Essential Physics of Low Temperature and Freezing - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 34

Figure 11 Undercooling and droplet freezing of water in saline solution ( ), aqueous
solution of polygalacturonic acid ( m ), fluids extracted from the efflorescence
of L. telekii ( ' ) and their polysaccharide fraction (3). Reproduced with
permission from the Royal Society of Chemistry from Franks 44

4.5 Ice: Crystallisation and Crystal Habits

In contrast to nucleation, the growth of ice crystals in undercooled water
is extremely rapid and displays Arrhenius kinetics. The temperature
dependence of the overall freezing rate is thus given by a combination of
two opposing processes in which the nucleation rate increases with
decreasing temperature, whereas ice crystal growth increases with in-
creasing temperature. The freezing process, as it occurs in an aqueous
solution, is affected by additional variables: temperature, pressure,
solute concentration, catalytically active ''impurities'', rates of cooling
and rewarming, where appropriate, and thermal history (annealing). 28
The crystal habits of ice are extremely complex so that, depending on the
environmental conditions, needles, feathers, spherulites or disc-type
crystals can be generated. 20,29 On annealing, they all eventually tend
to convert to the stable form, the familiar hexagonal stellar dendrites.
A distinction must be drawn between equilibrium freezing, as it occurs
under conditions of minimum undercooling, i.e. DT E 0, and perturbed
freezing, as observed for rapidly cooled solutions, where DT c 0. For
purposes of industrial-scale freeze-drying, the former process is of
greater significance. Cooling rates are invariably low where heat transfer
takes place between a liquid in a vial and a cooled metal shelf; typical
cooling rates are of the order of 1-301C min 1 . Perturbed freezing can
be achieved when small volumes, e.g. droplets, are sprayed into a
suitable cryogen or against a cold metal plate. In that case, cooling
rates well in excess of 10001Cs 1 can be reached, i.e. DT E 401. With