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     

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.     

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 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     

Determination of Operating Conditions of Ethylene/1-Octene Copolymerization Using Artificial Neural Network (ANN)

An artificial neural network (ANN) is applied to determine appropriate parameters in copolymerization of ethylene and 1-octene via metallocene catalytic system for producing a copolymer with desired chain microstructures. The polymerization parameters of interests are polymerization temperature, ethylene pressure, and the amount of hydrogen used. The ANN used is a feed-forward network with a back propagation learning method and has a 5-6-6-3 architecture. When comparing with both training and testing experimental data sets, it was found that ANN can provide a good guesstimation of polymerization parameters.     

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     

Estimation of Polymerization Conditions Needed to Make Ethylene/1‐olefin Copolymers with Specific Microstructures Using Artificial Neural Networks

Two artificial neural network models (forward and inverse) are developed to describe ethylene/1‐olefin copolymerization with a catalyst having two site types using training and testing datasets obtained from a polymerization kinetic model. The forward model is applied to predict the molecular weight and chemical composition distributions of the polymer from a set of polymerization conditions, such as ethylene concentration, 1‐olefin concentration, cocatalyst concentration, hydrogen concentration, and polymerization temperature. The results of the forward model agree well with those from the kinetic model. The inverse model is applied to determine the polymerization conditions to produce polymers with desired microstructures. Although the inverse model generates multiple solutions for the general case, unique solutions are obtained when one of the three key process parameters (ethylene concentration, 1‐olefin concentration, and polymerization temperature) is kept constant. The proposed model can be used as an efficient tool to design materials from a set of polymerization conditions.

     

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