12.3.3 Depletion Interaction
Assume a dispersion of particles of radius rp that also contains some
nonadsorbing polymer; the polymer molecules form random coils, radius of
gyrationrg. The situation is depicted in Figure 12.10. The center of mass of
the polymer molecules cannot come closer to the particles’ surface than at a
distance about equal torg. This means that a solvent layer around the
particle of thickness d&rg is not available for (is depleted of) polymer.
For the whole dispersion thisdepletion layerwould make up a fraction
A?d=ð 1 jÞof the solvent, whereAandjare specific surface area and
volume fraction of the particles, respectively. Consequently, the presence of
the particles causes the polymer concentration, and hence its contribution
to the osmotic pressurePpol, to be increased. If now two particles touch
each other, their depletion layers partly overlap, thereby increasing the
volume of solvent available for the polymer. Consequently, aggregation of
the particles will lead to a decrease in osmotic pressure, hence to a decrease
in free energy. This implies that there is a driving force for aggregation. In
other words, the presence of the dissolved polymer induces attraction
between the particles.
FIGURE12.10 Illustration of the depletion of polymer molecules, radius of
gyrationrg, from a layer around spherical particles, radiusrp, and of the decrease in
depletion volume resulting from particle aggregation.