Modelling of infectious spreading in heterogeneous polymer oxidation I. Development of a stochastic model

The heterogeneous features of the oxidation of polypropylene in the amorpho us region are consistent with infectious spreading from a small number of s ites, such as catalyst residues. A stochastic model was developed for demon strating the spatial and temporal development of oxidation from these sites . In this model, the probability of passing the infection from one site to an adjacent site could be used in place of conventional rate constants. The probability of spreading was assumed to be temperature dependent, and mode lled with Arrhenius behaviour. Each site was given a predefined lifetime su ch that the maximum probability of spreading coincided with the maximum rat e of oxidation at a particular site. This has enabled visualisation of the spatial development of oxidation within the amorphous region. The epidemiol ogical fractions corresponding to the remaining (unoxidised) polymer, the d ead (oxidised) polymer and the infectious (oxidising) polymer. were calcula ted and used to test the limitations of the simple epidemiological model. ( C) 2001 Elsevier Science Ltd. All rights reserved.