Chemistry Reference
In-Depth Information
Temperature decreases
-50
-100
-150
7.5 - 12.5
o
C min
-1
(T
p
=11
o
C)
0.5 - 1.5
o
C min
-1
(T
p
=20
o
C)
-200
-250
-300
-350
0.0
0.2
0.4
0.6
0.8
1.0
α
Fig. 3.63
The
E
ʱ
dependencies obtained by applying an advanced isoconversional method to DSC
data on gelation of 17 wt. % solution of gelatin in water.
Squares
and
circles
denote respectively
different intervals of cooling rates. The intervals differ in the mean value of the DSC peak tem-
perature,
T
p
, shown in parentheses. (Adapted from Chen and Vyazovkin [
165
] with permission of
Wiley)
The effect of temperature on the
E
ʱ
is even more evident when the
E
ʱ
dependen-
cies are evaluated from the data collected in different ranges of the cooling rates. As
already noted with increasing the cooling rate, the DSC peaks shift to lower tempera-
tures (Fig.
3.62
). For the range of faster cooling rates (7.5, 10, and 12.5 ﾰC min
−1
),
the average DSC peak temperature is ~ 11 ﾰC so that the average value of
E
ʱ
is about
− 90 kJ mol
−1
. However, at slower cooling rates (0.5, 1.0, and 1.5 ﾰC min
−1
), the aver-
age peak temperature is markedly higher (20 ﾰC), i.e., closer to
T
gel
so that the average
E
ʱ
estimated from the slower heating rates is around − 300 kJ mol
−1
[
165
]. Therefore,
isoconversional analysis of the continuous cooling DSC data demonstrates that under
these conditions the rate of sol-gel conversion has a negative temperature coefficient,
whose absolute value becomes larger when the process is measured closer to
T
gel
.
As already suggested, the kinetics of physical gelation can be reasonably well de-
scribed by the Turnbull-Fisher and Hoffman-Lauritzen models. This means that one
generally should be able to fit the temperature dependencies of the isoconversional
activation energy to Eqs. 3.45 and/or 3.60 by substituting
T
gel
for the equilibrium
temperature. For example, Eq. 3.45 derived from the Turnbull-Fisher model would
take the following form:
2
T
1
(3.90)
EE A
=−
−
.
D
(
)
3
(
)
2
TTTT
−
−
gel
gel
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