Counterion condensation theory constructed from different models

The primitive model and the line of charges model for ionized polymers both predict the emergence of a condensed counterion layer at a critical polymer charge density, but the two models describe the condensed layer in different ways. The Zimm-Le Bret and Ramanathan distributions for the condensed layer in the primitive model are reviewed. The extended Debye-Huckel theory of the line of charges model is recast in a more general form in an attempt to make its underlying assumptions transparent. We show that the counterion-polyion potential of mean force at great distances behaves differently for the two models.