Transport phenomena and ion binding in poly(styrenesulfonate) solutions containing mixtures of two counter ions differing in charge and size

Abstract

By the combination of electrical conductivity and polyion constituent transport number measurements, fractions of free counter ions were calculated in salt-free polyelectrolyte solutions containing mixtures of mono- and di-valent or mono- and tri-valent counter ions. The poly(styrenesulfonate) anion was chosen as the polyion and mixtures of hydrogen and magnesium or hydrogen and lanthanum ions were taken as counter ions. All measurements were performed in aqueous solutions at 25 °C in the concentration range from ca. 0.002 to 0.1 mol l^–1 for various equivalent fractions of the hydrogen ion in the counter ion mixture. The experimental results were compared with the theoretical predictions based on the analytical and numerical solution of the Poisson–Boltzmann equation for the cell model of a polyelectrolyte solution with mixtures of two counter ions differing in charge and size. A pronounced dependence of the fraction of free counter ions on the composition of the mixture has been found, a finding which is in agreement with the theory. The fraction of free monovalent counter ions is much higher than the fraction of free di- or tri-valent counter ions and decreases, whereas that for the multivalent ones increases upon increasing the corresponding equivalent fraction in the counter ion mixture.