Deformability of multilamellar vesicles

Although a free unilamellar vesicle has zero or almost zero genuine surface tension, the multilamellar vesicle ("onion") exhibits a nonzero effective surface tension sigma(eff). The expression for sigma(eff) used in the literature is sigma eff similar to root kappa B/d(0), where B is the interaction modulus between the vesicle bilayers, do the repeating distance between the bilayers in the droplet, and kappa their bending rigidity. In this paper we calculate the contributions to the effective surface tension of a lamellar droplet in the case when the layers interact with one another and when they are free. It is shown that the interaction contribution to the surface tension is small and sigma(eff) is determined mainly by kappa, the radius of the droplet R-0, and the number of the shape undulation modes l(max). A nonzero surface tension of the layers is also included in the calculation which is necessary when the vesicle membrane is stressed in the complex of other membranes.