Order parameter spatial variation and anchoring energy for nematic liquid crystals

A spatial variation of the nematic scalar order parameter leads to a surface anchoring energy renormalization. This renormalization is a consequence of torque conservation and of the ‘‘macroscopic’’ definition of the surface orientation. The order change comes from an assumed property of the boundary or from an external curvature constraint inducing surface melting. In both cases, the maximum effect leads to a surface extrapolation length comparable with the nematic-isotropic coherence length. Strong anchoring data should be remeasured and reinterpretated.