Generalized Gibbs-Thomson Equation and Surface Stiffness for Materials with an Orientational Order Parameter

A generalized Gibbs-Thomson equation for the interfacial equilibrium of “soft” materials is derived. It applies to liquid crystals in general, and to Langmuir monolayers. The transition temperature of a soft matter's interface is found to be shifted proportionally to the “curvatures” of the order-parameter field at the interface, in addition to the usual shift proportional to interface curvature. For materials presenting a curvaturelike elasticity, a generalized surface stiffness is defined, the sign of which yields an instability criterion for flat interfaces. As a by-product, rough smectic- $C$ interfaces parallel to the layers should always be unstable, in agreement with recent experimental observations.