Chemistry Reference
In-Depth Information
Figure 1.12.
Viscosity of amorphous tris-
α
-naphthylbenzene as a function of the reciprocal of
temperature (reproduced with permission from Ref. 21. Copyright 1968, AIP Publishing LLC).
fragility. Since extension of the VTF equation to temperatures below
T
g
assumes that the
supercooled liquid state continues down to
T
0
, one might expect that the VTF equation
would not be able to predict molecular mobility much below
T
g
. That this is so can be
observed in Figure 1.12 where a plot of log
-naph-
thylbenzene indicates that although a discontinuity does not occur at
T
g
, there is a distinct
discontinuity at a temperature that is roughly 15 K below
T
g
[21]. Below this temperature,
viscosity dependence on temperature appears to follow Arrhenius kinetics and exhibit
values that are signi
η
versus 1/
T
for amorphous tris-
α
cantly lower than those predicted from the VTF equation. Appar-
ently, closer to
T
g
there is very rapid aging of the glass toward the supercooled liquid over
the time period required to carry out the viscosity measurements (see Figure 1.4 and the
earlier discussion of aging of glasses) and viscosity values are those expected for the
supercooled liquid. The lower than expected viscosity in the glass would be consistent
with the general structure of glasses, as illustrated in Figure 1.8, that contains a
microstructure region in which molecules should have higher energy, less density,
and higher molecular mobility. Such behavior, that is, greater molecular mobility than
predicted from the VTF equation, has also been reported with measurements of relaxation
time for amorphous indomethacin at temperatures below
T
g
using DMA, DES, and
thermal analysis [22]. It has been shown further that the extrapolation of relaxation times
obtained in the glassy state of indomethacin leads to a value of 3 years (10
8
s) at
T
g
T
equal to 40 K, 3 years being the desired time of storage generally required for establishing
expiration dates of many solid drug products. Thus, long-term stability in this case would
require a storage temperature that is about 40 K below
T
g.
(there will be more discussion of
stability subsequently).
