Kinetic Analysis, Fitting and Teaching Design of Rubber Vulcanization Curve

ZHAI Jun-xue; LI Guo-jie

doi:10.14028/j.cnki.1003-3726.2026.26.085

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Kinetic Analysis, Fitting and Teaching Design of Rubber Vulcanization Curve

更新时间：2026-07-27

- Kinetic Analysis, Fitting and Teaching Design of Rubber Vulcanization Curve
- Polymer Bulletin Vol. 39, Issue 8, Pages: 1512-1518(2026)
- 作者机构：
  
  青岛科技大学高分子科学与工程学院橡塑材料与工程教育部重点实验室　青岛 266042
- 作者简介：
- 基金信息：
- DOI：10.14028/j.cnki.1003-3726.2026.26.085
  CLC：
- Received：25 February 2026，
  
  Accepted：28 April 2026，
  
  Online First：13 July 2026，
  
  Published：20 August 2026
- 稿件说明：
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翟俊学, 黎国杰. 橡胶硫化曲线动力学分析、拟合与教学设计. 高分子通报, 2026, 39(8), 1512–1518.

Zhai, J. X.; Li, G. J. Kinetic analysis, fitting and teaching design of rubber vulcanization curve. Polym. Bull. (in Chinese), 2026, 39(8), 1512–1518.
翟俊学, 黎国杰. 橡胶硫化曲线动力学分析、拟合与教学设计. 高分子通报, 2026, 39(8), 1512–1518. DOI： 10.14028/j.cnki.1003-3726.2026.26.085.

Zhai, J. X.; Li, G. J. Kinetic analysis, fitting and teaching design of rubber vulcanization curve. Polym. Bull. (in Chinese), 2026, 39(8), 1512–1518. DOI： 10.14028/j.cnki.1003-3726.2026.26.085.

摘要

橡胶硫化动力学分析是高分子学科的重要知识。为了系统学习橡胶硫化动力学知识和分析方法，学习用新的非等温动力学方法分析和拟合橡胶等温硫化曲线，本文首先总结了国内外文献中的橡胶硫化、交联反应动力学模型，然后将非等温动力学分析Málek法进行改进，用二元自催化模型结合改进的非等温动力学方法分析并拟合橡胶等温硫化曲线，进一步将其结合BOPPPS (知识导入(Bridge-in)，学习目标(Objective)，前测(Pre-assessment)，参与式学习(Participatory Learning)，后测(Post-assessment)，总结(Summary))方法进行教学设计。结果表明，文献认为机理动力学模型可以描述橡胶硫化反应历程，

级模型、K–S模型等经验模型能够更方便地拟合硫化动力学曲线；通常认为等温硫化是一级反应，示差扫描量热法(DSC)非等温动力学分析方法可以计算反应活化能和反应级数；将Málek法中的温度函数简化为不变量后可以分析橡胶等温硫化曲线，K–S模型比

级模型能够更好地描述硫化速率−反应度曲线。将上述文献分析、科研结果用于课堂教学，更新橡胶硫化反应动力学知识，学习二元K–S模型拟合方法并与

级模型对比，有助于加深理解、掌握橡胶硫化/交联动力学知识，培养分析和解决如何控制最佳硫化程度的工程实践能力。

Abstract

The analysis of rubber vulcanization kinetics is a fundamental discipline in polymer science. To systematically study rubber vulcanization kinetics and analytical methods

this study focuses on employing novel non-isothermal kinetic approaches to analyze and fit isothermal vulcanization curves. This study first synthesizes rubber vulcanization and crosslinking reaction kinetic models from domestic and international literature. Subsequently

the improved M

álek method for non-isothermal kinetic analysis was used to analyze and fit the isothermal vulcanization curves by integrating a binary autocatalytic model. These findings were further incorporated into the instructional design using the BOPPPS (Bridge-in

Objective

Pre-assessment

Participatory Learning

Post-assessment

Summary) methodology. The results demonstrate that

according to the literature analysis

the kinetic models effectively describe the vulcanization processes

while empirical models

such as the n-order and K-S models

facilitate curve fitting. Isothermal vulcanization reactions are generally classified as first-order processes

whereas differential canning calorimetry (DSC)-based non-isothermal kinetic analysis enables the calculation of the activation energy and reaction order. Simplifying the temperature function in the Málek method into invariant parameters allows effective curve analysis

with the K-S model outperforming the

-order model in describing vulcanization rate-reaction degree curves. Integrating these literature reviews and research findings into classroom teaching updates the knowledge of vulcanization kinetics. A comparative analysis between binary K-S model fitting methods and n-order models enhances the understanding of vulcanization/crosslinking kinetics

fostering practical engineering skills in optimizing vulcanization conditions.

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references

潘祖仁 . 高分子化学 , 第2版 . 北京 : 化学工业出版社 , 2011 . 234 .

吴其晔 , 张萍 , 杨文君 , 林润雄 . 高分子物理学 . 北京 : 高等教育出版社 , 2015 . 186 .

杨清芝 . 现代橡胶工艺学 . 北京 : 中国石化出版社 , 1997 . 658 .

曾宗强 , 李普旺 , 吕明哲 , 陈锦炜 . 热分析技术在天然橡胶研究中的应用 . 热带农业工程 , 2005 , 29 ( 1 ), 12 – 15 .

郭飞 , 张兆想 , 宋炜 , 贾晓红 . 橡胶硫化过程数值模拟研究进展 . 化工学报 , 2020 , 71 ( 8 ), 3393 – 3402 .

戈明亮 , 阚长华 , 易玉华 , 张海 . 橡胶硫化反应动力学研究概况 . 橡胶工业 , 2004 , 51 ( 10 ), 631 – 635 .

Coran, A. Y . Vulcanization. Part V. The formation of crosslinks in the system: natural rubber-sulfur-MBT-zinc ion . Rubber Chem. Technol. , 1964 , 37 ( 3 ), 679 – 688 .

Kissinger, H. E . Reaction kinetics in differential thermal analysis . Anal. Chem. , 1957 , 29 ( 11 ): 1702 – 1706 .

Kamal, M. R. ; Sourour, S . Kinetics and thermal characterization of thermoset cure . Polym. Eng. Sci. , 1973 , 13 ( 1 ), 59 – 64 .

Rafei, M. ; Ghoreishy, M. H. R. ; Naderi, G . Development of an advanced computer simulation technique for the modeling of rubber curing process . Comput. Mater. Sci. , 2009 , 47 ( 2 ), 539 – 547 .

Leroy, E. ; Souid, A. ; Sarda, A. ; Deterre, R . A knowledge based approach for elastomer cure kinetic parameters estimation . Polym. Test. , 2013 , 32 ( 1 ), 9 – 14 .

Yeoh, O. H . Mathematical modeling of vulcanization characteristics . Rubber Chem. Technol. , 2012 , 85 ( 3 ), 482 – 492 .

贾玉玺 , 孙胜 , 季忠 , 赵国群 . 硅橡胶硫化反应场的数值模拟 . 化学学报 , 2002 , 60 ( 8 ), 1368 – 1373 .

秦岩 , 刘海华 , 梅启林 , 黄志雄 . 低压SMC体系的固化动力学及凝胶化理论 . 高分子材料科学与工程 , 2008 , 24 ( 4 ), 105 – 108 .

张天萍 , 甄卫军 , 赵玲 . 配方对有机硅橡胶非等温硫化动力学的影响 . 高校化学工程学报 , 2020 , 34 ( 1 ), 222 – 229 .

刘慧娟 , 展喜兵 , 祝文亲 , 林欣 , 程珏 , 张军营 . 液体乙烯基硅树脂的制备及固化反应动力学 . 化工学报 , 2014 , 65 ( 4 ), 1509 – 1516 .

张晓林 , 梁栋 , 赵树高 . 不同硫化体系天然橡胶阻尼减震材料的硫化动力学及性能研究 . 橡胶工业 , 2018 , 65 ( 8 ), 845 – 849 .

Málek, J . A computer program for kinetic analysis of non-isothermal thermoanalytical data . Thermochim. Acta , 1989 , 138 ( 2 ), 337 – 346 .

Barghamadi, M. ; Ghoreishy, M. H. R. ; Karrabi, M. ; Mohammadian-Gezaz, S . Investigation on the kinetics of cure reaction of acrylonitrile-butadiene rubber (NBR)/polyvinyl chloride (PVC)/graphene nanocomposite using various models . J. Appl. Polym. Sci. , 2020 , 137 ( 18 ), 48632 .

艾娇艳 , 刘保华 , 宋丽娜 , 赵晨 . 《高分子物理》课程中交联相关知识的模块化教学 . 高分子通报 , 2024 , 37 ( 5 ), 707 – 712 .

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