Colloidal Aggregation FDSC400
Goals Aggregation rate Interaction potentials Electrostatic repulsion Van der Waals attraction DVLO theory Steric repulsion
Aggregation Rate Second order reaction (fast kinetics): or 2P P2
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
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
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.
Van der Waals Attraction Always attractive Very short range Hamaker constant ~5e-21 J
Surface Charge y=y0e-kh
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
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
DVLO Theory VDVLO=VVdW+Velectrostatic The height of the barrier increases with surface potential Its width increases with decreasing I
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?
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