Effective charge saturation in colloidal suspensions

Because micro-ions accumulate around highly charged colloidal particles in electrolyte solutions, the relevant parameter to compute their interactions is not the bare charge, but an effective (or renormalized) quantity, whose value is sensitive to the geometry of the colloid, the temperature or the presence of added-salt. This non-linear screening effect is a central feature in the field of colloidal suspensions or polyelectrolyte solutions. We propose a simple method to predict effective charges of highly charged macro-ions, that is reliable for mono-valent electrolytes (and counter-ions) in the colloidal limit (large size compared to both screening length and Bjerrum length). Taking reference to the non linear Poisson-Boltzmann theory, the method is successfully tested against the geometry of the macro-ions, the possible confinement in a Wigner-Seitz cell, and the presence of added salt. Moreover, our results are corroborated by various experimental measures reported in the literature. This approach provides a useful route to incorporate the non-linear effects of charge renormalization within a linear theory for systems where electrostatic interactions play an important role.