POLYELECTROLYTE THEORY .2. ACTIVITY-COEFFICIENTS IN POISSON-BOLTZMANN AND IN CONDENSATION THEORY - POLARIZABILITY OF THE COUNTERION SHEATH

We derive approximate formulas for the activities for counterions and co-ions in Poisson-Boltzmann theory. The counterion activities are very close to those of condensation theory. The co-ion activities are larger than one for small quantities of added salt. The activities are insensitive to the counterionic distribution near the polyelectrolyte or to site binding. Condensation and Poisson-Boltzmann theory both fit the experimental activity coefficient of counterions fairly well. Neither fits the co-ion measurements. Iwasa and Kwak have shown that the activity coefficient of the co-ion in condensation theory was derived incorrectly. Their procedure yields a coefficient larger than one, like Poisson-Boltzmann. This result from both theories is in contradiction with experiment. We propose two modifications in the derivation of activity coefficients in low salt concentrations. In particular we suggest that the polarization induced in the counterion sheath by an ion far from the polyelectrolyte may reduce the activity of counterions and co-ions significantly. The analysis of activity coefficients suggests that the experimental data cannot be called upon to support condensation theory. © 1979 American Chemical Society.