Planar nematic anchoring on rough anisotropic substrates: An elastic model

Rough anisotropic substrates, as SiO coated glass plates, can give uniform planar alignment for nematics. We quantify their surface anisotropy by means of the local fractal dimension D calculated from vertical profiles, An elastic model is proposed to explain the existence of the planar nematic easy axis: the elastic strain energy in the bulk of the nematic depends on D. The nematic aligns along the direction with lower D, which imposes the lower deformation. This model should hold for all substrates, with low apparent anisotropy, that can be described as self-affine surfaces.