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     

A Mathematical Model for the Kinetics of Crystallization in Crystaf

Summary : A series of ethylene homopolymers and ethylene/1-hexene copolymers with different molecular weight distributions (MWD) and chemical composition distributions (CCD) was analyzed by crystallization analysis fractionation (Crystaf) at several cooling rates to investigate the effect of MWD, CCD, and cooling rate on their Crystaf profiles. Using these results, we developed a mathematical model for Crystaf that considers crystallization kinetic effects ignored in all previous Crystaf models and can fit our experimental profiles very well.     

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.     

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     

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     

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     

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     

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.     

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.     

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     

Effect of 1‐hexene comonomer on polyethylene particle growth and copolymer chemical composition distribution

An investigation of the polymer particle growth characteristics and polymer molecular weight and composition distributions in ethylene homopolymerization and ethylene/1‐hexene copolymerization has been carried out with a catalyst comprising a zirconocene and methylaluminoxane immobilized on a silica support. The presence of 1‐hexene leads to higher productivity and easier fragmentation of the support during particle growth. Crystallization analysis fractionation and gel permeation chromatography analysis of ethylene/1‐hexene copolymers prepared at different polymerization times reveals a broadening of the chemical composition distribution with increasing polymerization time as a result of the gradual formation of a relatively high‐molecular‐weight, ethylene‐rich fraction. The results are indicative of significant monomer diffusion effects in both homopolymerization and copolymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2883–2890, 2006     

Correlation of the elution behavior in temperature rising elution fractionation and melting in the solid‐state and in the presence of a diluent of polyethylene copolymers

Compositionally homogeneous poly(ethylene‐α‐olefin) random copolymers with 1‐butene and 1‐hexene comonomers have been studied. The melting of solution‐crystallized specimens of these copolymers in the presence of trichlorobenzene as a diluent with differential scanning calorimetry (DSC) is well correlated with analytical temperature rising elution fractionation (A‐TREF) elution temperature profiles. This indicates that the A‐TREF experiment is essentially a diluent melting experiment. Furthermore, the correction of the corresponding solid‐state melting endotherms of these copolymers with Flory's diluent melting equation yields curves that also correlate very well with the DSC diluent melting curves and the A‐TREF elution temperature profiles. Values of χ, the Flory–Huggins interaction parameter, are determined for these copolymers in trichlorobenzene. χ decreases as short‐chain branching increases. The A‐TREF elution temperature profiles of one of these copolymers are the same, within experimental error, for dilute‐solution crystallizations of the copolymer performed over an extremely broad time schedule (10 s to 3 days). This indicates the profound effect of the branches, as limiting points of the ethylene sequences, in controlling the crystal thickness distribution, which in turn controls the melting point in the presence of the diluent, or the elution temperature from the A‐TREF. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2819–2832, 2001     

Polydispersity of ethylene sequence length in metallocene ethylene/α‐olefin copolymers. I. Characterized by thermal‐fractionation technique

In this article, the polydispersity of the ethylene sequence length (ESL) in ethylene/α‐olefin copolymers was studied by atomic force microscopy (AFM) and the thermal‐fractionation technique. The crystal morphology observation by AFM showed that morphology changed gradually with decreasing average ESL from complete lamellae over shorter and more curved lamellae to a granular‐like morphology, and the mixed morphology was observed after stepwise crystallization from phase‐separated melt. This result indicated that the ethylene sequence with different lengths crystallized into a crystalline phase with a different size and stability at the copolymer systems. The thermal‐fractionation technique was used to characterize the polydispersity of ESL. Three of the following statistical terms were introduced to describe the distribution of ESL and the lamellar thickness: the arithmetic mean L?_n, the weight mean L?_w, and the broadness index I = L?_w/L?_n. It was concluded that the polydispersity of ESL could be quantitatively characterized by the thermal‐fractionation technique. The effects of temperature range, temperature‐dependent specific heat capacity C_p of copolymer, and the molecular weight on the results of thermal fractionation were discussed. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 813–821, 2002     

Synthesis of ethylene‐1‐hexene copolymers from ethylene stock by tandem action of bis(2‐dodecylsulfanyl‐ethyl) amine‐CrCl3 and Et(Ind)2ZrCl2

In this work, ethylene‐1‐hexene copolymers were synthesized with a tandem catalysis system that consisted of a new trimerization catalyst bis(2‐dodecylsulfanyl‐ethyl) amine‐CrCl₃/MAO ( 1 /MAO) and copolymerization catalyst Et(Ind)₂ZrCl₂/MAO ( 2 /MAO) at atmosphere pressure. Catalyst 1 trimerized ethylene with high activity and excellent selectivity in the presence of a relatively low amount of MAO. Catalyst 2 incorporated the 1‐hexene content and produced ethylene‐1‐hexene copolymer from an ethylene‐only stock in the same reactor. Adjusting the Cr/Zr ratio and reaction temperature yielded various branching densities and thus melting temperatures. However, broad DSC curves were observed when low temperatures and/or high Cr/Zr ratios were employed due to an accumulation of 1‐hexene component and composition drifting during the copolymerization. It was found that a short pretrimerization period resulted in more homogeneous materials that gave unimodal DSC curves. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3562–3569, 2007     

Molecular heterogeneity of ethylene‐propylene rubbers: New insights through advanced crystallization‐based and chromatographic techniques

For a long time ethylene‐propylene rubber (EPR) copolymers with high comonomer contents were believed to be amorphous materials with a random copolymer composition. This is not completely correct as has been shown by temperature rising elution fractionation (TREF) combined with differential scanning calorimetry (DSC), crystallization analysis fractionation (CRYSTAF), and high temperature–high‐performance liquid chromatography (HT‐HPLC). When using only conventional crystallization‐based fractionation methods, the comprehensive compositional analysis of EPR copolymers was impossible due to the fact that large fractions of these copolymers do not crystallize under CRYSTAF conditions. In the present work, HT‐HPLC was used for the separation of the EPR copolymers according to their ethylene and propylene distributions along the polymer chains. These investigations showed the existence of long ethylene sequences in the bulk samples which was further confirmed by DSC. The results on the bulk samples prompted us to conduct preparative fractionations of EPR copolymers having varying ethylene contents using TREF. Surprisingly, significant amounts of crystallizing materials were obtained that were analyzed using a multistep protocol. CRYSTAF and DSC analyses of the TREF fractions revealed the presence of components with large crystallizable sequences that had not been detected by the bulk samples analyses. HT‐HPLC provided a comprehensive separation and characterization of both the amorphous and the crystalline TREF fractions. The TREF fractions eluting at higher temperatures showed the presence of ethylene‐rich copolymers and PE homopolymer. In order to obtain additional structural information on the separated fractions, HT‐HPLC was coupled to Fourier transform‐infrared (FT‐IR) spectroscopy. The FT‐IR data confirmed that the TREF fractions were separated according to the ethylene contents of the eluted samples. Preparative TREF analysis together with a combination of various analytical methods proved to be useful tools in understanding the complex molecular composition of these rubber samples. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 863–874     

Melting behavior of polyethylene/α‐olefin copolymers: Narrow composition distribution copolymers and fractions from Ziegler–Natta and single‐site catalyst products

The melting temperature and heat of fusion were measured for an extensive series of compositionally uniform copolymers of ethylene with butene‐1, hexene‐1, and octene‐1. Fractions and whole polymers that exhibited minimal interchain compositional heterogeneity were from commercial copolymers made with either Ziegler–Natta (ZN) or single‐site metallocene catalysts. The present results do not support recent claims that ZN and corresponding metallocene catalyst copolymers melt at significantly different temperatures, nor the implication that comonomer incorporation is “blocky” in ZN copolymers. In five of the six comonomer/catalyst systems the dependencies of the melting temperature on comonomer type and amount were scarcely distinguishable. This common behavior is the same as that for a model random copolymer, so we conclude that most ethylene/α‐olefin copolymers have random distributions of ethylene sequences. The exception in the present study is a metallocene ethylene/butene‐1 copolymer that melts at lower temperatures and apparently has perceptibly alternating sequence distributions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3416–3427, 2004     

Styrene‐ethylene co‐oligomerization with bis‐(diphenylphosphino)‐amine/chromium catalysts and the use of the co‐oligomerization products in copolymerization reactions with metallocenes

Ethylene‐styrene (or 4‐methylstyrene) co‐oligomerization using various bis(diphenylphoshino)amine ligands in combination with chromium is discussed. GC analysis of the reaction mixture shows that various phenyl‐hexene and phenyl‐octene isomers are formed either through cotrimerization or cotetramerization. It seems that the more bulky ligands display lower selectivity to co‐oligomerization and favor ethylene homo‐oligomerization. Subsequent copolymerization of the oligomerization reaction mixture using a metallocene polymerization catalyst results in a copolymer with a branched structure as indicated by Crystaf and ¹³C NMR analysis. Assignments of the ¹³C NMR spectrum are proposed from an APT NMR experiment combined with calculated NMR chemical shift data using additivity rules. An indication of the ability of the different co‐oligomerization products to copolymerize into the polyethylene chain could be established from these assignments. Unreacted styrene and the more bulky isomers, 3‐phenyl‐1‐hexene and 3‐phenyl‐1‐octene, are not readily incorporated while branches resulting from the other isomers present in the co‐oligomerization reaction mixture are detected in the NMR spectrum. © 2008 Wiley Periodicals, Inc. JPolym Sci Part A: Polym Chem 46: 1488–1501, 2008     

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.     

Copolymerization behavior of titanium imidazolin‐2‐iminato complexes

Monocyclopentadienyl titanium imidazolin‐2‐iminato complexes [Cp′Ti(L)X₂] 1a (Cp′ = cyclopentadienyl, L = 1,3‐di‐tert‐butylimidazolin‐2‐imide, X = Cl), 1b (X = CH₃); 2 (Cp′ = cyclopentadienyl, L = 1,3‐diisopropylimidazolin‐2‐imide, X = Cl); 3 (Cp′ = tert‐butylcyclopentadienyl, L = 1,3‐di‐tert‐butylimidazolin‐2‐imide, X = Cl), upon activation with methylaluminoxane (MAO) were active for the polymerization of ethylene and propylene and the copolymerization of ethylene and 1‐hexene. Catalysts derived from imidazolin‐2‐iminato tropidinyl titanium complex 4 = [(Trop)Ti(L)Cl₂] (Trop = tropidinyl, L = 1,3‐di‐tert‐butylimidazolin‐2‐imide) were much less active. Narrow polydispersities were observed for ethylene and propylene polymerization, but the copolymerization of ethylene/hexene led to bimodal molecular weight distributions. The productivity of catalysts derived from the dialkyl complex 1b activated with [Ph₃C][B(C₆F₅)₄] or B(C₆F₅)₃ were less active for ethylene/hexene copolymerization but yielded ethylene/hexene copolymers of narrower molecular weight distributions than those derived from 1a/MAO. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6064–6070, 2008