Bending elasticity of charged surfactant layers : the effect of mixing

Expressions have been derived from which the spontaneous curvature (H-0), bending rigidity (k(c)), and saddle-splay constant ((k) over bar (c)) of mixed monolayers and bilayers may be calculated from molecular and solution properties as well as experimentally available quantities such as the macroscopic hydrophobic-hydrophilic interfacial tension. Three different cases of binary surfactant mixtures have been treated in detail: (i) mixtures of an ionic and a nonionic surfactant, (ii) mixtures of two oppositely charged surfactants, and (iii) mixtures of two ionic surfactants with identical headgroups but different tail volumes. It is demonstrated that k(c)H(0), k(c), and (k) over bar (c) for mixtures of surfactants with flexible tails may be subdivided into one contribution that is due to bending properties of an infinitely thin surface as calculated from the Poisson-Boltzmann mean field theory and one contribution appearing as a result of the surfactant film having a finite thickness with the surface of charge located somewhat outside the hydrophobic-hydrophilic interface. As a matter of fact, the picture becomes completely different as finite layer thickness effects are taken into account, and as a result, the spontaneous curvature is extensively lowered whereas the bending rigidity is raised. Furthermore, an additional contribution to k(c) is present for surfactant mixtures but is absent for k(c)H(0) and (k) over bar (c). This contribution appears as a consequence of the minimization of the free energy with respect to the composition of a surfactant layer that is open in the thermodynamic sense and must always be negative (i.e., k(c) is generally found to be brought down by the process of mixing two or more surfactants). The magnitude of the reduction of kc increases with increasing asymmetry between two surfactants with respect to headgroup charge number and tail volume. As a consequence, the bending rigidity assumes the lowest values for layers formed in mixtures