Generalized van der Waals theory. XII. Application to ionic solutions

The recently developed generalized van der Waals (GvdW) theory of fluids is applied to ionic solutions, and shown to yield the Poisson-Boltzmann equation when short-range effects are neglected, and the Debye-Huckel theory when non-linear effects are also neglected. The linear GvdW theory, retaining excluded-volume and energetic correlation effects, then yields a corrected Debye-Huckel (CDH) theory. We consider electrolytes in the restricted primitive model and find that the excluded-volume effects then vanish. Two different methods for the evaluation of the energetic correlation effects are examined. In the first method, these effects are treated in a simple local approximation which leads to a DH theory with a decreased Debye length valid as long as this length is much greater than the hard-sphere diameter of the ions. In the second method, we assume a DH-type charge density, a constant number density and determine the Debye length by minimizing the linearized GvdW free-energy functional. The results for the internal energy, osmotic coefficient and mean ionic activity coefficient of 1-1 and 2-2 electrolytes in the concentration range 0-2 M are obtained and compared with corresponding simulation results. The agreement is good for 1-1 electrolytes, but significant deviations are observed for 2-2 electrolytes.