Sedimentation Equilibrium of Mixtures of Charged Colloids

0.10.08100.06η i 50 5 10 15 200.04i=2X (cm)0.02i=3ρ salt(µM)2015i=100 5 10 15 20X (cm)aE (mV/cm)21.510.50Q/2ρ ssinhφ(x)10 −6−10 −6 00 5 10 15 20X (cm)0 5 10 15 20X (cm)m 3g/Z 3ebm 2g/Z 2em 1g/Z 1eFigure A.2: Density profiles (a) and the electric field profile (b) of anequimolar ternary mixture of equally-sized colloids with charges Z i =(1000, 250, 125) and gravitational lengths L i = (1, 2, 1)mm with total packingfractions ¯η i = 0.005 in a 20cm ethanol suspension at room temperature,with monovalent ionic strength ρ s = 10µM in the reservoir. Almost completesegregation takes place into well-defined layers of pure components, with aslope η i(x) ′ = πρ s σ 3 /3Zi 2 L i and a constant electric field m i g/eZ i in the layerwith component i, as denoted by the dashed lines in (a) and (b), respectively.The inset in (b) shows a dimensionless measure for local charge neutrality(see main text).inset of Fig.2(b) shows the ratio of the total charge density Q(x) and the ioncharge density 2ρ s sinh φ(x), which is such that |Q(x)/2ρ s sinh φ(x)| ≪ 1 forall x except close to x = 0 and x = H where it is ∼ 1. This indicates that thesystem, with its inhomogeneous electric field, is yet essentially locally chargeneutral (but not exactly, and not at all at the boundaries), suggesting thata description on the basis of hydrostatic equilibrium within a local densityapproximation should be rather accurate [17].A.5 Polydisperse MixturesWe now extend our study to polydisperse mixtures, where one could expectsegregation into many layers on the basis of the results for two and threecomponents. We mimic the polydispersity by considering a system of n = 21components, with Z i distributed as a Gaussian with average of 250 and astandard deviation of 50. This distribution is shown in the inset of Fig. 3(a),where the vertical axis (¯η i ) is proportional to the relative frequency of speciesi in the sample. We consider two distributions for L i : (A) L i = 2mm for all59