Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 42

where a and b are the parameters of the compensation effect. The original work [ 57 ]
by Vyazovkin and Lesnikovich has demonstrated two important properties of the
compensation effect that are relevant to accurate evaluation of the preexponential
factor. First, even if the correct model is not included in the list of models used to
determine the ln A j and E j values and if none of these values matches the correct val-
ues ln A 0 and E 0 , the latter still lie on the compensation line determined by Eq. 2.28.
This means that if the correct value of the activation energy is known, one can esti-
mate the correct value of the preexponential factor by substituting E 0 into Eq. 2.28.
Second, although the parameters of the compensation effect depend on the heating
rate, the latter does not affect the value of the preexponential factor estimated by
substituting E 0 into Eq. 2.28 obtained at different heating rates. The property arises
from the fact [ 61 ] that the compensation lines related to different heating rates in-
tersect at the points ln A 0 and E 0 (Fig. 2.11 ). As a result, substitution of the correct
value of the activation energy into the compensation line equation yields the same
value of the preexponential factor regardless of the heating rate [ 57 ].
Overall, the method of estimating the preexponential factor boils down to the
following four steps. First, an isoconversional method is applied to determine the
activation energy, E ʱ , as a function of conversion. Second, a single-heating-rate
method is employed to determine several ln A j and E j pairs. Third, the ln A j and E j
values are fitted to Eq. 2.28. Fourth, the E ʱ values are substituted into Eq. 2.28 to
yield the respective value of the preexponential factor:

(2.29)

ln AEb

α =+

.

If E ʱ is independent of ʱ, as one would expect for a single-step process, the result-
ing ln A ʱ is also invariable. Substitution of variable E ʱ value obviously yields ln A ʱ
value that depends on ʱ, which would be the case of a multistep process. As shown
earlier [ 58 ], a dependence of ln A ʱ on ʱ can be used to estimate the preexponential
factors of a multistep process. This has been recently reconfirmed by Sbirrazzuoli

Fig. 2.11 Compensa-
tion lines ln A j = aE j + b
at three different heating
rates ʲ 1 < ʲ 2 < ʲ 3 . The lines
intersect at the correct values
of the activation energy and
preexponential factor. Circles
represent the actual values
of ln A j and E j estimated by
a single-heating-rate method
(e.g., Eq. 2.27) while using
different reaction models

β 1

β 2

β 3

lnA 0

E 0

E