Abstract
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.
Cited by
24 articles.
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