Mixed amphiphilic bilayers: Bending elasticity and formation of vesicles

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Abstract
In this article, we report on a theoretical investigation of the bending elasticity of fluid bilayers consisting of two amphiphilic species. According to the ideas of Safran et al. [Phys. Rev. A 43, 1071 (1991)], one expects that the corresponding composition degree of freedom couples to curvature playing so a significant role in the bending properties of the mixed membrane. We show that these properties can be interpreted in terms of the bending moduli of the individual constituting monolayers provided that these are calculated at fixed chemical potential μ and not at fixed composition. A simple general theory is built up, designed so that the μ moduli can be calculated in a consistent way. It is shown that the composition degree of freedom softens the mean curvature modulus κ but leaves the Gaussian modulus κ̄ unaffected. Finite thickness effects are also considered. They do not modify κ, whereas their influence on κ̄ just has the same value as formerly calculated for the case of no composition degree of freedom. Finally, this general approach is applied to more specific models of mixed membranes: (i) bilayers made of surfactant and cosurfactant; (ii) initially neutral membranes weakly charged by addition of a small amount of an ionic surfactant; and (iii) bilayers covered with a brush of adsorbed end‐functionalized polymers. New insights are also obtained on well known experimental facts such as the existence of spherulite textures in lamellar phases and spontaneous formation of vesicles and liposomes.