Highly Asymmetric Electrolytes in the Associative Mean-Spherical Approximation

Abstract

The associate mean-spherical approximation (AMSA) is used to derive the closed-form expressions for the thermodynamic properties of an (n+m)-component mixture of sticky charged hard spheres, with m components representing polyions and n components representing counterions. The present version of the AMSA explicitly takes into account association effects due to the high asymmetry in charge and size of the ions, assuming that counterions bind to only one polyion, while the polyions can bind to an arbitrary number of counterions. Within this formalism an extension of the Ebeling–Grigo choice for the association constant is proposed. The derived equations apply to an arbitrary number of components; however, the numerical results for thermodynamic properties presented here are obtained for a system containing one counterion and one macroion (1+1 component) species only. In our calculation the ions are pictured as charged spheres of different sizes (primitive model) embedded in a dielectric continuum. Asymmetries in charge of −10:+1, −10:+2, −20:+1, and −20:+2 and asymmetries in diameter of 2:0.4nm and 3:0.4nm are studied. Monte Carlo simulations are performed for the same model solution. By comparison with new and existing computer simulations it is demonstrated that the present version of the AMSA provides semiquantitative or better predictions for the excess internal energy and osmotic coefficient in the range of parameters where the regular hypernetted chain (HNC) and improved (associative) HNC do not yield convergent solutions. The AMSA liquid–gas phase diagram in the limit of complete association (infinitely strong sticky interaction) is calculated for models with different degrees of asymmetry.