Structure of Polyelectrolytes with Mixed Monovalent and Divalent Counterions: SAXS Measurements and Poisson−Boltzmann Analysis

Abstract

We have studied by small angle X-ray scattering (SAXS) the structure of salt-free polyelectrolytes solutions containing monovalent and divalent counterions. We have considered mixtures of sulfonated polystyrene with monovalent (Na+) and divalent (Ca2+) counterions and measured the position of the scattering peak, q*, as a function of the monomer concentration cp and the monovalent/divalent content. The aim is to understand the variations observed in q* position when the valence of the counterions is gradually increased. This work is a continuation of a previous study in which first measurements were performed on a rather small number of sodium−PSS/calcium−PSS mixtures. In the present work, we used synchrotron radiation to improve the quality of the data and vary the monovalent/divalent ratio with a much finer step. Indeed this gives new interesting results in the ranges of low and large divalent content. We analyzed SAXS results through the isotropic model and scaling approach description introduced by de...