Vesicles and onion phases in dilute surfactant solutions

. We study theoretically the stability of phases of unilamellar and multilamellar vesicles in bilayer-forming surfactant solutions. It is argued that these are likely to arise, instead of a bicontinuous "sponge" phase, when the elastic constants of the bilayer are chosen so that the curvature energy of a sphere is small. At very low volume fractions we predict a phase of noninteracting vesicles; as the concentration is increased these reach an overlap threshold, beyond which "nesting" can occur, giving a multilamellar vesicle or "onion" phase. At higher concentration still, a transition to the smectic (La) phase is predicted. This transition may be rather weak if the mean curvature rigidity is small. The relevance of our results to recent experimental work is briefly discussed.