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Open AccessFeature PaperArticle

Method of Moments Applied to Most-Likely High-Temperature Free-Radical Polymerization Reactions

1
Department of Chemical & Biomedical Engineering, Drexel University, Philadelphia, PA 19104, USA
2
Axalta Coating Systems, Philadelphia Navy Yard, PA 19112, USA
3
Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104-6323, USA
*
Author to whom correspondence should be addressed.
Processes 2019, 7(10), 656; https://doi.org/10.3390/pr7100656
Received: 13 July 2019 / Revised: 12 September 2019 / Accepted: 19 September 2019 / Published: 26 September 2019
(This article belongs to the Special Issue Computational Methods for Polymers)
Many widely-used polymers are made via free-radical polymerization. Mathematical models of polymerization reactors have many applications such as reactor design, operation, and intensification. The method of moments has been utilized extensively for many decades to derive rate equations needed to predict polymer bulk properties. In this article, for a comprehensive list consisting of more than 40 different reactions that are most likely to occur in high-temperature free-radical homopolymerization, moment rate equations are derived methodically. Three types of radicals—secondary radicals, tertiary radicals formed through backbiting reactions, and tertiary radicals produced by intermolecular chain transfer to polymer reactions—are accounted for. The former tertiary radicals generate short-chain branches, while the latter ones produce long-chain branches. In addition, two types of dead polymer chains, saturated and unsaturated, are considered. Using a step-by-step approach based on the method of moments, this article guides the reader to determine the contributions of each reaction to the production or consumption of each species as well as to the zeroth, first and second moments of chain-length distributions of live and dead polymer chains, in order to derive the overall rate equation for each species, and to derive the rate equations for the leading moments of different chain-length distributions. The closure problems that arise are addressed by assuming chain-length distribution models. As a case study, β-scission and backbiting rate coefficients of methyl acrylate are estimated using the model, and the model is then applied to batch spontaneous thermal polymerization to predict polymer average molecular weights and monomer conversion. These predictions are compared with experimental measurements. View Full-Text
Keywords: method of moments; free-radical polymerization; methyl acrylate; thermal polymerization; high-temperature polymerization method of moments; free-radical polymerization; methyl acrylate; thermal polymerization; high-temperature polymerization
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MDPI and ACS Style

Riazi, H.; Arabi Shamsabadi, A.; Grady, M.C.; Rappe, A.M.; Soroush, M. Method of Moments Applied to Most-Likely High-Temperature Free-Radical Polymerization Reactions. Processes 2019, 7, 656.

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