Counterion condensation as saturation effect under the influence of ion hydration

Polyelectrolyte solutions are often described by structural theories. These theories in some cases yield values for the counterion concentration at the charged monomer surface that exceed the saturation concentration. This means a change of the ion properties due to ion immobilization or ion condensation in close vicinity to the polymer chain. The extent of this counterion condensation (CIC) and the respective surface potential are calculated from the saturation concentrations of the electrolyte involved including the influence of ion hydration on the effective dielectric number. In this paper, we shall consider all these influences by a fundamental differential equation and a set of explicit formulae yielding quantitative expressions without linearization. All calculations are based on the abstraction of an idealized elementary cell.