NDLI: Closed form analytical approach for a second order non-linear ODE interpreting EPDM vulcanization with peroxides

Content Provider	Springer Nature Link
Author	Milani, G.
Copyright Year	2013
Abstract	In this paper, the recently presented kinetic model proposed in Milani and Milani (J Math Chem 51(3):1116–1133, 2013) to interpret EPDM peroxide vulcanization is extensively revised and the resultant second order ODE is solved by means of an approximate but effective closed form analytical approach. The model has kinetic base and it is aimed at predicting, by means of a very refined approach, the vulcanization degree of rubber vulcanized with peroxides. Such a procedure takes contemporarily into consideration, albeit within a simplified scheme, the actual reactions occurring during peroxidic curing, namely initiation, H-abstraction, combination and addition, and supersedes the simplified approach used in practice, which assumes for peroxidic curing a single first order reaction. The main drawback of the overall procedure proposed in Milani and Milani (J Math Chem 51(3):1116–1133, 2013) is that the single second order non-linear differential equation obtained mathematically and representing the crosslink evolution with respect to time, was solved numerically by means of a Runge–Kutta approach. Such a limitation is here superseded and a major improvement is proposed allowing the utilization of an approximate but still effective closed form solution. After some simplifications applied on some parts of the solving function not allowing direct closed form integration, an analytical function is proposed. Kinetic parameters within the analytical model are evaluated through least squares where target data are represented by few experimental normalized rheometer curve values. In order to have an insight into the reliability of the numerical approach proposed, a case of technical interest of an EPDM with low unsaturation and crosslinked with three different peroxides at three increasing temperatures is critically discussed.
Starting Page	2033
Ending Page	2061
Page Count	29
File Format	PDF
ISSN	02599791
Journal	Journal of Mathematical Chemistry
Volume Number	51
Issue Number	8
e-ISSN	15728897
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-06-06
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Vulcanization Peroxides Mathematical model Second order differential equation Closed form solution Physical Chemistry Theoretical and Computational Chemistry Math. Applications in Chemistry
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Chemistry

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