Essential Physics of Low Temperature and Freezing - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 31

Figure 9 Partial solid-liquid phase diagram of H 2 O, including the corresponding homo-
geneous nucleation temperature T h . Reproduced from Franks 17 with permission
from Cambridge University Press
the effects of pressure on the ice melting point T m and the nucleation
temperature T h , such that at a given pressure, T h is depressed by twice
the amount of the lowering of T m . It also appears from Figure 9 that the
undercooling limit of pure water is 901C.
Turning briefly to the nucleation of ice in undercooled aqueous
solutions, we find that here too, the effect of the molal concentration
is exactly analogous to that of the pressure, i.e. DT h ¼ 2DT m . Once
again, the reasons are not understood, since the phenomena underlying
the two temperature depression effects are quite unrelated. DT m is the
well-documented osmotic freezing point depression, whereas DT h is the
manifestation of a kinetic rate process. It is also unclear why this process
should be identical for equivalent molar concentrations of widely dif-
ferent types of solutes as illustrated in Figure 10.
Reference has also been made to ''clean'' or ''purified'' water. In fact,
all the numbers shown in Table 1 and Figure 7 are based on the
homogeneous nucleation model, according to which the generation of
nuclei is solely the result of random density fluctuations within the liquid
phase. It is, however, well known that nucleation can be catalysed by
internal and external factors, in which case the growth and persistence,
possibly also the dimensions and structures, of critical clusters are