Primary Drying: The Sublimation of Ice - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 105

concentration gradients (concentration polarisation, see Chapter 4);
formation of an amorphous, glassy product ''skin''.

Of these, the ice crystal size distribution is set early on in the process
during freezing by the nucleation and growth conditions of the ice
crystals, which, in principle, depend on the applied cooling rate. A
qualitative summary of the effects of cooling rate on ice crystal size
distribution is given in Table 1. Definitions of ''fast'' and ''slow'', as
applied to ice crystallisation, deserve a mention; they have already been
touched upon in Chapter 4. Since the linear growth rate of ice in pure
water and in dilute solutions is very high, then in industrial practice,
actual cooling rates must always be considered as low. High rates can be
achieved for small samples with the aid of cryogens by methods such as
spin freezing or drop freezing.
The details of ice growth set the texture and porosity of the final, dried
product. To illustrate this point, some examples of freeze-induced
textures are shown in Figure 2 in Chapter 7. Any thermal treatment
of the frozen solution, e.g. annealing or thermal cycling, can only lead to
an irreversible coarsening of the texture, referred to as ''maturation''.
The relative advantages and disadvantages of targeted maturation have
been discussed at length, especially in the food processing literature. An
example of maturation of ice crystals in frozen meat is shown in Figure
15 in Chapter 4. From the point of view of ice sublimation, a coarsened
ice crystal structure reduces t s , but it may also produce undesirable side
effects.
The other factors, mentioned earlier, relate to details of the particular
formulation. Thus, the effects of a high solid content, when coupled with
small ice crystals, increase the likelihood of a complete coating of ice
crystals by the glassy product matrix. Such a film coating would mark-
edly reduce the ice sublimation rate, as given by Equation (1), where a
''retardation factor'' would need to be introduced to allow for the water
vapour diffusion across the amorphous layer. High solid contents,
especially of polymers, would also give rise to solute concentration
polarisation ahead of the advancing freezing front (see Figure 14 in
Chapter 4) and, in extreme cases, would produce an almost impermeable

Table 1 Effect of cooling rate on ice crystal dimensions and primary drying time

Number of ice
crystals

Size of ice
crystals

Ice sublimation
time Cooling rate Nucleation rate

Low Low Small Large Shorter

High High Large Small Longer