Bending of ionic surfactant monolayers

The electrostatic contribution to the bending moduli and spontaneous curvature of monolayers formed by ionic surfactants in solution is calculated for all salt concentrations, ranging from no added salt (counterions only) to excess salt. This is accomplished using a perturbative expansion in curvature of the free energy of the Poisson-Boltzmann cell model, which is shown to give precisely the same results for the moduli as would an alternative calculation employing moments of the transverse pressure profile of the electric double layer. With this treatment, it is possible to quantify the dependence of the moduli and spontaneous curvature on surfactant concentration alone (i.e., with fixed average salt concentration), a point of central importance to the validity of the flexible surface model in the description of ionic surfactant systems. A manifestation of the counterion condensation phenomenon is also observed, as the monolayer rigidity saturates and becomes independent of the surface area per ionic headgroup.