Important practical questions:

Transcription

1 Colloidal stability

2 Important practical questions: - Does dispersion change when T, P or... is changed? - If T, P or... is changed and the dispersion phase separates, what are then the final products? - How fast does the phase separation take place? Examples: - Food processing - Protein crystal growing - Rain makers - Cataract (grauer Star) - Synthesis of monodisperse colloidal particles - Percipitation of CaCO 3

3 Dutch example: Cheese Depletion of Wey proteins by Extracellular Poly-Saccharides ρ(wey proteins) low ρ(wey proteins) high

4 Phase separation: System with concentration ρ 0 decomposes in to a phase with a higher concentration ρ and a phase with a lower concentration ρ - Two types of phase separation, two types of kinetics : Liquid-solid or Gas-Solid Gas-liquid

5 Molecular systems hard to study: - Phase separation is too fast - Particles are too small to be observed with a microscope - No control on/knowledge of the interaction potential Use Colloids: - Mesoscopic Brownian particles dispersed in solvent instead of molecules dispersed in vacuum consider Π instead of P. Advantages: - Potential can be tuned by choice of particles and solvent - Dynamics is slow - Particles are detectable by microscopy and light scattering

6 Simple estimation of spinodal When B becomes sufficiently negative demixing takes place ( Π v / kt) c c φ = 1 ( B / v ) φ... Estimation spinodal: φ spinodal v = c B c HS B ( ϕ ) /B ϕ

7 Colloid Dispersion with mediated by depletion forces q=a FOS /R a FOS R

8 Second virial coefficient B can be computed from depletion potential: ( r) ω B = π r 1 d e kt r 0 for r < σ ω ( r) = Π V () r for σ < r < σ δ p overlap 0 for r > σ δ σ δ Π V () r p ov B = 4V π r 1 exp d r HS kt σ

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10 Demixing concentrations estimated from B De Hek and Vrij, 1980: 1 wt% HS-like silica a=46 nm mixed with PS in CHX ( a ) ( b ) 4 c PS (%) log (M/g mol 1 )

11 Mao, Cates, Lekkerkerker JCP 97 Sphere Rod Mixtures R = 3 μm c TRIS = 1. mm κ -1 = 1.4 nm φ(h)/k B T ( h) Δφ Geff h φdepl = Bexp{ κh} kt kt kt B B B h / nm 41 fn B=1400 k B T κ -1 = 13. nm L=880 nm φ 3 depl N A h = π c RL 1 kt B 3 M fd L

12 Example: stearyl alcohol-coated silica in cyclohexane Tunable attraction, hard core repulsion R V T V r sphere r sphere r R V Potential of colloidal particles similar to non-ideal gas van der Waals-like behavior of osmotic pressure Π.

13 Unstable region Temperature quench Π Unstable region: < 0 Π ρ Π or > 0 v Π v Connection to free energy:π = A V N V/N = v = 1 ρ d ( A/ N) Unstable region: < 0 d v A/N v

14 Phase separation? Minimize Free Energy A/N A 0 A A - A/N A 0 A A - 1/c 1/ c0 1/c v 1/c 1/ c 1/c 0 v A 0 >A A - A 0 <A A - d ( A/ N) < d v Concave, : YES 0 Convex, d ( A/ N) d v > 0 : NO

15 Spinodal A/N Π Π V/N d ( A dv / N ) = 0 v

16 Meta-stable region A/N A A -- A 0 1 / c 1/ c0 1/c A A -- <A 0 Lower free energy for big fluctuations But small probability

17 Unstable: Spinodal decomposition Meta-stable: Nucleation and growth A/N A/N v - Small fluctuations grow - Instantaneous start of phase separation - Phase separation starts throughout the sample v - Only big fluctuations grow - Induction time before phase separation - Phase separation only local

18 Where does the phase separtion end up?

19 Concentrations of lowest energy: d ( A / N ) d ( A / N ) Π( c ) = ( ) dv end = Π c dend v C Equality of chemical potential end F / C end N = Π ρμ A/N A 0 A end A -end μ 1 / c end 1/ c 1/c 0 end The line of minimum energy We found the binodal points (which depend on T or )

20 Spinodal and Binodal A/N Critical point Π Π( c end ) = Π( c end ) Π V/N d ( A dv / N ) = 0 v

21 Small density fluctuation δρ Attractive potential between particles

22 gas-liquid Lennard-Jones interaction: f ( a ) polymer concentration inversed temperature! α β ϕ

23 Simulation of the spinodal decomposition followed by domain coarsening End states after demixing Cates and Wagner, Nov. 000

24 Attractive potential between particles Small density fluctuation δρ Hard sphere

25 Fluid-solid f ( b ) fluid-solid α β ϕ No attraction, so: 1) very simple phase diagram. ) use equation of state for fluid and FCC crystal

26 Nucleation and growth Colloidal hard spheres P. N. Pusey Glass (see Zorn) heterogeneous homogeneous

27 Shallow quench Small density fluctuation δρ N x N1 Big density fluctuation δρ nucleation

28 Very deep quench nucleation Δt

29 Nucleation and growth Concentrated hard spheres, initial stage: nuclei dissolve Gasser et al, Science 9, April 001

30 Nucleation and growth Full picture: Gasser et al, Science 9, April 001

31 Hard spheres freely overlapping spheres Depletion potential: W dep (r) = Π V overlap (r) larger chains longer range of W range. more chains depth, more attractive W depth at c=c*, a HS /a FOS =5/3, W min =.5 kt

32 f Phase behaviour from f gas-liquid ( a ) f ( b ) fluid-solid α β ϕ α β ϕ f close ( c ) to a triple point f Metastable ( d ) gas-liquid fluid-solid α βγ δ α β ϕ ϕ

33 Compare to atomic/molecular fluids with Lennard-Jones interaction: Lennard-Jones interaction: polymer concentration inversed temperature!

34 Compare to atomic/molecular fluids with Lennard-Jones interaction: Lennard-Jones fluid n=1: polymer mixture: colloid-

35 Is dv ρ 1 true? Π = ( V ct V red ) α( N / V )