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 (L$_{\alpha}$) 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