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A stochastic model for predicting the service life of photolytically degraded poly(methyl methacrylate) films
Author(s) -
Martin Jonathan W.
Publication year - 1984
Publication title -
journal of applied polymer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.575
H-Index - 166
eISSN - 1097-4628
pISSN - 0021-8995
DOI - 10.1002/app.1984.070290306
Subject(s) - poisson distribution , materials science , population , compound poisson distribution , service life , interval (graph theory) , stochastic modelling , polymer , compound poisson process , photodegradation , chain (unit) , poisson process , composite material , mathematics , poisson regression , physics , chemistry , statistics , organic chemistry , combinatorics , quantum mechanics , demography , photocatalysis , sociology , catalysis
A stochastic model has been proposed and partially validated for predicting the service life of a nominal population of polymethyl methacrylate films subjected to photolytic degradation. Here, service life is defined as the time after which an unacceptable portion of a nominal population of PMMA films subjected to photodegradation have failed; failure occurs when a performance property of the film falls below a predesignated minimum value. The stochastic model has two parts. The first part uses a Poisson distribution in computing the probability that exactly K photon related chain scissions will occur in the film in the interval [0, t ). The parameter of the Poisson distribution is made functionally dependent on temperature and the intensity of radiation absorbed. The second part determines the probability that a performance property will be greater than a minimum value after K chain scissions. This part is called the damage process. Together, the two parts of the model form a compound Poisson process. The main points of the models are validated against 25 published data sets. The plausibility of the Poisson process was substantiated for modeling the number of chain scissions occurring in the interval [0, t ). Also, it was demonstrated that the expected change in two performance properties of the films was functionally related to the expected number of chain scissions.