自由基聚合反应动力学的数学建模——多自由基数学模型

Modeling of Free-Radical Polymerization Kinetics --Polyradical Model

对自由基聚合过程进行数学建模多采用动力学机理模型。但在文献中的动力学数学建模多是利用了单自由基假设 :即假设每个自由基都位于不同的聚合物活性链上。当存在向聚合物的链转移和大分子反应等基元反应时 ,所得的数学模型是不封闭的 ,需经过近似处理后才能进行求解。研究表明 :若将聚合物活性链和非活性链等同对待 ,应用多自由基反应机理 ,根据矩法推导所得数学模型是封闭的 ,可直接求解。以包含有向聚合物链转移反应的自由基均聚反应机理为例 ,根据矩法分别建立了单自由基和多自由基数学模型 ,所得单自由基模型清楚表明了模型存在的不封闭性 ;而多自由基模型可以直接求解计算。模型中考察了数均和重均链长、数均和重均支化度等微观质量参数。对多自由基模型应用单自由基假设 ,并进一步假设仅仅有向非活性链聚合物的链转移后 。

In the literature kinetic models of free-radical polymerizationare widely developed. But most of models were based on the monoradicalassumption: each radical is located on a different polymer chain. The moment closure problems were existence when chain transfer reaction to polymer chain and double bond polymerization were considered. Other approximation must be imported to models. It is result of separately treated polymer radical chain and dead polymer as two components. But the closure problem vanishes by polyradical model base on polymer radical chain and dead polymer were treated to one component. A example, free-radical homopolymerization kinetics with transfer reaction to polymer chain, is presented. The monoradical and polyradical models are developed by moment method. The monoradical model is not closed and can not be directly integrated. But the polyradical model can be directly integrated. The number and weight average chain length and branching degree can be evaluated. By the assumption of monoradical and chain transfer only to dead polymer, the polyradical model can be returned to the conventional monoradical model.