1. Colloidal Stability Introduction Interparticle Repulsion
Interparticle Attraction
Hamaker constant
Measurement techniques
Solvent Effects
Electrostatic Stabilisation
Critical Coagulation Concentration
Kinetics of Coagulation

2. Introduction Colloid stability: ability of a colloidal
dispersion to avoid coagulation.
Kinetic vs thermodynamic parameters.
Two kinds of induced stability:
(1) Electrostatic induced stability:
(like) charges, repel
van der Waal’s forces, attract
+ve
repulsive
stable V
-ve
attractive
unstable
H=particle separation

3. (2) Polymer induced or Steric Stability:
Stability is a result of a steric effect,
where the two polymer layers on
interacting particles overlap and
repel one another.

4. Interparticle Repulsion
Goal is to calculate repulsive potential
VR between two particles Yd H
Two possibilities for Y:
Due to adsorption of charged species
Y remains constant, s decreases
Due to intrinsic charge on the particles
s constrained to remain constant,
Y increases as overlap increases

5. Derjaguin Approximation
Approximate sphere by a set of “rings”
Assumes:
Constant potential case.
Sphere radius much larger than
double layer thickness, ka>10.
NO assumptions on potentials. dH a1 a2 H
low potentials (D-H approx.)
both particles the same.

6. Summary Simplest form of repulsive interaction: spherical
like particles
low potentials
large interparticle distances.
As k increases, repulsion decreases, destabilisation occurs:
increase in electrolyte concentration
increase in counter-ion charge.
Like charged particles stabilise, unlike charges destabilise.

7. Interparticle Attraction
Van der Waal’s forces: exist for all particles
atom-sized and up.
permanent dipole-permanent dipole
Keesom interaction
permanent dipole-induced dipole
Debye interaction
induced dipole-induced dipole
London or dispersion interaction
ALWAYS PRESENT
always attractive (?)
long range ( nm)

8. Form of van der Waal’s Interactions
(single particle)
b includes contributions from London,
Keesom and Debye forces.
b = f(polarizability, dipole moment)
Relative contributions:
Compound m a b % % %
Debye x1030 m3 x1077 Jm6Keesom Debye London

9. Van der Waal’s interactions between
two particles
Must sum over each volume element
of a large particle -- introduces error!
For two spheres close together (H<<a):
Equal Spheres
Unequal Spheres
Hamaker Constant!
where...
units of Joules

10. Hamaker constant determined by both
polarizability and dipole moment of
material in question...
Material A
(x 1020 J)
Means of measuring
determine from
a and m
(approximate and not always possible to get values)
Measure using bulk properties:
Surface tension is an obvious one

11. Direct Measurement of forces
This is a difficult thing to do...
Insert Fig here

13. Solvent Effects Previous results were in vacuum.
Presence of a solvent between particles
will affect the overall Hamaker constant: 3
solvent 3
solvent 1 2 3
solvent 3
solvent 1 2

14. Net result:
If particles are the same reduces to...
If particles are the same…
Aeff is always positive -- i.e attractive.
If A’s are similar, attraction is weak.
If particles are different…
Aeff is positive if A33>A11,A22 or A33< A11,A22 attractive.
Aeff is negative if A11<A33<A22 i.e. repulsive interaction if the solvent Hamaker constant is intermediate to those of the particles.

15. Electrostatic Stabilisation
We may combine the two expressions for
the potential experienced as follows…
Effects of changing A
Least control, set
by system.
Effective over
long range.
A=2x10-20 J
5x10-20 J
1x10-19 J
2x10-19 J
Y = 100 mV
k = 1x108 m-1
a = 100 nm

16. Effects of changing Y (i.e. g):
Much shorter range
effect.
More effective at low
values of Y.
Experimentally,
we measure the
zeta potential.
A = 2x10-19 J
k = 1x108 m-1
a = 100 nm

17. Effects of changing k (i.e. electrolyte concentration):
This is the item
we have most
control over!
Affects potentials
at short distances.
For a 1:1 electro-
lyte, the transition
is about
molar.
A = 2x10-19 J
Y = 25 mV
a = 100 nm

18. Critical Coagulation Concentration The Schulze-Hardy Rule
C.C.C. is fairly ill-defined:
The concentration of electrolyte which is just sufficient to coagulate a dispersion to an arbitrarily chosen extent in an arbitrarily defined time.
At the C.C.C:
dV/dH = 0 at V= 0 V H

19. Assuming a symmetrical electrolyte
(i.e. z+ = z-):
As Y becomes large g®1
small g®ze Y/4kT
Thus:
c.c.c.µ 1/z6 at high potentials
c.c.c. µ 1/z2 at low potentials
Effect is independent of particle size!
Strongly dependent on temperature!

20. Critical Coagulation Concentrations
(mmol/L)
Stronger dependency is typical of
adsorption in the Stern layer: softer
species tend to adsorb better (more
polarizable) so have a slightly
stronger effect.
Any potential determining ion will
have a significant effect.

21. Kinetics of Coagulation
No dispersion is stable thermodynamically.
Always a potential well.
Two steps in mechanism:
(1) Colloids approach one another
diffusion controlled: perikinetic.
externally imposed velocity
gradient: orthokinetic
(e.g. sedimentation, stirring, etc.).
(2) Colloids stick to one another
(assume probability of unity).
Two forces then controlling approach:
(1) Rapid diffusion controlled.
(2) Interaction-force controlled
(potential barrier, slows approach).

22. The Stability Ratio W= Rate of diffusion-controlled collision
Rate of interaction-force controlled collision
W = large : particles are relatively stable.
W = 1 : rate unhindered, particles unstable.
Diffusion-controlled (Rapid) Rate: R R1 R2
R1+R2

23. Fick’s Second law can now be used:
Which can be used to show that for
identical particles, the collision rate:
Since 2 particles are involved, the reaction
follows second order kinetics:
Thus, the rate constant is given by:
Only binary collisions
occur (dilute solution).
Neglect solvent flow out
of gap.
For second relationship
Stokes-Einstein is used.

24. The stability ratio can thus be given by:
kslow will depend upon the potential
around the particles.
Can acquire an expression for kslow by
modifying Fick’s second law with an
“activation energy”, V(R), where V(R)
is the potential barrier previously dicussed.

25. Assume a (very simple) barrier such
as the following... V
Vmax
2a k-1
particles
touch
Then…

26. Critical Coagulation Concentration
Can solve previous simple expression
for W in terms of Vmax, determined from
when dV/dH = 0
For water as dispersion medium
AgI Particle Coagulation

27. Plot is linear
When log W =0 we are at the CCC, breaks in the curve appear as coagulation occurs at a rapid rate.
Coagulation rates cannot be measured in this system beyond about log W = 4. Corresponds to an energy barrier of about 15 kT.
Can use the slopes to analyze for Yo, if the particle size is known.