Cahn-Hoffman capillarity vector thermodynamics for liquid crystal interfaces.

The classical Cahn-Hoffman capillarity vector formalism for anisotropic interfaces, widely used to analyze capillary and surface patterning processes in metallurgical systems, is applied to nematic liquid crystalline interfaces. The nematic capillarity vector is derived and expressed in terms of nematic surface energies. Expressions for surface tension forces on surface line elements are derived and shown to include the usual tangential forces as well as normal forces driven by surface tension anisotropy. The connections between interfacial rotational effects, surface tension anisotropy, and bending stresses are established. The vector formalism is shown to be a tractable and simple method to analyze capillarity processes in nematic liquid crystals. The application of the formalism to a straight nematic triple line shows that the interface configuration should be such that the projection of the sum of the three capillarity vectors on a plane normal to the contact line vanishes.