A VARIATIONAL APPROACH TO CHARGED POLYMER-CHAINS - POLYMER MEDIATED INTERACTIONS

A variational approach, based on a quadratic trial Hamiltonian is used to determine the configurational as well as the mechanical properties of a system composed of two point charges plus a neutralizing charged polymer, considered as a model of polyelectrolyte-macroion interactio ns. The quadratic variational ansatz used in the context of charged po lymers presents a variant of the Feynman-Kleinert approach properly ge neralized to include polymer self-interactions. Conditions for chain l ocalization in the field of a point charge are derived and its consequ ences for polymer-mediated forces between two point charges are analyz ed. It is established that in three dimensions the polymer can confer long range attraction to nominally equally charged point ions. At smal l separations, the polymer mediated force is elastic in origin, stemmi ng from the soft electrostatic anchoring of the chain to both point ch arges but with a force constant much stronger than expected from entro pic elasticity alone. At large separations. the polymer mediated inter actions are of long range and are due to polymer-induced charge revers al on one of the external point charges.