Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 50

2.3 Kinetic Predictions

But it had been one thing to foresee it mentally, and it was
another to behold it actually.
Henry James, The Portrait of a Lady

2.3.1 Why Predictions?

Kinetic predictions constitute the most important practical aspect of kinetic analy-
sis. The essence of the latter is parameterization of the experimentally measured
process rate as a function of such variables as the temperature, extent of conver-
sion, and, sometimes, pressure. Parameterization means evaluating parameters of
the equations (i.e., models) that represent a response of the process rate to a change
in the aforementioned variables. Most commonly, one needs to parameterize the
rate in terms of the temperature and conversion. This type of parameterization is
accomplished by evaluating the kinetic triplet. Knowledge of a single kinetic triplet
should be sufficient to predict the kinetics of a single-step process. Prediction of
multistep kinetics would then require estimating multiple kinetic triplets, which
is accomplished through model-fitting computations. However, isoconversional
methods can be used to make adequate kinetic predictions for single- and multistep
processes without estimating either preexponential factor or reaction model.
When it comes to kinetic predictions, one is typically interested in extrapolat-
ing some experimental kinetic measurements outside the actual temperature range,
within which they were taken. The need in the extrapolations arises from practical
difficulties of measuring the kinetics in the temperature range of interest. The actual
measurements can be prohibitively difficult because the process is either too slow or
too fast to measure by regular methods. Excessive costs as well as time limitations
are among other practical factors that make one to choose predictions over actual
measurements. A typical practical situation would be when one needs to select the
most efficient stabilizer for a material that degrades slowly, e.g., on the scale of sev-
eral years, at an ambient temperature. Measuring kinetics for several samples on such
timescale would be unacceptably long and may require very expensive and sensitive
equipment. A practicable alternative is to measure the kinetics at 40-50 ﾰC above am-
bient temperature. This would accelerate the process and shorten its timescale from
years to hours. Then, the higher-temperature kinetic data can be parameterized with
respect to temperature and conversion, and the resulting parameters can be used to
predict the kinetics at ambient temperature. The procedure is based naturally on the
assumption that the kinetics would not change over the temperature range of ex-
trapolation. In other words, it has to be assumed that the kinetic parameters estimated
from higher temperature data should remain unchanged at ambient temperature. The
same assumption allows one to make predictions from lower to higher temperature
which is just as important. For instance, thermal stability of polymeric materials at