Colloid Stability ?

• A state of subdivision in which the particles, droplets, or bubbles dispersed in another phase have at least one dimension between 1 and 1000 nm

• all combinations are possible between :

gas, liquid, and solid W. Ostwald

Colloidal systems

Surface area of colloidal systems

• Cube (1cm; 1cm; 1cm) after size reduction to an edge length of 500 nm: surface area of 60 m2

• Spinning dope (1 cm3) after spinning to a fibre with diameter of 1000 nm:

fiber length of 1273 km

• 1 liter of a 0.1 M surfactant solution: interfacial area of 40000 m2

Surface atoms [in %] in dependence on the particle size [in nm]

0102030405060708090

100

20 10 5 2 1

part of surfaceatoms in %%

nm

Colloidal systems

• have large surface areas

• surface atoms become dominant

Colloid stability

• Colloidal gold: stabilized against coagulation !

• Creme: stabilized against coagulation !

• Milk: stabilized against coagulation !

Particle – Particle interactions

• Interaction Energy ( Vtot) – Distance of Separation (d) Relationship

d

Vtot(d) = Vattr(d) + Vrep(d)

- Van der Waals attraction - Electrostatic repulsion

- Steric repulsion

DLVO - Theory

• 1940 – Derjaguin; Landau; Verwey; Overbeek

• Long range attractive van der Waals forces

• Long range repulsive electrostatic forces

DLVO – TheoryVan der Waals attractive energy

a) between two plates:

b) between two spheres:

2.

12 d

AV attr

WaalsderVan

d

aAV attr

WaalsderVan 12.

Double layer models

• Helmholtz

• Gouy Chapman

• Stern

Gouy Chapman model

• planar double layer

• Ions as point charges

Electrolyte theory

kT

xez

iii

i

enezxd

xd

0

2

2 4

I distribution of ions in the diffuse double layer (Boltzmann equation)

II equation for the room charge density

III Poisson relation

Aus I, II und III folgt:

Poisson – Boltzmann - relation

kT

xezenxn i

ii

xnezx iii

02

2 4 x

xd

xd

Solution of the P-B equation

xekx

xxd

xd

0

22

2

For small potentials (< 25 mV) :

Integrable form

kT

xez

iii

i

enezdx

xd

0

2

2 4

DLVO – TheoryElectrostatic repulsive energy

Resulting repulsive overlap energy

a) Between two plates:

c° – volume concentration of the z – valent electrolyte

b) Between two spheres

drepelektrost e

kTcV

64

.

2

2

2

220

22

.

1

18

kT

ze

kT

ze

drepelektrost

e

ee

ze

TkV

Vtot(d) = Vattr(d) + Vrep(d)

Vvan der Waals = - A a / 12 d Velectrost. = k e-d

A – Hamaker constant

a – particle radius

d – distance between the particles

1/ - thickness of the double-layer

Electrostatic stabilization

stabilized against coagulation

Kinetically stable state

energetic metastable state in the secondary minimum with an energy barrier

Critical coagulation concentration (CCC)

• The energy barrier disappears by adding a critical amount of low molecular salts

DLVO – Theory

(CCC)

Vtot / dd = 0 Vtot = 0

 for two spheres:

2

266

30

3553

2

2

2

21

220

22

1

1

4

1039,3

121

18

kT

ze

kT

ze

kT

ze

kT

ze

e

e

Aze

Tkccc

d

aA

e

ee

ze

Tk

DLVO – Theory

(CCC)

• For two spheres the ccc should be related to the valency (1 : 2 : 3) of the counterions as:

1000 : 16 : 1,3

CCC of a colloidal dispersion as a function of the salt concentration

AlCl3

CaCl2

MgCl2

KCl

NaCl

electrolyte

1,79,3 10-5

136,5 10-4

137,2 10-4

10005,0 10-2

10005,1 10-2

Schulze-Hardy-ratioCCC of a

Arsensulfid -Dispersion

Steric stabilization

• What will be happen when we add polymers to a colloidal dispersion ?

Particle – Particle interactions

Polymer adsorption layer

Particle – Particle interactions

Overlap of the polymer adsorption layer

Overlap of the adsorption layer

• Osmotic repulsion

• Entropic repulsion

• Enthalpic repulsion

Sterically stabilized systems can be controlled by

• The thickness of the adsorption layer

• The density of the adsorption layer

• The temperature

Stabilization and destabilization in dependence on the molecular weight of the added polymer

Stabilization and destabilization in dependence on the

polymer-concentration