Long Chain Branching Distribution Research Articles

LDPE Production in Tubular Reactors: Comprehensive Model for the Prediction of the Joint Molecular Weight-Short (Long) Chain Branching Distributions

Good control on molecular properties, and as a consequence on end-use properties, is very important for low-density polyethylene (LDPE) manufacturers. However, the connection between the architecture of polymer chains and the kinetic mechanism and polymerization conditions is still a subject of study. In this work, we present a comprehensive model of the polymerization of ethylene in high-pressure tubular reactors. In addition to the usual predictions of conversion, temperature profiles, and average molecular properties, this model also provides bivariate distributions such as molecular-weight–long-chain branching distribution and molecular-weight–short-chain branching distribution of LDPE produced under different operating conditions. The 2D probability-generating function technique is applied to obtain the bivariate distributions. This is a deterministic technique that allows the calculation of the distributions without any prior assumption of their shape.

Linear viscoelastic model for elongational viscosity by control theory

Flows involving different types of chain branches have been modelled as functions of the uniaxial elongation using the recently generated constitutive model and molecular dynamics for linear viscoelasticity of polymers. Previously control theory was applied to model the relationship between the relaxation modulus, dynamic and shear viscosity, transient flow effects, power law and Cox–Merz rule related to the molecular weight distribution (MWD) by melt calibration. Temperature dependences and dimensions of statistical chain tubes were also modelled. The present study investigated the elongational viscosity. We introduced earlier the rheologically effective distribution (RED), which relates very accurately and linearly to the viscoelastic properties. The newly introduced effective strain-hardening distribution (REDH) is related to long-chain branching. This REDH is converted to real long-chain branching distribution by melt calibration and a simple relation formula. The presented procedure is very effective at characterizing long-chain branches, and also provides information on their structure and distribution. Accurate simulations of the elongational viscosities of low-density polyethylene, linear low-density polyethylene and polypropylene, and new types of MWDs are presented. Models are presented for strain-hardening that includes the monotonic increase and overshoot effects. Since the correct behaviour at large Hencky strains is still unclear, these theoretical models may aid further research and measurements.

Prediction of the molecular and polymer solution properties of LDPE in a high-pressure tubular reactor using a novel Monte Carlo approach

In the present work, a novel kinetic/topology Monte Carlo algorithm is developed for the prediction of molecular, topological and solution properties of highly branched low-density polyethylene (LDPE), produced in a high-pressure multi-zonal tubular reactor. It is shown that the combined kinetic/topology MC algorithm can provide comprehensive information regarding the distributed molecular and topological properties of LDPE (i.e., molecular weight distribution, short- and long-chain branching distributions, joint molecular weight-long chain branching distribution, branching order distribution, seniority/priority distributions, etc.) The molecular/topological results obtained from the MC algorithm are then introduced into a random-walk molecular simulator to calculate the solution properties of LDPE (i.e., the mean radius of gyration, R g , and the branching factor, g) in terms of the chain length of the branched polyethylene. The validity of the commonly applied approximation regarding the random scission of highly branched polymer chains is assessed by a direct comparison of the average molecular properties of LDPE (i.e., number and weight average molecular weights), calculated by the combined kinetic/topology MC algorithm, with the respective predictions obtained by the commonly applied method of moments (MOM). Through this comparison it is demonstrated that the ambiguous implementation of the random scission reaction in the MOM formulation can result in erroneous predictions of the weight average molecular weight and MWD of LDPE. Finally, the effects of two key process parameters, namely, the polymerization temperature profile and the solvent concentration, on the molecular, topological and polymer solution properties of LDPE produced in a multi-zonal tubular reactor are investigated.

Prediction of Bivariate Molecular Property Distributions in Free-Radical Polymerization Systems Using Monte Carlo and Sectional Grid Methods

An efficient Monte Carlo (MC) algorithm and a two-dimensional fixed pivot technique (2-D FPT) are described for the calculation of the average and distributed molecular properties of polymers in batch free-radical polymerization and copolymerization reactors. Simulations are carried out, under different reactor conditions, to calculate the individual monomer conversions, the leading moments of the 'live' and 'dead' polymer chain length distributions as well as the dynamic evolution of the distributed molecular properties (i.e., molecular weight distribution (MWD), long chain branching distribution (LCBD), copolymer composition distribution (CCD), joint LCB-MW and CC-MW distributions, etc.). The validity of the numerical calculations is examined via a direct comparison of the simulation results, obtained by the two numerical methods, with experimental data on the styrene-methyl methacrylate and vinyl acetate batch free-radical polymerization systems. Additional comparisons between the MC and the 2-D FPT methods are carried out for both polymerization systems, under different polymerization conditions. It is clearly shown that both numerical methods are capable of predicting the distributed molecular, branching and copolymer properties, with high accuracy, up to very high monomer conversions.

Molecular Topology Fractionation of Polystyrene Stars and Long Chain Branched Polyethylene Fractions

AbstractSummary: Control of long chain branching (LCB) architecture is an area of considerable interest in materials science because LCB can have a dominating effect on polymer rheology and properties. Currently no analytical technique provides a quantitative description of the LCB topologies in these materials beyond a basic estimation of the average number of branch points per molecule. Neither the molecular weight of the branch, nor the shape of the branched molecule (e. g. star, comb, “H” or other) can be determined using current state of the art methodology such as size exclusion chromatography (SEC) with molecular weight sensitive detectors or nuclear magnetic resonance spectroscopy.In our laboratory, we have developed a fractionation method that sorts polymer solutes based on LCB topology. The approach, which we term molecular topology fractionation (MTF), utilizes a separating medium comprising channels having dimensions similar in size to the dimensions of the macromolecules being analyzed. An applied flow field provides the driving force for the separation. Although the details of the separation mechanism are not well understood at this time, two possible mechanisms are being considered. In one, dissolved solute molecules are restricted by the channels such that the relaxation modes for reorientation determine the rate of transport. In the second, pinning (or entanglement) of molecules on the stationary phase determines the rate of transport. Both mechanisms result in the largest molecules eluting latest (opposite to the sequencing in SEC), and produce significant additional retardation for LCB chains above that of linear chains. This additional retardation leads to fractionation of an LCB distribution even if the hydrodynamic radii of the components are the same.In this paper, an overview of the MTF experiment will be provided. MTF fractionation of PS stars is presented to demonstrate the separation of LCB chains from linear chains and LCB chains based on topology. The application of MTF for characterizing LCB polyolefin fractions will be shown. The paper will also include a brief discussion of the coupling of MTF and SEC in an on line two dimensional approach for determination of LCB distributions.

SEC-MALS method for the determination of long-chain branching and long-chain branching distribution in polyethylene

This paper systematically describes a LCB determination method that can quantify both LCB content and LCB distribution across the molecular weight distribution in polyethylene homopolymers as well as copolymers. Coupling size-exclusion chromatography with multi-angle light scattering (SEC-MALS), this method quantifies molecular weights (MW) and radii of gyration ( R g) simultaneously. The number of LCB per molecule and LCB frequency as a function of MW can be calculated by comparing R g of a branched polymer with that of a linear control at the same MW using the Zimm–Stockmayer approach. Because the presence of short-chain branching in copolymers results in changes in R g of the copolymers, their LCB contents cannot be obtained before the short-chain branching (SCB) effect is corrected. Using well-characterized linear PE copolymers as standards, an empirical method is successfully established in this paper to correct the SCB effect. Consequently, this method can be applied to determine LCB in PE copolymers as well. Some practical aspects, such as the selection of formalism for data processing, the LCB detection sensitivity and precision, and long-term reproducibility of this method are also discussed. Finally, examples are given to demonstrate how this method is applied to determine LCB and LCB distribution in practical PE homopolymers and copolymers.

Comparison of the melt fracture behavior of metallocene and conventional polyethylenes

The influence of sparse long-chain branching and molecular weight distribution on the melt fracture behavior of polyethylene melts was investigated. Four commercial polyethylene resins were employed for this study: a conventional low-density polyethylene, a conventional linear low-density polyethylene, a linear metallocene polyethylene, and a sparsely branched metallocene polyethylene. Rheological measurements were obtained for both shear and extensional deformations, and melt fracture experiments were carried out using a controlled rate capillary rheometer. A single capillary geometry was used to focus on the effects of material properties rather than geometric factors. For the linear polyethylenes, surface melt fracture, slip-stick fracture, and gross melt fracture were all observed. Conversely, the branched PE resins did not exhibit a slip-stick regime and the degree of gross fracture was observed to be much more severe than the linear resins. These variations can be explained by the effects that long-chain branching has on the onset of shear-thinning behavior (slip-stick fracture) and the degree of extensional strain hardening (gross melt fracture). Although there is some indication that the breadth of molecular weight distribution indirectly influences surface melt fracture, the results remain inconclusive.

Separating the effects of sparse long-chain branching on rheology from those due to molecular weight in polyethylenes

The effects of sparse (<1 branch per chain) long-chain branching (LCB), molecular weight (MW), and molecular weight distribution on the shear rheological properties of commercial polyethylenes are often convoluted. In this paper a method for separating the effects of sparse LCB in metallocene-catalyzed polyethylenes (mPE) from those of molecular weight and its distribution based on time–molecular weight superposition is proposed. Four metallocene polyethylenes with degrees of long-chain branching [i.e., M of the arm (Ma) is greater than that for the onset of entanglements, Mc] as determined from dilute solution measurements ranging from zero (linear) to 0.79 LCB/104 CH2, along with a conventional Ziegler–Natta polymerized linear low-density polyethylene (LDPE), and a tubular free-radical polymerized LDPE are investigated. In general, it is observed that sparse LCB (for levels < 1.0 LCB/104 CH2) increases the zero shear viscosity, η0 (e.g., by a factor of 7) and decreases, but even to a greater degree, the critical shear rate (γ̇c) for the onset of shear thinning (e.g., by a factor of 100). The breadth of the molecular weight distribution just affects γ̇c but not η0 for the range of data used in this study. Furthermore, the dynamic storage modulus G′ shows similar enhancement at low frequencies as viscosity does, while the primary normal stress difference coefficient, Ψ1,0, exhibits a greater dependence on long-chain branching than that predicted from the zero-shear viscosity enhancement. The results for the mPEs are consistent with recent molecular theories for randomly branched molecules in that it is the spacing between branch points and not the number of branches at a point that is important. Furthermore, the results are consistent with the idea that the branches are located on the longest chains, and hence, have the greatest effects on the longest relaxation modes.

Modeling of Chain Length and Long-Chain Branching Distributions in Free-Radical Polymerization

The effect of long-chain branching and β- scission reactions on the complete molecular weight (MW) and branching density distributions of polymer pro- duced in a well-mixed continuous reactor has been sys- ematically studied. An improved statistical description of ow branch points on a scissioning chain distribute between the two resulting polymer fragments has been developed and implemented in the PREDICI® software package, Simulations are used to illustrate that the branching density distribution does not provide a good visual ndication of average brarching in the system; appropriate averaging aeross the chair, length distribution must be performed, It is shown that chain lengths tend to the most probable distribution even in the presence of branching when scission is the principle MW-controlling mechanιsm. Furthemore, a uniform branchingdensity distribution is obtained, provided that a sufficient number of sciston events occur per chain relative to its average residence time in the reactor. Smaller amounts of scission, when combined with another MW-controlling mechanism such as transfer to solvent, can lead to the formation of chain length distributions with asymmetric or bimodal features as well as reducing the high-MW tail and polydispersity.

A comprehensive model for the calculation of molecular weight–long-chain branching distribution in free-radical polymerizations

A new method for the calculation of the joint molecular weight–long-chain branching distribution in free-radical highly branched polymerizations is developed. The method is based on the numerical fractionation of the total polymer population into a series of ‘classes’, each one representing a population of polymer chains with the same long chain branching content (e.g., linear chains, chains with one long–chain branch, etc.). Accordingly, dynamic molar balance equations are derived for the leading moments of the molecular weight distribution (MWD) of each polymer class as well as for the moments of the overall ‘live’ and ‘dead’ polymer chain distributions. A two-parameter Wesslau distribution is employed to reconstruct the MWD of each class in terms of its leading moments. The overall distribution is then calculated by the weighted sum of all class distributions. Simulation results are presented for a high-pressure ethylene continuous stirred tank reactor (CSTR) and a series of two CSTRs with or without a recycle stream. The effect of process parameters (e.g. temperature, chain transfer agent concentration and reactor residence time) on the MWD of low-density polyethylene (LDPE) is analyzed. It is shown that under typical operating conditions the calculated MWD exhibits a bimodal character in agreement with experimental measurements on MWD of LDPE produced in industrial autoclaves.

Prediction of Molecular Weight Distribution and Long-Chain Branching Distribution of Low-Density Polyethylene from a Kinetic Model

The molecular weight distribution and the long-chain branching distribution of low-density polyethylene are predicted as a function of the synthesis conditions from a kinetic model for an autoclave reactor. The model includes initiations, propagation, termination by combination and disproportionation, and chain transfer to monomer, solvent, and polymer. Recursion formulas are developed to calculate the whole distribution density functions. A numerical method for solving the model equations is proposed. Several simulations have been performed to demonstrate the method, and predictions of long-chain branching distributions of an industrial autoclave reactor are compared with laboratory measuements.

Effects of molecular weight distribution and long‐chain branching on the viscoelastic properties of high‐ and low‐density polyethylene melts

AbstractUsing the Han slit/capillary rheometer, rheological measurements were taken of several commercially available low‐ and high‐density polyethylene melts, namely, three low‐density polyethylene samples of Chemplex Corp. (CX 1005, CX 1016, and CX 3020), three low‐density polyethylene samples of U.S. Industrial Chemicals Co. (NA 205, NA 244, and NA 279), two high‐density polyethylene samples of Union Carbide Corp. (DMDJ 5140 and DMDJ 4306), and two high‐density polyethylene samples of Mitsui Petrochemical Industries, LTD. Molecular characterization of these samples was carried out by the resin suppliers. The rheological measurements included (1) entrance pressure drop, (2) exit pressure, (3) pressure gradient, (4) die swell ratio. These then permitted us to determine the shear viscosity and normal stress differences. The rheological measurements were interpreted to identify the effects of long‐chain branching and molecular weight distribution on the rheological properties of polyethylenes in the light of the existing molecular viscoelasticity theories. It was found that fluid elasticity is greater for polymers having a broader molecular weight distribution and that, for polymers having more long‐chain branching, viscosities are lower while elasticities are higher.

Gel permeation chromatography of polyethylene. II. Rapid evaluation of long-chain branching and molecular weight distribution

A comparison is made of two methods by which one may derive molecular weight distribution and degree of long-chain branching using only the measured solution viscosity of a branched polyethylene whole polymer and its GPC trace. These are (a) Drott and Mendelson method and (b) Ram and Miltz procedure. In each case, the purpose of the method is to devise a means by which one may establish a relationship between solution viscosity and molecular weight for use in conjunction with the GPC universal calibration relationship of Benoit et al. The effectiveness of these theoretical approaches is evaluated by comparison with the true D and degree of long-chain branching data obtained using our complete iterative analysis method. Such a detailed comparison using low, moderate, and highly branched resins leads to a conclusion that both the techniques provide very good MWD and branching data and, further, that they may be considered interchangeable for most resins. For highly branched resins, the Ram and Miltz method, which is slightly more sensitive to the presence of a high degree of long-chain branching, is preferred. In practice, the Drott and Mendelson method has the advantage of using less computer time and providing a direct measure of degree of long-chain branching, and thus is likely to be used most frequently.