Free ions, polyelectrolyte-counterion interactions

Many theoretical models have been developed to describe the electrical polarizability of polyelectrolytes [2-4,13-40], The problem is, however, extremely complex and difficult, even if simple models are assumed for the geometry of the polyions [37]. This is because many fields are involved concentrations of small ions, the electrical potential, and the solvent velocity, to be determined as functions of space and time, which are coupled with each other through essentially nonlinear equations. Our numerical approach, however, need not introduce, as in most of the theories, somewhat ad hoc approximations such that counterions are classified into free and bound ions, only the latter contributing to the polarizability, nor neglect interactions between counterions. 

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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