Sylvio. May, 'Curvature elasticity and thermodynamic stability of electrically charged membranes', J.Chem.Phys. 105, 8314 (1996)

The elastic behavior and stability of electrically charged amphiphilic membranes is investigated. In the present study, we address the question whether the electrostatic contribution to the curvature elastic moduli of a uniformly charged symmetric membrane leads to a curvature instability. To this end we consider a membrane in which the overall number of molecules is conserved during any deformation. In order to estimate both the molecular equilibrium area and the position of the neutral surface of each monolayer during bending, we include in the expression of the bilayer free energy beside an electrostatic also a nonelectrostatic contribution. The former is described within the Gouy-Chapman theory of the diffuse double layer. The latter is a sum of a chain, an interfacial, and a nonelectrostatic head group contribution. The chain part is described using a detailed {\em mean-field} conformational free energy which is based on a molecular chain model. For the interfacial and nonelectrostatic head group contribution we use simple but general phenomenological expressions. It is shown that for medium and high membrane surface charge densities the electrostatic contribution to the bending moduli is not negligible. For highly charged membranes, the model predicts an instability with respect to a spherical deformation. This is discussed referring to the experimentally observed process of spontaneous vesiculation upon jump in pH of certain ionizable amphiphilic molecules.