Physical Chemistry of Foods

be described as a random chain ofn^0 ‘‘statistical chain elements’’

of average lengthb, wheren^0 b¼nL. Any statistical chain element

thus containsb=Lmonomers, and the ratiob=Lis a measure of the

stiffness of the chain.

Note Some theories use the concept of persistence lengthq, where

effectively 2q¼b.

Eq. (6.1) now reads

rm¼bHn^0 ð 6 : 3 Þ

This would imply that the specific volume occupied by the

polymer becomes larger than predicted by (6.1), by a factor

ðb=LÞ^1 :^5. Experimental values forb/Lrarely are below 4 and can

be much larger; Table 6.1 gives some examples.

It is also seen in Table 6.1 that the number of statistical

chain elementsnL/bmay be fairly small. Ifn^0 is smaller than about

25, Eq. (6.3) is not valid any more because the average distribution

of the segments is not gaussian any more. Instead, the molecule

assumes an elongated form, andrmwill be larger than predicted

by Eq. (6.3). The extreme is a stiff rodlike molecule of lengthnL.

Some linear homopolymers tend to form a regular helix. A

case in point is amylose, which tends to form a helix in aqueous

solutions. Nevertheless, also in this case Eq. (6.2) may remain

FIGURE6.4 The effect of the stiffness of a polymer chain on its conformational
freedom. This is illustrated for a two-dimensional case, with a fixed, obtuse bond
angle, implying two possible conformations at each bond. Although over a distance
of two or three segments, the position cannot vary at random, this is possible over a
distance of, say, 5 segments, as illustrated. The broken lines would then indicate the
statistical chain elements.