Counterion Condensation on Flexible Polyelectrolytes:  Dependence on Ionic Strength and Chain Concentration

We give a simple scaling picture for dilute and semidilute solutions of flexible polyelectrolytes including counterion condensation. It is shown that below a critical temperature a fraction of the counterions condenses on the chain. This leads to a renormalization of the total charge of the macroions as well as to a condensation-induced intrachain attraction resulting in a shrinkage of the chain. The paper extends the scaling picture of Schiessel and Pincus [Macromolecules 1998, 31, 7953] for dilute solutions without extra salt to higher ionic strengths and higher chain concentrations. The diagram of states for the different cases is presented.