A simple correlation-corrected Poisson-Boltzmann theory

A simple approach is used to introduce effects of ion-ion correlations into the Poisson-Boltzmann theory. The mean-field character of the theory is retained and correlations are approximated by an effective interaction potential, which differs from the Coulombic at short range. In particular, the severe overestimation of the average interaction energy between ions of like charge inherent in the original Poisson-Boltzmann theory, is accounted for by this effective potential. We show that important phenomena due to ion-ion correlations, such as net attraction between surfaces of like charge and charge reversal in double layer systems, are qualitatively and serniquantitatively reproduced by this correlation-corrected theory, which contains no adjustable parameter. The response of net surface interactions to the addition of salt is also captured by the theory and satisfactory quantitative agreement is found with simulation results, even at molar concentrations of divalent salt and in the presence of highly charged surfaces. The mean-field theory is furthermore able to qualitatively predict the way in which bulk salt properties such as the osmotic coefficient and the excess chemical potential depend on the salt concentration. The quantitative performance is poorer than for electric double layer systems, but there is still a substantial improvement relative to the ordinary Poisson-Boltzmann theory.