Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 39

Fig. 2.10 The E ʱ val-
ues estimated by flexible
(Vyazovkin, and Popescu and
Ortega) and rigid (Ozawa
and Flynn and Wall, and
Kissinger and Akahira and
Sunose) integral isoconver-
sional methods. The size of
the ∆ ʱ interval was taken to
be 0.02 in both Vyazovkin
and Popescu-Ortega methods

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become negative so that g ( ʱ ) remains positive as it should (see Eq. 2.8). If integra-
tion is done with respect to time, the integral (Eq. 2.6) remains positive regardless
of the direction in which temperature changes.
The appropriateness of the flexible integral methods for the processes occurring
on cooling can be illustrated by applying two flexible integral methods to simu-
lated data [ 52 ]. The data represent a process taking place on cooling with an activa-
tion energy 100 kJ mol −1 . The methods selected are that proposed by Vyazovkin
(Eqs. 2.18 and 2.20) and that proposed by Popescu and Ortega (Eq. 2.26). As seen
from Fig. 2.10 , both methods successfully retrieve the correct value of E from the
cooling data. To reinforce the earlier made point that the rigid integral methods
are not suitable for treating cooling data, we have applied the methods of Ozawa
and Flynn and Wall as well as of Kissinger, Akahira, and Sunose to the same data
set. These methods obviously produce erroneous values of the activation energy
(Fig. 2.10 ). The failure is the direct consequence of the aforementioned (Fig. 2.6
and related discussion) inability of the rigid integral methods to properly evaluate
the temperature integral on cooling.
As seen from the above brief overview, over a couple of past decades, isoconver-
sional methods have developed into quite sophisticated computational tools capable
of exploring thermally stimulated kinetics under a wide variety of temperature con-
ditions. They have now become the most popular methods for kinetic analysis of the
thermally stimulated processes. Per Scopus database, there are over two thousand
papers that report the use of isoconversional methods over the last 4 years (2011-
2014). However, the popularity of the methods started to grow quickly less than
a decade ago. Apparently, the process was accelerated by the results of the 2000
Kinetic Project sponsored by the International Confederation for Thermal Analy-
sis and Calorimetry (ICTAC) that once more highlighted critical deficiency of the
single-heating-rate methods and vigorously emphasized [ 53 - 56 ] the necessity of
abandoning them in favor of the methods based on multiple temperature programs.