Mathematical Modeling of the Grafting of Maleic Anhydride Onto Poly(propylene): Model Considering a Heterogeneous Medium

Aguiar, Leandro G.; Filho, Pedro de Alcântara Pessôa; Giudici, Reinaldo

doi:10.1002/mats.201100037

Cited by 16 publications

(27 citation statements)

References 22 publications

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“…Additionally, the MMD was calculated a posteriori by means of an integro-differential bivariate equation, which gives the mass fraction of polymer chains with a certain chain length (CL) and degree of scission. MoM was also applied by Aguiar et al 36 for the kinetic modeling of free-radical grafting of MAH onto PP. These authors included initiator decomposition, hydrogen abstraction, b-scission, monomer grafting, chain transfer, and termination.…”

Section: Introductionmentioning

confidence: 99%

Modeling the reaction event history and microstructure of individual macrospecies in postpolymerization modification

et al. 2017

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For postpolymerization modification, a novel kinetic Monte Carlo (kMC) modeling strategy for the description of the reaction event history and the evolution of the microstructure of individual macrospecies with a complex topology is presented. The kMC model allows the kinetic analysis of free radical induced grafting of vinyl monomers onto polyethylene (PE) chains, assuming isothermal conditions and perfect macromixing and accounting for diffusional limitations on the microscale. Not only average characteristics such as the monomer conversion, grafting selectivity and yield, but also the chain length distribution (CLD) of all macromolecular species types, the average “from/to” grafting and cross‐linking density, the number of grafts and cross‐links per individual macromolecule, the chain length of every graft, and the CLD of the grafted chains are calculated. Under typical grafting conditions, depropagation and diffusional limitations cannot be ignored. The functionalization occurs mainly on those macrospecies in the PE‐CLD with a high mass concentration. © 2017 American Institute of Chemical Engineers AIChE J, 2017

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Section: Introductionmentioning

confidence: 99%

Modeling the reaction event history and microstructure of individual macrospecies in postpolymerization modification

et al. 2017

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“…It should be noted that most parameters in Table are based on literature data validated based on independent experimental techniques. Mass transfer of species from one phase to the other needs to be also accounted for on the meso‐scale, as summarized in Table 2 . Based on previous work mass transfer is modeled in terms of the flux equations, considering the driving force for mass transfer as the difference in concentration of the component “

α

” in both phases with respect to their equilibrium values (key mass transfer equation: see Table ).…”

Section: Model Developmentmentioning

confidence: 99%

“…Moreover, phase segregation can exist due to imperfect mixing and solubility limits. This implies that besides kinetics, mass transfer phenomena need to be accounted for . Hence, a wide range of process parameters influences industrial FRIG, complicating the identification of the optimal large‐scale protocol.…”

Section: Introductionmentioning

confidence: 99%

“…In order to shed more light on the FRIG synthesis–structure relationship, several models have been proposed . One of the most detailed models is the stochastic one of Hernández‐Ortiz et al in which a monomer‐ and polymer‐rich phase are distinguished on the timescale of reactive processing (second to minute scale), with radical kinetics taking place in both phases, and corrections on the reactivities due to diffusional limitations in the polymer‐rich phase.…”

Section: Introductionmentioning

confidence: 99%

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The Relevance of Multi‐Injection and Temperature Profiles to Design Multi‐Phase Reactive Processing of Polyolefins

Hernández‐Ortiz

Steenberge

Duchateau

et al. 2019

Macro Theory & Simulations

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For industrial‐scale continuous free radical induced grafting of polyethylene, which involves the contact of a monomer‐ and polymer‐rich phase, it is demonstrated that the functionalization selectivity and grafting density can be significantly improved (e.g., 100%) by considering multiple injection of monomer and/or a temperature profile. With parameters taken from literature, it is highlighted through simulations that step‐wise addition of monomer allows to reduce the homopolymerization rate, and an increased temperature at the start of the reactive processing allows to increase the hydrogen abstraction rate, so that more potential grafting points can be generated. As this increased grafting density goes along with a lower reaction extent, a better process efficiency is obtained albeit at a lowering of the average chain length of the grafts and an increase of the crosslinking density. In any case, a broader span of polymer characteristics (e.g., ranges of grafting/crosslinking densities and functionalization yields) can be achieved by including variations in reactant addition and temperature profiles.

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“…Numerical simulations have been devoted to reactive extrusion processes for quantitatively analyzing the reaction trend and optimizing the processing conditions . Such simulations have been performed by Motha and Seppala for the grafting of carboxylic acids and silanes to ethylene polymers, Hojabr et al for the grafting of GMA onto PE, Fukuoka for the grafting between PE and vinylsilane, Keum and White, Zhu et al, and Aguiar et al for the grafting of maleic anhydride on PP, and Zhao et al for poly[ethylene‐ co ‐(vinyl alcohol)]‐graft‐poly(Ε‐caprolactone) . With accurate numerical models, evolutions of key variables such as monomer conversion, grafting degree and fluid viscosity can be quantitatively predicted.…”

Section: Introductionmentioning

confidence: 99%

Kinetic study on free radical grafting of polyethylene with acrylic acid by reactive extrusion

Zhang

Jia

2014

J of Applied Polymer Sci

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In the reactive extrusion process for the free radical grafting of acid monomers onto polyethylene, monomer grafting and homopolymerization occur simultaneously and interact with each other. Using an incremental theory, mathematical models of conversions for monomer grafting and homopolymerization were separately constructed to predict the grafting degree, mass of homopolymer and grafting efficiency. Effects of the barrel temperature, initial monomer and initiator concentrations on grafting behaviors were investigated. The barrel temperature and initial monomer concentration were shown to be the main process parameters for controlling the grafting degree. The grafting degree and mass of homopolymer increased significantly with increasing barrel temperature and monomer concentration and increased marginally with increasing initiator concentration. No significant improvement in the grafting efficiency was observed. The predictions of the models are in good agreement with experimental data. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40990.

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Mathematical Modeling of the Grafting of Maleic Anhydride Onto Poly(propylene): Model Considering a Heterogeneous Medium

Cited by 16 publications

References 22 publications

Modeling the reaction event history and microstructure of individual macrospecies in postpolymerization modification

Modeling the reaction event history and microstructure of individual macrospecies in postpolymerization modification

The Relevance of Multi‐Injection and Temperature Profiles to Design Multi‐Phase Reactive Processing of Polyolefins

Kinetic study on free radical grafting of polyethylene with acrylic acid by reactive extrusion

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