Sedimentation Equilibrium of Mixtures of Charged Colloids

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Other extensions are planned to include the high density regime, where packingeffects and excluded volume are important. For spherical particles theCarnahan-Starling approximation is thought to be suitable, for long rodsthe virial expansion, but this will be worked on in future. Charge regulation,strongly confined fluids, van der Waals forces. . . colloidal suspensionscan be made increasingly complicated, and their diversity will not be easilyexplained by a (simple) theory.The author is delighted to have the possibility to continue this work, participatingin the research on colloidal systems. For now, the reader will haveto wait. New problems, and new answers will follow in future.52
Appendix AArticleA.1 abstractWe theoretically study sedimentation-diffusion equilibrium of dilute binary,ternary, and polydisperse mixtures of colloidal particles with different buoyantmasses and/or charges. We focus on the low-salt regime, where theentropy of the screening ions drives spontaneous charge separation and theformation of an inhomogeneous macroscopic electric field. The resulting electricforce lifts the colloids against gravity, yielding highly nonbarometric andeven nonmonotonic colloidal density profiles. The most profound effect is thephenomenon of segregation into layers of colloids with equal mass-per-charge,including the possibility that heavy colloidal species float onto lighter ones.A.2 IntroductionSedimentation in a suspension of colloidal particles is of profound fundamentalimportance, and has been studied in detail for a long time. For instance,in 1910 Perrin determined the Boltzmann constant k B (and from this Avogadro’snumber) by comparing the measured equilibrium density profile ofa dilute suspension with the theoretically predicted barometric law [1], andmore recently the full hard-sphere equation of state was determined accuratelyfrom a single measurement of the sedimentation profile of a densesuspension of colloidal hard spheres [2, 3]. In rather dilute suspensions ofcharged colloids, however, strong deviations from the barometric distributionhave recently been theoretically predicted [4, 5, 6, 7, 8, 9], experimentally observed[10, 11, 12, 13], and simulated [14], at least in the regime of extremelylow salinity. The most striking phenomenon is that the distribution of colloidsextends to much higher altitudes than is to be expected on the basis of53
Page 1:
Sedimentation Equilibrium of Mixtur
Page 4 and 5:
5 Charge Regulation in the Low Dens
Page 6 and 7:
programming?Do I like programming?T
Page 8 and 9:
Additional information, often writt
Page 10 and 11: 1.2 Sedimentation equilibrium of mi
Page 12 and 13: make them spark. . . Wait, wait! I
Page 14: dG = −SdT − V dP + ∑ αµ α
Page 17: with ν λ = ν 0 +λw, the free en
Page 20 and 21: eservoir is:µ res± = k B T ln(ρ
Page 22 and 23: x-axis, only τ xx = −(ɛ/8π)E 2
Page 24 and 25: is denoted by ρ i . The salt ions
Page 26 and 27: numbers for the parameters Z i , L
Page 28 and 29: 2Case (a)4.5Case (a)ρ +E (mV/cm)1.
Page 30 and 31: is plotted as a function of Z 2 /Z
Page 32 and 33: 0.1i=320a0.080.06η i0 5 10 15 20ρ
Page 34 and 35: Z 16=2993a0.6210 3 η iZ 11=2500.40
Page 36 and 37: 0.02210.83E x(mV/cm)0.60.40.0140.25
Page 38 and 39: 4.6.1 The influence of the diameter
Page 40 and 41: 0.01ρ s=10 −3 Mρ s=10 −5 Mρ
Page 42 and 43: 0.03108642η i 0.01500 5 10 150.031
Page 44 and 45: The next constant that can be solve
Page 46 and 47: 4.6.5 Donnan-method for polydispers
Page 48 and 49: and try to fill the holes, or try t
Page 51 and 52: Chapter 5Charge Regulation in the L
Page 53 and 54: 5.1.2 Numerical resultsThe example
Page 55: Discussion The mean height of the s
Page 58 and 59: Z i (x) that converges, at least in
Page 62 and 63: their buoyant mass. The force that
Page 64 and 65: (π/6)ρ i (x)σi3 the local packin
Page 66 and 67: 0.010.008ρ +0.006 i=10.5hη i/σi
Page 68 and 69: species, and (B) L i = 2 × (250/Z
Page 70 and 71: A.7 AcknowledgementsIt is a pleasur
Page 72 and 73: length by Peter Debye. In dense col
Page 74 and 75: One quick check shows ∫ ∞dx Q(x
Page 77 and 78: Appendix CThe block modelThe model
Page 79: Index of frequently usedsymbols and
Page 83 and 84: Bibliography[1] J. Perrin, (1913),
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Sedimentation Equilibrium of Mixtures of Charged Colloids

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