Saddle-splay modulus of the AOT monolayer in the AOT-brine-oil system

Three parameters determine the geometry of monolayers in oil-brine-surfactant mixtures dilute in surfactant: the mean bending elastic modulus K, the saddle-splay modulus K¯, and the spontaneous curvature ${\mathit{C}}_0$ of the monolayer. It is found that K¯ and ${\mathit{C}}_0$ of an AOT monolayer vary linearly with ${\mathit{S}}^{\mathrm{-}0.5}$ and ${\mathit{S}}^{0.5}$, respectively (S is the salt concentration) as predicted for monolayers with high charge densities. K¯ is positive for a long-chain oil (12 carbon atoms) and negative for a shorter-chain oil in agreement with the geometry of the phases obtained at optimal salinity where ${\mathit{C}}_0$=0.