Tg^0 (generally read as ‘‘tee gee prime’’) may be called thespecial glass
transitiontemperature; it characterizes the glass transition in a maximally
freeze concentrated system. The corresponding valuec^0 W¼ 1 c^0 sis the
residual water content(often denotedWg^0 ), i.e., the proportion of water that
will not freeze, however low the temperature. Some time ago, it was
generally assumed that the residual water does not freeze because it is
‘‘bound’’ to the solute. As discussed in Section 8.3, this assumption is no
longer tenable. The explanation is that the freezing rate of the water
becomes infinitesimally small after the glassy state has been reached.
Figure 16.6 also gives a curve for the homogeneous nucleation of
water. It is seen thatThomdecreases ever more below the value of pure water
( 408 C) with increasing solute concentration. As a rule of thumb,Thom&
40 2 DTin 8 C, whereDTis the freezing point depression caused by the
solute. It may be clear that it is generally impossible to bring the solution
without freezing to a temperature below Tg, except at a high sucrose
concentration (above the eutectic point), with very rapid cooling or with
very rapid drying.
Stability. As long as the temperature remains below Tg^0 , the
composition of the system is virtually fixed. This implies physical stability:
crystallization, for instance, will not occur. As mentioned, some chemical
reactions may still proceed, albeit very slowly because of the high viscosity
and the low temperature. The parametersTg^0 andcsare, however, not
invariable: they are not thermodynamic quantities. Their values will depend
to some extent on the history of the system, such as the initial solute
concentration and the cooling rate. The curve in Figure 16.6 denotedTf,f
(for fast freezing) shows what the relation may become if the system is
cooled very fast. TheTgcurve is now reached at a lower ice content, so the
apparent Tg^0 and c^0 s values are smaller. However, the system now is
physically not fully ‘‘stable’’: water can freeze very slowly until the ‘‘true’’c^0 s
is reached.
Various Systems. Table 16.1 gives values ofTg^0 andc^0 Wfor some
substances. It is seen that the values ofTg^0 follow the same pattern as theTg
of the pure substance, e.g., increasing with increasing molar mass. However,
the temperature range is not nearly as wide, although the values ofc^0 Wdo
not vary greatly. The main variation seems to be in the steepness of theTg
curve betweenTg,SandTg^0 , at least for sugars.
Inmixturesof solutes there is not just one eutectic, and so in principle
more than one solute can crystallize. On the other hand, a wider
compositional range tends to make it easier to reach a glassy state, just as