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Fluctuation-entanglement mechanism for director anchoring at nematic polymer surfaces.

The existence of polymeric entanglements in a polymer nematic liquid crystal modifies the Frank elastic description governing director deformation. We present a calculation of the director fluctuation contribution to polymer nematic surface tension, in which we supplement the usual Frank terms with a damping term due to entanglements. We infer an effective surface anchoring potential, going to zero as n ln n in the limit of low entanglement density n. The anchoring easy axis depends on the relative magnitudes of the Frank constants governing director elasticity. We comment on generalizing the approach to take into account polydomain structure.