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

2][Pkdt

dP

Smoulokowski Kinetics

• Gives the rate of collision of freely diffusing particles

• We know the diffusion coefficient of spheres

• Combining

Drk 8

r

kTD

6

34kT

k

D =

dif

fusi

on c

oeff

icie

nt, r

= r

adiu

s,

=

cont

inuo

us p

hase

vis

cosi

ty

Slow Kinetics

• Smoulokowski kinetics assumes each collision leads to a droplet aggregation.

• In fact only a tiny proportion of collisions are reactive

2P

P2

G

G

kslow=kfast/W

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

-100

-50

0

0 20 40

Separation, nmV

A/k

T, J

h

ArVA 12

Hamaker constant~5e-21 J

• Always attractive

• Very short range

Surface Charge =0e-h

Effective Charge

0

2

4

6

8

10

12

0 10 20 30 40Distance

Pot

entia

l

Low ionic strength=long range

=0e-h

High ionic strength=short range

Effective charge at distance h

Surface charge

Distance from surface

Reciprocal Debye length – increases with ionic strength

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

)1ln(2 khE ekrV

0

100

200

0 10 20

Separation /nm

VE/k

T, J

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0 5 10 15 20

Separation

Inte

ract

ion

fre

e en

erg

y

I=0.3 I=0.4

I=0.5 I=0.6

• VDVLO=VVdW+Velectrostatic

• The height of the barrier increases with surface potential

• Its width increases with decreasing I

DVLO Theory

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