1. Colloids
1.1. Introduction
1.2. Types of colloids
1.3. Forces between colloidal particles
1.4. Charge stabilization
1.5. Steric stabilization
1.6. …
Hamley, chapter 3
Jacob Israelachvili: Intermolecular & Surface Forces,
2nd edition, Academic Press London 1992, chapters 10, 11
John C. Berg, An Introduction to Interfaces & Colloids,
World Scientific Singapore, 2010, chapters 6A-B, 7A-C,
1
1.1 Introduction
toothpaste
dispersed and
continuous phase
paint
milk:
colloidal
dispersion
aerogel
2
Definition of a colloid
* dispersed and continuous phase
* dimensions of one component between
• those of molecules and
• those of macroscopic particles
→ large surface-to-volume ratio
→ interface/surface chemistry very important
→ charge stabilization or steric stabilization
reversible aggregation: flocculation into flocs
irreversible aggregation: coagulation
→ sedimentation or creaming
3
Length scales
4
1.2 Types of colloids
here: two-phase dispersions
Continuous phase
(medium)
Dispersed phase
Gas
Liquid
Solid
Gas
All gases
are miscible.
Aerosol:
cloud, mist, fog
Solid aerosol:
smoke
Liquid
Foam:
Emulsion:
soap, detergents milk, mayonnaise
Sol:
Ink, blood, paint
Solid
Solid foam:
aerogel
Solid sol:
glass
Gel:
cheese, gelly
5
Foams and liquid foams
liquid foam: dispersion of a gas in a liquid
solid foams: dispersion of a gas in a solid
liquid foams
soaps and detergents
aerogel (solid foam)
99 % air
6
Aerosol
liquid particles dispersed in gas
mist
(visibility higher)
fog
(visibility < 1 km)
clouds
(liquid or frozen droplets)
7
Solid aerosol
solid particles dispersed in gas
fire extinguisher:
tiny solid particles
(40% alkaline metal oxide)
suspended in gas
(60% CO2, water vapor, N2)
particulates in air
8
Emulsion
mixture of 2 immiscible liquids:
liquid dispersed in another continuous liquid
emulsifier
emulsion
dispersed oil droplets in water
Ouzo:
• ~45% ethanol
• ~55% water
• trans-anethol (t-A):
soluble in ethanol,
insoluble in water
• addition of water
→ clear solution becomes
milky (opalescent)
see NSSM
NSSM--1
oil in water
9
Gel
3D solid network dispersed in liquid medium
silica gel structure
hair gel
(dilute crosslinked system
of cationic polymers)
solid phase:
• exhibits no flow
• weight similar to liquid
stickiness due to the 3D solid
10
Sols
solid particles in a liquid
paints
blood
red and white
blood cells
http://www.colloids.uni-freiburg.de
11
Solid sol
solid particles in another continuous solid
Metal oxide (pigments) in glass
Compounds
Colors
iron oxides
greens, browns
manganese oxide
deep amber
cobalt oxide
deep blue
gold chloride
ruby red
selenium compounds
reds
carbon oxides
amber/brown
lead with antimony
yellow
12
Sol-gel process
gel: solid 3D network in liquid medium
internal network structure due to
physical, chemical, or H-bonds
hydrogels:
solvent is water
organogels: in organic solvent
aerogels:
solvent is air
sol-gel process → light porous materials
crosslinking
sol
(solid in liquid)
replace liquid
with air
(heating)
gel
(liquid in solid network)
aerogel
13
1.3 Forces between colloidal particles
•
•
•
•
van der Waals forces
electric double-layer forces
entropic forces
excluded volume repulsion
1.3.1 Van der Waals forces
attractions between electric
dipoles of molecules
C
W =− 6
r
Keesom forces:
permanent dipole–permanent dipole forces
Debye forces:
permanent dipole–induced dipole forces
London dispersion forces:
instantaneous induced dipole-induced dipole
14
Van der Waals forces between surfaces
pairwise summation of potentials
between molecules in different particles
h
two flat infinite surfaces
in distance h in vacuum:
πCρ 2
AH
V ( h) = −
≡−
2
12h
12πh 2
AH: Hamaker constant:
effective strength of
van der Waals interaction
between particles
general expression:
AH = π 2Cρ1 ρ 2
15
Hamaker constant
typical values: 10-19 J across vacuum
even though polarizabilities and
molecular sizes are very different,
the Hamaker constants are very similar
16
Example for vdW forces: The Gecko
14,000 tiny
foot hairs/mm2
(Setae)
each tiny foot hair
has many spatulae
force per spatula: ~10-100 nN
40g gecko: total clinging force of about 20 N
→ using van der Waals forces,
the Gecko can walk along the ceiling
17
Maximum radius of Gecko foot spatula
radius R
Fadh
∂Vadh AH R
=−
=
∂h
6h 2
Fgrav
4 3
= πR ρg
3
6×10-20
AH R
Vadh (h) = −
6h
1/ 2
 AH 

→ R =  2
 8h πρg 
kg/m3,
J, ρ = 3000
AH =
g = 9.81 m/s2 , h = 1.7 Å
Force (mN)
distance h
spherical quartz particle
hangs on flat quartz surface
against the gravity force
if adhesive force = gravity:
3
2
Gravity
1
0
→ particle with R < 1.7 mm can hold
0
to the flat surface against gravity force
van der
Waals
1
2
Radius (mm)
3
Interaction between spheres
spheres of equal radius R
in distance h << R in vacuum
(Derjaguin approximation):
V =−
adhesion force:
F=
AH R
12h
AH R
12h 2
two spheres of radius R = 1 cm
in contact at h = 0.2 nm
(AH = 10-19 J):
F = 2 ×10 −3 N = 0.2 g
R = 10 nm, h = 0.2 nm:
F = 10 −6 N = 0.1mg
energy: E = −10 −14 J = 2 ×106 k BT
at distances above ~5 nm: retardation effects
19
Derjaguin approximation
spheres of equal radius R in distance D << R in vacuum:
consider not only
energies, but also
forces between
particles
integrate the force between small circular regions
of area 2πx dx on one surface and the opposite surface,
which is assumed to be locally flat and at a distance
Z = D + z1 + z2 away
20
Derjaguin approximation
F ( D) = ∫
Z =∞
Z =D
2πxdxf ( Z )
 RR 
→ F ( D) ≈ 2π  1 2 W ( D)
 R1 + R2 
f(Z): normal force per unit area
W(D): energy per unit area of
two flat surfaces at distance D
for sphere near flat surface: R2 >> R1:
→ F ( D) ≈ 2πR1W ( D)
for two equal spheres of radius R:
→ F ( D) ≈ πRW ( D)
for two spheres in contact:
W(D) = 2γ (surface tension)
adhesion force between two spheres
→ F ( D ) ≈ 4πγ
R1 R2
R1 + R2
21
Interaction between particles in a medium
two phases 1 in a liquid medium 2
→ reduction of the van der Waals interaction
→ effective Hamaker constant, which is sum of
particle-particle and medium-medium contributions
2
(
(
)
)
2 2
2
2 3/ 2
 ε 1 − ε 2  3hν e n − n
3
 +
AH = k BT 
2
4
 ε 1 + ε 2  16 2 n1 + n2
2
1
ε1,2: dielectric permittivity
ve:
main electronic absorption
frequency in the UV
ve ~ 3x1015 s-1
n1,2: refractive index in the visible
→ vdW force between identical bodies
in medium always attractive
interaction between hydrocarbon across water
is 10 % of the one across vacuum
22
Stability of colloids
The discussed forces due to
dispersion interactions are attractive
→ colloidal solutions not stable
→ possibly formation of aggregates
→ sedimentation or creaming
Repulsive forces are needed
to stabilize a colloidal solution:
• steric stabilization by
adsorption of polymers
• electrostatic stabilization
by electric charges
polymer
23