between the surfaces over which interaction forces are significant is nearly
always much smaller than the particle size. The interaction free energy is
often denotedV; it is often divided bykBT, the kinetic energy involved in the
encounter of two particles in Brownian motion. This is done because the
interaction curves (Vversush) are often used to predict whether particles
that encounter each other by Brownian motion will aggregate or not.
Interaction Curves. Figure 12.1 gives a hypothetical example of
such a curve. At very close distance (<0.5 nm), the interaction free energy is
always (large and) positive, due to hard-core repulsion (Section 3.1), but at
longer distances the shape of the curves can vary widely. In the drawn curve,
a primary minimumis shown at A, a maximumat B, and a secondary
minimumat C. Starting at largeh, the particles will at some time reach
position C. If it is a shallow minimum, the particles can diffuse away from
each other; if the minimum is deeper, they may stay aggregated without
actually touching each other. If the maximum at B is substantial, the
particles will not pass it. The maximum can be seen as a free energy barrier,
retarding or even preventing close approach. However, the maximum value
ofV cannotbe seen as representing an activation free energy as used in
molecular reaction kinetics (Section 4.3). The slowing down of aggregation
by an energy barrier will be further discussed in Section 13.2.1. If the
particles can come closer, i.e., pass the free energy barrier, they will reach the
primary minimum A.
The broken lines in Figure 12.1 give two extremes. In a situation
characterized by the upper curve, aggregation will never occur. In other
words, the dispersion is stable against aggregation. If the lower curve would
apply (no maximum and a deep minimum), particles will reach each other
and will stay forever at touching distance, provided that the external
conditions (temperature, pH, etc.) are kept constant. In other words,
irreversible aggregation has occurred. At intermediate situations, slow
aggregation may occur, or aggregation may be to some extent reversible.
Importance. Some situations in which colloidal interaction forces
play an essential role are the following:
Aggregation of particles, i.e., does it occur and if so at what rate?
The rheological properties of particle gels greatly depend on the
strength of the interaction forces between the particles (Section
17.2.3).
Thestability of thin filmsagainst rupture (Section 13.4.1).
In understanding the last case, the interaction between two flat plates
or surfaces is needed. Assuming the dimensions of the film to be much larger