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(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(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(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 k(c) 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 of two oppositely charged surfactants, and k(c) is further reduced in anionic/cationic surfactant mixtures where the surfactant in excess has the smaller tail volume. Likewise, the reduction of k(c) is enhanced in mixtures of an ionic and a nonionic surfactant where the ionic surfactant has the smaller tail. The effective bilayer bending constant (k(bi)) is also found to be reduced by mixing, and as a result, k(bi) is seen to go through a minimum at some intermediate composition. The reduction of k(bi) is expected to be most pronounced in mixtures of two oppositely charged surfactants where the surfactant in excess has the smaller tail in agreement with experimental observations.