Numerical Techniques for the Solution of the Molecular Weight Distribution in Polymerization Mechanisms, State of the Art,Macromolecular Reaction Engineering

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Numerical Techniques for the Solution of the Molecular Weight Distribution in Polymerization Mechanisms, State of the Art
Macromolecular Reaction Engineering ( IF 1.8 ) Pub Date : 2020-07-01 , DOI: 10.1002/mren.202000010
Enrique Saldívar‐Guerra ₁

Affiliation

The molecular weight distribution (MWD) is possibly the most important characteristic of a polymer. Polymers derive many of their physical properties from their MWD. Therefore, since the origins of polymer science, the theory provides a link between the kinetic mechanism and the mathematical expression of the MWD, and there are analytical solutions for ideal cases. However, the MWD formed in real‐life polymerization processes is usually more complex; the solution of the mathematical models that describe them can be quite challenging and has been the focus of enormous research efforts. These models may consist of systems of very large dimension: thousands of differential equations, often stiff, which demand special numerical techniques for their solution. In this paper the numerical techniques that can be used to solve this challenging problem are reviewed and contrasted, including weighted residual methods, direct integration, numerical inversion of transformed equations, and lumping methods. Stochastic techniques are also surveyed.

中文翻译：

解决聚合机理中分子量分布的数值技术，最新技术

分子量分布（MWD）可能是聚合物的最重要特征。聚合物从其MWD获得许多物理性质。因此，由于高分子科学的起源，该理论在MWD的动力学机理和数学表达式之间建立了联系，并为理想情况提供了解析解。然而，现实生活中聚合过程中形成的MWD通常更复杂。描述它们的数学模型的解决方案可能非常具有挑战性，并且一直是大量研究工作的重点。这些模型可能由非常大的系统组成：成千上万的常为刚性的微分方程，需要特殊的数值技术来求解。在本文中，对可用于解决这一难题的数值技术进行了回顾和对比，包括加权残差法，直接积分，变换方程的数值反演和集总法。还对随机技术进行了调查。

更新日期：2020-07-01

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