Copolymer Composition Distribution Research Articles

Modeling of the Copolymerization of Propylene with 1‐Hexene to Predict the Copolymer Molecular Weight and Composition

AbstractA detailed mathematical model of the propylene‐1‐hexene copolymerization based on the two‐dimensional probability generation function technique is developed. It calculates the joint molecular weight‐copolymer composition distribution (MWD‐CCD) of the copolymer, as well as the average copolymer composition distribution, the molecular weight distribution (MWD), the copolymer composition distribution (CCD), average molecular weights and composition, and yield. The parallelized execution of the model code allows for obtaining the different copolymer microstructure distributions efficiently. The model allows for reaching a thorough understanding of the copolymer microstructure under different operating conditions of a semibatch reactor. It also has the potential to become a powerful tool for selecting operating conditions to obtain a material with target molecular properties.

Modeling of the Activators Regenerated by Electron Transfer Copolymerization of Styrene-Acrylonitrile with Prediction of the Bivariate Molecular Weight Distribution─Copolymer Composition Distribution Using Parallel Computing and Probability Generating Functions

A mathematical model of the activators regenerated by electron transfer atom transfer radical polymerization copolymerization of styrene-acrylonitrile (SAN) is developed for the first time that calculates the bivariate molecular weight distribution (MWD)-copolymer composition distribution (CCD) of the copolymer. In addition, the model calculates the overall MWD, the overall CCD, average molecular weights and composition, and conversion. The model is implemented in the open-source programming language Julia, a high-level language designed for scientific computing, which is easy to use and that performs very fast calculations. The probability generating function technique is used to process the infinite population balances of the system. The mathematical model, composed of a very large system of equations, is solved by applying parallel computing to speed up its execution. In this way, the distributions of polymer properties are calculated in a very efficient manner. The evolution of the joint MWD–CCD and other molecular properties along the reaction path is analyzed under different operating conditions. The model allows obtaining very detailed insights into the copolymer microstructure during the polymerization reaction.

Determination of Chemical Composition and Monomer Sequence Distributions of Methacrylate Copolymers by Multivariate Analysis of NMR Spectra

Determination of Chemical Composition and Monomer Sequence Distributions of Methacrylate Copolymers by Multivariate Analysis of NMR Spectra

Free radical solution copolymerization of monomers of dissimilar reactivity - influencing chemical composition distribution and properties of copolymers of methyl methacrylate and N-vinyl imidazole by varying monomer feeding profiles

Copolymerization is one way of influencing the properties of polymers and the outcome of copolymerization between vinyl monomers is dependent on the reactivity ratios between the monomers. Incorporation of polar monomers into copolymers offer many benefits. In this regard, N-Vinyl imidazole (NVI) carries much significance as a comonomer. NVI is a specialty monomer. The high polarity and planarity of NVI can impart many beneficial characteristics upon copolymerization with other vinyl monomers. However, its unfavourable reactivity ratios with other vinyl monomers prevent the facile incorporation of NVI in the copolymers. In this work, a semi-continuous solution polymerization is employed with the help of software called Monomer Addition Profile (MAP) to predict the optimal addition profile of the more reactive monomer (methyl methacrylate) through an iterative approach in order to achieve uniform incorporation of less reactive comonomer in the copolymer chain. The predicted chemical composition distribution (CCD) of the copolymerization is used to determine the homogeneity of copolymers which is well supported by the glass transition temperature (Tg) of copolymers. Apart from the workflow of MAP, solubility characteristics of copolymers, microstructure and sequence length are also discussed in this article.

Influence of thermal runaway in styrene–acrylonitrile bulk copolymerization revealed by computational fluid dynamics modeling

AbstractThe computational fluid dynamics (CFD) and kinetic‐based moment methods coupled approach is adopted to simulate the bulk copolymerization of styrene–acrylonitrile (SAN) in a stirred tank reactor. Numerical simulations are carried out to investigate the impacts of impeller speed, monomer ratio, initiator ratio, and initial reaction temperature on the copolymerization process and product properties. Particularly, the Chaos theory is selected as a criterion for evaluating the occurrence of the thermal runaway. The Flory's and Stockmayer's distributions are employed to calculate chain length distribution and copolymer composition distribution of copolymer. The simulation results highlight that the appearance of thermal runaway can be postponed by properly increasing the rotation speed, decreasing the initiator loadings, initial acrylonitrile contents and initial reactor temperature. Furthermore, significant differences exist in the product properties that predicted by the ideal and non‐ideal models, which demonstrates that the temperature heterogeneity plays a crucial role in SAN copolymerization. This study could offer references for the safe operation and design of polymerization processes.

Facile Synthesis of CO2 -Responsive Nano-Objects: Batch versus Semi-Batch RAFT Copolymerization.

Precise polymer architecture and self-assembled morphological control are attractive due to their promising applications, such as drug delivery, biosensors, tissue engineering and "smart" optical systems. Herein, starting from the same hydrophilic units poly(ethylene glycol) (PEG), using CO2 -sensitive monomer N, N-diethylaminoethyl methacrylate (DEAEMA) and hydrophobic monomer benzyl methacrylate (BzMA), a series of well-defined statistical, block, and gradient copolymers is designed and synthesized with similar degree of polymerization but different monomer sequences by batch and semi-batch RAFT polymerization process and their CO2 -responsive behaviors of these nano-objects is systematically studied. The gradient copolymers are generated by using semi-batch methods with programmed monomer feed rate controlled by syringe pumps, achieving precise control over desired gradient copolymer composition distribution. In aqueous solution, the copolymers could self-assemble into various aggregates before CO2 stimulus. Upon bubbling CO2 , the gradient copolymers preferred to form nanosheet-like structures, while the block and statistical copolymers with similar molar mass could only form larger vesicles with thinner membrane thickness or disassemble. The semi-batch strategy to precisely control over the desired composition distribution of the gradient segment presents an emerging trend for the fabrication and application of stimuli-responsive polymers.

Application of Artificial Neural Networks for Producing an Estimation of High-Density Polyethylene.

Polyethylene as a thermoplastic has received the uppermost popularity in a vast variety of applied contexts. Polyethylene is produced by several commercially obtainable technologies. Since Ziegler–Natta catalysts generate polyolefin with broad molecular weight and copolymer composition distributions, this type of model was utilized to simulate the polymerization procedure. The EIX (ethylene index) is the critical controlling variable that indicates product characteristics. Since it is difficult to measure the EIX, estimation is a problem causing the greatest challenges in the applicability of production. To resolve such problems, ANNs (artificial neural networks) are utilized in the present paper to predict the EIX from some simply computed variables of the system. In fact, the EIX is calculated as a function of pressure, ethylene flow, hydrogen flow, 1-butane flow, catalyst flow, and TEA (triethylaluminium) flow. The estimation was accomplished via the Multi-Layer Perceptron, Radial Basis, Cascade Feed-forward, and Generalized Regression Neural Networks. According to the results, the superior performance of the Multi-Layer Perceptron model than other ANN models was clearly demonstrated. Based on our findings, this model can predict production levels with R2 (regression coefficient), MSE (mean square error), AARD% (average absolute relative deviation percent), and RMSE (root mean square error) of, respectively, 0.89413, 0.02217, 0.4213, and 0.1489.

Modeling of Reversible Deactivation Radical Polymerization of Vinyl Monomers Promoted by Redox Initiation Using NHPI and Xanthone

AbstractTwo mathematical approaches for modeling of the kinetics and evolution of molar mass distributions in the reversible deactivation radical polymerization of vinyl monomers promoted by redox reaction with N‐hydroxyphthalimide (NHPI) and xanthone (XT) are presented. In the first modeling approach, the polymerization scheme is implemented in the standard version of the Predici commercial software. In the second case, an accelerated, self‐implemented version of the so called kinetic Monte Carlo (kMC) approach, considering binary trees, is used. The effect of concentrations of XT and monomer, as well as monomer type, on monomer conversion, NHPI efficiency, molar mass averages, molar mass dispersity, and full molar mass distributions are studied. The models are validated using literature available experimental data of polymerizations of methyl methacrylate (MMA) and styrene, in toluene, at 70 °C. The calculated results indicate that NHPI initiator efficiencies are low (<0.2); polymer end‐group functionalities present a maximum value of about 0.8 with a subsequent decrease with monomer conversion; molar mass distributions are broad, exhibiting low molar mass tails. In addition, the hypothetical copolymerization of styrene and MMA is also considered. Copolymer composition distributions for short molecules are broader than those for large ones.

Heinz Gerrens Revisited: A New Look at the Impact of Reactor Type on Polymer Chain Morphology

AbstractThe equations for predicting molecular weight distribution, copolymer composition distribution, and copolymer sequence distribution for three polymerization mechanisms (monomer linkage with termination, monomer linkage without termination, and polymer linkage), and three reactor types (batch/plug flow, homogenous continuous stirred tank, and segregated continuous stirred tank) are assembled from various sources and compared and contrasted.

Miniemulsion RAFT Copolymerization of MMA with Acrylic Acid and Methacrylic Acid and Bioconjugation with BSA.

Polymerization through reversible addition-fragmentation chain-transfer (RAFT) polymerization has been extensively employed for the production of polymers with controlled molar mass, complex architectures and copolymer composition distributions intended for biomedical and pharmaceutical applications. In the present work, RAFT miniemulsion copolymerizations of methyl methacrylate with acrylic acid and methacrylic acid were conducted to prepare hydrophilic polymer nanoparticles and compare cell uptake results after bioconjugation with bovine serum albumin (BSA), used as a model biomolecule. Obtained results indicate that the RAFT agent 2-cyano-propyl-dithiobenzoate allowed for successful free radical controlled methyl methacrylate copolymerizations and performed better when methacrylic acid was used as comonomer. Results also indicate that poly(methyl methacrylate-co-methacrylic acid) nanoparticles prepared by RAFT copolymerization and bioconjugated with BSA were exceptionally well accepted by cells, when compared to the other produced polymer nanoparticles because cellular uptake levels were much higher for particles prepared in presence of methacrylic acid, which can probably be associated to its high hydrophilicity.

Modeling of molecular weight and copolymer composition distributions for ethylene‐propylene solution copolymerization

AbstractA comprehensive computational fluid dynamics (CFD) model was developed to investigate spatial distributions of molecular weight distribution (MWD) and copolymer composition distribution (CCD) for ethylene‐propylene (EPM) copolymers in a bubble column reactor. The CFD approach incorporated Euler–Euler two‐fluid model, copolymerization kinetics, and copolymer microstructural distribution model together by user‐defined functions for ethylene‐propylene heterogeneous copolymerization process. MWD and CCD distributions were calculated by introducing Flory's distribution and Stockmayer's distribution, respectively. CFD model results were validated with literature data. The multiphase hydrodynamics, interphase mass transfer, spatial–temporal variations of MWD and CCD distributions were analyzed. Both distributions are wider at the inlet of reactor for the inefficient mixing, but narrower at the outlet due to fully developed flow and polymerization. This model is beneficial to the improvement of polymer products and process control in industrial EPM reactor.

Catalyst: Size Distribution in Self-Assembly Matters

Dafni Moatsou completed her PhD in chemistry at the University of Warwick in 2015, was a Marie Sklodowska-Curie fellow at the Adolphe Merkle Institute until 2017, and is a junior research group leader at the Karlsruhe Institute of Technology, where she focuses on sequence control and self-assembly of polymers. Rachel O’Reilly completed her PhD in 2003 at Imperial College London. She currently holds a chair in chemistry within the College of Engineering and Physical Sciences at the University of Birmingham. In August 2018 she became the head of the School of Chemistry. Her research targets the design, synthesis, and application of polymeric materials, where control over architecture, functionality, and reactivity are central to their application.

Reaction: Size Distribution in Olefin Block Copolymers: Not Bad at All

Hongyu Chen completed his PhD in macromolecular science at Case Western Reserve University in 2010. He is a fellow of the Dow Chemical Company, where he focuses on developing new products. He is also a fellow of the American Physical Society and American Chemical Society. Valeriy Ginzburg completed his PhD in polymer physics at the Moscow Institute of Physics and Technology in 1992. He is a senior scientist at the Dow Chemical Company and a fellow of the American Physical Society.

Tailoring Uniform Copolymer Composition Distribution via Policy II RAFT Solution Copolymerization of Styrene and Butyl Acrylate

AbstractControlled radical polymerization (CRP) is regarded as a powerful method to design various chain structures. Semibatch monomer feeding strategies in CRP are widely used for targeting the polymer products with desired copolymer composition distribution (CCD) and molecular weight distribution, which define the properties of polymer materials. In this work, the uniform CCD in reversible addition–fragmentation transfer (RAFT) solution copolymerization is targeted via model‐based semibatch Policy II. A RAFT solution copolymerization model is first developed and correlated with batch styrene (St) and butyl acrylate (BA) copolymerization experimental data. St/BA copolymers having three different uniform compositions are produced by the comonomer feeding Policy II. Heat and concentration analysis prove feasibility of the policy. Simulation results show that the uniform CCD can be achieved by both Policy II and Policy I, compared with starved feeding and constant feeding. Policy II gives higher and more steady rates than Policy I.

An evaluation of the impact of SG1 disproportionation and the addition of styrene in NMP of methyl methacrylate

A kinetic modeling study is presented for batch nitroxide mediated polymerization (NMP) of methyl methacrylate (MMA; nitroxide: N‐tert‐butyl‐N‐[1‐diethylphosphono‐(2,2‐dimethylpropyl)] (SG1)). Arrhenius parameters for SG1 disproportionation (A = 1.4 107 L mol−1 s−1; Ea = 23 kJ mol−1) are reported, based on homopolymerization data accounting for unavoidable temperature variations with increasing time, that is, nonisothermicity. For low targeted chain lengths (TCLs ≤ 300), this nonisothermicity is also relevant for NMP of MMA with a small amount of styrene. Parameter tuning to copolymerization data confirms a penultimate monomer unit effect for activation (sa2 = ka12/ka22=6.7; 363 K; 1: MMA; 2: styrene). To obtain, for a broad TCL range (up to 800), a dispersity well below 1.3 an initial styrene mass fraction of ca. 10% is required. An interpretation of the comonomer incorporation is performed by calculating the fractions of activation‐growth‐deactivation cycles with a given amount of monomer units and the copolymer composition distribution. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2545–2559, 2018

Modeling of the bivariate molecular weight distribution-copolymer composition distribution in RAFT copolymerization using probability generating functions

In this work, we develop a mathematical model of a RAFT copolymerization process able to predict average molecular properties as well as the full bivariate molecular weight distribution – copolymer composition distribution (MWD-CCD) of the copolymer. This model takes into account the three main kinetic theories proposed in the literature. The bivariate MWD-CCD is obtained by means of the 2D probability generating function (pgf) technique. This modeling technique can be used without any simplifying assumptions or a priori knowledge of the distribution shape. The results highlight the advantages of simulation as a powerful tool to get insight in the relationship between operating conditions and molecular structure.

Transfer of Emulsion Polymerization of Styrene and n‐Butyl Acrylate from Semi‐Batch to a Continuous Tubular Reactor

The transfer of a semi‐batch emulsion copolymerization to a single feed continuous recipe is investigated herein. A single feed continuous tubular reactor is used in the presented study in accordance with the requirement of minimizing the number of dosing streams. The correlation between operating parameters and the product properties are experimentally presented for the semi‐batch as well as for the single feed continuous tubular reactor. It is shown that the transfer from semi‐batch to continuous smart‐scale tubular reactor needs to be direct as opposed to via a batch reactor. The particle sizes and molecular masses obtained in the tubular reactor are similar to those of the semi‐batch process. However, the adjustment of the polymer composition is challenging. Using monomer addition as a means to influence chemical composition is not applicable. Thus, in the tubular reactor the chemical composition of the resulting copolymer depends on the initial monomer composition and reaction temperature. Nevertheless, the mass transfer of the emulsion polymerization damps the copolymer composition distribution (CCD) drift for higher initial monomer contents compared to bulk polymerization. It is shown that transfer of a semi‐batch product to a continuous recipe is possible in early stages of process development. image

State‐of‐the‐Art and Progress in Method of Moments for the Model‐Based Reversible‐Deactivation Radical Polymerization

Reversible‐deactivation radical polymerization (RDRP) techniques have received lots of interest for the past 20 years, not only owing to their simple, mild reaction conditions and broad applicability, but also their accessibility to produce polymeric materials with well‐defined structures. Modeling is widely applied to optimize the polymerization conditions and processes. In addition, there are numerous literatures on the kinetic and reactor models for RDRP processes, which show the accessibility on polymerization kinetics insight, process optimization, and controlling over chain microstructure with predetermined molecular weight and low dispersity, copolymer composition distribution, and sequence distribution. This review highlights the facility of the method of moments in the modeling field and presents a summary of the present state‐of‐the‐art and future perspectives focusing on the model‐based RDRP processes based on the method of moments. Summary on the current status and challenges is discussed briefly. image

Mathematical Tools and Approaches for Polymerization Reaction Engineering II— Statistical Modeling Tools and Approaches

Mathematical Tools and Approaches for Polymerization Reaction Engineering II— Statistical Modeling Tools and Approaches

Model‐Based Production of Polymer Chains Having Precisely Designed End‐to‐End Gradient Copolymer Composition and Chain Topology Distributions in Controlled Radical Polymerization, A Review

Polymer chain microstructures, such as copolymer composition distribution (CCD) and topology, play an important role in determining materials properties of the polymer products. The design and control of polymer chain microstructures represents an important task in macromolecular reaction engineering. Semi‐batch copolymerization with the model‐based design of comonomer feeding policies provides a powerful approach enabling precision production of CCD, topology, and their combined structures in controlled radical copolymerization systems. Various novel polymer products with predesigned CCDs and topologies have been successfully prepared by the approach. This article highlights the recent progresses in this area.