in unfrozen systems. The values ofTg^0 andc^0 sare, however, more dependent
on temperature history.
Table 16.1 gives two example ofbiopolymers. It is seen thatTg^0 is not
far below zero, especially for starch. Again, the glassy state is reached easily
for polymers, although it may be difficult to establish a clear glass transition
point. This is illustrated in Figure 16.7, which shows freezing curves of some
complex systems. It is seen that at a considerable freeze concentration the
curves go steeply down, and near acsvalue of about 0.8 the curves tend to
become vertical. This means that no more ice crystallizes; presumably, the
system then is in a glassy state. Newer studies indicate that the ‘‘proper’’
values ofTg^0 can be substantially higher than those suggested by the figure.
Uncertainties. The value of Tg^0 is generally determined by
differential scanning calorimetry (DSC), and Figure 16.8a gives an
example of a curve near the glass transition. It is commonly seen that not
one but two second-order transitions occur, the first one being small
compared to the second. The existence of two transitions is generally
ascribed to two different physical relaxation mechanisms occurring in the
glass; currently, there is no agreement about the explanation. The results for
Tg^0 given in Table 16.1 represent the second, major, transition. Other
workers assume the first transition to represent properly the glass transition.
Also the ‘‘overshoot’’ often seen in the curve, which can be more prominent
in some systems, is still posing questions, since it seems to indicate a first-
FIGURE16.7 Freezing curves of various biological systems.Tis temperature,cS
mass fraction solid. Curve 1, human blood; 2, washed yeast cells in water; 3,
collagen; and 4, muscle tissue. (From results by A. P. MacKenzie. In: R. B.
Duckworth, ed. Water Relations of Foods. Academic Press, London, 1975, p. 477.)