Counterion condensation is a phenomenon described by Manning's theory (Manning 1969), which assumes that counterions can condense onto polyions until the charged density between neighboring monomer charges along the polyion chain is reduced below a certain critical value.
In the model the real polyion chain is replaced by an idealized line charge, where the polyion is represented by a uniformly charged thread of zero radius, infinite length and finite charge density, and the condensed counterion layer is assumed to be in physical equilibrium with the ionic atmosphere surrounding the polyion.
The uncondensed mobile ions in the ionic atmosphere are treated within the Debye–Hückel (DH) approximation.
The phenomenon of counterion condensation now takes place when the dimensionless Coulomb coupling strength where
For many standard polyelectrolytes, this phenomenon is relevant, since the distance between neighboring monomer charges typically ranges between 2 and 3 Å and
The Manning theory states that the fraction of "condensed" counter ions is