Thermodynamic and structural properties of the charged hard sphere model of polyelectrolytes: integral equation theories results

Dilute charged hard-sphere mixtures are investigated in a regime of charges and sizes of the ionic species which is typical of ionic micellar solutions and charged colloids. The adopted theoretical approaches are the hypernetted-chain (HNC) approximation and the mean spherical approximation (MSA). An extensive exploration of both thermodynamical and structural properties of the mixtures makes it possible to show the basic role played by the size asymmetry of the ionic species in favoring the onset of a well-defined ordering of the biggest particles, also called "micelles" in this paper. The structural arrangement of the micelles is compared to that of counterions and co-ions, which last are present when a salt is added to the micellar solution. The accurateness of the MSA vs the HNC is also discussed throughout the paper in order to identify the range of the physical parameters on which the MSA can be confidently used for the determination of thermodynamic and structural quantities of interest. Finally, the charge-charge and concentration-concentration structure factors, SQQ(q) and Scc(q), respectively, are studied as a function of the coupling strength Γ, defined as the ratio of the Coulombic to the thermal energy, and of the concentration c of the added salt. It appears that the increase of Γ, or the increase of the concentration, modifies the patterns of SQQ(q) and Scc(q) in a fashion indicating a trend to phase segregation of the solution, in qualitative agreement with recent experimental results.