Thermodynamics of ion-exchange equilibria in polyelectrolyte systems

Abstract

A general, simplified thermodynamic treatment of ion-exchange equilibria in polyelectrolyte systems is presented. The treatment unifies the approaches based on the Gibbs–Donnan phase equilibrium and the mass-action law. The ion-exchange equilibrium depends essentially on two effects, the electrostatic Donnan effect and specific local interactions manifest in the activity coefficients. If ions with different valences are present the Donnan effect dominates in dilute solutions, and in the limit of infinite dilution the exchange equilibrium is completely in favour of the counterion having the highest valence. In very dilute solutions effects arising from the self-ionisation of water are important and the system becomes partially hydrolysed. An equation for the quantitative evaluation of this effect is derived.