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The Colloidal Domain
Chapter 8
Colloidal Stability
1
Peter Schurtenberger
Specific colloid properties: Stability
lyophilic lyophobic
colloids
colloidal system: dispersion medium is notsimple mixing of a “solvent”: fat, oil,components inorganic particles (Au, TiO2,…)surfactants, polymers,…
colloidal system is thermodynamically
stable unstable
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Colloids in daily life
Colloids everywhere:
Milk, cheese, paint, foam, ceramics (teeth implants, coatings,...), drugs,...
The colloid scientistʼs daily quiz:
• Formation of a river delta near the sea. Sedimentation of small particles that would not sediment by gravity only.
Why?
• Carbon is insoluble in water. The egypts (2500 BC) already
How?
made ink dispersing smoke particles in water.
Aggregation and Gelation - From Ceramics to Yoghurt
4
Medicine:protein aggregation(protein condensation diseases)
Food sciences:yoghurt and cheese
Materials science:ceramics
Colloid stability: fundamentals and applications
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Aggregation and gel formation
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Ds(c)
gel formation
viscoelastic networkδ2, τc
model systems: latex (Φ = 0.1- 30 %)
real systems: Al2O3 suspensions;
biopolymer solutions
U(r)
[kT]
r/2a1
energy barrier Rc ≈ aΦ−1 /(3−dF )
Aggregation and cluster formation
screening
addition of salt,acid, enzymes...
Milk - a food colloid system
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water 87wt%lactose 4.6wt%fat 3.9wt%protein 3.3wt% casein, 80% whey, 20%salts 0.7wt%
Colloidal systemmade of 5
principal components:
A colloid scientists view of milk:
+ + =
hydrophobic core
hydrophilic shell: κ-casein molecules → “hairy layer” → steric stabilization
Casein micelle:
<R> ≈ 100 - 150nm
Production 85,000,000,000 kg/year
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YoghurtCheese
CreamButter
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Milk - composition and products
Casein micelles - a model colloid?
8
Latex: Solid particles with pH-dependent charge density
S.H. Behrens et. al. , Langmuir 16, 2566 (2000)
D.J. McMahon, W.R. McManus J. Dairy Sci. 81, 2985 (1998)
Casein micelles: Self assembled particleswith pH-dependent charge densitybut electro-sterically stabilized
Dual binding model of casein micellesD.S. Horne, Int. Dairy J. 8 (1998) 171
Casein interaction potentialR. Tuinier, C.G. de Kruif, J. Chem. Phys. 117 (2002) 1290
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Milk destabilization - cheese and yoghurt formation
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hydrophilic shell: κ-casein molecules → “hairy layer” → steric stabilization
flocculation or aggregation of the micelles: • hairs are removed enzymatically (cheese) • acidification (glucono-δ lactone): → brush
collapse (yoghurt)U(r)
r
removing thestabilizing ʻhairsʼ from
the surface
The sol-gel transition in skim milk
10
0.001
0.01
0.1
1
10
100
1000
4.5
4.7
4.9
5.1
5.3
5.5
5.7
5.9
6.1
6.3
6.5
0 100 200 300 400 500 600
pHG', G"[Pa]
time [min]
pH induced
sol-gel transition
rU(r)
P. Schurtenberger, A. Stradner, S. Romer, C. Urban, and F. Scheffold, Chimia 55, 155 (2001)
P. Aichinger, Nestlé
gel point(collapse of electrosteric layer)
Instead of lactobacilli:slow pH-shift by addition of GDL
A. Stradner et al., Prog. Colloid Polym. Sci. 118, 136-140 (2001)
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RLCA
Brownian motion results in collisions
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particles experience effective interaction forces
Colloid stability and interaction potential
Colloid stability and interaction potential
12
stability
coagulation
flocculation
reversiblevs.irreversible
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DLVO theory
Interaction potential as sum of two contributions:
el.stat.: U(D) ~ exp(-κD)
vdW: U(D) ~ 1/Dn
(Derjaguin and Landau (1941),
Verwey and Overbeek (1948))
explicit dependence on R
(small particles are difficult to stabilize)
addition of salt -> destabilization of
particles
U(D) ≈2πσ 2R
κ 2εε0e−κD −
AR
12DHR
DLVO potential for latex particles
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Example: 2 spheres in water, R = 10 or 200 nm, Hamakerconstant=1.3x10-20J (latex), Surface charge density= 0.02 C/m2
10 mM NaCl
75 mM NaCl
pure vdW
10 kT
R = 10 nm R = 200 nm
Small particles are difficult to stabilize with a DLVO potential!
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explicit size dependence
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-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
0.9
0.01 0.1 1 10 100
VdWkT
dlvo10
dlvo25
dlvo37.5
dlvo50
dlvo75
dlvo100
dlvo125
dlvo150
dlvo175
dlvo200
dlvo300
dlvo500
dlvo1000
U/kT
distance between surfaces [nm]
-10
-8
-6
-4
-2
0
2
4
6
8
10
0.01 0.1 1 10 100
VdWkT
dlvo10
dlvo25
dlvo37.5
dlvo50
dlvo75
dlvo100
dlvo125
dlvo162.5
dlvo150
dlvo175
dlvo187.5
dlvo200
dlvo
U/kT
distance between surfaces [nm]
weak vs. deep secondary minimum
CCC approx. 160 mM
steric stabilization
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steric repulsion
poor solvent condition
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steric stabilization
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assume steric layer with 1 nm
Colloids in daily life
Colloids everywhere:
Milk, cheese, paint, foam, ceramics (teeth implants, coatings,...), drugs,...
The colloid scientistʼs daily quiz:
• Formation of a river delta near the sea. Sedimentation of small particles that would not sediment by gravity only.
Why?
• Carbon is insoluble in water. The egypts (2500 BC) already
How?
made ink dispersing smoke particles in water.
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Colloid stability and aggregation: initial stages of aggregation
calculate rate constant by looking at particle flux through spherical shell at distance r around „stationary“ or central particle using Ficks law:
4πr2Jr( )i= − 4πr2( )Di
d X1[ ]dr
k =∞ −
4 22
1
π e
D r rdr
a ( )
Vr( )/kT
k TB≈ 8
3ηk k e Q/kT∝ −
fast slow
how to measure rate constants
different salt concentrations:
1 M
♦ 0.75 M
▼ 0.5 M
0.25 M
■ 0.2 M
Δ 0.075 M
fast aggregation limit
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cluster size distribution
W =k fastkexp
Colloid stability and aggregation: stability ratio W
Stability ratio W: Measurements using particles with low charge density:
SMOLUCHOWSKI THEOR Y
EXPERIMENT
CLASSICALDLVO-THEOR Y
DLVO-THEOR Y INCLUDINGHETEROGENEITIES
AGGREGA TION RA TE CONST ANTS OF SULF ATE LA TEX P ARTICLESELECTROL YTE NaClO , RADIUS 108 nm4
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Colloid stability and aggregation: stability ratio W
Stability ratio W: Measurements using particles with low charge density (S. H. Behrens et al., Langmuir (1998)):
• rate constant determined by barrier height
• DLVO breaks down at r < 1 nm
30.9.2011
24
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Colloid stability and aggregation: how to model aggregation
Computer simulations:
diffusion limited (DLA, fast) vs. reaction limited (RLA, slow) cluster growth
seed particle
starting circle
killing circle
DLA simulation: fractal growth
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DLA simulation: how to determine fractal diemnsion
Determination of the fractal dimension of a cluster generated via computer simulation ofmonomer-cluster aggregation:
i) "experiment counting numbers": N(r) ~ rdF
ii) determination of the density-density correlation function
g(r) ~ N(r)
rd ~ rdF - d , d: lattice dimension
→ S(q), d.h. direct comparison with results from scattering experiments
DLCA RLCA
power-law cluster size distribution
N(M;t) = A2M−τ exp −
MMc (t)
⎛
⎝ ⎜
⎞
⎠ ⎟
(slightly) peaked cluster size distribution
N(M;t) =A1
M2 (t)1−
2M2(t)
⎛
⎝ ⎜
⎞
⎠ ⎟ M−1
RLCA
Cluster-cluster aggregation - the two limiting regimes
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no barrier -> diffusion limited barrier ≥ kT -> reaction limited
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Colloid aggregation: DLCA and RLCA
Resulting clusters fractal, , dF fractal dimensionM ∝ RGa( )
dF
fractal aggregates
aggregation: formation of fractal structures