Physical Chemistry of Foods

as most salts, the discrepancies tend to be even greater. In fact, many
workers consider the theory to be essentially wrong, and try to develop other
theories of nucleation rate.
Considering the exponential factor, the basic problem is that the
magnitude ofggenerally cannot be determined, and it is therefore often used
as a fitting factor. Moreover, the value ofDHVmay be quite uncertain near
Thom, because of nonideality; this is especially important for the sucrose/
water system in Table 14.2, since tabulated values of the enthalpy of
dissolution refer to the addition of a small amount of solute to pure solvent,
whereas a saturated sucrose solution contains about 65%w/w solute. More
fundamental is the criticism that an embryo, i.e., a very small region, cannot
be treated as constituting a phase, with a clear phase boundary, especially
when it concerns formation of a crystalline phase. The results onrhomfor ice
and sucrose lead to nuclei of about 200 molecules, and such a region is
possibly large enough to be considered a phase. However, a nucleus of
tristearate would only contain 14 molecules, which implies that the
assumption is questionable. On the other hand, in the case of tristearate
the agreement between theory and experiment for the exponential factor is
quite good, presumably because the solution properties are almost ideal in
this case.
There are also great differences between predicted and observed values
of the preexponential factor. Assuming that the treatment is fundamentally
sound (which can be questioned on the same grounds as discussed in Section
4.3.5), it must be the magnitude ofDG that is much larger than predicted
from diffusional resistance. Nevertheless, the latter is of importance, since
nucleation rate tends to decrease again at very low temperature. This is
illustrated in Figure 14.3 (broken line). A strong decrease occurs near the
glass transition temperature, as is discussed in Section 16.1. Presumably, the
nucleation rate for ice is negligibly small at about
1408 C. In passing, it is
extremely difficult to cool water at such a rate that no nucleation occurs
before reaching this temperature.
Another factor that presumably contributes toDG is the loss of
orientational and conformational entropy of the molecules that become
incorporated in an embryo. It is seen that the difference between theory and
experiment of the preexponential factor increases when going from ice (five
orders of magnitude) to sucrose (seven) to tristearate (twelve), and this is at
least in qualitative agreement with the loss in entropy, which will be
larger for more anisometric and more flexible molecules. Especially
tristearate molecules will lose very much conformational freedom upon
crystallization.
In conclusion, classical nucleation theory is insufficient, and the results
on nucleation rate may be off by as much as ten orders of magnitude.