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

摘要

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.