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.     

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 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     

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     

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     

Correlation of the melting behavior and copolymer composition distribution of Ziegler–Natta‐catalyst and single‐site‐catalyst polyethylene copolymers

The multimodal differential scanning calorimetry melting endotherms observed for commercial linear low‐density polyethylenes are due to broad and multimodal short‐chain‐branching distributions. Multiple peaks, observed in melting endotherms of isothermally melt‐crystallized and compositionally homogeneous polyethylene copolymers are due to intrachain heterogeneity. This intrachain heterogeneity is quantified by the distribution of ethylene sequence lengths within the chains. These compositionally homogeneous copolymers undergo a primary crystallization, which produces a population of thicker lamellae, creating a network that places severe restrictions on segment transport in subsequent secondary crystallization, which produces a population of thinner crystals. The restrictions on segment transport imposed by the initial network created by the primary crystallization of thicker lamellae severely limits the total crystallinity achieved in the random copolymers studied. The solution crystallization of such copolymers produces a continuous distribution due to more facile segment transport in a dilute solution, in contradistinction to the multimodal distribution produced in the melt crystallization. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2800–2818, 2001     

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     

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     

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     

Computer modeling of the crystallization process of single‐chain ethylene/1‐hexene copolymers from dilute solutions

Langevin molecular dynamics (LMD) simulations have been performed to understand the role of the short chain branches (SCB) on the formation of ordered domains by cooling dilute solutions of ethylene/α‐olefins copolymer models. Three different long single‐chain models (C₂₀₀₀) with 0, 5, and 10 branches each 1000 carbons were selected. These models were equilibrated at high reduced temperature (T* = 13.3) and cooling in steps of 0.45 until the final temperature (T* = 6.2) by running a total of 35 × 10⁶ LMD steps. During the cooling process, global order parameter, torsion distribution, position of the branches, and local‐bond order parameter were calculated and monitored. The peaks of crystallization for each model were calculated by differentiating the global order parameter with temperature. The T_c (crystallization temperature) decreases as the number of branches increases as has been experimentally reported. The formation of order in the copolymers is affected by the amount of the SCB in the backbone of the polymer chain. Initially, the SCB move to the folding surface. Once the SCB are located near the folding surface the order starts to grow. In all cases here shown, the C₄ branches are excluded from the ordered domains. To take into account, the influence of the branch distribution, a different branch distribution model has been considered for the two‐branched systems. The crystallization fraction (α) and the density of the amorphous and ordered fractions was defined using the local‐bond order parameter. Both magnitudes decrease as the number of branches increases. These facts fairly agree with experimental literature data. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Novel characterization of the crystalline segment distribution and its effect on the crystallization of branched polyethylene by differential scanning calorimetry

Based on a thermal segregation treatment, a novel semiquantitative method for the characterization of the crystalline segment distribution in branched polyethylene copolymers was established by the results of differential scanning calorimetry being treated with the Gibbs–Thomson equation. The method was used to describe the segment distribution of Ziegler–Natta‐catalyzed linear low‐density polyethylene (Z–N LLDPE), metallocene‐catalyzed linear low‐density polyethylene (m‐LLDPE), and a commercial linear low‐density polyethylene with a wide molecular weight distribution. The isothermal crystallization kinetics of Z–N LLDPE and m‐LLDPE were studied to assess the effect of different segment distributions. According to their molecular characteristics, the crystallization behaviors were analyzed. They indicated that the different segment distributions of the two polymers resulted in different crystallization processes, including the nucleation and growth of crystals under various crystallization conditions. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2107–2118, 2002     

Short Chain Branches Distribution Characterization of Ethylene/1-Hexene Copolymers by Using TREF + 13C-NMR and TREF + SC Methods

Summary: Short chain branches distribution (SCBD) is the key factor for high density polyethylene (HDPE) pipe materials to achieve their excellent performance for long term (50 years) applications. However, the precise SCBD characterization of these HDPE materials with relatively low content of comonomer incorporation still remained as a challenge in this field. In this work, two characterization methods, namely temperature rising elution fractionation (TREF) cross step crystallization (SC) (TREF + SC) and TREF cross ¹³C-NMR (TREF + ¹³C-NMR), have been respectively used to qualitatively and quantitatively investigate the SCBD for two HDPE pipe materials (PE-1 and PE-2 with different long term performances) with small amount of 1-hexene incorporation prepared from SiO₂-supported silyl chromate catalyst system (S-2 catalyst) during UNIPOL gas phase polymerization. The comparison of SCBD between the two samples showed that: although short chain branches of PE-2 with good performance were less than those of PE-1 with bad performance, PE-2 showed less comonomer incorporation on the low crystallinity and low molecular weight (MW) fractions keeping even higher comonomer incorporation on the high crystallinity and high MW parts compared with PE-1. This difference on the SCBD for PE-1 and PE-2 was thought to be the key factor which is responsible for their great difference on environment slow crack resistance (ESCR). Moreover, TREF + SC method further reflected the intra- and inter-molecular heterogeneities of each fraction from the two HDPE samples through the lamella thickness distribution compared with TREF + ¹³C-NMR.     

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.     

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     

Polyolefin analysis by single‐step crystallization fractionation

Temperature rising elution fractionation (TREF) fractionates polymer chains with respect to their crystallizability, independently of molecular weight effects. In order to achieve a good fractionation, TREF requires a time‐consuming polymer deposition step over an inert support before the elution step. A single‐step crystallization fractionation method has been developed recently,^1,2 Crystallization Analysis Fractionation (CRYSTAF), in which the chemical composition (or short chain branching) distribution of olefin copolymers can be measured by monitoring on‐line polymer concentration in solution at decreasing temperatures. For the present experimental investigation, a CRYSTAF‐prototype has been assembled and used to fractionate several linear low‐density polyethylene (LLDPE) samples. These results were compared to the ones measured by the commercial CRYSTAF apparatus from Polymer ChAR. Additionally, CRYSTAF results from Polymer ChAR were compared to analytical TREF results. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 539–552, 1999     

Ethylene Polymerization over Supported Titanium-Magnesium Catalysts: Heterogeneity of Active Centers and Effect of Catalyst Composition on the Molecular Mass Distribution of Polymer

New experimental approach was used for analysis of molecular weight distribution (MWD) of polymers produced over titanium-magnesium catalysts (TMC). Polymers were fractionated on to fractions with narrow MWD (polydispersity (PD) values Mw/Mn ≤ 2). Then some of these fractions were combined to get the minimal quantity of fractions with PD values close to 2 (Flory components). It was found that three fractions corresponding to three groups of active centers are sufficient for proper fitting experimental MWD curve for PE obtained over TMC with different Ti content and with different hydrogen concentration in polymerization.     

Characterization of homogeneous ethylene/1‐octene copolymers made with a single‐site catalyst. CRYSTAF analysis and calibration

The crystallizability of narrow composition, homogeneous ethylene/1‐octene copolymers made with a constrained geometry catalyst, measured by CRYSTAF, follows a straight line correlation with the amount of total comonomer incorporated. The potential use of these resins as standards to calibrate CRYSTAF and TREF techniques is discussed. Although most of the resins analyzed have a narrow chemical composition distribution, there seems to be a relation between the broadness of the distribution and molecular weight, as predicted by Stockmayer's bivariate distribution. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 89–93, 1999