Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 52

= −−
−

ln( 1 α )

t ,

α

E
RT

(2.40)

A exp

0

where the value of E is estimated by the Flynn and Wall method (Eq. 2.11). Compar-
ison of Eqs. 2.40 and 2.39 suggests that g ( ʱ ) = − ln(1 − ʱ ), which means that Eq. 2.40
is based on the assumption that the process obeys first-order kinetics (Table 1.1).
This assumption is also used to estimate the preexponential factor in Eq. 2.41:

= −

β R

a

(2.41)

A ln( 1 0 − α ) ,

E r

where ʲ is the mean of the experimental heating rates used to determine E by
the Flynn and Wall method (Eq. 2.11). The E r value is the corrected value of the
activation energy. It is determined by dividing the experimental value of E by the
correction factor that compensates for the inaccuracy of Dolyle's approximation of
the temperature integral. The ASTM document [ 74 ] lists the values of both the cor-
rection factor and the parameter a in Eq. 2.41.
The predictive equation utilized by E698 is the same as the one used by E1641
(Eq. 2.40). The value of E is recommended to be estimated either by the method of
Kissinger [ 76 , 77 ] or by the methods of Ozawa and Flynn and Wall (Eq. 2.11). In
the latter case, the ASTM document [ 75 ] recommends replacing T ʱ in Eq. 2.11 with
the peak temperature, T p . Just as E1641, the E698 method makes the assumption of
the first-order kinetics in its predictive equation and in the equation for estimating
the preexponential factor:

E
RT

β E

RT

(2.42)

A =

2 exp

.

p

p

The major shortcoming of both ASTM methods is that the lifetime is predicted
by assuming the first-order kinetics as well as the constancy of the activation en-
ergy. If any of these assumptions does not hold, the prediction would be in error.
Figure 2.19 demonstrates a considerable deviation of the ASTM prediction from
the experimental data on the thermal degradation of poly(ethylene 2,6-naphthalate)
(PEN), the process that demonstrates a significant variation of E ʱ with ʱ [ 78 ]. More
examples of similar problems with the ASTM predictions are found elsewhere [ 73 ,
79 ]. Therefore, before using the ASTM methods, one should be advised to check
whether E ʱ does not vary significantly with ʱ and whether the reaction model is that
of first order.
The shortcomings of the ASTM methods are circumvented by employing the
model-free predictions. The latter utilize the dependence of E ʱ on ʱ evaluated by an