Counterion condensation-electrostatic interaction theory

Theoretical considerations of the coulombic interactions of dissolved biopolymers have produced a complete picture of the distributions of counter and coions under the influence of the electrostatic charge on the macroion(56,57). The counterion condensation theory of Manning(56) has stimulated a great deal of activity in the study of dissolved macroions, especially because it provides a group of limiting laws describing the contribution of electrostatic effects to the thermodynamic and transport properties of polyelectrolyte solutions. Data... 

From Figure 1 we can see that linear counterion condensation theory predicts that counterion condensation is only a function of charge density or titrated degree of neutralization, while nonlinear theory predicts that counterion condensation is not only a function of titrated degree of neutralization, but also a function of ionic strength. The lower is the ionic strength, the more obvious is the counterion condensation. In the later discussion, we will use nonlinear counterion condensation as the basis to calculate other electrostatic interactions. 

The first theory of polyelectrolyte complex formation was proposed by Voom and Overbeek [14, 15]. This mean field model was used to describe the binodal compositions, the water content and the critical salt concentration as a function of the polymer chain length. This theoretical description uses the Debye-Hiickel approximation the approximations within the derivation of the electrostatic interaction free energy are therefore only valid at low charge densities. The correlation effects at high concentrations of salt and monomeric units are neglected, and ion pairing effects such as counterion condensation are not taken into account. Despite these limitations, the experimental results could be described reasonably well [13]. 

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