In this work, we apply the variational field theory [3] to develop a model of polyelectrolyte chains in aqueous solution of salt. The model takes into account the connectivity of the charged monomers along the polyelectrolyte backbone and the hard-core interactions between these monomers and the counterions in solution. The charges are located off-center of ions; the electrical structure of the monomers and the counterions is described by the off-center distances and the variance of the charge distribution. The many-body Coulomb interactions in this system are treated in RPA approximation as pioneered by Borue and Erukhimovich [5], who only considered the point-charge ions in the system.
We derive expressions for the free energy, the osmotic pressure, the screening function and the partial structure factors, and apply our theory for calculating thermodynamic, conformational and structural characteristics for solutions of poly(dimethyl diallyl ammonium) salts in water (and in aqueous solution of sodium salts), with halide or amino acid counterions: PDADMAX where X=Cl, Lys(lysine), Leu(leucine), Gly (glycine). We demonstrate the effects of counterion size, asymmetry and spread of its charge on the predicted results.