Oblique anchoring at a free nematic surface

We generalize earlier density functional theories of the interface between an ordered nematic liquid crystal and its vapor to consider oblique anchoring. This is achieved by including a term with the symmetry of the electrostatic quadrupole in the model molecular interaction potential. As the bulk triple point of the liquid crystal is approached, the model exhibits the second-order oblique-to-homeotropic anchoring transition observed experimentally by Chiarelli et al. The result constitutes a thermodynamically consistent demonstration of this phenomenon using a microscopic theory. We plot the relevant anchoring phase diagrams, and compare them with constrained treatments of the density functional. By means of this comparison we assess to what extent the commonly adopted strategy of decoupling interfacial structure from anchoring is justified.