Colloid Stability ?
Colloidal systems
• 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
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]
100
90
80
70
60
% 50
40
30
20
10
0
part of surface
atoms in %
20
10
5
2
nm
1
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
d
• Interaction Energy ( Vtot) – Distance of
Separation (d) Relationship
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 – Theory
Van der Waals attractive energy
a) between two plates:
attr.
Van der Waals
V
A

12 d 2
b) between two spheres:
attr.
Van der Waals
V
Aa

12 d
Double layer models
• Helmholtz
• Gouy Chapman
• Stern
Gouy Chapman model
• planar double layer
• Ions as point charges
Electrolyte theory
I distribution of ions in the diffuse double layer
(Boltzmann equation)
ni  x   ni   e
 zi e   x 
kT
II equation for the room charge density
  x    zi e ni  x 
i
III Poisson relation
d 2  x   4   x 

2
dx
0 
Aus I, II und III folgt:
d 2  x   4 

 zi e ni   e
2
dx
0  i
Poisson – Boltzmann - relation
 zi e   x 
kT
Solution of the P-B equation
d 2  x 
4


zi e ni e

2
dx
 0 i

zi e  x 
kT
For small potentials (< 25 mV) :
d  x 
2

k
 x 
2
dx
2
 x   k  0  e kx
Integrable form
DLVO – Theory
Electrostatic repulsive energy
Resulting repulsive overlap energy
a)
Between two plates:
rep
elektrost.
V

64 c kT
k
e
kd
c° – volume concentration of the
z – valent electrolyte
b) Between two spheres
8 k T   0  k d

e
2 2
e z
2
rep
elektrost.
V
2
ze 
2 kT


 e  1
 ze 

 e 2 kT  1
2
Vtot(d) =
attr
V (d)
Vvan der Waals = - A a / 12 d
A – Hamaker constant
a – particle radius
d – distance between the particles
1/k - thickness of the double-layer
+
rep
V (d)
Velectrost. = k e-kd
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:
8k T  0
e
2 2
e z
2
2
1
2
ze 
2 kT


 1
Aa
e

 ze
 12 d 2
 e 2 kT  1
ze 
kT


ccc  3,39  10 6k 6T 2   e ze  1
4 e z A
 e kT  1
3
5
5
3
3
0
2
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
electrolyte
CCC of a
Arsensulfid -Dispersion
Schulze-Hardy-ratio
NaCl
5,1 10-2
1000
KCl
5,0 10-2
1000
MgCl2
7,2 10-4
13
CaCl2
6,5 10-4
13
AlCl3
9,3 10-5
1,7
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