New Features of Two-Dimensional Soft Matter Domains: Dips and Quasicusps

We determine the equilibrium shapes of Langmuir monolayer domains using a generalized Gibbs-Thomson equation. We obtain kinked domains whose scaling behavior agrees with that experimentally observed. We find new shape features characteristic of soft matter: dips and quasicusps. Soft matter exhibits two antagonistic trends: it gives rise to kinks even for very small anisotropies, due to the appearance of virtual textural defects, and it avoids true sharp singularities, due to the softness of its bulk.