On the use of the Gibbs free energy in macroionic solutions

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Abstract
We investigate a recent theory for macroionic dispersions due to Sogami and Ise, which advocates the use of the Gibbs free energy in place of the usual Helmholtz description of the counterion thermodynamics. Employing the Poisson–Boltzmann approximation, their model predicts an effective electrostatic interaction between macroions which is attractive for spheres, in contradiction to the much used DLVO potential. By applying their analysis to a planar geometry of charged walls with only counterions we make explicit the consequences of their assumption that the thermodynamic potentials are first-order homogeneous functions of the extensive parameters in the system. This is no longer the case of the nonuniform systems inherent in the calculation of effective potentials.

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