Colloidal Stability

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 Waals forces, attract

ve repulsive stable
V
0
-ve attractive unstable
Hparticle separation
3
(2) Polymer induced or Steric Stability Stabilit
y 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, kagt10.
• NO assumptions on potentials.

dH
a2
a1
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 Waals 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 (0.2 - 10 nm)

8
Form of van der Waals 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 Waals interactions between two particles
Must sum over each volume element of a large
particle -- introduces error!
For two spheres close together (Hltlta)
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. 1.27 here
12
(No Transcript)
13
Solvent Effects
Previous results were in vacuum. Presence of a
solvent between particles will affect the overall
Hamaker constant
1
2
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 As are similar, attraction is weak.
• If particles are different
• Aeff is positive if A33gtA11,A22 or A33lt A11,A22
  attractive.
• Aeff is negative if A11ltA33ltA22 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.
A2x10-20 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 concentrat
ion)
This is the item we have most control
over! Affects potentials at short
distances. For a 11 electro- lyte, the
transition is about 10-2 - 10-3 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
0
H
19
Assuming a symmetrical electrolyte (i.e. z z-)
As Y becomes large g1 small gze
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
23
Ficks 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
Ficks 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
0
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.