Dilute solutions of highly asymmetrical electrolytes in the primitive model approximation

The structure and thermodynamics of dilute solutions of a highly asymmetric electrolyte were studied in the primitive model approximation. Solutions of macroions and counterions in water with asymmetries in charge of 10:1 (10:2) and of 20:1 (20:2), and asymmetries in size of 10:2 and of 15:2 were considered. The calculations apply to the concentration range where, an otherwise quite successful theory, the so-called hypernetted chain approximation, does not provide convergent results. The pair correlation functions and thermodynamic parameters were calculated using recently developed two-density theory and the cluster expansion approach. The results of these two theories were compared with new Monte Carlo simulations for the same model solution. The two-density theory in the associated HNC approximation yields good agreement for both structure and thermodynamics in solutions with monovalent counterions; i.e. for 10:1 and 20:1 electrolytes. The cluster expansion approach, as used in this paper, is only applicable for low asymmetry in charge and for dilute solutions of macroions and monovalent counterions. Among the versions of the two-density theory studied here, only the mixed closure, i.e. associated MSA/HNC approximation, gives convergent solutions for systems of macroions and divalent counterions. The agreement of this theory with the Monte Carlo results is only qualitative.