Statistical thermodynamics of polyelectrolyte solutions. I. Activity coefficient of counter ion in salt‐free system

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Abstract
The authors investigated theoretically the activity coefficient of counter ion in the salt‐free polyelectrolyte solutions, by stressing the interionic interaction between the macro ion and counter ion. Assuming the Boltzmann distribution for the polyelectrolyte system and proposing a new linear approximation, the Poisson‐Boltzmann equation was solved for a model of spherical rigid macro ion, and then the free energy of the system was calculated by means of the charging‐up procedure. Applying this theory to the experimental data of activity coefficient of silver ion in the silver carboxymethyl cellulose solutions, the size of macro ion was computed, and the results are discussed from a purely theoretical standpoint. Thus, the authors have succeeded in giving a valid insight into the correlation between polyelectrolyte and simple electrolyte solutions as well as into some peculiar features of polyelectrolyte solutions.