An association theory for the formation of ion oligomers: Extensions from the low density limit

Abstract

A recently published ion association theory which includes the formation of trimers and tetramers has been further developed by accounting for density-dependent properties. This theory is developed in the framework of a primitive model and based on the completely dissociated reference system. The association constants of the equilibria between the ions and the clusters are related to an integral over the pair distribution function of the ionic fluid by an association balance. In order to calculate the fraction of trimers and larger ion clusters use has been made of the Kirkwood superposition approximation. For all calculations the dielectric constant of the pure solvent has been employed. In this paper an extension of the theory has been accomplished by replacing properties of the low density limit by density-dependent properties. The exponential low density pair correlation function has been replaced by the analytically available general mean spherical approximation expression. The covolumes of the clusters have been approximated with a perturbation approach for an effective Bjerrum distance. The ion clusters are modeled as hard spherocylinders. For the charged clusters the Coulomb interaction is described with the mean spherical approximation expression. Finally, the model is applied to some 1–1 electrolyte solutions in water. In the applications the dielectric constant of pure water has been used at a given temperature.