Bending rigidity of ionic surfactant interfaces with variable surface charge density: the salt-free case

The theoretical understanding of the electrostatic contribution to the bending constants of ionic surfactant interfaces has been extensively developed over the past decade. In this contribution, we deal with systems without added electrolyte, and allow for the interfacial charge density to vary with curvature, treating both an undulating sheet geometry and a spherical/cylindrical cell model. The rippled-plane case shows that the lowest free energy state is that for which the surface potential remains fixed, i.e. a conducting interface. Moreover, the deduced expression for the bending modulus agrees with that derived from the cell model, generalizing our previous result that the bending modulus is geometry-independent, even for systems without added salt, to cases where the surface charge is permitted to redistribute on bending. (C) 1997 Elsevier Science B.V.