Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 113

If one spreads this interval evenly between, say, five heating rates ranging from
2 to 20 ﾰC min −1 , the shift in DSC peaks related to two successive heating rates
would be about ~ 0.7 ﾰC. For an isoconversional method to work successfully, the
temperatures related to the same conversion, T ʱ , must increase systematically with
increasing ʲ for each value of ʱ . This condition is hard to fulfill at the smallest and
largest values of ʱ because the shifts in T ʱ are so small that they become comparable
to the T ʱ variation associated with the selection of the DSC peaks baseline.
Nonetheless, the baseline selection and adjustment does not affect practically the
DSC peak temperature. This brings about the idea [ 129 ] of adapting the Kissinger
method [ 99 , 100 ] for estimating the experimental dependence of E versus T . The
Kissinger method (Eq. 3.51) estimates the effective activation energy from the shift
of the DSC peak temperature ( T p ) with the heating rate. It should be noted that the
method is not exactly isoconversional, i.e., the conversion related to the peak tem-
perature may not be the same value at different heating rates [ 130 ]. Experimental
data need to fulfill the isoconversional condition because this is the condition under
which the theoretical E versus T dependence is derived (Eq. 3.72). The condition is
easy to check by determining the conversion at T p from the actual DSC peaks. For
example, the isoconversional condition appears to be fulfilled quite satisfactorily
for melting of PET and PCL because the respective conversions do not show any
systematic dependence on the heating rate giving rise to the value 0.59 0.02 [ 129 ]
and 0.61 0.03 [ 131 ]. Thus, the use of the Kissinger method for estimating the ex-
perimental E versus T dependence would be justified.
The Kissinger plots for melting of PET and PCL are presented in Fig. 3.43 . It
is immediately clear that the plots are nonlinear. Since at any given temperature
the slope of this plot is the effective activation energy, it can be concluded that the
effective activation energy of the melting process is temperature dependent. Fur-
Fig. 3.43 The Kissinger
plots for melting of PET
and PCL. The solid lines
represent interpolation of the
experimental points. PET
poly(ethylene terephthalate),
PCL poly(ε-caprolactone).
(Adapted from Vyazovkin
et al. [ 129 , 131 ] with
permission of Wiley)