Hypernetted chain calculation of static correlation function of macroions in solution using Allnatt equation

Abstract

Numerical results are reported on the calculation of the correlation function of macroions in solution using Allnatt's renormalized integral equation in the hypernetted chain (HNC) approximation for a three-component system of macroion, coion, and counterion in the framework of the primitive model. The dependence of the correlation function on the macroion radius, charge, concentration and concentration of added salt is discussed. The effective potential of interaction of a pair of macroions is calculated from these correlation functions. These potentials are found to be repulsive and have the same form as the well known DLVO potential at shorter distances, particularly for smaller macroion charge, size and concentration, but fall off more rapidly at larger distances. The qualitative dependence of these pair potentials on macroion concentration, charge, radius and concentration of added salt agrees with the predictions of the approximate theoretical analysis by B. Beresford-Smith, D. Y. C. Chan and D. J. Mitchell (1985, J. Colloid Interface Sci., 105, 216). It is found that the range of macroion parameters for which Allnatt equation gives a convergent solution is significantly larger than that reported in the literature for the HNC equation for a general fluid.