he order of the interaction range of the forces responsible for the ne matic phase. When the spatial variation of the elastic constants is la rge and the usual elastic approach does not work, the same analysis is performed in the framework of the second-order elasticity. In this ca se a nonlocal form for the surface energy is used. By considering simp le situations the equivalent surface anchoring energy is deduced. Our results generalize the conclusions obtained by other researchers for a similar problem.