Beyond the harmonic bending theory of ionic surfactant interfaces

There is now a broad understanding of how electrostatics, described by the nonlinear Poisson-Boltzmann equation, contributes to the phenomenological coupling (bending) constants of the flexible surface model as applied to ionic surfactant interfaces when the curvature energy density is truncated at harmonic order. Here, we extend this to the constants associated with anharmonic terms, specifically at third order in the interfacial curvatures, using model aggregates of spherical and cylindrical geometry. We analyze in detail the two limits of excess added salt and counterions only, and also provide a simple construction for bridging these two extremes using the theory of a functions. Further, we investigate the asymptotic nature of the curvature expansion for ionic membranes, showing that it progressively deteriorates as the aggregate curvature is increased, and offer an alternative approximation scheme for the full free energy, using the method of Pade approximants.