Chemistry Reference
In-Depth Information
controlled by
α
-relaxation in the material, while below
T
g
, the rate of crystallization was
controlled by
-relaxation processes.
Viscosity measurements have also been used to determine the molecular mobility in
glasses and supercooled liquids. The assumption here is that
β
Einstein
relationship holds, and that molecular diffusivity is inversely proportional to the
viscosity. Thus, samples with a higher viscosity will crystallize more slowly.
For example, samples with a higher viscosity at the melting point have been observed
to be more likely to form glasses on cooling than compounds with a lower melt viscosity,
which have a higher tendency to crystallize [34]. However, it has been observed that
crystal growth rates do not always scale in the expected way with viscosity for some
supercooled liquids. This is particularly true for fragile liquids such as APIs, where there
is a breakdown in scaling between the viscosity and growth rate, particularly in
the deeply supercooled region. In this region, the crystal growth rate is typically faster
than would be expected based on considering the viscosity [35].
Despite the dif
the Stokes
-
cultly in making
a priori
predictions of crystallization from
measurements of molecular mobility, it is clear that factors that increase molecular
mobility will enhance the risk for crystallization. Of the various factors that enhance
molecular mobility,
the two of greatest practical
importance are temperature and
moisture content.
The impact of temperature on mobility has already been discussed to some extent. As
temperature increases, the molecular mobility will increase; however, the typical Arrhe-
nius relationship does not usually hold. The most common models to describe the
temperature dependence of molecular mobility are the Adam
-
Gibbs
-
Vogel (AGV) [36],
Vogel
-
Tammann
-
Fulcher (VTF) [37], Adam
—
Gibbs (AG) [38], andWilliams
-
Landell
-
Ferry (WLF) [39] equations. The AGV equation relates the structural relaxation time
τ
of
a glassy material below
T
g
:
!
DT
0
T
1
T
0
=
τ
τ
0
exp
;
(5.10)
T
f
whereas the VTF (Equation 5.11) is one of the most common models used to describe the
temperature dependence of structural relaxation (or viscosity) above
T
g
:
;
DT
0
T
T
0
τ
τ
0
exp
(5.11)
where
τ
0
is the relaxation time constant for the
unrestricted material,
D
is the strength parameter,
T
f
is the
τ
is the mean molecular relaxation time,
fictive temperature, and
T
0
is
the zero mobility or Kauzmann [40] temperature. These equations clearly show the
strong dependence of the relaxation time on temperature.
Due to its very low
T
g
value (reported values range from 136 to 165 K) [41,42], the
presence of water lowers the
T
g
of amorphous systems, and there is a corresponding
increase in molecular mobility. The lowering of
T
g
is called a plasticizing effect
and is well-known consequence of water absorption by amorphous systems [43,44].
