more tenuous (rarefied, expanded) for a largerMorn. It also implies that
the viscosity of a polymer solution of a given concentration increases with
increasingM(see Section 6.2.2). This is illustrated by a simple experience in
everyday life. When eating a soup that has been thickened by starch, we can
generally observe that the viscosity of the soup decreases during eating. This
because the we contaminate the soup via the spoon with saliva. Saliva
contains amylase, an enzyme that hydrolyzes the large starch molecules into
smaller fragments. This means that the averageMwill gradually decrease,
with a concomitant effect on viscosity.
Complications. The above qualitative statements are generally
true, but Eq. (6.1) is mostly not obeyed precisely, because the theory is an
oversimplification. The main complications are
- Stiffness of chain. An actual polymer chain will always be less
flexible than the statistical chain considered above, because the
bond angle between monomers is fixed. Figure 6.3 demonstrates
that the position of a monomer–monomer bond with respect to
the next one can only be at any point of a circle, rather than at any
point of a sphere of radiusL. Bulky side groups of the monomer
may further restrict the freedom of orientation. Moreover, in the
case of polyelectrolytes, electrical repulsion between chain
segments may limit flexibility; this is discussed in Section 6.3.2.
Nevertheless, the same laws may hold for the polymer conforma-
tion, by taking into account that the position of a bond with
respect to another that is several monomers away can still be
random. This is illustrated in Figure 6.4. A long chain can always
FIGURE6.3 Orientational possibilities of two segments of a polymer, where a
segment is depicted by its axis. Segment 1 is fixed in the horizontal plane. (a) Ideal
chain; the anglesaandbcan assume any value. (b) More realistic chain; the bond
angleyis fixed (about 109 degrees for a C 22 C 22 C bond) and the end of segment 2
must be on the circle depicted.