Essential Chemistry and Biochemistry Associated with Low Temperature and Freezing - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 64

lifetimes are likely to be extremely long, so that few experimental data
for PHC crystallisation from part-frozen solutions exist. Notable excep-
tions are mannitol and lactose. The former can crystallise quite rapidly,
even at subfreezing temperatures, while the latter is known to crystallise,
often inadvertently, as in ice cream, even when stored at -201C.
The previous section dealt with equilibrium phase relationships during
freezing and drying, and it was shown that even they can be complex.
We now extend the discussions to non-equilibrium situations, such as
supersaturation, a common event, which has already been touched
upon. Where lifetimes of supersaturated solutions extend into years or
centuries, it becomes permissible to treat such mixtures as pseudo-
equilibrium solutions. Consider the case of a sucrose solution that is
being cooled at a constant rate. The phase rule predicts that at some
temperature, the eutectic point, sucrose should crystallise. However,
nucleation probabilities of PHCs, especially from aqueous solutions, are
generally very low. This arises from their complex crystal structures. As
in ice, PHC molecules in the crystals are linked by weak hydrogen bonds
between their many -OH groups to form infinite three-dimensional
chains and networks. 69,70 Furthermore, interactions between sugar -OH
groups and those between sugar -OH groups and water molecules are
closely similar in energy and configuration. For these reasons, most
PHCs are reluctant to crystallise, so that on cooling, even at quite low
rates, ice will continue to grow beyond the (notional) eutectic point and
the solution becomes increasingly supersaturated and viscous. The
increasing viscosity leads to a slowing down of ice crystallisation, until
at some characteristic temperature no further freezing can be detected in
real time. The solution is then said to have reached its glass transition
temperature, usually denoted by T g , the temperature of maximum
freeze-concentration. This temperature is of the utmost importance for
the development of rational and effective freeze-drying cycles. Its de-
pendence on the solution composition can be incorporated into the
solid-liquid phase diagram, but with the proviso that the glass transition
profile does not represent a solid-liquid phase coexistence curve and is
purely an isoviscosity profile; i.e. it connects the T g values of mixtures
that have the same viscosity, often taken as E 10 14 Pa s. This repre-
sentation of equilibrium phase data with kinetic (vitrification) data was
in the past described as a ''supplemented phase diagram'', 42 but it is
nowadays more commonly referred to as a ''state diagram''. 71 Such a
diagram is shown in Figure 10 for the system water-sucrose.
For many aqueous systems, especially PHC solutions, the actual
positions of their true eutectic points are quite uncertain, giving rise to
significant discrepancies in reported solubility data by different workers.