Arrhenius extrapolation

The data of aging obtained at elevated temperature are extrapolated to ambient conditions. The extrapolation is based on the law of Arrhenius (2). Thus a rate constant k is dependent on the absolute temperature T by the relation 

The parameter E is the energy of activation and R is the gas constant. Actually, the law of Arrhenius is valid for rather complex degradation processes, in that the individual rate constants may have different energies of activation. 

the application of the law of Arrhenius can be trusted to be an empirical relationship that is widely usable. 

However, sometimes a curvature in the logarithmic plot is observed. Most simply this curvature can be resolved in a low temperature and high temperature regime with different energy of activation Efl. 

When the curvature indicates lower activation energies at lower temperatures, the service time estimated from the high temperature region would be too optimistic. 

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Further problems arise if measurements of the rate of nitration have been made at temperatures other than 25 °C under these circumstances two procedures are feasible. The first is discussed in 8.2.2 below. In the second the rate profile for the compound imder investigation is corrected to 25 °C by use of the Arrhenius parameters, and then further corrected for protonation to give the calculated value of logio/i fb. at 25 °C, and thus the calculated rate profile for the free base at 25 °C. The obvious disadvantage is the inaccuracy which arises from the Arrhenius extrapolation, and the fact that, as mentioned above, it is not always known which acidity functions are appropriate. 

In summary, practical experience with predicting the hydrolytic degradation of polyethylene terephthalate is an example of the use of Arrhenius extrapolation, a demonstration of the problems encountered when there are changes in the state of the polymer as the temperature is raised, and an example of the large variability in prediction of lifetime due to the logarithmic scale. 

Such contradictory results obtained by different aging methods suggest that one should use Arrhenius extrapolations to predict service life only with great reservation. Obviously aging tests should be run over a wide spectrum of temperatures and as near as possible to the anticipated end-use temperature of the resin. One way to shorten the duration of the test at lower temperatures is to use thin specimens, such as microtome cuttings. Figures 5 and 6 show that acceleration by an order of magnitude may be obtained. 

Figure 17. Arrhenius extrapolation of In k vs. 1000/T (K). Key , light oxygen, warp O, light oxygen, weft , dark oxygen, warp , dark...

These observations emphasise the conclusion that a simple dependence on an Arrhenius extrapolation from high-temperature studies can be unreliable. In the worst case, the derived rate constant for a 1% formulation in the absence of Carbopol is 9 orders of magnitude in error at 298 K. 

The data from the three higher temperatures were used to calculate rate constants and in turn Arrhenius extrapolations for air containing the normal amount of oxygen yielding A = 1.713 x 10 and an activation energy of 17. 3 i 0.U9 Kcal/mol. 

The need to actual measure kinetic data, rather than extrapolating data from lower temperatures, is that the theoretical models are insufficiently sophisticated to accmately describe the transition from subcritical conditions to supercritical conditions, as is evident from the data plotted in Fig. 88. Thus, a simple Arrhenius extrapolation of Elhot s subcritical data or by using a multiple collision model does not produce the data at all well in the... 

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