Static correlations in macro-ionic suspensions: Analytic and numerical results in a hypernetted-chain–mean-spherical approximation

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Abstract
The static correlations in highly charged colloidal and micellar suspensions, with and without added electrolyte, are examined using the hypernetted-chain approximation (HNC) for the macro-ion–macro-ion correlations and the mean-spherical approximation for the other correlations. By taking the point-ion limit for the counter-ions, an analytic solution for the counter-ion part of the problem can be obtained; this maps the macro-ion part of the problem onto a one-component problem where the macro-ions interact via a screened Coulomb potential with the Gouy-Chapman form for the screening length and an effective charge that depends on the macro-ion–macro-ion pair correlations. Numerical solutions of the effective one-component equation in the HNC approximation are presented, and in particular, the effects of macro-ion charge, nonadditive core diameters, and added electrolyte are examined. As we show, there can be a strong renormalization of the effective macro-ion charge and reentrant melting in colloidal crystals.