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

TL;DR

This study investigates how counterion condensation in aqueous polyelectrolyte solutions varies across dilute, semidilute, and concentrated regimes, revealing distinct behaviors linked to polymer flexibility and concentration.

Contribution

It provides a comprehensive analysis of counterion condensation regimes in flexible and rigid polyions over a wide concentration range, combining experimental data with theoretical models.

Findings

Counterion condensation exhibits three distinct regimes depending on concentration.

The fraction of free counterions remains constant only in the semidilute (Manning) regime.

Both dilute and concentrated regimes show a marked dependence of free counterions on concentration.

Abstract

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.