Physical Properties of Crystalline and Amorphous Solids - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 74

The bottom line of this discussion is therefore that a study of the
science and technology of amorphous solids requires the introduction of
a kinetic element into classical thermodynamics. 87 Also, in practice, the
importance of kinetics far outweighs the predictions of the equilibrium
phase rule, because equilibrium might be hours, years, centuries or
millennia away.
6.2 Non-equilibrium Processes in Amorphous Solids
For kinetic processes that are slow, relative to the period of observation,
we need to be aware of the time evolution of equilibrium properties
(energy, volume, structure, solubility, etc.). Consider the reaction between
oxygen and hydrogen gases at 251C. According to textbook thermody-
namics, the gases should react to form liquid water because at that
temperature water has a lower free energy than the mixture of the two
gases. However, experience teaches that the reaction does not take place,
at least not within a measurable period of observation, because the kinetic
energy barrier is very high. It requires the addition of a catalyst, e.g.
MnO 2 , to cause the reaction to take place spontaneously and explosively!
The average structure in an amorphous (disordered) system is
constant with time but subject to spatial fluctuations (dynamic equili-
brium). Where such fluctuations involve the breaking and remaking of
bonds or spatial reorganisations of molecules or groups of molecules,
relaxation rates towards equilibrium may become very low (relative to
the period of observation). Such a system can then be considered as
petrified on the experimental time scale and take on some of the thermal
and mechanical properties of a crystalline solid. All thermodynamic
properties will, however, remain partially time dependent. If such a
system is subjected to a sudden perturbation, e.g. a pressure or tem-
perature jump, one observes an immediate response, followed by a slow
approach (relaxation) to quasi-equilibrium. 88 The process of structural
relaxation is shown schematically in Figure 3 for a fused system that has
been subjected to a temperature jump (quenching). The initial, rapid
response is due to an elastic, crystal-like increase in the density, but
without concomitant changes in the bonding pattern. The following,
slow relaxation process involves a rearrangement of bonds between
atoms or molecules, to yield a structure of lower energy that may more
closely resemble the equilibrium structure. In the case of amorphous
polyhydroxy compounds (PHCs), such relaxations involve rearrange-
ments of intermolecular hydrogen bonding patterns, until a new struc-
ture with a lower energy has been achieved.