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To explain the observed deviation from the Rapini-Papoular surface energy of nematic-liquid-crystals, we propose a model of the form Tr (Q₈₉-Q₀₈₉) ^2 (Q₈₉ is the quadrupolar order parameter of the nematic-liquid-crystal and Q₀₈₉ a quadrupolar surface field). For a broken anchoring, this model predicts a surface order decrease 3/2 (/d) S₁ where and d are the coherence and surface extrapolation lengths of the nematic liquid crystal and S₁ is the bulk order parameter. A quantitative check is presented on planar anchoring of various strengths and temperatures.
Nobili et al. (1992) studied this question.