The Dried Product - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 140

universally guarantee an acceptable long-term stability. The higher mole-
cular mobility in the amorphous state, relative to the crystal, can lead to
processes such as crystallisation or chemical degradation. Angell 137 first
suggested that glasses can generally be classified into two types, according
to the temperature dependence of their thermomechanical behaviour. He
introduced a so-called fragility parameter, which is now often employed
to describe the temperature dependence of molecular motions in an
amorphous material, and the estimation of the fragility parameter is
potentially useful for predictions of long-term product stability (shelf life).
Thermal analysis, used to estimate the temperature dependence of the
mean relaxation time t, or the viscosity Z, offers a practical method for
estimating glass fragility (see later).
Figure 4 shows the extremes of the two types of behaviour: a scaling
temperature was chosen (the notional glass temperature) at which the
viscosity Z reaches 10 12 Pa s. The strong liquids display Arrhenius
behaviour, i.e. ln Z is linear in T/T g . By contrast, the viscosities of
fragile fluids decrease more rapidly at temperatures above T g ; this
behaviour is described by the VTF equation. SiO 2 and Ge 2 O are typical
examples of strong fluids; they have tetrahedrally coordinated structures
(like ice!), remnants of which apparently persist when the glasses are
heated across the glass transition. Curiously, it has been found that,
according to the fragility classification, globular proteins are also strong
fluids. In fragile fluids, on the other hand, any residual structural order
in the glass is rapidly destroyed above T g . This is the case for substances
Figure 4 Temperature dependence of viscosity: limits for strong and fragile fluids