Counterion and Coion Distribution Functions in the Counterion Condensation Theory of Polyelectrolytes

We develop formulas for the counterion−polyion and coion−polyion potentials of mean force in the context of counterion condensation theory. For separation distances on the scale of a Debye screening length, both potentials conform to Debye−Hückel screening behavior. Close to the polyion, in the region defining the layer of condensed counterions, the counterion potential is attractive and unscreened. A coion in this region acts like a charged group on the polyion; its potential is repulsive, and it augments the ability of the polymer to condense counterions. There is an interfacial region between condensed layer and diffuse cloud from which counterions are expelled back into the cloud but which accumulates coions. The associated radial distribution functions exhibit two peaks for the counterion and a single peak for the coion.