Sedimentation Equilibrium of Mixtures of Charged Colloids

Z 16 =29932a10 3 η iZ 11 =2500.60.40.20150 200 250 300 350Z i10 3 η i0 5 10 15 201.5bA1010 3 η totB51010 3 0 5 10 15 20η i X (cm)151Z 14 =2790.500 5 10 15 20X (cm)00 5 10 15 20X (cm)Figure A.3: Density profiles of a 21-component colloidal suspension with aGaussian charge distribution as illustrated in the inset of (a), at total packingfraction 0.005, reservoir salt concentration ρ s = 3µM, and Bjerrum lengthλ B = 2.3nm. The gravitational lengths are as in case A (see main text) in(a), and case B in (b). In (b) the solid curves are for Z i > 250, and thedashed ones for Z i ≤ 250. The inset of (b) shows the total packing fractionprofile for case A and B, together with that of the underlying one-componentsystem (see main text).systems [15], it is tempting to argue that the theory is also (qualitatively)reliable for ternary or polydisperse systems, i.e. the predicted segregationand layering should be experimentally observable. One should bare in mind,however, that the present theory ignores the hard-core of the colloidal particles,and is therefore expected to break down at higher packing fractions(say η > 0.1) . It also ignores effects due to charge renormalisation, whichbecomes relevant when Z i λ B /σ i ≫ 1. Work on extending the theory in thesedirections is in progress [18, 17].All results presented in this paper were obtained with the zero-field boundaryconditions φ ′ (0) = φ ′ (H) = 0. We checked explicitly, however, thatother boundary conditions that respect global charge neutrality, such asφ ′ (0) = φ ′ (H) = eE ext /k B T (describing a suspension in a homogeneous externalelectric field E ext ) or φ(0) = φ(H) and φ ′ (0) = φ ′ (H) (describing ashort-circuited bottom and meniscus) give indistinguishable density profiles,except in two layers of thickness ∼ κ −1 ≪ 10µm in the vicinity of the bottomand the meniscus. This insensitivity to the boundary conditions is not surprising:the whole phenomenology in these systems is driven by the entropyof the microscopic ions, i.e. a bulk contribution to the grand potential thatshould dominate any boundary (surface) contribution.61