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The low-frequency limit of the electrical conductivity (d.c. conductivity) ofdifferently flexible polyions in aqueous solutions has been measured over anextended polyion concentration range, covering both the dilute and semidilute(entangled and unentangled) regime, up to the concentrated regime. The datahave been analyzed taking into account the different flexibility of the polymerchains according to the scaling theory of polyion solutions, in the case offlexible polyions, and according to the Manning model, in the case of rigidpolyions. In both cases, the fraction f of free counterions, released into theaqueous phase from the ionizable polyion groups, has been evaluated and itsdependence on the polyion concentration determined. Our results show that thecounterion condensation follows at least three different regimes in dependenceon the polyion concentration. The fraction f of free counterions remainsconstant only in the semidilute regime (a region that we have named the Manningregime), while there is a marked dependence on the polyion concentration bothin the dilute and in the concentrated regime. These results are brieflydiscussed at the light of the aqueous ionic solutions.

The counterion condensation of differently flexible polyelectrolyte aqueous solutions in the dilute and semidilute regime