Abstract
One of the main drawbacks of EPM/EPDM rubber vulcanization by peroxides is the lack of selectivity, which leads to a number of side reactions. The reaction mechanisms at the base of peroxides crosslinking are generally known and include the formation of alkyl and allyl (in the EPDM case) macro-radicals through H-abstraction from the macromolecular chains and the combination of these macro-radicals, which macroscopically is known with the term “vulcanization”. In the paper, a simple but effective mathematical model having kinetic base, to predict the vulcanization degree of rubber vulcanized with peroxides, is presented. The approach 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. After a suitable re-arrangement of the first order system of differential equations obtained from the actual kinetic system adopted, a single second order non-linear differential equation is obtained and numerically solved by means of a Runge–Kutta approach. Kinetic parameters to set are evaluated by means of a standard least squares procedure where target data are represented by experimental values available, i.e. normalized rheometer curves or percentage crosslink density experimentally evaluated by means of more sophisticated procedures. In order to have an insight into the reliability of the numerical approach proposed, two cases of technical interest are investigated in detail: the first is an EPDM crosslinked with two different peroxides, whereas the second is a compound with high level of unsaturation, showing reversion at medium-high vulcanization temperature (\(175^\circ \text{ C}\)).
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References
G. Milani, F. Milani, J. Math. Chem. 47(1), 229–267 (2010)
E. Di Giulio, G. Ballini. Kautschuk gummi, kunststoffe 15, 6–11 (1962)
A.Y. Coran, Vulcanization, in Science and technology of rubber, Chapter 7, ed. by F.R. Eirich (Academic Press, New York, 1978)
M. Morton (ed.), Rubber technology (van Nostrand Reinhold, New York, 1981)
G. Milani, F. Milani, J. Math. Chem. 48, 530–557 (2011)
G. Milani, F. Milani, J. Appl. Polym. Sci. 124(1), 311–324 (2012)
G. Milani, F. Milani, Comput. Chem. Eng. 43, 173–190 (2012)
W. Hofmann, Rubber technology handbook (Hanser Publishers, Munich, 1989)
J.A. Riedel, R. Vander Laan, Ethylene propylene rubbers. in The vanderbilt rubber handbook, 13th edn. (R.T. Vanderbilt Co., Inc., Norwalk, CT, 1973), pp. 123–148
P.S. Ravishankar, Rubber World, 219(3), pp. 23+57 (1998)
G. Milani, F. Milani, Kinetic finite element model to optimize sulfur vulcanization: application to extruded EPDM weather-strips. Polym. Eng. Sci. (2013, in press)
F.P. Baldwin, P. Borzel, C.A. Cohen, H. Makowski, J.F. van de Castle, Rubber Chem. Technol. 43, 522 (1970)
M. van Duin, H.G. Dikland, Rubber Chem. Technol. 76, 132 (2003)
M. van Duin, M. Dees, H.G. Dikland, Kautsch. Gummi Kunstst 61, 233 (2008)
M. Dees, M. van Duin, Rubber World, 238(5), 19–25 (Aug, Sept 2008)
M. van Duin, Kautsch. Gummi Kunstst 55, 150 (2002)
B.E. Knox, B. Palmer, Chem. Rev. 61, 247 (1961)
R. Peters, M. van Duin, D. Tonoli, G. Kawakkenbos, Y. Mengerink, R. van Benthem, C. de Koster, P.J. Schoenmakers, S. van der Wal, J. Chromatogr. A 1201, 151 (2008)
R. Orza, P.C.M.M. Magusin, V.M. Litvinov, M. van Duin, M.A.J. Michels, Macromolecules 42, 8914–8924 (2009)
H.G. Dikland, M. van Duin, Crosslinking of EPDM and polydiene rubbers studied by optical spectroscopy. in Spectroscopy of rubbers and rubbery materials, Rapra Technology Ltd., ed. by V.M. Litvinov, P.P. De (Shawbury, Shrewsbury, Shropshire, 207, 2002)
M. van Duin, R. Orza, R. Peters, V. Chechik, Macromol. Symp. 291–292, 66–74 (2010)
W.C. Endstra, C.T.J. Wreesman, in Elastomer Technology Handbook, ed. by N.P. Cheremisinoff (CRC Press, Boca Raton, 1993), p. 495
P. Dluzneski, Rubber Chem. Technol. 74, 451 (2001)
R. Orza, Investigation of peroxide crosslinking of EPDM rubber by solid-state NMR. PhD thesis Technische Universiteit Eindhoven (2008)
J.M. Kranenburg, M. van Duin, U.S. Schubert, Screening of EPDM cure states using depth-sensing indentation. Macromol. Chem. Phys. 208, 915–923 (2007)
Matlab User’s Guide (2007). http://www.mathworks.com/products/matlab/
G. Milani, A. Galanti, C. Cardelli, F. Milani, Peroxide cross-linking of EPDM for medium voltage cable applications: experimental insight. in Proceedings of 183rd technical meeting Akron, Ohio Monday April 22–Wednesday April 24 (2013)
AkzoNobel (2012). Brochure of organic peroxides, available at http://www.akzonobel.com/polymer/
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Milani, G., Milani, F. Differential model accounting for reversion for EPDM vulcanized with peroxides. J Math Chem 51, 1116–1133 (2013). https://doi.org/10.1007/s10910-012-0140-5
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DOI: https://doi.org/10.1007/s10910-012-0140-5