Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 41

The equation is readily obtained by rearranging Eq. 2.2. The kinetic triplet is esti-
mated by substituting some reaction model f j ( ʱ ) in the left-hand side of Eq. 2.27 and
fitting its dependence on the reciprocal temperature to a straight line. The intercept
and slope of the line would, respectively, yield ln A j and − E j / R . Such model-fitting
results in obtaining as many kinetic triplets as the number of the reaction models
one chooses to substitute in Eq. 2.27. Then, out of the multitude of obtained triplets,
one picks a triplet whose E j value matches best the activation energy value obtained
by an isoconversional method. Such approach is unsound because of several meth-
odological flaws. First, the E j value frequently does not match the isoconversional
activation energy with sufficient accuracy. Second, it is also not uncommon when
more than one reaction model yields E j values that match the isoconversional value
within its confidence limits. Third, for the same reaction model, the E j and A j values
commonly change with the heating rate. These factors introduce considerable inac-
curacy in evaluation of the reaction models and preexponential factors.
On the other hand, the two methods discussed further afford accurate evaluation
of the reaction model and preexponential factor subject to one important condition.
The condition is that the process under study can be adequately represented by the
single-step Eq. 2.2. This is readily verifiable by means of an isoconversional meth-
od. The condition is satisfied when the E ʱ values do not demonstrate a systematic
dependence on ʱ within a reasonably wide range of ʱ , e.g., 0.1-0.9. It is practically
acceptable when the difference between the maximum and minimum values of E ʱ is
less than 10 % of the average E ʱ value. In the case of larger variability, the process
cannot be considered as a single-step one. Any attempts to describe a multistep pro-
cess by a single-reaction model and a value of the preexponential factor would give
rise to inaccurate estimates of both.

2.2.2 The Use of the Compensation Effect

The first method we are going to discuss here allows one to employ the compensa-
tion effect for evaluation of the preexponential factor and the reaction model [ 29 ].
The method was originally proposed [ 57 ] for a single-step process. Later it was
demonstrated [ 58 ] to work for estimating the preexponential factors of multistep
processes. The method has been perfected by Sbirrazzuoli [ 59 ]. The compensation
effect was already discussed briefly in Chap. 1 (Eq. 1.11). More detailed informa-
tion is furnished elsewhere [ 60 ].
For the purpose of the present discussion, it would suffice to mention that the
Arrhenius parameters ln A j and E j estimated by a single-heating-rate method (e.g.,
Eq. 2.27) are strongly correlated in the form of a linear relationship known as the
compensation effect:

(2.28)

ln AEb

j =+

,