Doubly-periodic instability pattern in a smectic A liquid crystal

We report the observation of a doubly-periodic surface defect-pattern in the liquid crystal 8CB, formed during the nematic--smectic A phase transition. The pattern results from the antagonistic alignment of the 8CB molecules, which is homeotropic at the surface and planar in the bulk of the sample cell. Within the continuum Landau-deGennes theory of smectic liquid crystals, we find that the long period (~10 \mu m) of the pattern is given by the balance between the surface anchoring and the elastic energy of curvature wall defects. The short period (~1 \mu m) we attribute to a saddle-splay distortion, leading to a non-zero Gaussian curvature and causing the curvature walls to break up.