Case studies with mathematical modeling of free-radical multi-component bulk/solution polymerizations: Part 2

Dorschner, David; Jung, Woo-Sung; Riahinezhad, Marzieh; Duever, Thomas A.; Penlidis, Alexander

doi:10.1080/10601325.2017.1312678

Cited by 4 publications

(4 citation statements)

References 153 publications

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“…Once a chain propagates an irreversible comonomer, all sequence information preceding that unit in the chain has no influence on any subsequent (de)propagation reactions, and thus, tracking it is not required. While methods exist to further reduce the number of equations required, as demonstrated by Hutchinson ,, and Penlidis, , these methods rely on implementing an analogous assumption as that of Lowry, Izu, Witter, and Krüger in their copolymer equation derivations ( vide infra ).…”

Section: Survey Of Methodsmentioning

confidence: 99%

Accurate Determination of Reactivity Ratios for Copolymerization Reactions with Reversible Propagation Mechanisms

Lundberg,

Kilgallon,

Cooper

et al. 2024

Macromolecules

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An understanding of monomer sequence is required to predict and engineer the properties of copolymers. In stochastic polymerizations involving more than one monomer, monomer sequence is typically inferred or determined from reactivity ratios, which are measured through copolymerization experiments. The accurate determination of reactivity ratios from copolymerizations where one or both monomers undergo reversible propagation, however, has been complicated by the difficulty in solving the underlying population balance equations, the presence of myriad copolymer equations in the literature derived under varying assumptions and simplifications, and lack of an easy-to-fit integrated model. Here, we rectify and assert the consistency between previously reported copolymer equations of disparate forms, introduce a new method to explicitly solve the underlying population balance equations, and perform stochastic copolymerization simulations to evaluate the ability of these three methods to produce consistent comonomer consumption predictions and fits to simulated copolymerization data. We find that all methods produce consistent predictions given the same input parameters, which implies both accuracy and precision when modeling copolymerization, fitting experimental data, and making predictions of comonomer sequence. Considering this consistency, we make a recommendation to use numerical integration of the appropriate copolymer equation to fit real copolymerization data due to its ease of implementation. We further identify the minimum number of parameters required for accurate data fitting and suggest ways to measure other information ex situ from copolymerization to expedite accurate fitting. Finally, the practical utility of the methods developed herein is demonstrated through fitting seven distinct copolymerization data sets, which span a wide range of copolymerization reactivities.

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Section: Survey Of Methodsmentioning

confidence: 99%

Accurate Determination of Reactivity Ratios for Copolymerization Reactions with Reversible Propagation Mechanisms

Lundberg,

Kilgallon,

Cooper

et al. 2024

Macromolecules

View full text Add to dashboard Cite

show abstract

“…46 Once a chain propagates an irreversible comonomer, all sequence information preceding that unit in the chain has no influence on any subsequent (de)propagation reactions and thus tracking it is not required. While methods exist to further reduce the number of equations required, as demonstrated by Hutchinson 52,76,77 and Penlidis, 78,79 these methods rely on implementing an analogous assumption as that of Lowry, Izu, Witter, and Kruger in their copolymer equation derivations (vide infra).…”

Section: Kinetic and Population Balance Modeling Of Equilibrium Copol...mentioning

confidence: 99%

Accurate Determination of Reactivity Ratios for Copolymerization Reactions with Reversible Propagation Mechanisms

Lundberg,

Kilgallon,

Cooper

et al. 2024

Preprint

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An understanding of monomer sequence is required to predict and engineer the properties of copolymers. Typically, comonomer sequence is inferred or determined from reactivity ratios, which are measured through copolymerization experiments. The accurate determination of reactivity ratios from copolymerizations where one or both monomers undergo reversible propagation, however, has been complicated by difficulty in solving the underlying population balance equations, the presence of myriad copolymer equations in the literature derived under varying assumptions and simplifications, and lack of an easy to fit integrated model. Here, we rectify and assert the consistency between previously reported copolymer equations of disparate form, introduce a new method to explicitly solve the underlying population balance equations, and perform stochastic copolymerization simulations to evaluate the ability of these three methods to produce consistent comonomer consumption predictions and fits to simulated copolymerization data. We find that all methods produce consistent predictions given the same input parameters, which implies both accuracy and precision when modeling copolymerization, fitting experimental data, and making predictions of comonomer sequence. Considering this consistency, we make a recommendation to use numerical integration of the appropriate copolymer equation to fit real copolymerization data due to its ease of implementation and single subjective parameter for implementation. We further identify the minimum number of parameters required for accurate data fitting and suggest ways to measure other information ex situ from copolymerization to expediate accurate fitting. Finally, the practical utility of the methods developed herein is demonstrated through fitting seven distinct copolymerization datasets which span a wide range of copolymerization reactivities.

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“…To the authors’ best knowledge, all models applicable to systems with three or more comonomers − assume the presence of only one acrylate, or in other words, that only one of the monomers may undergo backbiting and scission in a given system. Moreover, the active radical fractions are computed only for secondary propagating radicals (SPRs), and they are assumed to be affected only by propagation and depropagation, neglecting the impact of backbiting, scission, tertiary propagation, and transfer to polymer.…”

Section: Introductionmentioning

confidence: 99%

“…A more general approach was developed by Dorschner et al, 17 who developed a framework able to account for up to six comonomers, while gathering a significant amount of literature data and kinetic parameter values. Their model can describe depropagation of up to six monomers, while only one acrylate monomer is considered, meaning that the backbiting and scission kinetic steps are implemented for one of the six monomers.…”

Section: Introductionmentioning

confidence: 99%

A General Approach for Modeling Acrylate and Methacrylate Solution Copolymerizations

Fleckenstein

Alter²,

Lazzari

et al. 2021

Ind. Eng. Chem. Res.

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Acrylate and methacrylate solution polymers are ubiquitous in day-to-day life. Very often a combination of monomers belonging to these two families is necessary to achieve the desired material properties. First-principles reaction models help provide good control over acrylate/ methacrylate solution polymerizations, especially since light has been shed on relevant side-reactions occurring (backbiting, scission, depropagation, etc.). However, the complicated reaction network necessary to describe these systems has typically limited models to specific combinations of monomers, involving only one type of acrylate. In this work, we propose a general deterministic framework to describe the radical polymerization of any number of acrylates and methacrylates. Besides tracking the chain length of several active and inactive polymer chains by means of population balance equations (PBEs), we describe the radical fractions of secondary and midchain radicals, as well as those of the terminal, penultimate, and pen-penultimate composition of the secondary propagating radicals (SPRs). After introducing the kinetic model and performing a parametric study to assess its potential, we validate the model against a new set of experimental data involving a five-monomer polymerization.

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Case studies with mathematical modeling of free-radical multi-component bulk/solution polymerizations: Part 2

Cited by 4 publications

References 153 publications

Accurate Determination of Reactivity Ratios for Copolymerization Reactions with Reversible Propagation Mechanisms

Accurate Determination of Reactivity Ratios for Copolymerization Reactions with Reversible Propagation Mechanisms

Accurate Determination of Reactivity Ratios for Copolymerization Reactions with Reversible Propagation Mechanisms

A General Approach for Modeling Acrylate and Methacrylate Solution Copolymerizations

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