Abstract
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.
Highlights
IntroductionFree-radical polymerization has been used widely to produce a variety of synthetic polymers
Free-radical polymerization has been used widely to produce a variety of synthetic polymers.The polymerization involves three main reactions: initiation, propagation and termination [1].In the initiation reaction, an initiator such as a thermal initiator usually generates free radicals at temperatures above 60 ◦ C [2,3]
The zeroth moment of the chain-length distribution (CLD) of a polymer class is the molar concentration of the polymer class, and the first moment times the monomer molecular weight is the mass concentration of the polymer class [39,40]
Summary
Free-radical polymerization has been used widely to produce a variety of synthetic polymers. Mastan and Zhu [25] published a tutorial paper on the method of moments They considered free-radical polymerization reactions such as initiation, propagation, and termination, but did not account for secondary reactions like monomer self-initiation, backbiting or β-scission [25]. Based on a comprehensive list of the most likely reactions in high-temperature free-radical homo-polymerization of acrylates, Table S1 (Supporting Information) [31,32,33,34,35,36,37,38], the reader learns how to systematically calculate the contributions of each reaction to different moments and to the production or consumption of different species. Method of moments predictions of conversion and polymer average molecular weights are compared with measurements from polymer sample analyses
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