(83h) A New Perturbation Approach for Electrolyte Solutions

The treatment of electrolyte systems in fluid theories is demanding because of the long-range decay of the coulombic interactions. Integral equation approaches are the most prominent path to developing theoretical descriptions of electrolyte solutions. A promising perturbation approach, however, has been formulated by Henderson et al. [1]. The problem of diverging correlation integrals is alleviated by resumming the perturbation terms of different order and approximating a converging expression from the sum of diverging integral equations. The initial theory is of third order and the resulting equations are formulated in powers of ½ in inverse temperature. Due to inaccurate approximations and erroneous angle averaging, this approach does not predict the Helmholtz energy of the system correctly.

In this contribution we present a new approach of a perturbation theory for electrolyte solutions. Similar to the ewald sum the electrostatic potential is subdivided into a short ranged part and a long raged tail. The long-range contribution of the electrostatic potentials is accounted for in a powerful analytical theory (local molecular field theory, LMF) proposed by Rodgers and Weeks [2, 3]. We reformulate the correlation integrals up to third order for only the short-ranged part of the pair potentials. Diverging integrals and thus inaccurate approximations are avoided.
The underlying LMF theory is validated by computer simulations comparing the  results with ewald summation calculations. Furthermore, the theoretical work is supplemented with molecular simulations applying thermodynamic integration for the estimation of the Helmholtz energy of charged and dipolar hard spheres. This allows us to test the theory without any further assumptions.

[1]   D. Henderson, L. Blum, A. Tani: Equation of state of ionic fluids. ACS Symp. Ser. No. 300 (1986), 281.

[2] J. M. Rodgers, J. D. Weeks: Local molecular field theory for the treatment of electrostatics. J. Phys.: Condens. Matter 20. (2008), 494206.

[3] J. M. Rodgers, J. D. Weeks: Accurate Thermodynamics for Short-Ranged Truncations of Coulomb Interactions in Site-Site Molecular Models. J. Chem. Phys. 131. (2009), 244108.