Physical Chemistry of Foods

of the system will become so high as to hinder greatly the diffusion of
crystallizable components.
Mixtures of a polymer, say starch, with a small molecule, say glucose,
can also be made. To be sure, such a mixture will also contain water, since
(a) starch, whether native or gelatinized, contains water; (b) glucose has to
be dissolved before a homogeneous mixture can be made; and (c) it is
virtually impossible to remove all water from the mixture. Having made a
mixture with a low water content, theglucosethen acts as aplasticizer,
meaning that it lowers the apparent viscosity as compared to a system
without glucose at the same starch–water ratio. This is, again, because
glucose molecules are much smaller, hence more mobile, than those of
starch.
In many mixtures, the value ofTgis uncertain:Tgis not an equilibrium
parameter and its value will depend to some extent on the temperature
history of the system. Moreover, it is often difficult to determine theTgof
mixed systems (more about this in Section 16.2). Several equations have
been proposed for calculatingTgof mixtures from the data for pure systems.
A simple equation directly relates it to the mass fractions ci of each
componenti, according to

1

Tg

&

Xci

Tg;i

ð 16 : 1 Þ

This equation well describes the relation between water content of potato
starch andTgas given in Figure 16.3a; the relation is less perfect for several
other binary mixtures. Many low-moisture foods are mixtures of polymers,
water, and several other small-molecule components. Prediction ofTgfrom
composition then is generally uncertain; in practice a (narrow) transition
range rather than a sharp transition point is often observed.
For pure substances and their mixtures with water, the ratioTg/Tm
varies between about 0.85 and 0.50. See further Table 16.1. For polymer–
water systems that form crystallites, the ratio tends to be smaller than for
dry systems, e.g., 0.7 for gelatinized starch with 30%water as compared to
0.8 for dry starch.

Viscosity Relations. Several equations have been proposed to
describe the dependence of the viscosity of the system on temperature. For
polymer systems theWilliams–Landel–Ferry(WLF) equation is often used.
It reads

log

Z

Zg

!

¼

C 1 ðT
TgÞ

C 2 þðT
TgÞ

ð 16 : 2 Þ