Editorial

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4 pages, 184 KiB

Open AccessEditorial

Special Issue on “Computational Methods for Polymers”

by Masoud Soroush

Processes 2020, 8(4), 386; https://doi.org/10.3390/pr8040386 - 26 Mar 2020

Cited by 1 | Viewed by 1728

Abstract

Polymers play a key role in our daily lives [...] Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

Research

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18 pages, 3832 KiB

Open AccessFeature PaperArticle

Modeling, Simulation, and Operability Analysis of a Nonisothermal, Countercurrent, Polymer Membrane Reactor

by Brent A. Bishop and Fernando V. Lima

Processes 2020, 8(1), 78; https://doi.org/10.3390/pr8010078 - 07 Jan 2020

Cited by 15 | Viewed by 3520

Abstract

As interest in the modularization and intensification of chemical processes continues to grow, more research must be directed towards the modeling and analysis of these units. Intensified process units such as polymer membrane reactors pose unique challenges pertaining to design and operation that [...] Read more.

As interest in the modularization and intensification of chemical processes continues to grow, more research must be directed towards the modeling and analysis of these units. Intensified process units such as polymer membrane reactors pose unique challenges pertaining to design and operation that have not been fully addressed. In this work, a novel approach for modeling membrane reactors is developed in AVEVA’s Simcentral Simulation Platform. The produced model allows for the simulation of polymer membrane reactors under nonisothermal and countercurrent operation for the first time. This model is then applied to generate an operability mapping to study how operating points translate to overall unit performance. This work demonstrates how operability analyses can be used to identify areas of improvement in membrane reactor design, other than just using operability mapping studies to identify optimal input conditions. The performed analysis enables the quantification of the Pareto frontier that ultimately leads to design improvements that both increase overall performance and decreases the cost of the unit. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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12 pages, 1841 KiB

Open AccessFeature PaperArticle

Numerical Simulations of Polymer Solution Droplet Impact on Surfaces of Different Wettabilities

by Moussa Tembely, Damien Vadillo, Arthur Soucemarianadin and Ali Dolatabadi

Processes 2019, 7(11), 798; https://doi.org/10.3390/pr7110798 - 02 Nov 2019

Cited by 15 | Viewed by 4118

Abstract

This paper presents a physically based numerical model to simulate droplet impact, spreading, and eventually rebound of a viscoelastic droplet. The simulations were based on the volume of fluid (VOF) method in conjunction with a dynamic contact model accounting for the hysteresis between [...] Read more.

This paper presents a physically based numerical model to simulate droplet impact, spreading, and eventually rebound of a viscoelastic droplet. The simulations were based on the volume of fluid (VOF) method in conjunction with a dynamic contact model accounting for the hysteresis between droplet and substrate. The non-Newtonian nature of the fluid was handled using FENE-CR constitutive equations which model a polymeric fluid based on its rheological properties. A comparative simulation was carried out between a Newtonian solvent and a viscoelastic dilute polymer solution droplet. Droplet impact analysis was performed on hydrophilic and superhydrophobic substrates, both exhibiting contact angle hysteresis. The effect of substrates’ wettability on droplet impact dynamics was determined the evolution of the spreading diameter. While the kinematic phase of droplet spreading seemed to be independent of both the substrate and fluid rheology, the recoiling phase seemed highly influenced by those operating parameters. Furthermore, our results implied a critical polymer concentration in solution, between 0.25 and 2.5% of polystyrene (PS), above which droplet rebound from a superhydrophobic substrate could be curbed. The present model could be of particular interest for optimized 2D/3D printing of complex fluids. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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25 pages, 1741 KiB

Open AccessFeature PaperArticle

Modeling and Observer-Based Monitoring of RAFT Homopolymerization Reactions

by Patrick M. Lathrop, Zhaoyang Duan, Chen Ling, Yossef A. Elabd and Costas Kravaris

Processes 2019, 7(10), 768; https://doi.org/10.3390/pr7100768 - 20 Oct 2019

Cited by 7 | Viewed by 3465

Abstract

Reversible addition–fragmentation chain–transfer (RAFT) polymerization of methyl methacrylate (MMA) is modeled and monitored using a multi-rate multi-delay observer in this work. First, to fit the RAFT reaction rate coefficients and the initiator efficiency in the model, in situ

^{1}

H nuclear magnetic resonance [...] Read more.

Reversible addition–fragmentation chain–transfer (RAFT) polymerization of methyl methacrylate (MMA) is modeled and monitored using a multi-rate multi-delay observer in this work. First, to fit the RAFT reaction rate coefficients and the initiator efficiency in the model, in situ

^{1}

H nuclear magnetic resonance (NMR) experimental data from small-scale (<2 mL) NMR tube reactions is obtained and a least squares optimization is performed.

^{1}

H NMR and size exclusion chromatography (SEC) experimental data from large-scale (>400 mL) reflux reactions is then used to validate the fitted model. The fitted model accurately predicts the polymer properties of the large-scale reactions with slight discordance at late reaction times. Based on the fitted model, a multi-rate multi-delay observer coupled with an inter-sample predictor and dead time compensator is designed, to account for the asynchronous multi-rate measurements with non-constant delays. The multi-rate multi-delay observer shows perfect convergence after a few sampling times when tested against the fitted model, and is in fair agreement with the real data at late reaction times when implemented based on the experimental measurements. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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18 pages, 5519 KiB

Open AccessArticle

A Theoretical and Experimental Study for Screening Inhibitors for Styrene Polymerization

by Ali Darvishi, Mohammad Reza Rahimpour and Sona Raeissi

Processes 2019, 7(10), 677; https://doi.org/10.3390/pr7100677 - 01 Oct 2019

Cited by 13 | Viewed by 9748

Abstract

Styrene is one of the most important monomers utilized in the synthesis of various polymers. Nevertheless, during distillation, storage, and transportation of ST, undesired polymer (i.e., UP) formation can take place. Thus, the control of undesired polymerization of styrene is a challenging issue [...] Read more.

Styrene is one of the most important monomers utilized in the synthesis of various polymers. Nevertheless, during distillation, storage, and transportation of ST, undesired polymer (i.e., UP) formation can take place. Thus, the control of undesired polymerization of styrene is a challenging issue facing industry. To tackle the mentioned issue, the antipolymer and antioxidant activity of stable nitroxide radicals (i.e., SNRs) and phenolics in styrene polymerization were studied by density functional theory (DFT) calculation and experimental approach. The electrophilicity index and growth percentage have been determined by DFT calculation and experimental approach, respectively. It is depicted that 2,6-di-tert-butyl-4-methoxyphenol (DTBMP) and 2,6-di-tert-butyl-4-methylphenol (BHT) from phenolics, and 4-hydroxy-2,2,6,6-tetramethyl piperidine 1-Oxyl (4-hydroxy-TEMPO) and 4-oxo-2,2,6,6-tetramethylpiperidine 1-Oxyl (4-oxo-TEMPO) from stable nitroxide radicals were the most effective inhibitors. Also, the growth percentage of DTMBP, BHT, 4-hydroxy-TEMPO, and 4-oxo-TEMPO after 4 h were 16.40, 42.50, 24.85, and 46.8, respectively. In addition, the conversion percentage of DTMBP, BHT, 4-hydroxy-TEMPO, and 4-oxo-TEMPO after 4 h were obtained to be 0.048, 0.111, 0.065, and 0.134, respectively. Furthermore, the synergistic effect of these inhibitors was investigated experimentally, indicating that DTMBP/4-hydroxy-TEMPO exerted the best synergistic effects on the inhibition of polymerization. The optimum inhibition effect was observed at the blend of 4-hydroxy-TEMPO (25 wt.%) and DTMBP (75 wt.%) corresponding to 6.8% polymer growth after 4 h. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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14 pages, 640 KiB

Open AccessArticle

Comparison of Irregularity Indices of Several Dendrimers Structures

by Dongming Zhao, Zahid Iqbal, Rida Irfan, Muhammad Anwar Chaudhry, Muhammad Ishaq, Muhammad Kamran Jamil and Asfand Fahad

Processes 2019, 7(10), 662; https://doi.org/10.3390/pr7100662 - 27 Sep 2019

Cited by 17 | Viewed by 2486

Abstract

Irregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, [...] Read more.

Irregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, the evaluation of the irregularity of graphs is valuable not only for quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies but also for various physical and chemical properties, including entropy, enthalpy of vaporization, melting and boiling points, resistance, and toxicity. In this paper, we will restrict our attention to the computation and comparison of the irregularity measures of different classes of dendrimers. The four irregularity indices which we are going to investigate are

σ

irregularity index, the irregularity index by Albertson, the variance of vertex degrees, and the total irregularity index. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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25 pages, 1257 KiB

Open AccessFeature PaperArticle

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

by Hossein Riazi, Ahmad Arabi Shamsabadi, Michael C. Grady, Andrew M. Rappe and Masoud Soroush

Processes 2019, 7(10), 656; https://doi.org/10.3390/pr7100656 - 26 Sep 2019

Cited by 9 | Viewed by 4153

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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14 pages, 3941 KiB

Open AccessFeature PaperArticle

Handling Constraints and Raw Material Variability in Rotomolding through Data-Driven Model Predictive Control

by Abhinav Garg, Hassan A. Abdulhussain, Prashant Mhaskar and Michael R. Thompson

Processes 2019, 7(9), 610; https://doi.org/10.3390/pr7090610 - 10 Sep 2019

Cited by 6 | Viewed by 2585

Abstract

This work addresses the problems of uniquely specifying and robustly achieving user-specified product quality in a complex industrial batch process, which has been demonstrated using a lab-scale uni-axial rotational molding process. In particular, a data-driven modeling and control framework is developed that is [...] Read more.

This work addresses the problems of uniquely specifying and robustly achieving user-specified product quality in a complex industrial batch process, which has been demonstrated using a lab-scale uni-axial rotational molding process. In particular, a data-driven modeling and control framework is developed that is able to reject raw material variation and achieve product quality which is specified through constraints on quality variables. To this end, a subspace state-space model of the rotational molding process is first identified from historical data generated in the lab. This dynamic model predicts the evolution of the internal mold temperature for a given set of input move trajectory (heater and compressed air profiles). Further, this dynamic model is augmented with a linear least-squares based quality model, which relates its terminal (states) prediction with key quality variables. For the lab-scale process, the chosen quality variables are sinkhole area, ultrasonic spectra amplitude, impact energy and shear viscosity. The complete model is then deployed within a model-based control scheme that facilitates specifying on-spec products via limits on the quality variables. Further, this framework is demonstrated to be capable of rejecting raw material variability to achieve the desired specifications. To replicate raw material variability observed in practice, in this work, the raw material is obtained by blending the matrix resin with a resin of slightly different viscosity at varying weight fractions. Results obtained from experimental studies demonstrate the capability of the proposed model predictive control (MPC) in meeting process specifications and rejecting raw material variability. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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16 pages, 1657 KiB

Open AccessArticle

Imbalance-Based Irregularity Molecular Descriptors of Nanostar Dendrimers

by Zafar Hussain, Mobeen Munir, Shazia Rafique, Tayyab Hussnain, Haseeb Ahmad, Young Chel Kwun and Shin Min Kang

Processes 2019, 7(8), 517; https://doi.org/10.3390/pr7080517 - 06 Aug 2019

Cited by 11 | Viewed by 2518

Abstract

Dendrimers are branched organic macromolecules with successive layers of branch units surrounding a central core. The molecular topology and the irregularity of their structure plays a central role in determining structural properties like enthalpy and entropy. Irregularity indices which are based on the [...] Read more.

Dendrimers are branched organic macromolecules with successive layers of branch units surrounding a central core. The molecular topology and the irregularity of their structure plays a central role in determining structural properties like enthalpy and entropy. Irregularity indices which are based on the imbalance of edges are determined for the molecular graphs associated with some general classes of dendrimers. We also provide graphical analysis of these indices for the above said classes of dendrimers. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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14 pages, 3113 KiB

Open AccessFeature PaperArticle

On the Recovery of PLP-Molar Mass Distribution at High Laser Frequencies: A Simulation Study

by Shaghayegh Hamzehlou, M. Ali Aboudzadeh and Yuri Reyes

Processes 2019, 7(8), 501; https://doi.org/10.3390/pr7080501 - 02 Aug 2019

Cited by 2 | Viewed by 2569

Abstract

Due to the inherent difficulties in determination of the degree of branching for polymers produced in pulsed laser polymerization (PLP) experiments, the behavior of the degree of branching and backbiting reaction in high laser frequency and relatively high reaction temperatures have not been [...] Read more.

Due to the inherent difficulties in determination of the degree of branching for polymers produced in pulsed laser polymerization (PLP) experiments, the behavior of the degree of branching and backbiting reaction in high laser frequency and relatively high reaction temperatures have not been well-established. Herein, through a simulation study, the validity of different explanations on the recovery of PLP-molar mass distribution at high laser frequencies is discussed. It is shown that the reduction of the backbiting reaction rate at high laser frequency, and consequent decrease in the degree of branching, is not a necessary condition for recovering the PLP-molar mass distribution. The findings of this work provide simulation support to a previous explanation about the possibility of using high laser frequency for reliable determination of the propagation rate coefficient for acrylic monomers. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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23 pages, 3265 KiB

Open AccessFeature PaperArticle

Making the Most of Parameter Estimation: Terpolymerization Troubleshooting Tips

by Alison J. Scott, Vida A. Gabriel, Marc A. Dubé and Alexander Penlidis

Processes 2019, 7(7), 444; https://doi.org/10.3390/pr7070444 - 12 Jul 2019

Cited by 5 | Viewed by 2818

Abstract

Multi-component polymers can provide many advantages over their homopolymer counterparts. Terpolymers are formed from the combination of three unique monomers, thus creating a new material that will exhibit desirable properties based on all three of the original comonomers. To ensure that all three [...] Read more.

Multi-component polymers can provide many advantages over their homopolymer counterparts. Terpolymers are formed from the combination of three unique monomers, thus creating a new material that will exhibit desirable properties based on all three of the original comonomers. To ensure that all three comonomers are incorporated (and to understand and/or predict the degree of incorporation of each comonomer), accurate reactivity ratios are vital. In this study, five terpolymerization studies from the literature are revisited and the ‘ternary’ reactivity ratios are re-estimated. Some recent studies have shown that binary reactivity ratios (that is, from the related copolymer systems) do not always apply to ternary systems. In other reports, binary reactivity ratios are in good agreement with terpolymer data. This investigation allows for the comparison between previously determined binary reactivity ratios and newly estimated ‘ternary’ reactivity ratios for several systems. In some of the case studies presented herein, reactivity ratio estimation directly from terpolymerization data is limited by composition restrictions or ill-conditioned systems. In other cases, we observe similar or improved prediction performance (for ternary systems) when ‘ternary’ reactivity ratios are estimated directly from terpolymerization data (compared to the traditionally used binary reactivity ratios). In order to demonstrate the advantages and challenges associated with ‘ternary’ reactivity ratio estimation, five case studies are presented (with examples and counter-examples) and troubleshooting suggestions are provided to inform future work. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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14 pages, 413 KiB

Open AccessArticle

Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

by Jialin Zheng, Zahid Iqbal, Asfand Fahad, Asim Zafar, Adnan Aslam, Muhammad Imran Qureshi and Rida Irfan

Processes 2019, 7(7), 433; https://doi.org/10.3390/pr7070433 - 09 Jul 2019

Cited by 27 | Viewed by 3375

Abstract

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability [...] Read more.

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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14 pages, 1539 KiB

Open AccessFeature PaperArticle

Separating Electronic from Steric Effects in Ethene/α-Olefin Copolymerization: A Case Study on Octahedral [ONNO] Zr-Catalysts

by Francesco Zaccaria, Roberta Cipullo, Andrea Correa, Peter H. M. Budzelaar, Vincenzo Busico and Christian Ehm

Processes 2019, 7(6), 384; https://doi.org/10.3390/pr7060384 - 20 Jun 2019

Cited by 8 | Viewed by 3534

Abstract

Four Cl/Me substituted [ONNO] Zr-catalysts have been tested in ethene/α-olefin polymerization. Replacing electron-donating methyl with isosteric but electron-withdrawing chlorine substituents results in a significant increase of comonomer incorporation. Exploration of steric and electronic properties of the ancillary ligand by DFT confirm that relative [...] Read more.

Four Cl/Me substituted [ONNO] Zr-catalysts have been tested in ethene/α-olefin polymerization. Replacing electron-donating methyl with isosteric but electron-withdrawing chlorine substituents results in a significant increase of comonomer incorporation. Exploration of steric and electronic properties of the ancillary ligand by DFT confirm that relative reactivity ratios are mainly determined by the electrophilicity of the metal center. Furthermore, quantitative DFT modeling of propagation barriers that determine polymerization kinetics reveals that electronic effects observed in these catalysts affect relative barriers for insertion and a capture-like transition state (TS). Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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23 pages, 6126 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Data-Driven Estimation of Significant Kinetic Parameters Applied to the Synthesis of Polyolefins

by Santiago D. Salas, Amanda L. T. Brandão, João B. P. Soares and José A. Romagnoli

Processes 2019, 7(5), 309; https://doi.org/10.3390/pr7050309 - 22 May 2019

Cited by 7 | Viewed by 3411

Abstract

A data-driven strategy for the online estimation of important kinetic parameters was assessed for the copolymerization of ethylene with 1,9-decadiene using a metallocene catalyst at different diene concentrations and reaction temperatures. An initial global sensitivity analysis selected the significant kinetic parameters of the [...] Read more.

A data-driven strategy for the online estimation of important kinetic parameters was assessed for the copolymerization of ethylene with 1,9-decadiene using a metallocene catalyst at different diene concentrations and reaction temperatures. An initial global sensitivity analysis selected the significant kinetic parameters of the system. The retrospective cost model refinement (RCMR) algorithm was adapted and implemented to estimate the significant kinetic parameters of the model in real time. After verifying stability and robustness, experimental data validated the algorithm performance. Results demonstrate the estimated kinetic parameters converge close to theoretical values without requiring prior knowledge of the polymerization model and the original kinetic values. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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18 pages, 23166 KiB

Open AccessFeature PaperArticle

Universal Relationships in Hyperbranched Polymer Architecture for Batch and Continuous Step Growth Polymerization of AB₂-Type Monomers

by Hidetaka Tobita

Processes 2019, 7(4), 220; https://doi.org/10.3390/pr7040220 - 17 Apr 2019

Cited by 14 | Viewed by 3577

Abstract

Design and control of hyperbranched (HB) polymer architecture by way of reactor operation is key to a successful production of higher-valued HB polymers, and it is essential in order to clarify the fundamental structural characteristics formed in representative types of reactors. In this [...] Read more.

Design and control of hyperbranched (HB) polymer architecture by way of reactor operation is key to a successful production of higher-valued HB polymers, and it is essential in order to clarify the fundamental structural characteristics formed in representative types of reactors. In this article, the irreversible step growth polymerization of AB₂ type monomer is investigated by a Monte Carlo simulation method, and the calculation was conducted for a batch and a continuous stirred-tank reactor (CSTR). In a CSTR, a highly branched core region consisting of units with large residence times is formed to give much more compact architecture, compared to batch polymerization. The universal relationships, unchanged by the conversion levels and/or the reactivity ratio, are found for the mean-square radius of gyration Rg², and the maximum span length L_MS. For batch polymerization, the g-ratio of Rg² of the HB molecule to that for a linear molecule conforms to that for the random branched polymers represented by the Zimm-Stockmayer equation. A single linear equation represents the relationship between Rg² and L_MS, both for batch and CSTR. Appropriate process control in combination with the chemical control of the reactivity of the second B-group promises to produce tailor-made HB polymer architecture. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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19 pages, 4885 KiB

Open AccessArticle

Categorization of Failures in Polymer Rapid Tools Used for Injection Molding

by Anurag Bagalkot, Dirk Pons, Digby Symons and Don Clucas

Processes 2019, 7(1), 17; https://doi.org/10.3390/pr7010017 - 02 Jan 2019

Cited by 15 | Viewed by 3973

Abstract

Background—Polymer rapid tooling (PRT) inserts for injection molding (IM) are a cost-effective method for prototyping and low-volume manufacturing. However, PRT inserts lack the robustness of steel inserts, leading to progressive deterioration and failure. This causes quality issues and reduced part numbers. Approach—Case studies [...] Read more.

Background—Polymer rapid tooling (PRT) inserts for injection molding (IM) are a cost-effective method for prototyping and low-volume manufacturing. However, PRT inserts lack the robustness of steel inserts, leading to progressive deterioration and failure. This causes quality issues and reduced part numbers. Approach—Case studies were performed on PRT inserts, and different failures were observed over the life of the tool. Parts molded from the tool were examined to further understand the failures, and root causes were identified. Findings—Critical parameters affecting the tool life, and the effect of these parameters on different areas of tool are identified. A categorization of the different failure modes and the underlying mechanisms are presented. The main failure modes are: surface deterioration; surface scalding; avulsion; shear failure; bending failure; edge failure. The failure modes influence each other, and they may be connected in cascade sequences. Originality—The original contributions of this work are the identification of the failure modes and their relationships with the root causes. Suggestions are given for prolonging tool life via design practices and molding parameters. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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Review

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33 pages, 772 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Advances in Mathematical Modeling of Gas-Phase Olefin Polymerization

by Mohd Farid Atan, Mohd Azlan Hussain, Mohammad Reza Abbasi, Mohammad Jakir Hossain Khan and Muhamad Fazly Abdul Patah

Processes 2019, 7(2), 67; https://doi.org/10.3390/pr7020067 - 30 Jan 2019

Cited by 14 | Viewed by 5459

Abstract

Mathematical modeling of olefin polymerization processes has advanced significantly, driven by factors such as the need for higher-quality end products and more environmentally-friendly processes. The modeling studies have had a wide scope, from reactant and catalyst characterization and polymer synthesis to model validation [...] Read more.

Mathematical modeling of olefin polymerization processes has advanced significantly, driven by factors such as the need for higher-quality end products and more environmentally-friendly processes. The modeling studies have had a wide scope, from reactant and catalyst characterization and polymer synthesis to model validation with plant data. This article reviews mathematical models developed for olefin polymerization processes. Coordination and free-radical mechanisms occurring in different types of reactors, such as fluidized bed reactor (FBR), horizontal-stirred-bed reactor (HSBR), vertical-stirred-bed reactor (VSBR), and tubular reactor are reviewed. A guideline for the development of mathematical models of gas-phase olefin polymerization processes is presented. Full article

(This article belongs to the Special Issue Computational Methods for Polymers)

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