Counterion and colon distribution functions in the counterion condensationtheory of polyelectrolytes

We develop formulas for the counterion-polyion and coion-polyion potentials of mean force in the context of counterion condensation theory. For separa tion distances on the scale of a Debye screening length, both potentials co nform to Debye-Huckel screening behavior. Close to the polyion, in the regi on defining the layer of condensed counterions, the counterion potential is attractive and unscreened. A colon in this region acts like a charged grou p on the polyion; its potential is repulsive, and it augments the ability o f the polymer to condense counterions. There is an interfacial region betwe en condensed layer and diffuse cloud from which counterions are expelled ba ck into the cloud but which accumulates colons. The associated radial distr ibution functions exhibit two peaks for the counterion and a single peak fo r the coion.