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A new perturbation theory for electrolyte solutions.

Developing physically based equations of state for electrolyte solutions is demanding due to the long range behaviour of the Coulombic interaction potentials. In this work, we present a new perturbation approach for nonprimitive model electrolyte solutions consisting of hard spheres with a positive or negative point charge or with point dipoles. We overcome the problem of diverging correlation integrals by separating the interaction potentials into short ranged parts and a long ranged contribution. For the point charges, the division is done like in most implementations of the Ewald sum. The perturbation expansion to 3rd order is formulated using the short ranged part of the potentials only, which results in converging correlation integrals for which we provide simple analytical expressions. The long range contribution to the Helmholtz energy is taken into account by a analytical term that has recently been presented by Rodgers and Weeks [J. M. Rodgers and J. D. Weeks, J. Chem. Phys. 131, 244108 (2009)]. In order to assess the proposed theory, we present molecular simulation data for Helmholtz energies of the same model electrolyte solutions. Predictions for the Helmholtz energy from the new theory are found to be in very good agreement with results from the molecular simulations for all state points we regarded.