Although the average value ofGwould be the same as in the former case,
copious aggregation occurs due to bridging. A bare particle that meets a
particle with a polymer layer will immediately stick to it, because
some segments of a protruding polymer chain can adsorb onto the bare
surface.
This example also shows that bridging is more likely if the total
amount of polymer is small compared to the amount that can become
adsorbed, i.e.,A?Gplateau. Since aggregation causes a dispersion to attain a
greatly increased viscosity, we can thus have a situation where addition of
more polymer (often called a thickening agent) leads to a lower viscosity.
Similar situations can be observed if O–W emulsions are made by
homogenization with variable amounts of protein, provided that the protein
has high molar mass. A small protein concentration in the aqueous phase
may then result in a highly aggregated emulsion, whereas a normal emulsion
is obtained if more protein is added before homogenization. (Adding it
afterwards does not help, since it will take a very long time before
equilibrium adsorption layers have been formed.)
One would thus expect that a dispersion of particles having a suitable
polymer layer that causes steric repulsion will always be stable against
aggregation, as long as no bridging adsorption occurs. This is not always
true. Figure 12.8b illustrates another type of bridging, i.e., bycross-linking.
Steric repulsion does not prevent contact between particles. On the contrary,
it only works when the polymer layers overlap, which implies that segments
of polymer chains from two particles will frequently touch each other. If
these segments can react with each other, a bridge is formed. An example is
the formation of 22 S 22 S 22 bridges between protein layers. This may
especially happen during heat-treatment of the system, but for some
proteins even at room temperature.
Another case concerns particles stabilized by apolyelectrolyte brush;
suppose that the charges on the chains are negative and that the solvent
contains divalent cations, e.g., Ca^2 þ. 22 Ca 22 bridges may now be formed,
and although such bonds have a short lifetime, the particles will become
permanently bridged if the number of bonds per particle pair is sufficiently
high. The forces involved can be measured, and an approximate example is
illustrated in Figure 12.9. Here the forceF(¼dVT/dh) needed to bring the
two particle surfaces to a distance his shown. Starting at point (a),F
increases ashis decreased. At (b), 22 Ca 22 bridges must have formed, and
now the increase ofFwith decreasinghis much stronger. Moreover, when
the distance is subsequently increased, hysteresis occurs:Fdecreases and
then becomes attractive, e.g., at (d). If no external force is acting, the
particles will assume a mutual distance corresponding to point (c), and they
are thus bridged. When pulling the particles apart with sufficient force, they
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