Prediction of Thermal Aging of Materials by Modified Kinetic Analysis based on Limited Amount of Experimental Points
The investigation of materials aging at ambient temperatures is experimentally very difficult due to its very low rate, small changes of physicochemical properties and, very often, limited amount of experimental data. Commonly applied methods of thermal-aging determination are therefore based on kinetic analysis carried out by measuring material properties at several elevated temperatures. Kinetic analysis can be applied to evaluate not only one-step reactions but also the multi-step reactions proceeding by several consequent or parallel steps that can be the combination of chemical or physical sub-stages. With today’s computers there are almost no limitations concerning the type of the reaction models applied and number of reaction steps during kinetic computations. The only limitations usually arise from the experimental procedure when the number of experimental points is in the range of ca. 30 or less. If only such scarce experimental points collected in discontinuous mode are available, we propose in the current study to modify both the kinetic analysis and the model selection approach in the way which still allows the correct description of investigated processes despite of experimental limitations. Applying simultaneous combination of two Sesták Berggren models enables to consider all the specific forms of the kinetic equations commonly applied in kinetic computations including also the peculiarities of the models applied to autocatalytic-type reactions (Kamal-Sourour (KS) or Finke-Watzky (FW) models). The difficult task of discriminating best kinetic reaction model among all models, when having scarce data points only, is solved by the application of Akaike and Bayesian Information Criteria (AIC/BIC). This approach allows successful discrimination between an unlimited numbers of kinetic models even if the total number of available data points is very limited. Using additionally the bootstrap method it is possible to calculate the prediction band, being particularly useful in reliable estimation of long-term properties of the materials. The method is illustrated by the experimental simulations of the depletion of the stabilizer Akardite-1 (1,1-Diphenylurea) in a single base propellant, the prediction of the thermal stability of freeze-dried measles vaccine and the determination of the long-term hydrostatic strength of thermoplastics materials in pipe form (ß-Nucleated PP-H).
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