Surface Tension of Liquid Crystals

The problem of finding the equilibrium shape of a small particle by the Wulff construction is reviewed briefly, with emphasis on its applications to liquid crystals. The proof of Wulff's theorem is stated in a concise mathematical form. Some typical equilibrium shapes of liquid crystalline drops are described. When there is orientational order of the molecules in the liquid crystal but no translational order, the equilibrium shape may be an ellipsoid or a tactoid; when there is translational order as well, the shape may have plane faces, possibly with sharp edges and corners. The formation of the stepped drop, goutte à gradins, is interpreted as analogous to the stepwise roughening of a flat crystal surface whose orientation does not occur amongst the boundary surfaces of the Wulff shape.