Ionic condensation and charge renormalization in colloidal suspensions

The very popular notion of effective or renormalized polyion charge is a concept of fundamental importance in the held of highly charged colloidal or polyelectrolyte solutions. In such suspensions, the electrostatic coupling between oppositely charged species induces a strong accumulation (or electrostatic "condensation") of counterions in the vicinity of the macroion surface. The basic idea is thus to consider the structural colloid and the condensed counterionic shell as a whole which carries an effective charge, Z(eff), much weaker than the structural one, Z(str). Consequently, as long as what happens far from the colloid is concerned, all Debye-Huckel-like linearized approaches which fail to correctly treat the nonlinear condensation phenomenon can still be used if Z(str) is more or less replaced by Z(eff). Beyond this basic idea, it remains to estimate a priori the value of Z(eff) It will be discussed how to deduce simple laws for the effective charge of spherical colloids from the Poisson-Boltzmann approach, analogous to Manning's law for linear polyelectrolytes. The validity of these laws will be tested, against more complete treatments. Lastly, it will be shown that while the notion of colloidal charge renormalization remains clear for dilute suspensions, it becomes incorrect at higher densities where the condensed counterionic shells overlap. (C) 1998 Elsevier Science B.V. All rights reserved.