Nematic films at chemically structured surfaces

We investigate theoretically the morphology of a thin nematic film adsorbed at flat substrate patterned by stripes with alternating aligning properties, normal and tangential respectively. We construct a simple 'exactly-solvable' effective interfacial model where the liquid crystal distortions are accounted for via an effective interface potential. We find that chemically patterned substrates can strongly deform the nematic-air interface. The amplitude of this substrate-induced undulations increases with decreasing average film thickness and with increasing surface pattern pitch. We find a regime where the interfacial deformation may be described in terms of a material-independent universal scaling function. Surprisingly, the predictions of the effective interfacial model agree semi-quantitatively with the results of the numerical solution of a full model based on the Landau-de Gennes theory coupled to a square-gradient phase field free energy functional for a two phase system.