Chemistry Reference
In-Depth Information
relaxation of an amorphous SDD is too slow for it to be measured reliably on an
experimental timescale. To circumvent this problem, we accelerated the study by
inducing relaxation at higher
temperatures, and then extrapolating back to the
temperature of interest. First,
the observed relaxation data were
t
to the Kohl-
rausch
-
Williams
-
Watts [25] stretched exponential function:
hi
β
;
t
τ
ϕ
t
exp
where
ϕ
(
t
) is the extent of relaxation at time
t
,
τ
is the relaxation time constant, and
β
is
known as the stretch function, a nonlinearity function that ranges between 0
1
and represents the heterogeneity of the system. With this, the maximum relaxation is
de
<
β
<
ned as
C
T
g
p
Δ
H
∞
Δ
T
g
T
;
where
T
is the
“
aging
”
temperature, or temperature at which the material was held. The
resulting values for
τ
and
β
were extrapolated to lower temperatures on an Arrhenius plot
(
versus 1/
T
).
The commercially approved SDD of telaprevir is one example of a material that
relaxes too slowly to be observed in an experimental time frame. Hence, the development
team measured enthalpic relaxation by DSC at temperatures close to
T
g
(
T
g
15
β
ln
τ
C,
°
T
g
20
t the data to the KWW
equation by nonlinear least squares analysis to determine the degree of molecular
mobility at lower temperature. With Arrhenius analysis, relaxation of these materials
was extrapolated to room temperature (Figure 7.9). The time constant for relaxation
at 25
C, and
T
g
35
C), as shown in Figure 7.8, and then
°
°
C proved to be 10
7
years
—
which we took to be, on a clinical timescale, clearly
°
suf
cient.
Figure 7.8.
Extent of relaxation as a function of time at
xed temperatures.
