Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 38

temperature increases linearly, stays constant, or changes nonlinearly. Figure 2.9
demonstrates the efficiency of the method as applied to a simulated process under
conditions of linear heating. It is seen that approximating the temperature integral
via the mean value theorem while keeping ∆ ʱ as small as 0.02 allows one to evalu-
ate the correct E ʱ dependence. The accuracy of this method appears to be compa-
rable to that of the methods proposed by Vyazovkin (Eqs. 2.18 and 2.20) and by
Friedman (Eq. 2.5). Not surprisingly, the methods of Ozawa and Flynn and Wall
(Eq. 2.11) as well as of Kissinger, Akahira, and Sunose (Eq. 2.13) cannot retrieve
the correct E ʱ dependence because the integration used in these methods is not ca-
pable of accounting for variability of E ʱ .
Note that the equation derived by Ortega for linear heating conditions is similar
to Eq. 2.26 obtained by Popescu, the only difference being that T ξ is taken as T ʱ ,
i.e., the upper limit of integration. The use of a single rather than averaged value
of temperature as T ξ can be a source of an unnecessary error as mentioned by Han
et al., [ 47 ] who proposed to evaluate T ξ as the mean of five temperatures from the
interval T ʱ −∆ ʱ − T ʱ . This simple modification has been shown [ 47 ] to improve the
accuracy of the method in the case of noisy simulated and actual experimental data.
All flexible integral isoconversional methods should in principle be applicable to
treat processes that take place on cooling. This expands the application area of the
methods to such processes as crystallization [ 48 , 49 ], gelation [ 50 ], as well as some
other phase transitions [ 51 ] that can be initiated by decreasing temperature. If a
flexible method is based on integration with respect to temperature (e.g., Eq. 2.21 or
2.24), then under conditions of cooling, both temperature integral and heating rate
Fig. 2.9 The process was simulated to have E ʱ to vary linearly with ʱ . Solid line represents the
simulated E ʱ versus ʱ dependence. Open circles, triangles, and squares represent the E ʱ values
estimated according to the methods proposed, respectively, by Ortega, Vyazovkin, and Friedman.
All three methods yield the E ʱ values that coincide with the simulated ones. FWO and KAS rep-
resent the values estimated by the method of Flynn and Wall and Ozawa and by the method of
Kissinger, Akahira, and Sunose. (Reproduced from Ortega [ 42 ] with permission of Elsevier)