Abstract
A simple electrolyte in a polar solvent is modelled by a mixture of polar hard spheres and equal diameter charged hard spheres with the possibility of ionic dimerization. The analytical solution of the associative mean spherical approximation (AMSA) for this model is derived to its full extent. Explicit expressions for pair correlation functions and dielectric constant in terms of the AMSA are established. Some numerical calculations illustrate the role of ionic association.
Highlights
The mean spherical approximation (MSA) is an analytical theory for electrolyte solutions in the ionic approach [1,2,3], as well as in the ion-molecular approach [412]
The MSA corresponds to the well-known DebyeHuckel (DH) theory [16] in the low coupling Mayer limit The MSA is asymptotically correct in the high coupling Onsager limit [17], where, unlike the DH theory, it satisfies the exact Onsager bounds [18] for the Helmholtz free energy and the internal energy of the system
A simple and natural way to correct the theory of electrolyte solutions was proposed by Bjerrum [20] who developed the theory of an ionic association in conjunction with the DH theory
Summary
The mean spherical approximation (MSA) is an analytical theory for electrolyte solutions in the ionic approach [1,2,3], as well as in the ion-molecular approach [412]. A multidensity integral equation theory which correctly accounts for the effects of association in ionic systems has been proposed [20,21,22,23] It is based on the multidensity formalism for associating fluids of Wertheim [36,37] and combines a description in terms of the activity and density expansions. The explicit expression for thermodynamical properties of a mixture of dimerizing ions was obtained with the application of the exponential approximation for the contact values of a non-associated part of pair distribution functions ga0b0 which was used for the calculation of the degree of association [36,37] Such an approximation yields the correct Bjerrum limit for very dilute solutions and the AMSA corresponds to the DH theory with the Bjerrum corection for an ionic association in the limit of point ions. As well as some conclusions are given in the fourth section
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