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[
59
], who also demonstrated that highly accurate values of the preexponential factor
can be obtained when one evaluates the parameters of the compensation effect from
only four pairs of
A
j
and
E
i
estimated by the single-heating-rate method of Tang
et al. [
62
] when using the reaction models of Mampel (F1) and Avrami-Erofeev
(A2, A3, A4).
Once both
E
ʱ
and
A
ʱ
have been evaluated, it becomes possible to reconstruct nu-
merically the reaction model in either integral or differential form [
63
]. The integral
reaction model is reconstructed as follows:
T
A
α
−
E
α
α
∫
g
(
α
)
=
exp
d
T
.
(2.30)
β
RT
0
Inserting in Eq. 2.30 the values of
E
ʱ
,
A
ʱ
,
and
T
ʱ
for each value of
ʱ
yields numeri-
cal values of
g
(
ʱ
) that can be matched to the theoretical g(α) models (Fig.
2.12
). In
Eq. 2.30,
T
ʱ
is the experimentally measured temperature of reaching a certain
ʱ
at a
given heating rate,
ʲ
. However, the resulting values of
g
(
ʱ
) should not demonstrate
any significant difference when using the
T
ʱ
values related to different heating rates.
Note that the independence of the g(
ʱ
) dependences on
ʲ
should be expected when
E
ʱ
(and thus
A
ʱ
) are independent of
ʱ,
i.e., for a single-step process. As a matter of
fact, accurate values of
g
(
ʱ
) can generally be evaluated when the process is a single-
step one, because only in this case, the process can be described by a single-reaction
model. When a process demonstrates significant variability of
E
ʱ
,
its accurate de-
scription would require in general more than one kinetic triplet and in particular
more than one reaction model. Nevertheless, analysis of the single
g
(
ʱ
) evaluated
for a multistep process in some cases may provide useful insights [
59
].
Similar procedure and principles are applied when restoring the differential reac-
tion model. The respective equation is obtained by rearranging Eq. 2.2 as follows:
Fig. 2.12
Theoretical
g
(
ʱ
)
dependencies. The numbers
correspond to the model
numbers from Table 1.1
2.0
9
8
1.5
6
7
1.0
1
2
3
5
4
0.5
12
11
13
10
0.0
0.0 .2
0.4 .6
0.8 .0
α
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