Lifetime prediction kinetic model

Aging becomes a difficult problem to study in practice, because it proceeds too slow in use conditions (typical lifetime of years). It is then necessary to make accelerated aging tests to build kinetic models that describe the time changes of the material s behaviour, and to use these models to predict the durability from a conventional lifetime criterion. Indeed, the pertinence of the choice of accelerated aging conditions, the mathematical form of kinetic model, and lifetime criterion has to be proved. Empirical models are highly questionable in this domain because they have to be used in extrapolations for which they are not appropriate. 

The most important achievement of the kinetic model is its capability to describe almost all the experimental data on SMIE available so far.6-8 It means that the above equation may be used for prediction of the lifetime in industrial applications where LMPM are used, for example as protective coatings. 

This paper presents a non-empirical kinetic model for the lifetime prediction of polymers exposed in their normal use conditions. After having described the different components (the core, the optional layers) of the model, its efficiency is demonstrated for polyethylene in large temperature and y dose rate ranges. Future developments are briefly presented. 

Since the end of the 90 s, our group has been developing a non-empirical kinetic model, named KINOXAM, for the lifetime prediction of polymers and polymer matrix composites in their use conditions. The model is totally open. It is composed of a core, common to all types of polymers, derived from the now well-known closed-loop mechanistic scheme (/). Around this core, various optional layers can be added according to the complexity of oxidation mechanisms and the relationships between the structural changes taking place at the molecular scale and the resulting ones at larger scales (the macromolecular and macroscopic scales). 

A non-empirical kinetic model was developed for the lifetime prediction of polymer parts in their normal use conditions. This model gives access to the spatial distribution (in the sample thickness) of the structural changes at the different scales and the resulting changes of normal use properties. Its efficiency was demonstrated for many substrates in large temperature and dose rate ranges. Here, we have paid special attention to PE radio-thermal oxidation. 

Future work will include combining the chain scission kinetics of ester hydrolysis (/) with crosslinking kinetics of urethane oxidation to provide an overall kinetic model of Estane molecular weight change. This combined hydrolysis/oxidation kinetic model will allow us to make lifetime predictions for the PBX 9501 binder. 

The model derived from the above procedure compares quite favorably with experiment, see Fig. 10. We are now ready to combine the model with the coking kinetic model to predict the observed changes in the reforming rate constants during the lifetime of the catalyst. 

The recently developed nonhomogeneous kinetics model for the reaction of ions produced during radiolysis of dielectric liquids is applied to the estimation of the lifetimes of these ions in water, ethyl alcohol, acetone, and cyclohexane. Calculated lifetime spectra are given. The use of the complex dielectric constant in the calculations is discussed and found to be necessary for alcohols, but not for water, acetone, or hydrocarbons. The model predicts that the yield of ions observed at time t after an instantaneous pulse of radiation would be about 10% greater than G,< at 0.3 nsec, in water, 2 nsec, in ethyl alcohol, 3 nsec, in acetone, and 400 nsec, in cyclohexane. The calculated results are consistent with the limited measurements that have been published. 

In view of the moderate success of the kinetics model in its present form, it might be useful to present the radiolytic ion lifetime spectra that are predicted by the model for several different dielectric liquids. In anticipation of what follows, the very limited results of the few experiments that have attempted to measure these lifetimes [in cyclohexane (11) and in water (9)] are consistent with the present calculations. More extensive experiments are needed. 

As an input for this model, one has to understand the fundamentals of performance losses and degradation. Specific experimental data is needed, to correlate degradation and deterioration phenomena to operating conditions for stationary applications, and identify the paths leading to failure phenomena. This experimental part is an effort to obtain data on degradation quantitatively and reproducibly, since the understanding of kinetics of various degradation processes are the key of final performance and lifetime prediction. 

The real breakthrough in terms of kinetic theory was published in 1973 by Aniansson and Wall [80, 81], who provided much more applicable kinetic equations for stepwise micelle formation using a polydisperse model. In a substantial paper two years later they were able to predict the first-order rate constants for the dis-sociation/association of surfactant ions to and from micelles (and hence residence times/lifetimes of surfactant monomers within micelles) [82]. They found values for the association and dissociation of surfactants into/from micelles (Ar and k , respectively) for sodium dodecyl sulfate (SDS) as 1 x 10 s and 1.2 x 10 mok s". Their kinetic model still remains essentially unchanged as a basis for the kinetics of micellar formation and breakdown. Modifications made to existing theory also allowed them to offer a significant thermodynamic explanation for the low enthalpy change upon micellization. 

The second-order kinetics cause some surprising conclusions. In general, RH decreases as the temperature increases and vice versa. When the Ea is low as for PC, the fact that the RH term is squared approximately cancels the effect of temperature. When the Ea is high as for PET, the temperature effect still dominates but not as much. As a result, the lifetime prediction is not very sensitive toward the accuracy of the temperature model. The results were also not very sensitive toward the time interval used in parsing the climatic data for both PC and PET 10 min and 2 h parsing surprisingly gave nearly the same results. 

A Kinetic Model for Predicting Polymeric Neutron Shieldings Lifetime... 

Such methods include predictions from tests of accelerated aging [7-23] and from weatherability based on empirical formulas (extrapolation, ageing kinetics model derivation) [5, 6], while others exploit new ways for detection of service lifetime [24—26]. Some methods are based on monitoring of cumulative damage [27-30], etc. [31]. 

In principle, the same rules hold true when zeolitic alkylation catalysts are used. A detailed study of the influence of PO and OSV on the performance of zeolite H-BEA in a backmix reactor was reported by de Jong et al. (80). The authors developed a simple model of the kinetics, which predicted catalyst lifetimes as a function of P/O and OSV. Catalyst lifetime (which is equivalent to the catalyst productivity, the reciprocal of acid consumption) increased with increasing P/O ratio and decreasing OSV. Furthermore, the authors persuasively demonstrated the superiority of a backmix reactor over a plug flow reactor. Qualitatively similar results were obtained by Taylor and Sherwood (222) employing a USY zeolite catalyst in a backmix reactor. The authors stressed the detrimental effect of unreacted alkene on the catalyst lifetime and product quality. Feller et al. (89) tested LaX zeolites in a backmix reactor and found the catalyst productivity to be nearly independent of the OSV within the examined OSV range. At higher values of OSV, the catalyst life was shorter, but in this shorter time the same total amount of product was produced. The P/O ratio had only a moderate influence on the catalyst performance. 

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