Ion correlations in a micellar solution studied by small-angle neutron and x-ray scattering

We propose a general and consistent scheme for the analysis of small-angle x-ray and neutron data from quasispherical ionic surfactant micelles in aqueous solution. A two-shell model for the micellar particle structure factor is used, which models the structure in terms of a compact hydrophobic core and a hydrophilic outer shell. The hydrophilic shell contains head groups of the surfactant, water molecules of hydration, and a number of counterions, the number being determined by the counterion condensation mechanism. The partial structure factors for micelle-micelle, micelle-counterion, and counterion-counterion correlations are calculated by a multicomponent mean spherical model (MMSA) of Ronis and Khan. This model can be solved analytically under the conditions of penetrable spheres for pointlike counterions. The former condition is essential for treating the highly charged macroion system such as micelles by MMSA. This scheme is applied to a micellar solution composed of an ionic surfactant, cesium dodecyl sulfate. The presence of heavy counterions provides the sensitivity necessary to test the accuracy of the calculated degree of counterion condensation into the outer shell of the micelle.