Theory of counter-ion condensation on flexible polyelectrolytes: adsorption mechanism.

A new model is presented for counterion distribution around flexible polyelectrolytes by considering (i) free energy of the polyelectrolyte chain, (ii) translational entropy of adsorbed counterions, (iii) adsorption energy, (iv) translational entropy of unadsorbed counterions, (v) fluctuations of dissociated ions, and (vi) correlation among ion-pairs formed by adsorbed counterions on the polymer. The effective charge and size of the polymer are calculated self-consistently. The degree of ionization f of the polymer decreases continuously with 1/epsilonT (epsilon and T are the dielectric constant of the solvent and temperature, respectively), depending sensitively on local dielectric heterogeneity. Further, f decreases with an increase in salt concentration, monomer concentration, or chain flexibility. The polymer size, accompanying the changes in f, depends nonmonotonically on 1/epsilonT. The predictions of the model are consistent with all trends observed previously in simulations and are distinctly different from the Manning argument for rodlike chains.