Cluster Theory of Polyelectrolyte Solutions. I. Activity Coefficients of the Mobile Ions

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Abstract
In an effort to calculate thermodynamic properties of polyelectrolyte solutions with as few assumptions as possible, we have utilized the Mayer cluster theory of ionic solutions as our starting point rather than the Poisson—Boltzmann equation. We show that the use of the Debye—Hückel screened Coulomb potential between charged sites on the polyion is an adequate first approximation for the mean activity coefficient of mobile ions, although single‐ion activity coefficients require additional terms for their description. Satisfactory agreement with experiment is obtained.