newtons, for films in pascals (N?m^2 ). The net pressure in a film due to
interaction forces is called thedisjoining pressure.
The nature of the various attractive and repulsive forces that can act is
discussed in the rest of this chapter. Because entropic contributions often are
involved, we need to consider free energy (more precisely Gibbs energy)
rather than internal energy. Especially the repulsive forces tend to depend
greatly on the substances adsorbed onto particles or film surfaces, i.e., on
surfactant properties and concentration.
12.2 DLVO THEORY
The first useful theory of colloidal interaction forces and colloid stability
(against aggregation) was developed independently by Deryagin and
Landau and by Verwey and Overbeek. Hence it is called the DLVO theory.
It takes into account the combined effects of van der Waals attraction and
electrostatic repulsion.
12.2.1 Van der Waals Attraction
Van der Waals forces are briefly discussed in Section 3.1; for interaction
between atoms or small molecules, their strength decays with intermolecular
distance to the power 6. In the Hamaker–de Boer treatment, two
macroscopic bodies are considered, and the van der Waals interaction
between each atom in one of the bodies with all of the atoms in the other
body are summed (actually a double integration procedure is applied). The
result is that the total interaction energyVcan be given by the product of a
material property, called the Hamaker constantA(expressed in J or units of
kBT), and a term depending on the geometry of the system. These relations
are relatively simple.
Geometry. For two spheres, radii R 1 and R 2 , separated at a
distancehbetween the particle surfaces, and ifh 5 R 1 ;R 2 , the result is
VvdW;s¼AR
12 h
R¼2 R 1 R 2
R 1 þR 2
ð 12 : 1 ÞHence the repulsive energy is inversely proportional to interparticle
distance. For two parallel flat plates of a size 4 hand a thickness larger