Sedimentation Equilibrium of Mixtures of Charged Colloids

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widths ξ i and block heights b i :n∑ξ i = Hi=1n∑b i ξ i = H ¯ηi=1(C.4)(C.5)Figure C.1 shows the full numerical solutions of a ternary system, with standardparameters as in tab. 4.1, charge number Z = (3000, 2500, 2000) andgravitational length L = (4, 3, 2)mm, together with the approximation withthe block model.0.010.008η i0.0060.0040.00200 5 10 15 20x (cm)Figure C.1: The full numerical solutions of a ternary system, with standardparameters as in tab. 4.1, charge number Z = (3000, 2500, 2000) and gravitationallength L = (4, 3, 2)mm, together with the approximation with theblock modelConclusion The block model is not accurate. It needs a fit parameter forthe jump constant t i . Moreover, the crossovers do not seem to be proportionalto ((Z N L n ) −2 − (Z n−1 L n−1 ) −2 ). A reason can be given by the lengths overwhich the crossovers take place, about 4 cm per crossover. A second reasonis the fact that the slopes of the profiles are not taken into account. Theslope model is therefore more accurate, and does not provide (much) morework.70
Index of frequently usedsymbols and namesBjerrum length? Dimensionless density? κ −1 ?!Here they are:symbol name relation to other symbols section of explanationLgravitational lengthk B TmgB.2λ B Bjerrum lengthe 2k B T ɛB.1κ −1 Debye screening length κ 2 = 8ρ s πλ B = 8ρ sπe 2k B T ɛB.1σ colloidal diameter B.3Z colloidal charge numbere elementary charge e1β inverse thermal energyk B TN number of particles 2µ chemical potential 2V (system) volume 2p pressure 2T temperature 2S entropy 2ˆρ microsc. number dens.∑ Ni=1 δ(r − r i) 2.3ρ number density 〈ˆρ〉 2.3η packing fraction πσ 3 ρ/6 B.2ψ electrostatic potential 3.2eψφ dimensionless potentialk B T3.2E(x) electric field ψ ′ (x) 3.2F intrinsic Helholtz free en. 2Ω grand potential 2k B Tmg71
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Sedimentation Equilibrium of Mixtur
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5 Charge Regulation in the Low Dens
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programming?Do I like programming?T
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Additional information, often writt
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1.2 Sedimentation equilibrium of mi
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make them spark. . . Wait, wait! I
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dG = −SdT − V dP + ∑ αµ α
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with ν λ = ν 0 +λw, the free en
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eservoir is:µ res± = k B T ln(ρ
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x-axis, only τ xx = −(ɛ/8π)E 2
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is denoted by ρ i . The salt ions
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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 60 and 61: Other extensions are planned to inc
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: Appendix CThe block modelThe model
Page 83 and 84: Bibliography[1] J. Perrin, (1913),
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Sedimentation Equilibrium of Mixtures of Charged Colloids

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