- Polydispersity. As mentioned, most polymers show a range in
degree of polymerization or molar mass. This means that suitable
averages should be taken. The theory is fairly involved and will
not be discussed here. - Branched polymers. Some polymers are highly branched, and
amylopectin is a prime example. In such a case, the volume taken
up by a polymer molecule will be much smaller than that of a
linear molecule of the same number of the same segments. The
exponent in the relation betweenrmorrgandn^0 will generally be
smaller than 0.5. For amylopectin, exponents of 0.41 to 0.43 have
been observed. Calculation of the conformation of branched
polymer molecules is generally not possible. - Heteropolymers. Several complications may arise. The stiffness
and the bulkiness of the chain may be different in different
stretches. The same may be true for the quality of the solvent,
which implies that the excluded volume parameter of the polymer
is a kind of average value. Specific interactions may occur between
different side groups. Simple theory is not available.
Moreover, polymers may bepolyelectrolytes, which are discussed in
Section 6.3. The electric charge generally causes the chains to be stiffer.
Polysaccharides. Many natural or modified natural polymers
exhibit most or all of the complications mentioned. This is especially true
for many polysaccharides, which tend to be fairly stiff molecules; see Table
6.1. Thebvalues are generally small, often< 0 :1. The chemical constitution
varies considerably, some polysaccharides (e.g., xanthan) having very large
side groups on the primary chain. Besides causing steric hindrance, which
also makes the chain stiffer, side groups may exhibit (weak) mutual
attraction. Some of these polymers tend to form helices in solution.
Altogether, polysaccharides vary widely in such properties as solubility,
tendency to form a gel, and extent of expansion. When characterizing the
latter by the hydrodynamic voluminosity, i.e., the hydrodynamic volume of
a polymer molecule per unit dry mass of polymer, values ranging from 10 to
more than 10^3 ml=g have been observed for polysaccharides ofM¼ 106 Da.
Notice the extremely large values possible (largely due to the stiffness
mentioned), which would even be larger for higherM.
The complications mentioned imply that the average conformation
can mostly not be calculated from first principles. However, many of the
parameters mentioned can be determined, such as molar mass and
composition. The radius of gyrationrgcan be obtained from light scattering
experiments,bfrom osmometry. If molecules of varying (average) molar