Effect of finite ion size on the ''overbeek correction'' to the Sogami-Ise interaction potential between macroions of like charge

The Sogami-Ise (SI) interaction potential has a ''long range attraction'' tail that is not present in the DLVO potential. Overbeek suggested that an ''error'' was present in the SI theory and that the inclusion of the solvent contribution eliminated the source of this long range attraction. The model used by Overbeek assumed that the macroions, by virtue of being fixed in their equilibrium positions, did not contribute to the electrical free energy of the solution. It is shown herein that the ''Overbeek correction'' is not rigorously zero for arbitrary polyion concentrations, as it must be in order to eliminate the Gibbs minimum for actual experimental conditions. It is shown herein on the basis of standard statistical thermodynamics expressions that the presence of a minimum in the pairwise Gibbs electrical free energy occurs for all screened Coulombic expressions for the Helmholtz electrical free energy, and therefore the correction term of Overbeek is in error. It is concluded that the concepts of screened Coulombic interactions and the equivalence of the pairwise Gibbs and Helmholtz electrical free energies are incompatible: one concept must be discarded if the other is to be retained.