In this chapter, the properties of ‘‘hydrocolloids,’’ i.e., water-soluble
polymers, are primarily discussed, in relation to the functions mentioned in
the previous paragraphs. It concerns mainly polysaccharides and gelatin.
The emphasis will be on fairly dilute solutions, but concentrated systems are
also discussed. Use will be made of polymer science to explain general
principles, but it makes little sense to give much quantitative theory, since
the polymers involved generally are too heterogeneous to follow the rules
derived for the more simple synthetic polymers for which the theory has
been derived. Proteins have very specific properties and will for the most
part be discussed in Chapter 7.
6.2 VERY DILUTE SOLUTIONS
In this section, uncharged polymers in very small concentrations will be
considered. This means that the behavior of a polymer molecule will not be
affected by the presence of other polymer molecules, but only by the solvent.
6.2.1 Conformation
Ideal Polymer Chain. The simplest model of a polymer molecule is
a linear chain ofnsegments, each of a lengthL, where each segment is free
to assume any orientation with respect to its neighbors, and where all
orientations have equal probability. The molecule as a whole then has a
conformation that can be described by a random walk through space: all
steps have the same lengthLbut can be in any direction. This is very much
like the path that a diffusing molecule or particle follows in time, and it can
be described by the same statistics. An example of such a statistical or
random chain is depicted in Figure 6.2. If we take theaverage conformation,
i.e., the average over the conformation of the same molecule at various
moments or over the conformation of various molecules at the same time,
the distribution of chain segments over space is Gaussian (Fig. 6.5, later on,
gives examples). If the number of segments is much larger than in Figure 6.2,
also each individual molecule has at any moment a more or less Gaussian
segment distribution. The end-to-end distance of the chainr(see Figure 6.2)
is on average zero, since r actually is a vector that can assume any
orientation. Theory shows that for largenthe root-mean-square distancerm
is given by
rm:hr^2 i^0 :^5 ¼Ln^0 :^5 ð 6 : 1 Þrmis also called the Flory radius. Theradius of gyration rg, which is defined
as the root-mean-square distance of all segments with respect to the center