Mathematical modeling of crystallization analysis fractionation (Crystaf) of polyethylene

Four polyethylene samples (PE) with different molecular weight distributions (MWD) were analyzed by crystallization analysis fractionation (Crystaf) at several cooling rates to investigate the effect of MWD and cooling rate on their Crystaf profiles. Using these results, we developed a mathematical model for Crystaf that considers crystallization kinetic effects, which are ignored in all previous Crystaf models. The Crystaf model we proposed can fit the experimental Crystaf profiles of the 4 polyethylene resins very well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2749–2759, 2006     

Application of a crystallization kinetics model to simulate the effect of operation conditions on Crystaf profiles and calibration curves

Crystallization analysis fractionation (Crystaf) is a polymer characterization technique used to estimate chemical composition distributions (CCDs) of semicrystalline copolymers. The Crystaf profile can be transformed into a CCD using a calibration curve that relates average comonomer content to peak crystallization temperature. The calibration curve depends on copolymer molecular properties and Crystaf operation conditions. In this investigation, we applied a crystallization kinetics model to simulate Crystaf calibration curves and to quantify how Crystaf calibration curves depend on these factors. We applied the model to estimate the CCDs of three ethylene/1‐hexene copolymers from Crystaf profiles measured at different cooling rates and showed that our predictions agree well with the CCDs described by Stockmayer's distribution. We have also used this new methodology to investigate the effects of cooling rate, molecular weight, and comonomer type on Crystaf profiles and calibration curves. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 866–876, 2009     

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

Summary: 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.     

An experimental and numerical study on crystallization analysis fractionation (Crystaf)

Crystallization analysis fractionation (Crystaf) is a new technique used to estimate the chemical composition distribution (CCD) of semi-crystalline copolymers. In this study, the effect of chain microstructure and operation parameters on Crystaf profiles was investigated using a series of ethylene/1-hexene copolymers and their blends. The Crystaf profiles were also modeled via stochastic simulation based on the distribution of average ethylene sequence lengths.     

Mathematical modeling of crystallization analysis fractionation of ethylene/1‐hexene copolymers

Crystallization analysis fractionation (Crystaf) is a polymer characterization technique for estimating the chemical composition distributions of semicrystalline copolymers. Although Crystaf has been widely used during the recent years, it is still a relatively new polymer characterization technique. More quantitative understanding of its fractionation mechanism is essential for further developments. In this work, three ethylene/1‐hexene copolymers with different 1‐hexene fractions, but similar number‐average molecular weights, were analyzed by Crystaf at several cooling rates. A mathematical model was proposed to describe the effect of comonomer fraction and cooling rate on Crystaf fractionation from a fundamental point of view. The model describes the experimental Crystaf profiles of ethylene/1‐hexene copolymers with different 1‐hexene fractions measured at distinct cooling rates very well. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1010–1017, 2007     

Simultaneous Deconvolution of the Molecular Weight and Chemical Composition Distribution of Polyolefins Made with Ziegler-Natta Catalysts

Heterogeneous Ziegler-Natta catalysts produce polyolefins that have broad distributions of molecular weight (MWD) and chemical composition (CCD). For such broad distributions, mathematical models are useful to quantify the information provided by polyolefin analytical techniques such as high-temperature gel permeation chromatography (GPC), temperature rising elution fractionation (TREF), and crystallization analysis fractionation (CRYSTAF). In this paper, we developed a mathematical model to deconvolute the MWD and CCD of polyolefins simultaneously, using Flory's most probable distribution and the cumulative CCD component of Stockmayer's distribution. We have applied this procedure to “model” polyolefin resins and to one industrial linear low-density polyethylene (LLDPE) resin. The proposed methodology is able to deconvolute theoretical distributions even when random noise is added to the MWDs and CCDs, and it can be used to calculate the minimum number of active site types on heterogeneous Ziegler-Natta catalysts.     

Simultaneous Deconvolution of Molecular Weight Distribution and Chemical Composition Distribution of Ethylene/1-Olefin Copolymers Synthesized with Multiple-Site-Type Catalytic Systems

Summary: Ethylene/1-olefin copolymers synthesized with multiple-site-type catalytic systems typically exhibit broad molecular weight distribution (MWD) and chemical composition distribution (CCD). These microstrucral characteristics can be described by the presence of several active site types, each of which produces chains with distinct chain microstructures. In this work, a new approach to identify the number of active site types and chain microstructures produced on each active site type was developed based on simultaneous deconvolution of the bivariate MWD/CCD information. Chain microstructures produced on each active site type are assumed to follow Stockmayer's bivariate distribution. The proposed approach was validated with simulated data of model ethylene/1-butene and ethylene/1-octene copolymers.     

Estimation of Average Comonomer Content of Ethylene/1-Olefin Copolymers Using Crystallization Analysis Fractionation (Crystaf) and Artificial Neural Network (ANN)

Summary: An artificial neural network (ANN) with a 4-3-3-1 architecture was developed to estimate average comonomer content of ethylene/1-olefin copolymers from crystallization analysis fractionation (Crystaf) results. The ANN was trained with a back propagation algorithm. It was found that average comonomer contents predicted from ANN agree well with experimental results for both training and testing data sets. The developed ANN was also used to systematically investigate the effects of chain microstructures and Crystaf operating conditions on Crystaf calibration curves.     

Cocrystallization of ethylene/1‐octene copolymer blends during crystallization analysis fractionation and crystallization elution fractionation

Blending of ethylene/1‐octene copolymers can be used to achieve a well‐controlled broad chemical composition distribution (CCD) required in several polyolefin applications. The CCD of copolymer blends can be estimated using crystallization analysis fractionation (CRYSTAF) or crystallization elution fractionation (CEF). Unfortunately, both techniques may be affected by the cocrystallization of chains with different compositions, leading to profiles that do not truly reflect the actual CCD of the polymer. Therefore, understanding how the polymer microstructure and the analytical conditions influence copolymer cocrystallization is critical for the proper interpretation of CRYSTAF and CEF curves. In this investigation, we studied the effect of chain crystallizabilities, blend compositions, and cooling rates on cocrystallization during CEF and CRYSTAF analysis. Cocrystallization is more prevalent when the copolymer blend has components with similar crystallizabilities, one of the components is present in much higher amount, and fast cooling rates are used. CEF was found to provide better CCD estimates than CRYSTAF in a much shorter analysis time. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Ethylene Polymerization by Metallocene Catalysts Supported over Siliceous Materials with Bimodal Pore Size Distribution

Summary: As known, the pore structure of the catalytic support plays a decisive role during the polymerization reactions determining intra-particle mass and heat transport phenomena. In this work, several ethylene polymerizations have been carried out by using as catalytic support different mesostructured materials with unimodal and bimodal pore size distributions in order to evaluate the influence of this pore size distribution on the catalytic behavior. Calcined mesoporous materials were impregnated with the catalytic system MAO/(nBuCp)₂ZrCl₂ and used for ethylene polymerization and ethylene/1-hexene copolymerizations, at 70 °C and 5 bar of ethylene pressure. Polyethylenes obtained were characterized by GPC, DSC and Crystaf. Results indicate that porous structure of the support has a significant influence on polymerization activity and polymer properties. Despite the catalyst bimodal pore size distribution, only ethylene/1-hexene copolymers presented a bimodal chemical composition distribution.     

Copolymerization of ethylene and α‐olefins with combined metallocene catalysts. II. Mathematical modeling of polymerization with single metallocene catalysts

The relation between the polymerization conditions and the distributions of molecular weight (MWD) and chemical composition (CCD) of poly(ethylene‐co‐1‐hexene) made with single supported metallocene catalysts was investigated. Understanding the behavior of each metallocene under different polymerization conditions is necessary for designing combined metallocene catalysts to produce tailor‐made polyolefins. In this article, a simple mathematical model based on experimental results is developed and combined with the bimodality criterion developed in Part I of this series to predict polymerization conditions and metallocene combinations that will produce polymers with desired MWDs and CCDs. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1417–1426, 2000     

Ethylene/1‐hexene copolymers synthesized with a single‐site catalyst: Crystallization analysis fractionation,modeling, and reactivity ratio estimation

A series of poly(ethylene‐co‐1‐hexene) samples made with rac‐ethylene bis(indenyl)zirconium dichloride/methylaluminoxane were analyzed by crystallization analysis fractionation (CRYSTAF). The nine samples had comonomer contents of 0–4.2 mol % 1‐hexene with a narrow range of molecular weights (34,000–39,000 g/mol). Because all the copolymer samples had narrow, unimodal chemical composition distributions, they were ideal as calibration standards for CRYSTAF. A linear calibration curve was constructed relating the peak crystallization temperature from CRYSTAF operated at a cooling rate of 0.1 °C/min and the comonomer content as determined by ¹³C NMR. Reactivity ratios for ethylene and 1‐hexene were estimated by the fitting of reactant liquid‐phase compositional data to the Mayo–Lewis equation. It was found that a value of the 1‐hexene reactivity ratio could not be unequivocally determined from the set of samples analyzed because the range of comonomer incorporation was too narrow. Stockmayer's bivariate distribution was used to model the fractionation process in CRYSTAF, and although a good fit to experimental CRYSTAF profiles was attained, the model did not fully describe the underlying crystallization phenomena. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2595–2611, 2002     

Simulation of Crystallization Analysis Fractionation (Crystaf) of Linear Olefin Block Copolymers

Summary: Linear olefin block copolymers (OBCs) have microstructures that are unique among polyolefins and exhibit properties that are different from those of other polyolefin elastomers. Characterizing their chain microstructures is a challenging task, as conventional characterization techniques cannot probe directly block length distribution or composition. In this work, we used a Monte Carlo model to predict the microstructure details of OBCs and a modified version of the Crystaf model previously developed in our groups to describe theoretical Crystaf profiles for model OBCs. This model can be used as a tool to interpret Crystaf results of these interesting new polyolefins and to relate them to OBC microstructures. Effects of polymerization parameters on OBC microstructure and Crystaf profiles were also discussed.     

Kinetics of ethylene polymerization reactions with chromium oxide catalysts

Principal kinetic data are presented for ethylene homopolymerization and ethylene/1‐hexene copolymerization reactions with two types of chromium oxide catalyst. The reaction rate of the homopolymerization reaction is first order with respect to ethylene concentration (both for gas‐phase and slurry reactions); its effective activation energy is 10.2 kcal/mol (42.8 kJ/mol). The r₁ value for ethylene/1‐hexene copolymerization reactions with the catalysts is ～30, which places these catalysts in terms of efficiency of α‐olefin copolymerization with ethylene between metallocene catalysts (r₁ ～ 20) and Ti‐based Ziegler‐Natta catalysts (r₁ in the 80–120 range). GPC, DSC, and Crystaf data for ethylene/1‐hexene copolymers of different compositions produced with the catalysts show that the reaction products have broad molecular weight and compositional distributions. A combination of kinetic data and structural data for the copolymers provided detailed information about the frequency of chain transfer reactions for several types of active centers present in the catalysts, their copolymerization efficiency, and stability. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5315–5329, 2008     

Effects of branching characteristics and copolymer composition distribution on non-isothermal crystallization kinetics of metallocene LLDPEs

The effects of branch content (BC) and copolymer composition distribution (CCD) on the non-isothermal crystallization kinetics of metallocene m-LLDPEs were studied using modified Avrami analysis, modulated differential scanning calorimetry (MDSC), and Crystaf. Several m-LLDPEs and an m-HDPE - all having comparable M_w and PDI - were experimented. In addition, a ZN-LLDPE was used for comparison purposes. The branch content, unlike the used cooling rates (2-6 °C/min), significantly affected the crystallization behavior. Crystallization peak temperature, , decreased linearly with increasing BC. All the m-LLDPEs showed primary and secondary crystallizations. The secondary crystallization showed to be more pronounced at high BC. The primary crystallization Avrami parameter n for m-HDPE ranged between 3.72 and 4.50, indicating spherulitic crystal growth whereas that for the m-LLDPEs, varied from 2.02 to 5.70. The ZN-LLDPE (having broader composition distribution) offered higher values of and than the m-LLDPEs with similar BC, M_w, and PDI. It, unlike the m-LLDPEs and m-HDPE, fairly agreed with the crystallization kinetic model proposed by Liu et al. The lamella thickness of the m-LLDPEs, L, calculated as per Gibbs-Thomson equation, showed to be in the range 2-16 nm, depending on BC and it decreased approximately following the relationship: L (nm) = 15.0 e^{(−0.0498BC)}.     

On the Production of Polyolefins with Bimodal Molecular Weight and Copolymer Composition Distributions in Catalytic Gas‐Phase Fluidized‐Bed Reactors

A comprehensive mathematical model is developed for the dynamic calculation of the molecular distributed properties (i.e. MWD and CCD) in a gas‐phase, catalytic, ethylene‐1‐butene copolymerization, FBR, taking into account the various kinetic, micro‐ and macroscopic phenomena in the reactor. The effects of the two single‐site catalyst mass fractions and reactor operating conditions on the production of polyolefins with ‘tailor‐made’ bimodal molecular properties are investigated. It is shown that PE grades with either a bimodal MWD or CCD can be produced in a single FBR, using a mixture of two single‐site catalysts under properly selected operating conditions.

     

Effect of operation parameters on temperature rising elution fractionation and crystallization analysis fractionation

Crystallization analysis fractionation and temperature rising elution fractionation are two techniques used to estimate the chemical composition distributions of semicrystalline copolymers. This study investigates the cooling rate and cocrystallization effects for both techniques with a series of ethylene/1‐olefin copolymers and their blends. Ideally, both techniques should operate in the vicinity of thermodynamic equilibrium so that crystallization kinetic effects are avoided. The results show that, in fact, crystallization kinetic effects play an important role at the typical cooling rate used with both techniques. Cocrystallization is significant when fast cooling rates are used. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1762–1778, 2003     

乙烯与甲基丙烯酸二甲氨基乙酯共聚物序列结构与结晶结构关系的研究

乙烯与甲基丙烯酸二甲氨基乙酯共聚物序列结构与结晶结构关系的研究＊陈群罗会浚杨光（华东师范大学分析测试中心上海２０００６２）徐端夫（中国科学院化学所北京１０００８０）关键词乙烯共聚物，高分辨核磁共振，序列结构，最小可结晶序列长度乙烯与甲基丙烯酸二甲氨基...     

Polyethylene with bimodal molecular weight distribution synthesized by 2,6-bis(imino)pyridyl complexes of Fe(II) activated with various activators

Polyethylenes with bimodal molecular weight distribution (MWD) were synthesized by 2,6-bis(imino)pyridyl complexes of Fe(II) combined with different activators, which were prepared from alkylaluminium. It is found that the molecular weight (MW) and MWD was influenced by not only iron complexes but activators as well. The activator plays key important role in determination of the MW and MWD of final polymer and the MWD shape could be regulated by selection of various activators and polymerization conditions. The study on the variation of the MWD with the polymerization time and fitting of bimodal MWD with two Flory distributions suggests that bimodal MWD is caused by chain transfer reaction to activator or two active sites.