Thermodynamic equilibrium of lipid mixtures on curved substrates

It has been known since long that thermodynamic stability of two-dimensional lipid mixtures is influenced by curvature. Inspired by recent experimental results on lipid membranes coated on colloidal scaffolds, we propose a simple and general framework for interpreting the phase diagram of inhomogeneous closed systems. When the critical behaviour of a system is affected by its shape, we further show how new thermodynamic states can arise in the phase diagram, where lipids are in a mixed phase yet exhibit strong lateral segregation. We prove how different types of inhomogeneous couplings must induce qualitatively different phenomena - such as a curvature dependent line tension - and thus provide a way to distinguish different types of curvature interactions.