Sedimentation Equilibrium of Mixtures of Charged Colloids

5.2 Ideal distributionsCharge regulating systems have an additional degree of freedom to lowerthe energy, when compared to systems containing colloids of fixed charge.Therefore the equilibrium free energy of a charge fixed system is expected tobe an upper bound of a regulating system. A regulating system will now beimitated by a series of calculations of polydisperse systems (n=21) of colloidsof fixed charge. The total charge of the colloids∑21Q c =i=1∫ H0dx Z i ρ i (x), (5.8)is kept fixed, while the distribution is changed. The system with the lowestmean height is considered the equilibrium distribution of a regulating systemwith total colloid charge Q c , and free exchange of charge between the colloids(only). Actually we should consider the system with the lowest grandpotential, see discussion below. The sedimentation is pictured in figure 5.2.The distribution is chosen to be Gaussian.Z mean=250, 21 components, λ B=2.3nm, κ −1 =98nm, D=150, L=1mm, η mean=0.0050.020.015Center of mass4.53.50 1 2 3η tot 0.01Gauβwidth/Z meanequimolar case0.00500 5 10 15 20X (cm)Figure 5.2:046