SCALING ANALYSIS OF NARROW NECKS IN CURVATURE MODELS OF FLUID LIPID-BILAYER VESICLES

Under appropriate conditions fluid lipid-bilayer vesicles in aqueous solution take the form of two (or more) compact shapes connected by a narrow neck (or necks). We study the limit (termed ''vesiculation'') in which the neck radius a approaches zero. On the basis of elastic equations, derived originally by Deuling and Helfrich [J. Phys. (Paris) 37, 1335 (1976)] for a bending-energy model (the spontaneous-curvature model), we show analytically that, at vesiculation, the local curvatures of the two regions joined by the neck satisfy a simple, universal ''kissing'' (osculation) condition. Furthermore, for points near but not at the vesiculation limit, a is small but nonzero and there is characteristic scaling behavior. For example, in the surface tension (sigma) and pressure (p) variables, the vesiculation boundary is a line in the (sigma,p) plane, and the quantity a Ina scales linearly with the distance (DELTAsigma,DELTAp) from the boundary. These relations have been observed numerically, but no analytic discussion has previously appeared in the literature. Results for the spontaneous-curvature model generalize easily to other (more physical) bending-energy models.