Physical Properties of Crystalline and Amorphous Solids - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 77

to recover after each step for fixed time periods of Dt. It is seen that after
the first step, the resting time is suciently long to enable the material to
recover to its previous state. After the second step, a lag is already
apparent that increases at the third step. At the fourth step, the material
begins to behave as a solid, because no recovery is observed during the
resting interval.
Considering now the responses when the material is reheated (marked
by crosses in Figure 5b) under the same conditions, the apparent solid
state persists until the second temperature jump, when the material first
begins to relax, but from its previous vitrified state, which had been
reached after the third cooling step. Thereafter relaxation is as expected,
until the resting time Dt is once again sucient for equilibrium to be
attained. This description and an inspection of Figures 4 and 5 demon-
strate that the responses of the material during cooling and heating are
not identical. The intermediate temperature region in which the system
passes from the fluid to a glassy response is identified with the glass
transition region (where Dt E t). In this region, the H(T) and V(T)
curves for cooling differ from the corresponding heating curves. The
glass transition region is thus seen to be cooling/heating rate dependent,
i.e. it depends on (dT/dt). Whereas enthalpy and volume change
monotonically with temperature, their temperature derivatives (specific
heat and coecient of expansion) display a sigmoid temperature depen-
dence. This point is important for the experimental determination of
glass temperatures and relaxation rates.
6.4 Glass Transition: A Summary
In light of this discussion, the glass transition can now be described as a
narrow temperature range over which the specific heat and thermal
expansion coecient of amorphous materials undergo more or less
sudden changes due to relaxation effects. In laboratory practice, recov-
ery times might lie in the range of 10 min to 1 h. It is thus important to
realise that the glass transition is not a first-order phase transition in the
sense of crystallisation, melting or polymorphism, but a kinetic phe-
nomenon that extends over a narrow temperature range and is depen-
dent on heating/cooling rates and the thermal history of a material. A
corollary is that the density of a glass depends on the temperature at
which it was formed, and also on the time for which it was stored
(annealed). Some practical aspects of relaxation phenomena as they
relate to the behaviour of freeze-dried pharmaceutical products will be
further explored in Chapter 11.