  The low-frequency limit of the electrical conductivity (d.c. conductivity) of
differently flexible polyions in aqueous solutions has been measured over an
extended polyion concentration range, covering both the dilute and semidilute
(entangled and unentangled) regime, up to the concentrated regime. The data
have been analyzed taking into account the different flexibility of the polymer
chains according to the scaling theory of polyion solutions, in the case of
flexible polyions, and according to the Manning model, in the case of rigid
polyions. In both cases, the fraction f of free counterions, released into the
aqueous phase from the ionizable polyion groups, has been evaluated and its
dependence on the polyion concentration determined. Our results show that the
counterion condensation follows at least three different regimes in dependence
on the polyion concentration. The fraction f of free counterions remains
constant only in the semidilute regime (a region that we have named the Manning
regime), while there is a marked dependence on the polyion concentration both
in the dilute and in the concentrated regime. These results are briefly
discussed at the light of the aqueous ionic solutions.
