A simple molecular model for the spontaneous curvature and the bending constants of nonionic surfactant monolayers at the oil/water interface

A simple analytical model for the spontaneous curvature and the bending con stants of nonionic surfactant monolayers at an oil/water interface is devel oped with the goal of allowing correlation and prediction of phase behavior . The surfactant molecules are treated as diblock copolymers grafted to the interface. The change in the free energy of the surfactant monolayer due t o the bending of the interface is calculated as a sum of the contributions of the hydrophobic and the hydrophilic blocks. The equilibrium thickness of a spherical and cylindrical surfactant monolayer is found by minimizing th e sum of the free energy of mixing and the stretching energy of the hydroph ilic and the hydrophobic blocks. Comparison with the Helfrich model gives e xpressions for the spontaneous curvature Ho, the bending elasticity kappa, and the saddle splay modulus ii, of the surfactant monolayer. An analytical expression is obtained for the phase inversion temperature, which correlat es well with experimental data for a wide series of nonionic surfactants Ci Ej and oils (n-alkanes). The model gives the temperature dependence of the spontaneous curvature and the bending parameters of nonionic surfactant mon olayers. Phase boundaries in C12E5/octane/water microemulsions are calculat ed without use of any adjustable parameters and are in a good agreement wit h experimental data.