Charge reversal of colloidal particles

– A theory is presented for the effective charge of colloidal particles in suspensions containing multivalent counterions. It is shown that if colloids are sufficiently strongly charged, the number of condensed multivalent counterion can exceed the bare colloidal charge leading to charge reversal. Charge renormalization in suspensions with multivalent counterions depends on a subtle interplay between the solvation energies of the multivalent counterions in the bulk and near the colloidal surface. We find that the effective charge is not a monotonically decreasing function of the multivalent salt concentration. Furthermore, contrary to the previous theories, it is found that except at very low concentrations, monovalent salt hinders the charge reversal. This conclusion is in agreement with the recent experiments and simulations. Introduction. – When a colloidal particle is placed inside a suspension containing multivalent ions its electrophoretic mobility can become reversed [1,2]. If this happens, an applied electric field will produce a drift of a colloid in the direction opposite to the one expected based purely on its chemical charge [3–5]. Somehow an excessive number of counterions must become associated with the colloid forming an overcharged (charge reversed) complex [6–11]. What is the cause of this curious behavior? There is a significant clues to the mechanism of charge reversal: the mean-field Poisson Boltzmann (PB) theory completely fails to account for its existence [12–15]. Since the PB theory does not take into account the ionic correlations, it is reasonable to suppose that they are the ones responsible for the colloidal charge reversal. Indeed, recently a number of theories have been advanced to establish the mechanism through which the counterion correlations lead to overcharging [3, 6, 7, 16, 17]. Unfortunately none of the theories can fully account for the experimental findings. While all the theories predict that addition of monovalent salt should greatly increase the amount of charge reversal, quite opposite is found experimentally and in the molecular dynamics simulations [4, 18, 19]. In fact it is observed experimentally that while small concentrations of 1:1 electrolyte have little effect on the charge reversal, larger concentrations destroy it completely [4]. Similar behavior has also been seen in recent molecular dynamics simulations [18, 19]. In this paper we will present a theory of charge reversal which accounts for the behavior observed in the experiments and simulations. The Model. – Consider a colloidal particle of radius a and charge −Zq, distributed uniformly over its surface, inside a suspension containing monovalent salt at concentration C and α-valent salt at concentration Cα. All ions are modeled as hard spheres of diameter ac. We shall assume that both salts are strong electrolytes so that in aqueous solution there