A mathematical model for the kinetics and chain length development in A₂ + B₂ step‐growth polymerization with competition between cyclization and linear chain growth is presented. The model requires two kinetic rate constants, one for the several reactions producing linear polymer molecules (k), and another one for chain length dependent cyclization (k_c). The model describes well the qualitative behavior of the system, including the effects of initial monomer concentration and ratio of limiting to excess functional groups on degree of cyclization. The model is validated using two polymerization systems, a conventional A₂ + B₂ polymerization of hexamethylene diisocyanate (HDI) and poly(ethylene glycol) (PEG200), as well as the superacid catalyzed polyhydroxyalkylation of modified isatin and biphenyl. Four different kinetic rate constants for the four reactions producing linear polymer molecules are required in the second case.

中文翻译：

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使用建模工具分析动力学控制的A2 + B2逐步增长聚合中环化和线性链增长之间的竞争

提出了在A ₂  + B ₂逐步增长聚合反应中动力学和链长发展以及环化和线性链增长之间竞争的数学模型。该模型需要两个动力学速率常数，一个动力学常数用于产生线性聚合物分子的多个反应（k），另一个动力学常数用于依赖链长的环化（k _c）。该模型很好地描述了系统的定性行为，包括初始单体浓度和过量官能团的限制比例对环化程度的影响。使用两个聚合系统（常规的A ₂  + B ₂）验证了该模型六亚甲基二异氰酸酯（HDI）和聚乙二醇（PEG200）的聚合反应，以及超酸催化的改性靛红和联苯的多羟基烷基化反应。在第二种情况下，对于产生线性聚合物分子的四个反应，需要四个不同的动力学速率常数。