Closed form numerical approach for a kinetic interpretation of high-cis polybutadiene rubber vulcanization with sulphur

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• 作者：G. Milani ; F. Milani
• 关键词：Vulcanization ; High ; cis polybutadiene ; Mathematical model ; Closed form solution
• 刊名：Journal of Mathematical Chemistry
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：55
• 期：2
• 页码：552-583
• 全文大小：
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Physical Chemistry; Theoretical and Computational Chemistry; Math. Applications in Chemistry;
• 出版者：Springer International Publishing
• ISSN：1572-8897
• 卷排序：55

文摘

A novel mathematical approach to predict the vulcanization degree of high-cis polybutadiene rubber vulcanized with sulphur is presented. The model has kinetic base, it is constituted by four reactions occurring in series and parallel and takes contemporarily into consideration, within a simplified but reliable scheme, the actual reactions occurring during polybutadiene sulphur curing, namely primary crosslinking and possible de-vulcanization. The first order differential equation system obtained is suitably rearranged and a closed form expression for the vulcanization degree is derived, depending the four kinetic constants characterizing the chemistry describing reactions. Instead of using classic least-squares optimization routines to characterize kinetic constants on experimental data, a simplified but reliable approach is proposed, where a system of four non-linear equations is solved with a recursive strategy, allowing estimating kinetic constants that proved to fit well normalized experimental data. The procedure is fast and its reliability is tested on a number of experimental data available, relying into a high-cis polybutadiene rubber cured under different temperatures and accelerators concentrations. Very good approximations of experimental data are obtained, also in comparison with a heuristic numerical approach where optimization is obtained interactively.