repulsion hardly depends on pH or ionic strength but becomes greatly
reduced at high temperatures, say over 60 8 C.
Question
In the discussion of Figure 12.7 it is stated that ‘‘the steric repulsion will hardly
depend on particle size (unless the particles are very small:Rcomparable tod).’’ Can
you explain why the particle size has little effect? Can you explain the caveat? Would
the small effect of particle size also hold for steric attraction? You may assume that
the particles are equal-sized spheres.
Answer
The area over which the polymer layers of two particles overlap, say athbeing
somewhat below 2d, will be larger for larger particles. Geometrical consideration
shows that the area will be about proportional toRfor the same value ofh(provided
h 5 R). This means that for largerRa greater number of polymer chains will be
involved, hence stronger repulsion at the same distance. However, the steric
repulsion increases so very steeply with decreasinghvalue that an extremely small
decrease ofhwill increase the repulsion for small particles to the value obtained for
large particles. In other words, the effect of particle size on repulsion can hardly be
measured. But if the particles are very small, sayR<d, their surface area may be too
small to accommodate sufficient polymer to give a reasonably dense layer at a
distancedfrom the particle surface.
The attractive force occurring when the solvent quality of the adsorbed (or
grafted) polymer is poor—i.e.,b<0—will often be weak, sincebmay only be very
slightly below zero. In that case, the number of chains participating in the interaction
would become an important variable. Larger particles would then be less stable to
aggregation.
12.3.2 Bridging
Consider two particles with an adsorbed layer of a homopolymer, where
part of the chains protrude from the particle surface. When these particles
are brought close together, theory predicts that at equilibrium some of the
polymer molecules will become adsorbed onto both particles, forming a
bridge. Suchbridging by adsorptionis depicted in Figure 12.8a. It implies, of
course, that the particles are aggregated. The same situation may occur with
several kinds of copolymers (though not for a diblock copolymer with one
part of the molecule being hydrophobic and adsorbed and the other part
hydrophilic and protruding into the solvent).