Wetting of Nematic Liquid Crystals on Crenellated Substrates: A Frank-Oseen Approach

We revisit the wetting of nematic liquid crystals in contact with crenellated substrates, studied previously using the Landau-de Gennes formalism. However, due to computational limitations, the characteristic length scales of the substrate relief considered in that study limited to less than 100 nematic correlation lengths. The current work uses an extended Frank-Oseen formalism, which includes not only the free-energy contribution due to the elastic deformations but also the surface tension contributions and, if disclinations or other orientational field singularities are present, their core contributions. Within this framework, which was successfully applied to the anchoring transitions of a nematic liquid crystal in contact with structured substrates, we extended the study to much larger length scales including the macroscopic scale. In particular, we analyzed the interfacial states and the transitions between them at the nematic-isotropic coexistence.