Copolymer Composition Distribution Research Articles

Mathematical Modeling of Crystallization Elution Fractionation of Ethylene/1‐Octene Copolymers

Crystallization elution fractionation (CEF) is a relatively new polyolefin characterization technique used to estimate the chemical composition distribution (CCD) of semicrystalline copolymers. CEF is developed to enhance the resolution and reduce the analysis time of temperature rising elution fractionation (TREF) by separating polymer samples in both the crystallization and elution steps. A model based on the concept of population balance, crystallization/dissolution kinetics, and dispersion model is developed to understand the CEF fractionation mechanisms. The proposed CEF model is found to describe well the experimental CEF profiles of a series of ethylene/1‐octene copolymers with different comonomer contents. image

Targeting Copolymer Composition Distribution via Model-Based Monomer Feeding Policy in Semibatch RAFT Mini-Emulsion Copolymerization of Styrene and Butyl Acrylate

Copolymer composition distribution (CCD) is an important parameter of chain microstructure that has significant impact on the material properties of polymer products. Controlled/living radical polymerization (CLRP) has provided a great opportunity in producing polymers with predesigned CCDs through a model-based monomer feeding policy (MMFP) in homogeneous systems. In this work, the MMFP has been expanded to heterogeneous systems. Reversible addition–fragmentation transfer (RAFT) mini-emulsion polymerizations of styrene (St) and butyl acrylate (BA) were carried out with 3-benzyltrithiocarbonyl propionic acid (BCPA) used as a RAFT agent. A kinetic model was developed and correlated to the batch St/BA RAFT mini-emulsion experimental data for parameter estimation. The MMFP was then developed by combining the kinetic model with a semibatch reactor model and applied to the semibatch St/BA RAFT mini-emulsion copolymerization for the synthesis of targeted CCDs. The model agreed well with the polymerization kinetics. A series of St/BA copolymers with predesigned CCDs were successfully synthesized.

Mathematical Tools and Approaches for Polymerization Reaction Engineering

Mathematical Tools and Approaches for Polymerization Reaction Engineering

The evolutionary development of chain microstructure during tandem polymerization of ethylene: A Monte Carlo simulation study

Employing a Kinetic Monte Carlo (KMC) simulation algorithm, tandem polymerization of ethylene is thoroughly investigated. To do this, the evolution of ethylene copolymerization is evaluated in terms of ethylene consumption and 1-hexene accumulation. The results obtained are in good agreement with the existing experimental kinetic data. It is revealed that the pre-trimerization time is a key factor in controlling the architecture of copolymer chains. Moreover, the precise computation of instantaneous and cumulative comonomer contents along with the chemical composition distribution of simulated copolymers provides a comprehensive image of the growing chains during tandem polymerization. A well-established crystallization fractionation (CRYSTAF) analysis mathematical model is applied to delve into the molecular architecture and the crystallization fractionation behavior of the produced polyolefins.

Modeling the Mini-Emulsion Copolymerization of N-Butyl Acrylate with a Water-Soluble Monomer: A Monte Carlo Approach

A Monte Carlo approach has been developed to simulate the miniemulsion polymerization of n-butyl acrylate with a water-soluble monomer, 2-hydroxyethyl methacrylate. The proposed simulation takes into account all the reactions in the aqueous and organic phases, as well as the entry of oligoradicals into the polymer particles by absorption and precipitation. The effect of the water-soluble monomer on the polymerization rate and on the molecular weight distribution of the polymer in the aqueous and organic phases has been studied. The addition of the water-soluble monomer retards the polymerization, though it had no significant effect on the molecular weight of the polymer produced in the particles; however, it increased the concentration of water-soluble polymer and its molecular weight. By this approach, it is possible to extract detailed information of polymer in the aqueous phase, such as the copolymer composition distribution.

Effect of Operating Conditions on Dynamic Crystallization of Ethylene/1‐Octene Copolymers

Dynamic crystallization (DC) is a new characterization technique for measuring the chemical composition distribution (CCD) of semicrystalline copolymers. This technique fractionates polymers based on chain crystallizabilities under a constant cooling rate; a solvent is also fed through the column at a constant flow rate during the crystallization to enhance the physical separation of the polymer fractions. In this work, a DC model for ethylene/1‐olefin copolymers on the basis of population balance, crystallization kinetics, and axial dispersion is proposed. This model is found to describe the experimental DC profiles of an ethylene/1‐octene copolymer at various operation conditions very well. image

Separation and composition distribution determination of triblock copolymers by thermal field-flow fractionation

Thermal field-flow fractionation (ThFFF) is used to separate a linear triblock copolymer of polystyrene, poly(tert-butyl acrylate), and poly(methyl methacrylate) by composition. Fractions were collected and subjected to off-line NMR analysis. The resultant mole fraction versus retention time plots for each of the three polymer components confirmed the success of the separation and yielded the composition distribution of the copolymer. The composition distribution was also obtained using a second approach that involved solving a series of equations comprised of polymer thermal diffusion coefficients and quasi-elastic light scattering, differential refractometry, and UV detector responses. Both sets of data showed similar trends of composition variations in each polymer component as a function of retention time. However, discrepancies were observed in the mole fraction values. The ability to compositionally separate and to determine composition distribution of copolymers is important as demonstrated by the presence of diblock impurities in the ThFFF with off-line NMR results.

Silica-supported (n BuCp)2 ZrCl2 : effect of catalyst active center distribution on ethylene-1-hexene copolymerization

Metallocenes are a modern innovation in polyolefin catalysis research. Therefore, two supported metallocene catalysts—silica/MAO/(nBuCp)2ZrCl2 (Catalyst 1) and silica/nBuSnCl3/MAO/(nBuCp)2ZrCl2 (Catalyst 2), where MAO is methylaluminoxane—were synthesized, and subsequently used to prepare, without separate feeding of MAO, ethylene–1-hexene Copolymer 1 and Copolymer 2, respectively. Fouling-free copolymerization, catalyst kinetic stability and production of free-flowing polymer particles (replicating the catalyst particle size distribution) confirmed the occurrence of heterogeneous catalysis. The catalyst active center distribution was modeled by deconvoluting the measured molecular weight distribution and copolymer composition distribution. Five different active center types were predicted for each catalyst, which was corroborated by successive self-nucleation and annealing experiments, as well as by an extended X-ray absorption fine structure spectroscopy report published in the literature. Hence, metallocenes impregnated particularly on an MAO-pretreated support may be rightly envisioned to comprise an ensemble of isolated single sites that have varying coordination environments. This study shows how the active center distribution and the design of supported MAO anions affect copolymerization activity, polymerization mechanism and the resulting polymer microstructures. Catalyst 2 showed less copolymerization activity than Catalyst 1. Strong chain transfer and positive co-monomer effect—both by 1-hexene—were common. Each copolymer demonstrated vinyl, vinylidene and trans-vinylene end groups, and compositional heterogeneity. All these findings were explained, as appropriate, considering the modeled active center distribution, MAO cage structure repeat units, proposed catalyst surface chemistry, segregation effects and the literature that concerns and supports this study. While doing so, new insights were obtained. Additionally, future research, along the direction of the present work, is recommended. © 2013 Society of Chemical Industry

Multistage dynamic optimization of a copolymerization reactor using differential evolution

ABSTRACTA multistage dynamic optimization methodology with sequential implementation procedure is proposed, and the evolutionary optimizing features of differential evolution (DE) are exploited to implement the methodology for optimal control of a semi‐batch copolymerization reactor. DE is designed and implemented to determine the optimal control policies for monomer addition rate and reactor temperature to produce a polymer with the desired copolymer composition and molecular weight distribution. Further, a similar multistage dynamic optimization strategy based on iterative dynamic programming is used for optimal control of copolymerization reactor and to compare with DE. The results show the effectiveness of the DE‐based multistage dynamic optimization strategy in determining the optimal control policies that yield the desired polymer product characteristics. © 2013 Curtin University of Technology and John Wiley & Sons, Ltd.

Self-assembly of amphiphilic random co-poly(ionic liquid)s: the effect of anions, molecular weight, and molecular weight distribution

Self-assembly behavior of amphiphilic random co-poly(ionic liquid)s in aqueous solution was investigated in this work. An imidazolium-type homopolymer, poly(1-(4-vinylbenzyl)-3-methyl imidazolium chloride) (denoted as PIL-[Cl]), was synthesized via reversible addition fragmentation chain transfer (RAFT) polymerization of p-chloromethyl styrene, and followed by post-polymerization with methylimidazole (or vinylimidazole). Partial anion-exchange of PIL-[Cl] with PF6− anions yielded amphiphilic random copolymers, PIL-[Cl]x[PF6]y (suffixes x, y represent the relative molar ratio of Cl− and PF6− anions). Self-assembly morphologies of PIL-[Cl]x[PF6]y in aqueous solution as a function of copolymer composition (anions), molecular weight, and molecular weight distribution were investigated. The size of well-defined PIL-[Cl]x[PF6]y spherical micelles increased dramatically with increasing molecular weight distribution, while the anions and molecular weight show little effect on the micelle size. Furthermore, self-assembly of amphiphilic random ionic copolymers with the vinylimidazole groups yielded colloidosomes, which might be due to the polymerization of vinylimidazole groups.

Mathematical Modeling of Temperature Rising Elution Fractionation (TREF) of Polyethylene and Ethylene/1‐Olefin Copolymers

AbstractTemperature rising elution fractionation (TREF) is a characterization technique widely used to estimate chemical composition distribution (CCD) of semicrystalline copolymers. Although several mathematical models have been previously proposed to elucidate the TREF fractionation mechanism, all previous TREF models assume equilibrium fractionation; thus, they cannot describe important kinetics effects observed in TREF experiments. In this work, a new TREF model is developed incorporating crystallization and dissolution kinetic models during the fractionation process. The proposed model describes the effects of molecular weight, comonomer content, cooling rate, heating rate, and solvent flow rate on experimental TREF profiles for both polyethylene and ethylene/1‐olefin copolymers very well.

Graft Copolymers for Blend Compatibilization: Mathematical Modeling of the Grafting Process

AbstractThe grafting of PE onto PS through a Friedel‐Crafts reaction, which results in a mixture of PE‐g‐PS copolymer, unmodified PE, and modified PS, is investigated. The copolymer may be suitable for compatibilization of immiscible mixtures in the household plastic waste stream, where PE and PS are majority components. Since the compatibilization effect depends on the composition and block lengths in the copolymer, a model is presented for predicting the complete molecular weight distribution of the homopolymers and the chemical composition distribution of the graft copolymer. The model has potential for application in an optimization tool for the compatibilization process, as it is able to account for the opposing effects of competing reactions that characterize the graft reaction. magnified image

Analysis of polystyrene‐b‐polyisoprene copolymers by coupling of liquid chromatography at critical conditions to NMR at critical conditions of polystyrene and polyisoprene

For the investigation of the molecular heterogeneity of polystyrene-b-polyisoprene block copolymers, a chromatographic separation method, namely liquid chromatography at critical conditions was developed. This method was coupled on-line with (1)H-NMR(where NMR stands for nuclear magnetic resonance) for the comprehensive analysis of the polystyrene-b-polyisoprene copolymers. The copolymers were synthesized by two different methods: sequential living anionic polymerization and coupling of living precursor blocks. While (1)H-NMR allows just for the analysis of the bulk chemical composition of the block copolymers, the coupling with liquid chromatography at critical conditions provides selective molar mass information on the polystyrene and polyisoprene blocks within the copolymers. The polyisoprene block molar mass is determined by operating at chromatographic conditions corresponding to the critical point of adsorption of polystyrene and size exclusion chromatography mode for polyisoprene. The molar mass of the polystyrene block is determined by operating at the critical conditions of polyisoprene. In addition to the molar mass of each block of the copolymers, the chemical composition distribution of the block copolymers was determined. By using the coupling of liquid chromatography at critical conditions to (1)H-NMR, one can also detect the homopolymers formed during synthesis. Finally the microstructure of the polyisoprene block in the copolymers was evaluated as a function of molar mass.

Composition control through pH and ionic strength during acrylic acid/acrylamide copolymerization

AbstractThe possibility of controlling the composition of acrylic acid/acrylamide copolymers by controlling the pH and the ionic strength of the reaction medium is investigated. The reactivity ratios of charged monomers depend on the pH of the medium, acrylic acid is the more reactive monomer below pH 3 and acrylamide above pH 4. The working pH was set at 3.6, a candidate for the crossover point, where no composition drift is expected. Copolymerization kinetics is investigated at this pH at various ionic strengths and a reaction without composition drift up to 80% conversion was achieved. All the chains produced in this reaction contain 30% ± 3% acrylic acid. Copolymer conversions, molecular weights, and composition distributions were measured through Automatic Continuous Online Monitoring of Polymerization (ACOMP) system. The copolymerization data were analyzed by a recent error in variables method (EVM) and reactivity ratios are calculated. The results show that in salt free conditions, the reactivity ratios depend on the ionic monomer concentration (ionic strength) in addition to the pH of the reaction medium. The effect of polyelectrolytic interactions on the reactivity ratios and the resulting composition drift during the reaction, sequence length distribution, and Stockmayer bivariate distribution are discussed in detail. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

Aqueous‐Phase Copolymerization of N‐Vinylpyrrolidone and N‐Vinylformamide

AbstractAqueous‐phase batch free‐radical copolymerization of NVP and NVF is studied at 60 and 85 °C with varying initial monomer mixture compositions and monomer to water ratios. The rate of monomer conversion is found to increase with increasing NVP molar fraction and with decreasing total monomer concentration, in accordance with the expected behavior based on homopolymerization kinetics. The copolymer composition is equal to the initial comonomer composition, indicating monomer reactivity ratios to be unity. A terminal copolymerization model provides a good description of polymerization rate, copolymer composition, and polymer molar mass distributions using the same kinetic rate coefficients as used to previously describe the homopolymerization of the two monomers.

Chromatographic examination of the chemical composition and sequence distribution of copolymers from ethyl and benzyl diazoacetate

Polymers, especially copolymers, are highly complex samples and, therefore, require various setups for their thorough characterization. In this work, one- and two-dimensional chromatographic approaches were applied to characterize two homopolymers and two dissimilar copolymers prepared by rhodium-mediated carbene polymerization using ethyl and benzyl diazoacetate as the monomers: poly-(EA-ran-BnA) and poly((EA)b-(BnA-ran-EA)b). Different strategies of synthesis suggested that poly-(EA-ran-BnA) was an approximately 1:1 random copolymer and that poly((EA)b-(BnA-ran-EA)b) was a block-type copolymer of which the (BnA-ran-EA)b block is dominated by BnA. The hydrodynamic volume of the investigated polymers turned out to be comparable, i.e. size exclusion chromatography (SEC) did not separate them. Temperature-gradient interaction chromatography was not feasible and one-dimensional (solvent-)gradient-elution liquid chromatography (GELC) suffered from coelution problems. Pyrolysis-gas-chromatography (Py-GC–MS) experiments allowed determining the monomer ratio. SEC with UV and refractive-index detection indicated the presence of molecular-weight-dependent chemical heterogeneity for the poly((EA)b-(BnA-ran-EA)b) copolymer. This finding was confirmed with off-line SEC//Py-GC–MS. Only a comprehensive two-dimensional GELC×SEC setup enabled the separation of high-molecular-weight material of the less-retained homopolymer from low-molecular-weight copolymeric material. In this way it was possible to detect some high-molecular-weight homopolymeric material in one of the copolymers.

Effect of Chain Microstructure and Cooling Rate on Crystaf Calibration Curves: An Experimental Study

AbstractSummary: Crystallization analysis fractionation (Crystaf) is a polymer characterization technique based on differences in chain crystallizabilities in a dilute solution during non‐isothermal crystallization. Crystaf profiles, a weight distribution function of chains crystallized at each temperature, can be used to infer the chemical composition distribution (CCD) of copolymers when a Crystaf calibration curve, a relationship between peak crystallization temperature and average comonomer content, is known. In this investigation, the effect of the number average molecular weight, comonomer type, and cooling rate on Crystaf calibration curves were experimentally investigated. It was found that the cooling rate and comonomer type may strongly affect Crystaf calibration curves, while the influence of molecular weight is relatively subtle.

Influence of chain microstructure on ethylene–norbornene copolymer film properties

AbstractThe effects of copolymer composition, copolymer composition distribution, and polar α‐olefin incorporation on transparency, refractive index, and hydrophilicity of resultant ethylene–norbornene copolymer films were investigated. It has been found that the transparency is mainly determined by the copolymer composition distribution. The samples having uniform compositions gave better transparency. However, the copolymer composition distribution had little effect on refractive index. The refractive index increased linearly with increasing norbornene content. Furthermore, the incorporation of polar α‐olefin with long carbon chain improved refractive index and hydrophilicity of the films. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Characterization of ethylene/propylene copolymers by means of a GPC-4D technique

Copolymer composition and comonomer distribution are important magnitudes in polymer material that have a big effect on different kind of properties and consequently there are several ways to study. In this work several ethylene/propylene copolymers synthesized with two different metallocene catalysts and a Ziegler–Natta catalyst and covering a wide composition range were studied. Characterization was carried out by nuclear magnetic resonance ( 13C NMR) and by gel permeation chromatography with 4 detectors (GPC-4D): refractive index, viscosity, multi-angle light scattering and infrared detectors. Different behaviour in the comonomer distribution along the molecular weight was obtained for metallocene and for ZN copolymers as expected due to the differences between these catalytic systems. Nevertheless, Ziegler–Natta copolymers present more homogeneous comonomer distribution due to the synthesis method. Study of conformation of chains in solution was improved by defining the scaling law of R g against the number of repeat units because it avoids the effect of the repetitive unit size. Both metallocene copolymer sets show similar dependence of q value with the copolymer composition, however Ziegler–Natta copolymers show different behaviour with q values independent on copolymer composition. This different behaviour has been related with the effects of the heterogeneity of the ethylene distribution and of the molecular weight of the samples.

Characterization of New Amphiphilic Block Copolymers of N‐Vinyl Pyrrolidone and Vinyl Acetate, 1 – Analysis of Copolymer Composition, End Groups, Molar Masses and Molar Mass Distributions

AbstractNew amphiphilic block copolymers consisting of N‐vinyl pyrrolidone and vinyl acetate were synthesized via controlled radical polymerization using a reversible addition/fragmentation chain transfer (RAFT)/macromolecular design via the interchange of xanthates (MADIX) system. The synthesis was carried out in 1,4‐dioxane as process solvent. In order to get conclusions on the mechanism of the polymerization the molecular structure of formed copolymers was analysed by means of different analytical techniques. 13C NMR spectroscopy was used for the determination of the monomer ratios. End groups were analysed by means of matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry. This technique was also used to determine possible fragmentations of the RAFT end groups. By means of a combination of size exclusion chromatography, 13C NMR and static light scattering molar mass distributions and absolute molar masses could be analysed. The results clearly show a non‐ideal RAFT mechanism.magnified image