Effect of Counterion Condensation on Rigidity of Semiflexible Polyelectrolytes

I have calculated the effect of counterion condensation on the electrostatic persistence length of semiflexible polyelectrolytes. There are two contributions to the electrostatic persistence length. The first contribution is due to neutralization of the ionized groups by condensed ions that changes the effective linear charge density along the polymer backbone, weakening intrachain electrostatic repulsion. In the case of the monovalent counterions this contribution to the chain persistence length is proportional to the Debye screening length, underlining the fact of the exponential screening of electrostatic interactions on the length scales of the order of Debye screening length. The second contribution is due to correlation/fluctuation-induced attractive interactions between condensed counterions that result in a negative contribution to the chain persistence length. In the case of multivalent ions these interactions are assumed to be due to strong lateral correlations between condensed multivalent ions and were accounted for in the framework of the strongly correlated Wigner liquid approximation.