Ion correlations and counter-ion condensation in ionic micellar solutions

Abstract

We present a general method for obtaining various ion correlations in ionic micellar solutions. This is based on combined small-angle x-ray and neutron scattering intensity measurements and their analyses using Khan - Ronis theory. The K - R theory of ionic solutions is a multicomponent mean-spherical approximation with non-additive diameters within the primitive model. We first extract an accurate macro-ion - macro-ion structure factor from analyses of SANS and SAXS data, including an accurate estimate of the renormalized micellar charge, , and then use the K - R theory to compute all the other partial structure factors. We demonstrate the validity and practicality of the method using micellar solutions made of caesium alkyl sulphate of various chain lengths. The charge renormalization phenomenon is then shown to be the consequence of condensation of counter-ions into the outer hydrophilic layers of micelles. The renormalized charge of a micelle is obtained for different types of monovalent counter-ion. In particular, we are able to determine the macro-ion - counter-ion pair correlation function which gives the distribution of counter-ions near the surface of a micelle.