Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 138

Fig. 3.65 DSC curves
for heating of methylcel-
lulose solutions of different
concentration at 10 ﾰC min −1 .
(Reproduced from Chen et al.
[ 169 ] with permission of
Wiley)

2%
4%
8%

0.0

-2.0

-4.0

-6.0

60 65 70 75 80 85

T / o C

The E ʱ versus T plots obtained from the E ʱ dependencies estimated by an iso-
conversional method are shown in Fig. 3.66 . All three plots have a similar concave
downward shape but shift to higher E ʱ values with increasing the concentration of the
solutions. The initial decreasing portion of the E ʱ versus T dependence is consistent
with that predicted by the Turnbull and Fisher model. Indeed, Eq. 3.90 suggests that
just above T gel , the E ʱ values should be large but decrease toward E D as temperature
continues to rise above T gel (see Fig. 3.50 and related discussion). However, the final
increasing portion cannot be rationalized within the aforementioned model.
An increase in E ʱ in the later stages of gelation (Fig. 3.66 ) is likely to be associat-
ed with changing conditions of diffusion. Cross-linking of polymer chains obstructs
their mobility so that the formation of new cross-links may encounter continuously
growing energy barrier to diffusion. This means that the constant activation energy

Fig. 3.66 Fits of Eq. 3.91
to experimental E ʱ versus T
dependencies. (Reproduced
from Chen et al. [ 169 ] with
permission of Wiley)

2%
4%
8%

250

200

150

100

335 340 345 350 355

T / K