Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 114

thermore, the effective activation energy decreases with increasing temperature as
predicted by Eq. 3.72. This certainly lends support to the nucleation model because
the Kissinger plot is obtained directly from the experimental data without making
any assumption about nucleation.
In order to convert the Kissinger plot to the experimental E versus T depen-
dence, one needs to differentiate the plot numerically and then replace the recipro-
cal temperature with temperature. To get around the problems of dealing with noisy
numerical derivative of experimental data, the Kissinger plot can be replaced with
some interpolating function. Differentiation of the latter would result in smooth
numerical derivative.
The E versus T dependencies derived from the Kissinger plots for melting of
PET and PCL are shown in Fig. 3.44 . A striking feature of these dependencies is
the enormous values of the effective activation energy. Lippits et al. [ 132 ] have
reported similarly large values for melting of ultrahigh molecular weight polyeth-
ylene. This fact has been rationalized [ 132 ] by hypothesizing that detachment of
polymer chain from the crystalline surface occurs in highly cooperative manner,
i.e., by simultaneously breaking multiple bonds. However, the nucleation model
suggests (Eq. 3.72) that the absolute value of E cannot be interpreted directly as
the energy barrier height. Furthermore, interpretation of the large magnitude of the
activation energy does not require invoking the hypothesis of cooperativity. Instead,
the nucleation model provides a straightforward explanation that the E value is nec-
essarily large because in Eq. 3.72 the Δ T is very small.
Fitting of the theoretical E versus T dependence (Eq. 3.72) to the experimental
one requires estimating the nonequilibrium melting temperature because it is a part
3(7
3&/
7.
Fig. 3.44 Temperature dependence of the effective activation energy for melting of PET
and PCL. Points connected by dash line represent the experimental dependence derived from
the Kissinger plot. The solid lines are fits of Eq. 3.72. PET poly(ethylene terephthalate), PCL
poly(ε-caprolactone). (Adapted from Vyazovkin et al. [ 129 , 131 ] with permission of Wiley)