Some Basics En Route to Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 8

conversions but with another at larger ones, or do not follow any model within a
certain range conversions. This creates a serious problem of identifying the reaction
models by means of the model-fitting procedure.
The problem of identifying the reaction models becomes practically insurmount-
able when model fitting is performed on experimental data obtained in a noniso-
thermal run at a single heating rate, ʲ . Note that under isothermal conditions the
conversion dependence of the reaction rate (i.e., an experimental dependence of f ( ʱ )
on ʱ ) is easy to isolate because the rate is directly proportional to f ( ʱ ) (see Eq. 1.9).
However, under nonisothermal conditions when the temperature changes linearly
with the time:

β= d
d

T
t

,

(1.10)

both ʱ and T change simultaneously that thwarts clean separation of f ( ʱ ) and k ( T )
in Eq. 1.1. That is, when Eq. 1.1 is fitted to nonisothermal data, any inaccuracy in
selecting the reaction model becomes compensated by the respective inaccuracy in
the rate constant. As a result of this compensation, there always is more than one set
of k ( T ) and f ( ʱ ) that can fit the experimental data equally well from the statistical
point of view [ 14 ]. The resulting different rate constants give rise to widely differ-
ing pairs of the Arrhenius parameters, E and A, which, however, are strongly cor-
related via the so-called compensation effect [ 15 ]:

ln AEb

j =+

,

(1.11)

where the subscript j denotes a particular reaction model f j ( ʱ ) that is used in the
model-fitting procedure. A set of f j ( ʱ ), E j , and A j is frequently called a kinetic trip-
let. Experimental examples of the problem have been considered by Vyazovkin and
Wight [ 14 ]. Instructive simulated examples are found in the papers by Criado et al.
[ 16 , 17 ], who have demonstrated that three different kinetic triplets can give rise to
exactly the same kinetic curve ʱ versus T (Fig. 1.6 ). Note that the respective Ar-
rhenius parameters are strongly correlated via the compensation effect (Fig. 1.7 ).
Although the deficiency of single-heating-rate kinetic analyses had been empha-
sized repeatedly, their general inability to produce reliable kinetic triplets was offi-
cially recognized by the community only in the discussions [ 18 - 21 ] of the results of
the 2000 Kinetic Project sponsored by the International Confederation of Thermal
Analysis and Calorimetry (ICTAC). One of the most important conclusions of that
project was that the single-heating-rate kinetic analyses should be avoided. As an al-
ternative, one should use kinetic analyses based on the simultaneous use of multiple
heating rates or, more, generally, multiple temperature programs. According to the
2011 recommendations [ 22 ] of the ICTAC Kinetics Committee, such kinetic analy-
ses should be performed by using either model-fitting or isoconversional (model-
free) kinetic methodologies. The use of the model-fitting methodology is outside
this topic's scope. The topic focuses entirely on the applications of the isoconver-
sional kinetic methodology or, simply, isoconversional kinetics.