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

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

Aggregation and gel formation

5

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

6

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

YoghurtCheese

CreamButter

7

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

Milk destabilization - cheese and yoghurt formation

9

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)

RLCA

Brownian motion results in collisions

11

particles experience effective interaction forces

Colloid stability and interaction potential

Colloid stability and interaction potential

12

stability

coagulation

flocculation

reversiblevs.irreversible

13

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

14

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!

explicit size dependence

15

-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

16

steric repulsion

poor solvent condition

steric stabilization

17

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.

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

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

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

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

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

28

no barrier -> diffusion limited barrier ≥ kT -> reaction limited

Colloid aggregation: DLCA and RLCA

Resulting clusters fractal, , dF fractal dimensionM ∝ RGa( )

dF

fractal aggregates

aggregation: formation of fractal structures