Physical Chemistry of Foods

of mass, is now given by

rg¼

rm

H 6

¼ 0 : 41 Ln^0 :^5 ð 6 : 2 Þ

The volume that the random coil occupies, including entrapped solvent, can
be defined in various ways, but it will anyway be proportional tor^3 g. Because
rgis proportional to

ffiffiffi

n

p
andnis proportional to the molar massMof the
(hypothetical) macromolecule, the said volume will be proportional toM^1 :^5.
Since the mass of polymer present in each coil is proportional toM, the
specific volume—i.e., the volume occupied per unit mass of polymer—is
proportional toM^0 :^5.
This is an important conclusion. It implies that the volume occupied
by a certain mass quantity of polymer increases with increasing molar mass
or molecular length, other things being equal; in other words, the coils are

FIGURE6.2 Example of a projection of a calculated random coil of 250 segments.r
is the end-to-end distance. (Adapted from L. R. G. Treloar. The Physics of Rubber
Elasticity. Clarendon, Oxford, 1975.)