T. Alfrey et al., THE COUNTERION DISTRIBUTION IN SOLUTIONS OF ROD-SHAPED POLYELECTROLYTES (REPRINTED FROM JOURNAL-OF-POLYMER-SCIENCE, VOL 7, PG 543-547), Journal of polymer science. Part B, Polymer physics, 34(3), 1996, pp. 395-399
For solutions containing rod-shaped polyelectrolytes and their counter
ions only, the Poisson-Boltzmann equation can be solved explicitly wit
hout the usual assumption of the Deybe-Huckel theory. At charge densit
ies corresponding to half-neutralized polyacrylic acid a large proport
ion of monovalent counterions is located close to the polyion even in
solutions as dilute as 1/800 base molar.