Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 55

1.0

0.8

0.6 280

260

0.4

240

220

0.2

200

0.0 0.2 0.4 0.6 0.81.0

0.0 α

0 500 1000 1500 2000 2500

t / s

Fig. 2.19 ASTM E1641 ( solid line ) and model-free ( dash-dot line ) predictions of the thermal
degradation of PEN in nitrogen at 420 °C compared to the actually measured data ( circles, the
initial portion is not shown to avoid overcrowding). Inset shows the E ʱ dependence evaluated by
an isoconversional method from nonisothermal TGA data. (Reproduced from Prime et al. [ 78 ]
with permission of Wiley.) ASTM American Society for Testing and Materials, PEN poly(ethylene
2,6-naphthalate)

**

JE Tt JE Tt [, ( ] = [ , ()]. (2.48)

α 0 α α α

In Eq. 2.48, the right-hand side represents the integral (Eq. 2.21) over a particular
experimental temperature program, T * ( t ). Then the lifetime t ʱ at any desired tem-
perature program T 0 ( t ) is estimated as a numerical solution of Eq. 2.48.

2.3.3 Understanding Precision and Accuracy of Predictions

It is important to keep in mind that any kinetic prediction has its inherent limits in
terms of precision and accuracy. Unavoidable noise in experimental measurements
(i.e., T , ʱ , d ʱ /d t ) leads to random errors in estimating the kinetic triplet. These ran-
dom errors further propagate into the error of the lifetime value. For example, the
relative error in the lifetime predicted by Eq. 2.43 is estimated [ 82 ] approximately
to be

∆ t 1 1 1

(2.49)

α

≈ ∆ E − − .

α

t RT RT E

α 0 α α

This equation suggests that as the temperature of prediction, T 0 , moves further away
from the experimental temperature, T ʱ , the relative error in the lifetime increases