92168.pdf

Colloid stability 219

If the two particles are of the same material, this expression becomes

m = (8,13)

giving values of Ai3l for hydrosols of up to about 10" I9 J.

A 132 will be positive (interparticle attraction) where AH and A 22

are either both greater than or both less than A 33. However, in the

unusual situation where A 33 has a value intermediate between those

of AH and A 2 2, then Ai32 is negative - i.e. a repulsive van der Waals

interaction between the particles is predicted,

Am for the interaction of particles of the same material is always

positive - i.e. the van der Waals interaction energy is always one of

attraction. This interaction will be weakest when the particles and the

dispersion medium are chemically similar, since AH and A 33 will be

of similar magnitude and the value of Am will therefore, be low.

Potential energy curves

The total energy of interaction between the particles in a lyophobic
sol is obtained by summation of the electric double layer and van der
Waais energies, as illustrated in Figure 8.2.
The general character of the resulting potential energy-distance
curve can be deduced from the properties of the two components.
For the interaction between particles of the same material, the
double-layer repulsion energy (equation (8.5)) is an approximately
exponential function of the distance between the particles with a
range of the order of the thickness of the double layer (I/), and the
van der Waals attraction energy (equation (8.10)) decreases as an
inverse power of the distance between the particles. Consequently,
van der Waals attraction will predominate at small and at large
interparticle distances. At intermediate distances double-layer repul-
sion may predominate,* depending on the actual values of the two
forces. Figure 8.2 shows the two general types of potential energy
curve which are possible. The total potential energy curve V(l) shows
a repulsive energy maximum, whereas in curve V(2) the double-layer
repulsion does not predominate over van der Waals attraction at any
interparticle distance.
'Repulsion due to overlapping of electron clouds (Born repulsion) predominates at
very small distances when the particles come into contact, and so there is a deep
minimum in the potential energy curve which is not shown in Figures 8.2-8.4.