Abstract
A simple model is used to study the equilibrium of lipid domains on two-phase vesicles. Two classes of configurations are considered: multidomain and ground state configurations. For multidomain configurations, the vesicle has a finite number of identical lipid domains. For ground state configurations, the vesicle is fully phase separated into two coexisting domains. Whereas the volume enclosed by a vesicle with multidomains is fixed, the volume enclosed by a vesicle in a ground state is allowed to vary with the osmotic pressure. Guided by experimental observations, all domains are assumed to be spherical caps. In a multidomain configuration, the line tension is found to decrease with the number of domains present, with possible exceptions when the number of domains is very small. The importance of a critical osmotic pressure and a critical excess radius on ground state configurations is explored. Emphasis is placed on understanding the variations of these critical quantities with relevant parameters.