Sedimentation Equilibrium of Mixtures of Charged Colloids

Chapter 7Conclusions and OutlookWithin the framework of density functional theory we derived a Poisson-Boltzmann theory to describe the equilibrium of diluted systems of chargedcolloids under sedimentation. The numerical solutions for monodisperse(n=1) cases show strong deviations from the barometric distribution in thelow salt limit, as was already shown in experiments [11]. For binary (n=2)and ternary (n=3) systems the solutions show segregation of components aswell. The salt entropy is seen to be the driving mechanism behind theseeffects. The colloids are lifted by an electric field that cancels gravity. Sincecomponents of different mass per charge cannot be lifted by the same electricfield, the components order according to their mass per charge and formlayers. Although the ordering still lacks experimental confirmation, the numericalsolutions agree very well with Monte Carlo simulations [15, 22]. Forpolydisperse systems (n=10,n=21), the same effects are predicted by the theory,although the segregation is in many cases weaker than in the binary andternary examples.An extension of the theory to charge regulating systems can be made byconsidering the colloidal charge to be dependent on the electrostatic potential,according to the Langmuir isotherm. The numerical results from thisextension do not show the linear density profiles, and constant electric fieldsas calculated from the theory describing charge stabilised colloids. Althoughthe solutions show the same phenomena, the profiles decrease more stronglywith height. This can be understood by comparing monodisperse systemsof charge regulating colloids with polydisperse systems of charge stabilisedcolloids.The exact dependence of the charge still lacks a proper derivation, and thenumerical calculations are not confirmed by simulation data or experiments,making the extension less underpinned than the PB theory for charge stabilisedsystems.51