Sedimentation Equilibrium of Mixtures of Charged Colloids

4.6.1 The influence of the diameterThe volume of the colloids plays no part in the theory of section 4.2. Changingthe diameter σ i will therefore not lead to different solutions for the densityprofiles and potential. The origin of the independency of size lies in the densityregion for which the theory applies. Since the density is low, the colloidsare considered an ideal gas, interacting as point particles, although having aspecific size σ. As already shown in figures 4.4 and 4.6, this approximationis not that bad, when comparing to simulations that do include size. Althoughthe density profiles ρ i (x) and the potential φ(x) do not change, thedimensionless packing fraction η can have spectacular solutions, though. Intheory, every colloidal family with charge number Z, gravitational length Land diameter σ, can be positioned at a desirable height, by adding ’invisible’small components of other colloids. Also the dimensionless density distributioncan be adjusted as well, by adding the right components. This maysound remarkable, but it is nothing more than a magic trick. The diameterof the particles is just a scaling factor for the density profiles. By choosing avery low diameter for some components it looks like if the others ’float’ in thesuspension. An example, figure 4.11, shows the deceitful packing fraction.0.02110.80.012E x(mV/cm)0.60.40.2η i0 20 40 60 80 100304x (cm)500 20 40 60 80 100x (cm)Figure 4.11: An example of a 10 component system. Components 1 - 5 havea particle radius σ big = 1500nm. Components 6 - 10 cannot be seen, becausetheir radius σ small is too small: σ small ≪ 0.01σ big . The number density isidentical to the number density of figure 4.9. The packing fraction though,looks spectacular. The diameter of the particles is just a scaling factor of thepacking fractions in our theory.It remains a question for experimentalists how big they can make their particlediameters in order to get results like figure 4.11. For our theoreticalobservations though, this factor does not play a role until we are going to30