Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 33

Fig. 2.5 Relative error in the
activation energy as a func-
tion of x E RT ; nonlinear
method, Eq. 2.16 ( circles ),
linear Kissinger-Akahira-
Sunose equation, Eq. 2.13
( squares ). (Reproduced from
Vyazovkin and Dollimore
[ 34 ] with permission of ACS)

rigid) integral methods, the resulting activation energies are estimated in accord
with a set of built-in assumptions. While maybe not obvious, these assumptions
cannot be changed because they are a part of the final equation used for estimating
the activation energy.
There are four built-in assumptions that affect the estimates of the activation
energy determined with the rigid integral methods. The first one is using 0 instead
of T 0 for the lower integration limit in I ( E, T ) has already been mentioned. Since in
a flexible method (e.g., Eq. 2.17) both integration limits are controlled by the user,
one can perform integration from the actual value of T 0 .
The second assumption is that the process occurs on heating making the tra-
ditional methods inapplicable to the processes that take place on cooling, such as
crystallization. The heating-only assumption arises from the fact that I ( E, T ) is ap-
proximated as S ( T ) and not as the difference shown in Eq. 2.10. As cooling starts
from the upper temperature T 0 and T continuously decreases, the extent of conver-
sion should increase in proportion to the increasing area S ( T 0 )− S ( T ) (Fig. 2.6 ). In
the traditional integral methods, this area is approximated as S ( T ) and thus it would
decrease with deceasing T . This is equivalent to a continuous decrease in the extent
of conversion that obviously does not make sense. However, the area S ( T 0 )− S ( T )
can be determined correctly when using the flexible integral methods that make
them suitable for treating a process that takes place on cooling.
The third built-in assumption is that the process temperature at any moment of
time is determined entirely by the value of ʲ (Eq. 2.7 ). In reality, the temperature
estimated by Eq. 2.7 is the so-called reference temperature or simply the furnace
temperature. The process temperature, though, is the sample temperature that can
deviate from that of the reference due to either self-heating or self-cooling caused
by the thermal effect of the process. Unless the deviations are negligible, one has to
use the actual sample temperature in kinetic computations. The sample temperature
can be used directly in the differential method such as that by Friedman (Eq. 2.5).
However, it cannot be used in the integral methods whose equations include a sin-
gle constant value of ʲ . The fact that such value is included in the equation of an