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Polymer Reaction Modeling and Kinetics

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A special issue of Polymers (ISSN 2073-4360). This special issue belongs to the section "Polymer Chemistry".

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 23918

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Dr. Enrique Saldivar-Guerra

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Guest Editor

Polymerization Processes Department, Centro de Investigación en Química Aplicada, 25294 Saltillo Coahuila, Mexico
Interests: polymer reaction engineering; polymerization kinetics; mathematical modeling of polymerization; reversible deactivation radical polymerization synthesis
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Prof. Dr. Dagmar R. D'hooge

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Centre for Textiles Science and Engineering, Ghent University, Technologiepark 70a, 9052 Ghent, Belgium
Interests: multi-scale modeling; polymer design; polymerization kinetics; polymer processing; polymer reycling
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Special Issue Information

Dear Colleagues,

The mathematical modeling of polymerization reactions lies at the heart of the methods used in polymer reaction engineering. They are useful for testing assumptions related to the kinetics and basic mechanistic understanding of the process and, depending on their type and level of detail, can be used for operation troubleshooting, process monitoring and control, and optimization, among other applications. The models are especially useful in elucidating the mechanisms governing heterogeneous processes in which mass transfer phenomena between phases and thermodynamic issues play a substantial role.

This Special Issue of Polymers: “Polymer Reaction Modeling and Kinetics” will be especially focused on mathematical models for free-radical, reversible deactivation radical polymerization (RDRP), coordination, ionic (anionic and cationic) polymerization, ring-opening, and pyrolysis, including homogeneous (one-phase) and heterogeneous systems (aqueous dispersions, slurry, and suspension polymerization, reactions in fluid-bed reactors, etc.). Works dealing with deterministic, stochastic, and hybrid models will be featured.

Papers that emphasize the mechanistic understanding of the process, advanced applications strongly based on mathematical models, as well as papers dealing with new processes or novel modeling approaches will be especially appreciated.

Dr. Enrique Saldivar-Guerra
Prof. Dr. Dagmar R. D'hooge
Guest Editors

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Polymers is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

polymerization processes
polymerization kinetics
mathematical modeling
reaction mechanisms
model-based design

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Published Papers (9 papers)

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Research

14 pages, 4190 KiB

Open AccessArticle

Measurement and Modeling of Semi-Batch Solution Radical Copolymerization of N-tert-Butyl Acrylamide with Methyl Acrylate in Ethanol/Water

by Gagandeep Kaur, Maryam Agboluaje and Robin A. Hutchinson

Polymers 2023, 15(1), 215; https://doi.org/10.3390/polym15010215 - 31 Dec 2022

Cited by 1 | Viewed by 2107

Abstract

The synthetic polymer industry is transitioning from the use of organic solvents to aqueous media in order to reduce environmental impact. However, with radical polymerization kinetics affected by hydrogen-bonding solvents, there is limited information regarding the use of water as a solvent for sparingly soluble monomers. Thus, in this paper, the radical polymerization of methyl acrylate (MA) and N-tert-butylacrylamide (t-BuAAm) is studied in water and ethanol (EtOH), as the copolymer product is of commercial interest. A series of semi-batch reactions are conducted under a range of operating conditions (i.e., reaction temperature, solvent-to-monomer ratio, and comonomer composition) to demonstrate that the copolymer can be successfully synthesized without significant drifts in product molar masses or composition. The experiments provide additional data to probe the influence of the solvent on the polymerization rate and copolymer properties, as the low monomer concentration maintained under starved-feed operation leads to a solvent-to-monomer ratio different from that in a batch system. A model that captures the influence of backbiting and solvent effects on rate, previously developed and tested against batch polymerizations, also provides an excellent description of semi-batch operation, validating the set of mechanisms and kinetic coefficients developed to represent the system. Full article

(This article belongs to the Special Issue Polymer Reaction Modeling and Kinetics)

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27 pages, 7066 KiB

Open AccessArticle

Evolution of Molar Mass Distributions Using a Method of Partial Moments: Initiation of RAFT Polymerization

by Charles H. J. Johnson, Thomas H. Spurling and Graeme Moad

Polymers 2022, 14(22), 5013; https://doi.org/10.3390/polym14225013 - 18 Nov 2022

Cited by 7 | Viewed by 2285

Abstract

We describe a method of partial moments devised for accurate simulation of the time/conversion evolution of polymer composition and molar mass. Expressions were derived that enable rigorous evaluation of the complete molar mass and composition distribution for shorter chain lengths (e.g., degree of polymerization, X_n = N < 200 units) while longer chains (X_n ≥ 200 units) are not neglected, rather they are explicitly considered in terms of partial moments of the molar mass distribution,

μ_{x}^{N} (P) = \sum_{n = N + 1}^{\infty} n^{x} [P_{n}]

(where P is a polymeric species and n is its’ chain length). The methodology provides the exact molar mass distribution for chains X_n < N, allows accurate calculation of the overall molar mass averages, the molar mass dispersity and standard deviations of the distributions, provides closure to what would otherwise be an infinite series of differential equations, and reduces the stiffness of the system. The method also allows for the inclusion of the chain length dependence of the rate coefficients associated with the various reaction steps (in particular, termination and propagation) and the various side reactions that may complicate initiation or initialization. The method is particularly suited for the detailed analysis of the low molar mass portion of molar mass distributions of polymers formed by radical polymerization with reversible addition-fragmentation chain transfer (RAFT) and is relevant to designing the RAFT-synthesis of sequence-defined polymers. In this paper, we successfully apply the method to compare the behavior of thermally initiated (with an added dialkyldiazene initiator) and photo-initiated (with a RAFT agent as a direct photo-iniferter) RAFT-single-unit monomer insertion (RAFT-SUMI) and oligomerization of N,N-dimethylacrylamide (DMAm). Full article

(This article belongs to the Special Issue Polymer Reaction Modeling and Kinetics)

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19 pages, 3112 KiB

Open AccessArticle

Emulsion Polymerization Using an Amphiphilic Oligoether Ionic Liquid as a Surfactant

by Ariadna Jiménez-Victoria, René D. Peralta-Rodríguez, Enrique Saldívar-Guerra, Gladis Y. Cortez-Mazatán, Lluvia de Abril A. Soriano-Melgar and Carlos Guerrero-Sánchez

Polymers 2022, 14(17), 3475; https://doi.org/10.3390/polym14173475 - 25 Aug 2022

Cited by 1 | Viewed by 2224

Abstract

We investigate the use of an ionic liquid (IL) as a surfactant in emulsion polymerization (EP) reactions. ILs have been proposed as surfactants for micellar dispersions, emulsions, micro-emulsions and suspensions. Thus, it is important to acquire knowledge of the application of ILs in heterogeneous polymerizations. We selected the amphiphile cationic oligoether IoLiLyte C1EG™ as an IL for this purpose and compared its performance to that of the conventional surfactant dodecyl trimethyl ammonium bromide (DTAB) in the EP of methyl methacrylate and styrene. After we found the proper concentration range of the IL, this amphiphile showed similar polymerization rates to those observed with DTAB for both monomers. The evolution of monomer conversion and the final average diameter of formed polymeric particles were similar for both evaluated surfactants, demonstrating their capability to stabilize the EPs of the investigated monomers. We simulated the evolution of monomer conversion and particle size using a conventional model for emulsion polymerization, which showed good agreement with the experimental data, suggesting that the EP with this IL follows Smith-Ewart kinetics. Full article

(This article belongs to the Special Issue Polymer Reaction Modeling and Kinetics)

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26 pages, 7267 KiB

Open AccessArticle

Terpene Coordinative Chain Transfer Polymerization: Understanding the Process through Kinetic Modeling

by Andrés Ubaldo-Alarcón, Florentino Soriano-Corral, Teresa Córdova, Iván Zapata-González and Ramón Díaz-de-León

Polymers 2022, 14(12), 2352; https://doi.org/10.3390/polym14122352 - 10 Jun 2022

Cited by 6 | Viewed by 2101

Abstract

The interest in the Coordinative Chain Transfer Polymerization (CCTP) of a family of naturally occurring hydrocarbon monomers, namely terpenes, for the production of high-performance rubbers is increasing year by year. In this work, the synthesis of poly(β-myrcene) via CCTP is introduced, using neodymium versatate (NdV₃), diisobutylaluminum hydrade (DIBAH) as the catalytic system and dimethyldichlorosilane (Me₂SiCl₂) as the activator. A bimodal distribution in the GPC signal reveals the presence of two populations at low conversions, attributable to dormants (arising from reversible chain transfer reactions) and dead chains (arising from termination and irreversible chain transfer reactions); a unimodal distribution is generated at medium and high conversions, corresponding to the dominant species, the dormant chains. Additionally, a mathematical kinetic model was developed based on the Method of Moments to study a set of selected experiments: ([β-myrcene]₀:[NdV₃]₀:[DIBAH]₀:[Me₂SiCl₂]₀ = 660:1:2:1, 885:1:2:1, and 533:1:2:1). In order to estimate the kinetic rate constant of the systems, a minimization of the sum of squared errors (SSE) between the model predicted values and the experimental measurements was carried out, resulting in an excellent fit. A set of the Arrhenius parameters were estimated for the ratio [β-myrcene]₀:[NdV₃]₀:[DIBAH]₀:[Me₂SiCl₂]₀ = 660:1:2:1 in a temperature range between 50 to 70 °C. While the end-group functionality (EGF) was predominantly preserved as the ratio [β-myrcene]₀:[NdV₃]₀ was decreased, higher catalytic activity was obtained with a high ratio. Full article

(This article belongs to the Special Issue Polymer Reaction Modeling and Kinetics)

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14 pages, 3800 KiB

Open AccessArticle

Ionic Liquids as Homogeneous Catalysts for Glycerol Oligomerization

by Dawid Kansy, Krystyna Czaja, Kornelia Bosowska and Paweł Groch

Polymers 2022, 14(6), 1200; https://doi.org/10.3390/polym14061200 - 16 Mar 2022

Cited by 3 | Viewed by 2438

Abstract

Ionic liquids (ILs) were used for the first time as catalysts for the glycerin condensation reaction. A series of imidazolium and ammonium ionic liquids differing in the length of the alkyl substituent (C₂, C₁₂, and C₁₄) and the type of anion (Br⁻, CH₃COO⁻, and NaHPO₄⁻) were synthesized using a typical two-step method. The structure of the obtained ILs was confirmed by nuclear magnetic resonance ¹³C NMR, and their base power was determined on the basis of the Hammett function. The oligomerization of glycerin with the participation of the obtained ionic liquids and, for comparison, in the presence of a homogeneous basic catalyst Na₂CO₃, was carried out for 3 h at 180 °C, under a pressure of 0.4 bar, where the highest conversion, i.e., 92%, was obtained against 1-dodecyl-N,N,N-triethylammonium acetate. The course of the reaction was monitored using a reaction system coupled with a FTIR spectrometer, which allowed for the tracking of changes in product concentration over time and the assessment of glycerin oligomerization kinetics. The reaction products were analyzed by positive electrospray ionization mass spectrometry (ESI-MS), ¹³C NMR, and infrared absorption spectroscopy (FTIR). Full article

(This article belongs to the Special Issue Polymer Reaction Modeling and Kinetics)

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32 pages, 9114 KiB

Open AccessArticle

Anionic Polymerization of Para-Diethynylbenzene: Synthesis of a Strictly Linear Polymer

by Vyacheslav M. Misin, Irina E. Maltseva, Alexander A. Maltsev, Alexander V. Naumkin and Mark E. Kazakov

Polymers 2022, 14(5), 900; https://doi.org/10.3390/polym14050900 - 24 Feb 2022

Cited by 3 | Viewed by 2532

Abstract

Anionic homo- and copolymerization of p-diethynylbenzene in the presence of n-BuLi in polar solvents was carried out. The use of hexamethylphosphortriamide (HMPA) makes it possible to synthesize a completely linear soluble polymer that does not have branching and phenylene fragments. A copolymer of p-diethynylbenzene with diphenyldiacetylene was synthesized. Homo- and copolymers of p-diethynylbenzene have high thermo- and thermo-oxidative stability. By the interaction of side reactive ethynylphenylene groups with various reagents, it is proposed to synthesize clusters along the conducting chain of poly-p-diethynylbenzene. Due to presenting C≡CH side groups, boron, copper, and cobalt derivatives were synthesized. It is shown that not all theoretically possible stereoisomers can be formed as a result of the polymerization. The application of p-diethynylbenzene polymers for the modification of industrial samples of epoxy novolac resin, oligoester acrylates, and carbon fibers has been demonstrated. Full article

(This article belongs to the Special Issue Polymer Reaction Modeling and Kinetics)

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28 pages, 3585 KiB

Open AccessArticle

Thermal Pyrolysis of Polystyrene Aided by a Nitroxide End-Functionality Improved Process and Modeling of the Full Molecular Weight Distribution

by Antonio Monroy-Alonso, Almendra Ordaz-Quintero, Jorge C. Ramirez and Enrique Saldívar-Guerra

Polymers 2022, 14(1), 160; https://doi.org/10.3390/polym14010160 - 31 Dec 2021

Cited by 6 | Viewed by 2060

Abstract

A significantly improved thermal pyrolysis process for polystyrene (PS) is reported and mathematically modeled, including the description of the time evolution of the full molecular weight distribution of the polymer during its degradation by direct integration of the balance equations without simplifications. The process improves the styrene yield from 28–39%, reached in our previous report, to 58–75% by optimizing the heating ramp during the initial stage of the pyrolysis process. The process was tested at 390 and 420 °C on samples of conventional PS synthesized via free-radical polymerization (FRP) and PS with a nitroxide end-functionality synthesized via nitroxide mediated polymerization (NMP) with three levels of the nitroxide to initiator (N/I) molar ratio: 0.9, 1.1 and 1.3. The NMP-PS produced with N/I = 1.3 generates the highest styrene yield (75.2 ± 6.7%) with respect to the best FRP-PS yield (64.9 ± 1.2%), confirming the trends observed in our previous study. The mathematical model corrects some problems of a previous model that was based on assumptions that led to significant errors in the predictions; this is achieved by solving the full molecular weight distribution (MWD) without assumptions. The model provides further insight into the initial stages of the pyrolysis process which seem to be crucial to determine the chemical paths of the process and the styrene yield, as well as the influences of the initial heating ramp used and the presence of a nitroxide end-functionality in the polymer. Full article

(This article belongs to the Special Issue Polymer Reaction Modeling and Kinetics)

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12 pages, 3679 KiB

Open AccessArticle

Material Modeling of PMMA Film for Hot Embossing Process

by Dongwon Yun and Jong-Bong Kim

Polymers 2021, 13(19), 3398; https://doi.org/10.3390/polym13193398 - 2 Oct 2021

Cited by 9 | Viewed by 3409

Abstract

This study provides an analysis of the hot embossing process with poly methyl methacrylate (PMMA) film. The hot embossing process engraves a fine pattern on a flexible film using a stamp, applied heat and pressure. As the quality of the embossing pattern varies according to various process variables, the mechanism of making the embossed shape is complicated and difficult to analyze. Therefore, analysis takes much time and cost because it usually has to perform a lot of experiments to find an appropriate process condition. In this paper, the hot embossing process was analyzed using a computational analysis method to quickly find the optimal process. To do this, we analyzed the embossing phenomenon using the finite element method (FEM) and arbitrary Lagrangian–Eulerian (ALE) re-mesh technique. For this purpose, we developed a constitutive model considering the strain, strain rate, temperature-dependent stress and softening of the flexible film. Work hardening, strain softening, and temperature-softening behavior of PMMA materials were well described by the proposed method. The developed constitutive model were applied in the embossing analysis via user-subroutine. This proposed method allowed a precise analysis of the phenomenon of film change during the hot embossing process. Full article

(This article belongs to the Special Issue Polymer Reaction Modeling and Kinetics)

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15 pages, 2420 KiB

Open AccessArticle

Kinetics and Mechanism of Synthesis of Carboxyl-Containing N-Vinyl-2-Pyrrolidone Telehelics for Pharmacological Use

by Andrey N. Kuskov, Anna L. Luss, Inessa A. Gritskova, Mikhail I. Shtilman, Mikhail V. Motyakin, Irina I. Levina, Anna M. Nechaeva, Oksana Yu. Sizova, Aristidis M. Tsatsakis and Yaroslav O. Mezhuev

Polymers 2021, 13(15), 2569; https://doi.org/10.3390/polym13152569 - 1 Aug 2021

Cited by 11 | Viewed by 3151

Abstract

It was found that sulfanylethanoic and 3-sulfanylpropanoic acids are effective regulators of molecular weight with chain transfer constants of 0.441 and 0.317, respectively, and show an unexpected acceleration effect on the radical polymerization of N-vinyl-2-pyrrolidone, initiated by 2,2’-azobisisobutyronitrile. It was determined for the first time that the thiolate anions of mercapto acids form a high-temperature redox initiating system with 2,2’-azobisisobutyronitrile during the radical polymerization of N-vinyl-2-pyrrolidone in 1,4-dioxane. Considering the peculiarities of initiation, a kinetic model of the polymerization of N-vinyl-2-pyrrolidone is proposed, and it is shown that the theoretical orders of the reaction rate, with respect to the monomer, initiator, and chain transfer agent, are 1, 0.75, 0.25, and are close to their experimentally determined values. Carboxyl-containing techelics of N-vinyl-2-pyrrolidone were synthesized so that it can slow down the release of the anticancer drug, doxorubicin, from aqueous solutions, which can find its application in the pharmacological field. Full article

(This article belongs to the Special Issue Polymer Reaction Modeling and Kinetics)

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