Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 106

Fig. 3.37 Isoconversional
values of the effective
activation energy for glass
and melt crystallization of
poly(ethylene terephthalate).
(Adapted from Vyazovkin
et al. [ 107 , 108 ] with permis-
sion of Wiley)

100

0

Glass crystallization
Melt crystallization

-100

-200

-300

0.0 .2 0.4 .6 0.8 .0

α

Once an appropriate method is selected, it can be applied to a set of DSC curves
collected at several heating or cooling rates. As a result, one obtains a dependence
of the effective activation energy on the extent of conversion from the amorphous to
crystalline state. Example of such dependencies for crystallization of PET is shown in
Fig. 3.37 . In agreement with the earlier discussion (Fig. 3.36 ), the activation energies
for the melt crystallization are negative and for the glass crystallization positive. It is
also seen that in both cases the E values tend to zero as crystallization progresses from
ʱ = 0 to 1. Again, this is consistent with the temperature-dependent trends for E pre-
sented in Fig. 3.36 . Recall that an increase in ʱ represents an increase in temperature
for the glass crystallization and a decrease in temperature for the melt crystallization.
In order to be able to parameterize the obtained isoconversional activation en-
ergies in terms of the Hoffman-Lauritzen theory, one needs to switch from a de-
pendence of E ʱ versus ʱ to a dependence of E ʱ versus T . Since any given val-
ue ʱ is reached at different temperatures, depending on the heating (or cooling)
rate (Fig. 1.8), the respective set of temperatures is replaced with a single mean
value. Then, by replacing each value of ʱ with the mean temperature related to it
(Fig. 3.38 ), one obtains a dependence of E ʱ versus T .
The E ʱ versus T dependence for the melt crystallization of PET is shown in
Fig. 3.39 . As follows from Fig. 3.36 , the E ʱ values are expected to be negative at
temperatures below T max that is experimentally found for PET in the region 170-
190 ﾰC [ 109 ]. A remarkable feature of the dependence is a break point at ~ 475 K
(i.e., ~ 202 ﾰC) that signals a change in the crystallization mechanism. For isothermal
PET crystallization, Lu and Hay [ 110 ] and Rahman and Nandi [ 111 ] have reported
a change in the crystallization mechanism revealed as a break point in the Hoff-
man-Lauritzen plot (Eq. 3.54) at the respective temperatures 217 and 236 ﾰC. Also,
Okamoto et al. [ 112 ] have observed a change in the crystallization regime at 202 ﾰC.
Because of the change in the crystallization mechanism, the higher temperature
( T > 475 K) and lower temperature ( T < 475 K) portions of the E ʱ versus T depen-
dence should be analyzed separately. It means that Eq. 3.60 should be fitted individ-