1. Colloidal Aggregation
FDSC400

2. Goals Aggregation rate Interaction potentials Electrostatic repulsion
Van der Waals attraction
DVLO theory
Steric repulsion

3. Aggregation Rate
Second order reaction (fast kinetics): or
2P P2

4. Smoulokowski Kinetics
Gives the rate of collision of freely diffusing particles
We know the diffusion coefficient of spheres
Combining
D = diffusion coefficient, r = radius, h = continuous phase viscosity

5. Slow Kinetics kslow=kfast/W
Smoulokowski kinetics assumes each collision leads to a droplet aggregation.
In fact only a tiny proportion of collisions are reactive DG 2P G
kslow=kfast/W P2
Function of energy barrier

6. An Interaction Potential
A plot showing energy to move a particle from an infinite distance to a given distance from a second particle.
The pair of particles will try to find the optimum separation to minimize energy but can be blocked by a significant (>2-3 kT) energy barrier.

7. Van der Waals Attraction
Always attractive
Very short range
Hamaker constant
~5e-21 J

8. Surface Charge
y=y0e-kh

9. Effective Charge y=y0e-kh Low ionic strength=long range
Surface charge
Effective charge at distance h
y=y0e-kh
Distance from surface
Reciprocal Debye length
– increases with ionic strength
Low ionic strength=long range
High ionic strength=short range

10. Electrostatic Repulsion
Repulsive or attractive depending on sign of charges
Magnitude depends on magnitude of the charge
Gets weaker with distance but reasonably long range
Short range at high I

11. DVLO Theory VDVLO=VVdW+Velectrostatic
The height of the barrier increases with surface potential
Its width increases with decreasing I

12. Steric Repulsion Droplets approach each other Protein layers overlap
Proteins repel each other mechanically & by osmotic dehydration
What happens when protein molecules on different droplets are reactive?

13. Dispersed Systems -summary-
Types of dispersed system
Surface tension
Surface active materials
Properties of emulsions
Mechanisms of emulsion destabilization (stabilization)
Foams
Aggregation kinetics
DVLO theory and modifications