Disorientation-induced disordering at a nematic-liquid-crystal–solid interface

To explain the observed deviation from the Rapini-Papoular surface energy of nematic-liquid-crystals, we propose a model of the form Tr[(${\mathit{Q}}_{\mathit{i}\mathit{j}}$-${\mathit{Q}}_{0\mathit{i}\mathit{j}}$ ${)}^2$] (${\mathit{Q}}_{\mathit{i}\mathit{j}}$ is the quadrupolar order parameter of the nematic-liquid-crystal and ${\mathit{Q}}_{0\mathit{i}\mathit{j}}$ a quadrupolar surface field). For a broken anchoring, this model predicts a surface order decrease ΔS≊3/2(ξ/d)${\mathit{S}}_{\mathit{B}}$ where ξ and d are the coherence and surface extrapolation lengths of the nematic liquid crystal and ${\mathit{S}}_{\mathit{B}}$ is the bulk order parameter. A quantitative check is presented on planar anchoring of various strengths and temperatures.