The renormalized jellium model for spherical and cylindrical colloids

Abstract

Starting from a mean-field description for a dispersion of highly charged spherical or (parallel) rodlike colloids, we introduce the simplification of a homogeneous background to include the contribution of other polyions to the static field created by a tagged polyion. The charge of this background is selfconsistently renormalized to coincide with the polyion effective charge, the latter quantity thereby exhibiting a non-trivial density dependence, which directly enters into the equation of state through a simple analytical expression. The good agreement observed between the pressure calculated using the renormalized jellium and Monte Carlo simulations confirms the relevance of the renormalized jellium model for theoretical and experimental purposes and provides an alternative to the PoissonBoltzmann cell model since it is free of some of the intrinsic limitations of this approach.

Hydrodynamic and electrokinetic effects on the dynamics of charged colloids and macromolecules

“…Likewise, a renormalized value for κ should be used. Several schemes have been developed to relate the effective Z and κ to the bare ones [5,6,7,8]. The outcome of these schemes depends on the approximation made for the free energy functional, and on additional simplifications used such as the spherical cell or macroion jellium models.…”

Renormalized jellium model for colloidal mixtures

“…The dimensionless electrostatic potential around a given colloid of type i, centered at position r = 0 then obeys [8,[10][11][12] …”

“…The key point in the jellium approach is that the charge of other colloids around a given tagged macroion is smeared out to form a homogeneous background of charge density ρ eZ back , in which the small ions are then immersed. A self-consistency requirement connects this background charge with the effective charge of the various species, see Refs [8,[10][11][12] for more details.…”

“…First, we present in section II the main ingredients of the jellium model, together with a new procedure that allows to solve the problem self-consistently for mixtures, in a more efficient way than hitherto proposed. Compared to the method used in Refs [8,10] for monodisperse colloids, an elegant reformulation was reported in [11,12], that significantly speeds up the resolution. We shall argue that this reformulation looses its suitability when dealing with mixtures.…”

“…As an alternative to the cell picture, a renormalized jellium model was proposed in Ref. [8], elaborating on an idea put forward by Beresford-Smith et al [9], who nevertheless did not implement the renormalization procedure, which turns out crucial [8,[10][11][12].…”