W. Richard Bowen and Nidal Hilal 4

44 2. MEASUREMENT OF PARTICLE ANd SURFACE INTERACTIONS
model. These models will be described in more detail later in this chapter.
The particular relationship between W a and A H depends again upon the particular
geometry of the interaction. For a sphere–plane interaction [21],
AH � 6D0 Wa
(2.25)
This is essentially the same as the force laws found in Table 2.1, replacing
the minimum separation distance, D, with an interatomic spacing
value. In turn, W a may be related to the interfacial energies by the following
relationship:
Wa � � � � � �
13 23 12
(2.26)
where � is the interfacial energy, subscripts 1 and 2 denote the two solid
bodies (in this case, the probe and the surface) and 3 denotes the intervening
medium. With this method, there is great potential for error. Care
must be taken when calculating surface forces from adhesion measurements.
Interactions not present at long range may be present when contact
is made, such as solvation forces as well as the effects of roughness
and deformations. In one study [23], both long-range forces and adhesion
measurements were observed between latex spheres and glass surfaces
in aqueous solution using the colloidal probe technique. Adhesion values
were estimated on the basis of the long-range interaction forces. These
calculated adhesion values were approximately 20–30 times greater than
the adhesion values actually measured.
2.3.2 Electrical double layer Forces
As stated above, van der Waals interactions between identical particles
are always attractive. If this was the only force present between colloidal
particles in solution, then dispersions would be unstable due to aggregation,
leading to the formation of a precipitate. Fortunately, this is not the
case as particles in water or any liquid of high dielectric constant usually
possess charges on their surfaces. Repulsion between identically charged
particles is long range in character and is often sufficient to overcome the
aggregating effects of attractive van der Waals interactions.
2.3.2.1 The Electrical Double Layer
From observations of colloidal systems, it can be concluded that particles
dispersed in water or any liquid with a high dielectric constant will
usually develop a surface charge. The charging of a surface in a liquid
can be brought about by one of two charging mechanisms [2]:
1. By the ionisation or dissociation of surface groups, which leaves
behind a charged surface (e.g. the dissociation of protons from carboxylic
acid groups, which leaves behind a negatively charged surface).