Self-consistent integral equation applied to the highly charged primitive model

Abstract

We apply the mixed integral equation (ZH) proposed recently by Zerah and Hansen to highly asymmetrical polyelectrolytes within the primitive model. The closure interpolates continuously between the Percus–Yevick and the hypernetted chain closures for charges of same sign and between the HNC and mean spherical approximations for charges of opposite sign. The thermodynamic consistency between the virial and compressibility equations of state is obtained by varying the single parameter in the switching functions. In weakly screened and highly charged suspensions, the new ZH equation improves appreciably the HNC results. The structure factors are essentially modified in the infinite wavelength limit. The two-phase region in the phase diagram is shifted towards the low temperature or the high charge region which allows us to study more asymmetrical systems than with the HNC equation. Since no simulation data are available, the ZH equation is useful to quantify the accuracy of the HNC closure for such systems.