interaction, van der Waals attraction is taken into account. The number
densitysof polymer molecules at the surface is kept constant. Three factors
have been varied. If thesolvent quality is poor (b<0), a deep energy
minimum can occur, causing strong attraction. Curves (c) and (d) refer to
the same polymer and only the composition of the solvent is different.
Notice that the layer thickness is smaller for a lower solvent quality, which
means that the polymer chains are less stretched. In other words, the
configuration tends to change from what is depicted in Figure 12.5c in the
direction of b, if solvent quality is decreased. Even if the solvent quality is
very good, but thepolymer layer thicknessis small due to low molar mass
of the polymer, sayd<5 nm, van der Waals attraction may prevail at
some distance, at least if the particles are fairly large (curve a). Van der
Waals attraction is proportional toparticle radius, as discussed, whereas the
steric repulsion will hardly depend on particle size (unless the particles are
very small:Rcomparable tod). The ratio of d/Rthus is an important
variable. If the ratio is not very small,sis high, and the solvent quality is
good (b>0), repulsion will always be strong and very stable dispersions
result.
It may further be noted that polymers that do adsorb onto particles,
and then stabilize them against aggregation, are nearly alwayscopolymers,
where some segments have affinity for the particle surface, while for other
segments the solvent quality is good enough for them to prefer being in the
continuous phase. It is very difficult to have a homopolymer that adsorbs
onto a particle without assuming a conformation as depicted in Figure
12.5b, or an even flatter one, which would generally imply steric repulsion to
be weak.
Polyelectrolytes. Several kinds of polymers bear electric charges,
and these polyelectrolytes are discussed in Section 6.3. An important
characteristic is the charge density 1/bch, wherebchis the average linear
distance between charged groups. If the charge density is high and the
charges are all (or predominantly) of the same sign, an adsorbed or grafted
layer of polymer chains of sufficient number densitysreadily forms a brush
that causes strong electrostatic plus steric repulsion. Another crucial
variable is the ionic strength I, and basically three cases can be
distinguished.
IfIis high, say>1 molar, the thickness of the electric double layer 1/k
is very small; electrostatic repulsion then acts over distances far smaller than
bchand the effect of charge is small. The result is aneutral brush, i.e., the
situation discussed above.