Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 57

Fig. 2.20 Model-free predictions ( dash lines ) of epoxy-amine curing reaction at a series of tem-
peratures from 60 to 160 C. Dots represent the actually measured data. Solid lines are predictions
corrected for vitrification. (Reproduced from Schawe [ 86 ] with permission of Elsevier)

This happens when ʱ reaches the detection limit, ʱ 0 . This obviously occurs at a non-
zero value of the time, t 0 . Therefore, accepting the ʱ 0 and t 0 values as being negligi-
bly different from zero introduces some systematic error into Eq. 2.39. As a result,
the lifetimes predicted by Eq. 2.39 are underestimated by the actual value of t 0 :

= ()

g
kT

α

0

t

() .

(2.50)

0

Equation 2.50 indicates that the error depends on the type of g ( ʱ ). As seen from
Fig. 2.12 , in the vicinity of ʱ 0 ≈ 0, the value of g ( ʱ 0 ) is vanishingly small for some
models (e.g., diffusion and contracting geometry type) but relatively large for others
(e.g., Avrami-Eroffev and power law models). This means that the assumption that
ʱ 0 and t 0 being zero would introduce negligible errors for the first type of the models
but may result in significant error for the second kind of the models. Recall that the
models of the first type belong to the class of decelerating models (see Sect. 1.1,
Fig. 1.5). They represent processes whose rate under isothermal conditions is the
fastest at ʱ = 0. For this reason, the process tends to become detectable at negligibly
small values of t 0 .
The second type of models is from the class of either accelerating or sigmoid
models. Under isothermal conditions, the respective processes have the slowest rate
at ʱ = 0 (Fig. 1.5). More importantly, these models represent the processes that tend
to have an induction period. In this case, the process may become detectable when