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We consider the effective pseudo-Casimir interaction forces mediated by anematic liquid-crystalline film bounded by two planar surfaces, one of whichimposes a random (disordered) distribution of the preferred anchoring axis inthe so-called easy direction. We consider both the case of a quenched as wellas an annealed disorder for the easy direction on the disordered surface andanalyze the resultant fluctuation-induced interaction between the surfaces. Inthe case of quenched disorder, we show that the disorder effects appearadditively in the total interaction and are dominant at intermediateinter-surface separations. Disorder effects are shown to be unimportant at bothvery small and very large separations. In the case of annealed disorder itseffects are non-additive in the total inter-surface interaction and can berationalized in terms of a renormalized extrapolation length.

Pseudo-Casimir interactions across nematic films with disordered anchoring axis