Counterion condensation in polyelectrolyte solutions

The fraction of dissociated counterions for several anionic and cationic polyelectrolytes in semidilute solution in aqueous and organic media was estimated from measurements of the osmotic pressure, electrical conductivity and scattering properties. The systems studied include polystyrene sulfonate, carboxymethyl cellulose and a poly(ionic liquid). The effect of counterion valence, size and solvophilicity are systematically studied. The data show that, for a fixed valence, the fraction of dissociated counterions does not depend on counterion type within the experimental error of our measurements. Next, we study the influence of the dielectric permittivity of the solvent media. As expected by the Oosawa-Manning theory, the fraction of free counterions decreases as the Bjerrum length increases. However, the charge fraction is found to be somewhat lower than the Manning condensation limit.