The arrangement of electric charge on the ionic species is among the key issues of molecular theory of solutions that contain large ions. An extension of the classical Debye-Huckel theory to ions that have complex electric structure has been developed by Lue, using a variational-field approach. In the recent years, the field theory techniques have been advanced systematically [2]; charge distribution functions have been introduced as an input that sets the arrangement of the electric charge within an ion. Within the Random Phase Approximation (RPA) this approach leads to an analytical description of a number of complex systems, including those containing ionic, dipolar, and/or polarizable species, and even ionic micellar aggregates.
In this work, we apply the variational field theory to develop a model of polyelectrolyte chains in an aqueous solution of salt. This model takes into account the connectivity of the polyelectrolyte chain and the hard-core interactions between the monomers and mobile ions in solution. The charges are located off-center of ions. The electrical structure of the monomers and of the mobile ions is reflected by setting the off-center distances and the variances of the charge distributions. The many-body Coulomb interactions in this system are treated in RPA approximation as pioneered by Borue and Erukhimovich, who only considered the point-charge ions.