Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 53

isoconversional method. Originally, the model-free predictive equation was derived
[ 29 , 80 ] in the following form:

T

α

− E

∫

α

exp d T

RT

0

t = .

(2.43)

α

− E

RT

α

β exp

0

This equation is derived by equating the right-hand sides of Eqs. 2.3 and 2.8 and
cancelling the A values. This action is justified by the aforementioned assumption
that the kinetic triplet does not change over the temperature range of extrapolation.
There is an important methodological difference between Eqs. 2.43 and 2.39. The
latter does not directly use any experimentally measured kinetic curves to make the
predictions. The kinetic curves are replaced with the kinetic triplet. On the other
hand, Eq. 2.43 makes use of the kinetic curve ʱ versus T measured at certain heating
rate ʲ . In other words, Eq. 2.43 is a way of converting actually measured noniso-
thermal kinetic data into isothermal data expected at a given temperature T 0 . Since
several heating rates are used to evaluate the E ʱ dependence, any of the respective
ʱ versus T curves can be used for making predictions by Eq. 2.43. In theory, there
should be no significant difference between the lifetimes predicted when using the
ʱ versus T curves obtained at different ʲ . This is because the numerator of Eq. 2.43
divided over ʲ is g ( ʱ ), whose value is constant at ʱ = const for all heating rates
involved. In practice, the lifetime predicted from different heating rates can demon-
strate some variability that is reduced by replacing the respective t ʱ values with the
mean or median value.
Since Eq. 2.43 performs integration from 0 to T ʱ , assuming that E ʱ remains con-
stant from 0 to ʱ, it cannot properly account for variability of the activation energy
with the extent of conversion. As mentioned earlier, this can lead to significant
systematic errors in the case of a strong variation of E ʱ with ʱ . For this reason,
the original Eq. 2.43 was later [ 81 ] modified to account for such variations. The
latter are accounted properly when performing integration by small segments (see
Eq. 2.21). Then, if the interval from 0 to ʱ is split in k segments, Eq. 2.43 can be
used to predict time for each individual segment:

T

α , i

− E

α , i

∫

exp d T

RT

T

(2.44)

α ,1 i −

t = .

α , i

− E

RT

α , i

β exp

0

Then, the total time to reach ʱ will be the sum of the times for all k segments: