Physical Properties of Crystalline and Amorphous Solids - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 79

(ii) The abruptness of the transition indicates that relaxation pro-
cesses have very large temperature coecients, i.e. the potential
energy barrier that the relaxing unit needs to overcome must be
considerably higher than those associated with the mean thermal
energy (or equilibrium energy fluctuations).
(iii) Close relationships exist between dielectric relaxation and glass
transformation, suggesting that relaxation processes, which lead
to vitrification involve motions that are related to those per-
formed by dipoles (and other molecules) when they jump from
one quasi-equilibrium position to another one.
(iv) All liquids are believed to have (almost) the same viscosity at their
glass transitions, usually taken as 10 12 -10 14 Pa s. This corre-
sponds to a viscous flow rate of ca. mm year 1 or mm century 1 .
6.5 Amorphous States and Freezing Behaviour
Most materials destined for eventual freeze-drying are supplied in the
form of unsaturated aqueous solutions; but the dried product is a solid.
The drying process involves several phase transitions, e.g. liquid-solid
and solid-gas, but water and solutes do not necessarily undergo the
same phase transitions or at the same time. As discussed in previous
chapters, when the temperature is lowered, solutions tend to undercool
(i.e. remain liquid below the equilibrium freezing temperature) before
freezing actually occurs. After the onset of freezing, and given moderate
cooling rates, the solution will then remain in equilibrium with the solid
phase (i.e. ice). The solutes remain in the concentrated, residual liquid
phase. As the temperature is lowered further, the solution will become
increasingly more concentrated. In principle, variations in the rate of
cooling can affect the morphology of the product (e.g. ice crystal size
distribution and specific surface area). In production-scale pharmaceu-
tical freeze-drying, the rate of cooling (typically 0.2-0.31 min 1 or less)
can always be considered as low, and minor variations hardly affect the
dried product morphology. The situation is different for spray freezing,
film freezing or hyperquenching, where cooling rates up to 10 4 deg s 1
can be achieved.
In multicomponent systems, solute primary crystallisation may or
may not occur during freezing; it may also be incomplete, depending on
formulation details. Solutions tend to supersaturation, i.e. water con-
tinues to freeze, but at a decreasing rate, and the solutes remain in a true
solution of increasing concentration. At some characteristic temperature
and composition, freezing stops, at least at a measurable rate. The