Topographical variations in thin liquid crystal films

A thin film of isotropic fluid with a free interface is always perfectly flat far away from boundaries and inclusions. In contrast, liquid crystals can, in principle, sustain a surface topography because elastic distortions in the bulk can be relaxed by deformation(s) of the surface. In practice, surface tension tends to dominate over elastic forces and so boundary deformations are usually neglected. (However, these have been observed in smectics and in nematics, as De Gennes famously predicted, where defects are confined to the boundary.) Here we present a different scenario: Topography at the free interface is induced by surface patterning of the substrate in a thin, hybrid-aligned nematic liquid crystal. The proposed mechanism requires finite anchoring at the free interface leading to modulation of the nematic orientation; deformation of the surface then allows the nematic to better satisfy the anchoring condition. We present analytical and numerical theory for several surface patterns, which are compared with our experimental actualizations.