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Title of Journal: J Math Chem

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Abbravation: Journal of Mathematical Chemistry

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Springer Netherlands

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DOI

10.1007/s10587-011-0039-5

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ISSN

1572-8897

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Closed form analytical approach for a second order

Authors: G Milani
Publish Date: 2013/06/06
Volume: 51, Issue: 8, Pages: 2033-2061
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Abstract

In this paper the recently presented kinetic model proposed in Milani and Milani J Math Chem 5131116–1133 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 Habstraction 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 5131116–1133 2013 is that the single second order nonlinear 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evolution with respect to time was solved numerically by means of a Runge–Kutta approach Such a limitation is here superseded and a major improvement is proposed allowing the utilization of an approximate but still effective closed form solution After some simplifications applied on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

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