Sedimentation Equilibrium of Mixtures of Charged Colloids

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make them spark. . . Wait, wait! I’ve got it! Then you’ve got a polydisperse.. . suspension. . . of charged colloids!Exactly. You speak the language. Now, if you wait for several days or weeks,or years, you will see the colloids sinking slowly, until they reach the bottomor just stop sinking.They just stop? While they are in the air?Yes, well, in the water you mean. They want to go down to the bottom,but not all together. By entropy, a certain love or longing for chaos. Justbelieve me. What I want to say is that this sinking of the colloids is calledsedimentation, and when they all stop sinking they’ve reached equilibrium.Sedimentation equilibrium of mixtures of charged colloids?Sedimentation equilibrium of mixtures of charged colloids! You’re great!My brain hurts.4
Chapter 2Overview of required statisticalmechanics2.1 Thermodynamics and Legendre transformsThe first and second law of thermodynamics provide the relationsdE = T dS − P dV + ∑ αµ α dN α (2.1)dS ≥ 0 (2.2)between the internal energy E = E(S, V, {N α }) and the entropy S of aclosed system of volume V and N α particles of species α. The intensivefield variables T , P and {µ α }, where T is the temperature, P the pressureand {µ α } the chemical potential, are conjugate to the extensive variables S,V and N α . The entropy S is experimentally hard to control, and can bereplaced by its conjugate field variable T by a Legendre transfomation:F (T, V, {N α }) = E(S, V, {N α }) − T S (2.3)dF = −SdT − P dV + ∑ αµ α dN α (2.4)where F is called the Helmholtz free energy. If one is still left with fieldvariables that are difficult to handle in experiments, more potentials can befound with Legendre transformations. The Gibbs free energy, or free enthalpyisG(T, P, {N α }) = F (T, V, {N α }) + P V (2.5)5
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 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 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
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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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