Sedimentation Equilibrium of Mixtures of Charged Colloids

Chapter 5Charge Regulation in the LowDensity RegimeAgain, a new chapter is going to disturb the equilibrium we found. Thesediment of charged particles, with differing properties, is now shaken again,and is given new degrees of freedom with the magic pen of the theorist. Thecolloidal particles so far had a fixed charge. In the suspensions we are goingto describe the colloids have the ability to adapt, to change their charge.This phenomenon is called charge regulation and complicates the systems wehave discussed so far considerably. The next sections show several attemptsto describe sedimentation of regulating colloids. The first attempt describesmultiple polydisperse systems of colloids of fixed charge. The systems onlydiffer in the charge distribution of the colloids. By comparing the sedimentswe will see what charge distribution has the lowest energy, or in other words,what distribution is favored by the colloids. This will be seen as the equilibriumdensity of regulating colloids that can exchange charge for free withother colloids, but not with the solvent.The next section is based on an article written by Biesheuvel [9]. The model isbased on a monodisperse system, where the colloidal charge number dependson the potential, by the so-called Langmuir isotherm.5.1 Regulation, the next challengeThe first model that we build to describe regulating systems is an extension ofthe PB theory of 4.2, and considers a monodisperse colloidal suspension, witha potential-dependent charge. This dependence is governed by the Langmuirisotherm (5.1.1).43