LDPE Melt Research Articles

Fracture in elongational flow of two low-density polyethylene melts

Samples of two commercial low-density polyethylene melts were investigated with respect to their fracture behavior in controlled uniaxial extensional flow at constant strain rate in a filament stretching rheometer. In order to assess the possible influence of grain boundaries on fracture, the samples were prepared by three different types of pre-treatment: by compression molding of (1) virgin pellets used as received, (2) pellets homogenized in a twin-screw extruder, and (3) pellets that were milled into powder by cryogenic grinding under liquid nitrogen. The elongational stress growth data were analyzed by the Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model developed by Wagner et al. (Rheol. Acta 61, 281-298 (2022)) for long-chain branched (LCB) polymer melts. The EHMMSF model quantifies the elongational stress growth including the maximum in the elongational viscosity of LDPE melts based solely on the linear-viscoelastic relaxation spectrum and two nonlinear material parameters, the dilution modulus GD and a characteristic stretch parameter {overline{lambda}}_m. Within experimental accuracy, model predictions are in excellent agreement with the elongational stress growth data of the two LDPE melts, independent of the preparation method used. At sufficiently high strain rates, the fracture of the polymer filaments was observed and is in general accordance with the entropic fracture criterion implemented in the EHMMSF model. High-speed videography reveals that fracture is preceded by parabolic crack opening, which is characteristic for elastic fracture and which has been observed earlier in filament stretching of monodisperse polystyrene solutions. Here, for the first time, we demonstrate the appearance of a parabolic crack opening in the fracture process of polydisperse long-chain branched polyethylene melts.

Low-density polyethylene simulated production in high pressure tubular reactor

The importance of the LDPE polymerization process has spawned a slew of LDPE tubular reactor modelling and simulation projects. Through adjusting input parameters, the sensitivity study of input parameters in an industrial low density polyethylene tube reactor was addressed in this paper. This work's innovation was highlighted with the incorporation of the LDPE melt flow index in the reactor output. The highest temperature peak and monomer conversion were obtained when initiator concentration were increased by 1.06 factor, whereas the highest melt flow index was obtained when the inlet temperature was increased by 1.07 factor. The monomer flow rate, initiator flow rate, and solvent flow rate all had a substantial impact on the LDPE process performance in a tubular reactor.

An Experimental Investigation of Viscoelastic Flow in a Contraction Channel.

In order to assess the predictive capability of the S–MDCPP model, which may describe the viscoelastic behavior of the low-density polyethylene melts, a planar contraction flow benchmark problem is calculated in this investigation. A pressure-stabilized iterative fractional step algorithm based on the finite increment calculus (FIC) method is adopted to overcome oscillations of the pressure field due to the incompressibility of fluids. The discrete elastic viscous stress splitting (DEVSS) technique in combination with the streamline upwind Petrov-Galerkin (SUPG) method are employed to calculate the viscoelastic flow. The equal low-order finite elements interpolation approximations for velocity-pressure-stress variables can be applied to calculate the viscoelastic contraction flows for LDPE melts. The predicted velocities agree well with the experimental results of particle imagine velocity (PIV) method, and the pattern of principal stress difference calculated by the S-MDCPP model has good agreement with the results measured by the flow induced birefringence (FIB) device. Numerical and experimental results show that the S-MDCPP model is capable of accurately capturing the rheological behaviors of branched polymers in complex flow.

Prediction of the Viscoelastic Behavior of Low‐Density Polyethylene Produced in High‐Pressure Tubular Reactors

In the open literature, there is a lack of comprehensive predictive models that can provide detailed information on the distributed molecular properties of LDPE (e.g bivariate molecular weight‐long‐chain distribution, seniority–priority long‐chain branching distributions, etc.) produced in a high‐pressure process. To address this problem, Meimaroglou and Kiparissides (2010) developed a novel kinetic–molecular topology Monte Carlo (MC) algorithm to predict the exact molecular architecture of nonlinear polyethylene chains. In the present paper, the molecular information obtained from the kinetic–topology MC algorithm is introduced into a comprehensive rheological model, the so‐called “branch on branch” model of Das et al. (2006), to predict the rheological behavior of the LDPE melt in a high‐pressure ethylene polymerization tubular reactor. The model uses an ensemble of branched polymer chains generated by the kinetic–chain topology MC algorithm to calculate several important viscoelastic properties, including the viscosity–shear rate curve, the storage and loss moduli, etc. The predictive capabilities of the new proposed computational approach, combining the solutions of kinetic, chain topology, and rheology models, are fully assessed via a direct comparison of model predictions with available experimental measurements on the molecular weight distribution, long‐chain branching, and linear viscoelastic properties of two LDPE grades produced in industrial‐scale reactors.

Melt Strength and Extensional Viscosity of Low-Density Polyethylene and Poly(butylene succinate) Blends Using a Melt-Spinning Technique

The melt strength (MS) and extensional viscosity of low-density polyethylene/poly(butylene succinate) (LDPE/PBS) blends were measured using a melt-spinning technique to investigate the effects of extrusion conditions and mixing ratios on the extensional flow. The experimental results indicated that maximal extensional length and MS of the LDPE/PBS blends decreased with an increase of PBS content. The response of the MS to the extrusion rate depended on the components of the blends. The extensional viscosity of the LDPE/PBS blends decreased with the increases of PBS content, extrusion rate, and extensional strain rate. Extensional master curves were suitable for the LDPE/PBS blends, and the scaling factor decreased with the increase of extrusion rate according to a power law. When the PBS content was not more than 40%, with the further increase of the PBS content, the sensitivity of the scaling factor to the extrusion rate decreased. However, when the PBS content was 60%, the sensitivity of the scaling factor to the extrusion rate increased, and was close to the sensitivity of the LDPE melt. Based on the extensional master curve and the back propagation (BP) neural network model, predicted extensional viscosities were compared with the experimental results.

Modelling of stress and strain amplification effects in filled polymer melts

When hard filler particles are added to a polymer melt, it is usually assumed that its zero-shear viscosity and therefore the stress increase according to Einstein’s or a similar formula. In some papers one finds an alternative approach in which the local strain field is increased according to these formulas. Although both approaches provide the same increase of the shear stress in the linear limit, it can be shown that the second approach violates the energy conservation law as the macroscopic and microscopic dissipated energies are not equal anymore. In this contribution we propose a new stress and strain amplification approach in which both the stress and strain tensors are modified to describe the behavior of filled polymer melts in the non-linear shearing regime. The new approach is tested using two relatively simple constitutive models: the Wagner model [1] and the original Doi–Edwards model [2]. This combined approach enables us to explain, for example, the peculiar behavior of the overshoot peak observed recently in filled LDPE melts [3].

Rheological characterizations and extrudate swell predictions of an LDPE melt by two KBKZ-type constitutive equations

The shear viscoelastic properties of an LDPE (1I2A-1) melt at 160°C were described by using two KBKZ integral type constitutive equations, i.e. Wagner model and the three- parameter rational type model. The present characterizations were compared with the previous calculations by using PSM model. The results show that there are differences between the descriptions on the stress relaxation property in step strain and the first normal stress difference for the three models, and however, all the three models show the almost same predictions on the shear-thinning viscosity of the ldpe melt. Both Wagner model and PSM model are good choice in describing the rheological properties of the melt due to theirs simplicity. The Tanner theory combined with the Wagner model or the three-parameter rational type model was used to predict the swell ratio of the LDPE melt through a long capillary die, which was also compared with the experimental results and the previous calculations on swell. The predictions by Tanner theory combined with the three different constitutive models on the swell ratio of the LDPE melt are similar, which are apparently lower than the experiments and numerical simulations over the whole experimental shear rate range. The results further indicate that Tanner theory cannot predict the swell ratio of the LDPE melt precisely.

A numerical study of constitutive models endowed with Pom-Pom molecular attributes

The branched polymer melts are modeled respectively in this investigation by the existing XPP and PTT–XPP models, along with the proposed S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model developed on the basis of the existing MDCPP model. A pressure stabilized mass equation is formulated with the finite increment calculus (FIC) process to restrain and further eliminate spurious oscillations of pressure field due to the incompressibility of fluids. The discrete elastic viscous stress splitting (DEVSS) technique is employed, in order to retain an elliptic contribution in the weak form of the momentum equation. An inconsistent streamline-upwind (SU) method is applied to spatially discretize the constitutive equations. The mass, momentum conservation and constitutive equations are discretized and solved by the iterative stabilized fractional step algorithm along with the Crank–Nicolson implicit difference scheme. Thus the finite elements with equal low-order interpolation approximations for velocity–pressure–stress variables can be devised to numerically simulate the viscoelastic contraction flows for branched LDPE melts. The influences of the three viscoelastic constitutive models and the branched arms at the end of the Pom-Pom molecule on the rheological behaviors occurring in this complex flow are discussed. The numerical results demonstrate that the proposed S-MDCPP model is capable of reproducing some properties similar to those predicted by the XPP model in high shear flow and, on the other hand, reproducing some properties similar to those predicted by the PTT–XPP model in high elongational flow. Furthermore, the proposed S-MDCPP model is capable of well identifying the macromolecule topological structures of branched polymer melts.

Numerical simulation of contraction and expansion flows of Langmuir monolayers

Langmuir monolayers consist of amphiphilic molecules at the air–water interface and can be modeled as two-dimensional fluids. Earlier experiments [D.J. Olson, G.G. Fuller, J. Non-Newtonian Fluid Mech. 89 (2000) 187–207] on 4:1 contraction and 4:1 expansion flows have been simulated using an integral constitutive equation of the K-BKZ type, suitably modified to account for strain-thickening in the planar extensional viscosity. The model has been used to fit linear viscoelastic data ( G′ and G″) and the shear viscosity ( η S ), while the amount of strain-hardening is assumed, due to lack of experimental data. The simulations are in good agreement with the experiments on Newtonian monolayers, which show no vortices in the contraction but large inertial vortices in the expansion. For the viscoelastic monolayer (a poly-octadecyl methacrylate or PODMA), the opposite is true. The contraction flow shows vortices, while in the expansion flow the vortex activity is substantially reduced compared with the Newtonian one. The viscoelastic behavior is well captured by the model, provided that substantial strain-thickening is exhibited by the monolayer in planar extension. The latter behavior is very much like that for a branched LDPE melt, which also shows big vortices due to strain-hardening in planar as well as in uniaxial extension.

Imaging and analysis of wave type interfacial instability in the coextrusion of low-density polyethylene melts

This report covers experimental studies and numerical modelling of interfacial instability in the bi-layer coextrusion flow of two low-density polyethylene melts. Melt streams are converged at an angle of 30° to a common die land. Melt stream confluence was observed in two coextrusion die arrangements. In one die design, which we term ‘bifurcated’ the melt stream is split by a divider plate in the die after being delivered from a single extruder. In the other design melt streams are delivered to a die from two separate extruders. In each die design melt flow in the confluent region and die land to the die exit was observed through side windows of a visualization cell. Velocity ratios of the two melt streams were varied and layer thickness ratios producing wave type interfacial instability determined for each melt for a variety of flow conditions. Stress and velocity fields in the coextrusion arrangements were quantified using stress birefringence and particle image velocimetry techniques. Wave type interfacial instability occurred in the processing of the low-density polyethylene melts at specific, repeatable, stream layer ratios. The birefringent pattern in the confluence region and the beginning of the die land appeared stable even when the extrudate exhibited instability. However, disturbances were observed in the flow field near the exit of the die land. The study demonstrates conclusively it is possible for interfacial instability to occur in the coextrusion of the same melt. The study also shows that wave type interfacial instability in the coextrusion process is not caused by process perturbations of extruder screw rotation. Increased melt elasticity appears to promote this type of instability. A modified Leonov model and Flow 2000™ software was used to simulate the LDPE melt flows through these geometries. There was reasonable agreement between modelled at experimentally determined stress fields. Modelling however provided far more detailed stress gradient information than could be resolved from the optical techniques. A total normal stress difference (TNSD) sign criterion was used to predict the critical layer ratio for the onset of the interfacial instability in one die arrangement and good agreement between theory and experiment has been obtained.

Influence of molecular architecture and melt rheological characteristic on the optical properties of LDPE blown films

A systematic investigation on the origin of the haze of LDPE blown films was conducted, aiming to correlate the film haze with the molecular architecture and melt rheological properties. First of all, the haze measurement indicated that the surface haze, rather than the bulk haze, is the dominating factor for the total haze of the investigated films. No spherulitic crystals or other superstructures were observed for the LDPE blown films, implying that the crystallites formed in the film-blowing process are too small to be responsible for the optical haze. Rheological study revealed that the surface roughness was originated from the irregular flow of LDPE melt during the extrusion process. NMR, GPC and parallel-plate rheology were applied to study the molecular architecture of the LDPE resins. It was found that the LDPE sample with higher haze value exhibits distinctly larger portion of higher molecular weight component, broader molar mass distribution, significantly higher side chain branch density.

Measurements of first and second normal stress differences in a polymer melt

A study of the first and second normal stress differences was made in order to determine the properties for an LDPE melt at high shear rates. Time dependent measurements of N 1 and N 2 were carried out using cone/plate and plate/plate rheometry, in order to extend the shear rate for rotational rheometry up to 120 s −1. Measurements utilizing the pressure hole method extended the shear rate range to approximately 1000 s −1. For N 1 there is an overlap in the data, that is within the experimental error, for N 2 the data is inconsistent in behaviour. Both N 1 and N 2 initially demonstrated a power law behaviour, but converged to a plateau at high shear rates. This behaviour is believed to be a true response of an oriented polymer network and not slip.

Thixotropy-loop tests by using upper convected differential Maxwell-type model with kinetic theory

The thixotropy-loop tests of a LDPE (PE-FSB-23D022/Q200) melt were described in the present paper by using the simplified Acierno-type constitutive equation, which was formed by a modified upper convected Maxwell model and a kinetic equation. The simplified Acierno model is a single-mode equation and only contains three parameters. The descriptions of the simplified Acierno model show partial agreements with the triangular-form thixotropy loop tests of the LDPE melt, in which the calculations of the model show agreement with the tests experiencing short- and medium-time shearing, but show some deviation with the experiment experiencing long-time shearing. The simplified Acierno model can reflect some typical viscoelastic properties of the melt.

Exploring the utility of an axisymmetric semi-hyperbolic die for determining the transient uniaxial elongation viscosity of polymer melts

The estimation of elongation viscosity of polymeric fluids from pressure drop measurements across converging dies remains an attractive method due to its cost effectiveness. However, the elongation viscosity so measured can be contaminated by large shear effects at the walls unless specific stress boundary conditions can be imposed. Such experiments are in general difficult to perform. In this work we examine an alternative simpler method that relies on a combination of experimental pressure drop measurements in semi-hyperbolic dies and matching viscoelastic CFD simulations to obtain the transient elongation viscosity data. The calculations of the transient uniaxial elongation viscosity from this methodology for an LDPE melt are compared with data obtained using extensional rheometers in order to explore the utility of the strategy.

Analysis of the rheotens experiment with viscoelastic constitutive equations for probing extensional rheology of polymer melts

A model for the rheotens experiment is proposed to probe extensional rheology of polymer melts relevant to fabrication. The philosophy of the model is the coupling of the filament transport phenomena equations with kinetic theory constitutive equations of the differential type. A modified Giesekus (MG) constitutive equation seems to outperform other constitutive equations of the kinetic theory type, such as original Giesekus (OG) and finitely extensible non-linear elastic (FENE)-like, in terms of fitting and predictive capability of force rheotens curves at different process conditions for (i) substantially linear homogeneously branched polymers (AFFINITY™ polyolefin plastomers), (ii) linear low density polyethylene (LLDPE) (ASPUN™ fiber grade resins) and (iii) dow LDPE melts, with a variety of melt indexes and polydispersities (Mw∕Mn). The model is a useful tool for estimation of an apparent elongational viscosity versus strain rate curve from raw rheotens data. It predicts a dominating extension thinnin...

Polymer Melt Flow Through Capillary with an Additional Vibration Component

The dynamic shear flow of a polymer melt in a capillary was analyzed deeply based on a novel rheological measuring apparatus which has an additional sinusoidal vibration component, then the rheological model of polymer melt under the action of vibration was set up. Through measuring and analyzing the instantaneous rheological data of a LDPE melt, including the capillary entry pressure, the volume flow rate and their phase-difference under a preset frequency and amplitude of vibration, the capillary pressure drop and the apparent viscosity of LDPE melt within a capillary were obtained. It was discovered that the capillary pressure drop and the apparent viscosity of LDPE melt under various amplitudes and frequencies of vibration emerge a tendency of nonlinear change; compared with the stable state extrusion, the capillary pressure drop and the apparent viscosity of LDPE melt decrease after introducing a sinusoidal vibration.

Time-dependent Viscoelastic Behavior of an LDPE Melt

Two differential constitutive equations, i.e. Giesekus model and Johnson–Segalman model were employed here to predict the time-dependent viscoelastic behavior of an LDPE melt in thixotropy-loop experiments and step shear rate experiment. Multiple relaxation modes were adopted, and the parameters used to describe the nonlinear viscoelasticity in the two models were obtained by fitting the shear-thinning viscosity. The predictions on those transient shear characteristics by the two models are found in qualitative agreement with our previous experiments. Johnson– Segalman model predicts oscillation behavior in the thixotropy-loop and step shear rate experiments, whereas Giesekus model does not. Both models predict higher shear stresses than the experimental data in the case of long time shearing, implying that both models are not able to completely characterize the time-dependent shear stress of the melt at high shear rate.

On the predictive/fitting capabilities of the advanced differential constitutive equations for branched LDPE melts

Predictive/fitting capabilities of the XPP, PTT–XPP and modified Leonov constitutive equations are compared in both steady as well as transient shear and uniaxial elongational flows using two, highly branched LDPE materials (Escorene LD165BW1 and Bralen RB0323). It has been found that even if all three tested models exhibit very good fitting capability for steady uniaxial extensional viscosity curve, their predicting capabilities may differ significantly for shear viscosity as well as first and second normal stress coefficients.

Elastic Behavior Analysis of Polymer Melt Extruding through Capillary with An Additional Sinusoidal Vibration

A novel rheological measuring apparatus was designed by the authors, which introduced an additional sinusoidal vibration in parallel on the extruding direction of polymer melt and was called as Constant Velocity Dynamic Capillary Rheometer in this article. After introducing different melt extrusion speeds and different intensities of vibration, the rheological measuring experiments for a LDPE melt were done respectively by using above-mentioned apparatus, and a mathematical model for the primary normal stress difference of polymer melt under the action of vibration was set up accordingly. Then, the change laws of die swell ratio and those of the primary normal stress difference under different frequencies and amplitudes of vibration were obtained. Compared with the stable state extrusion, after introducing an additional sinusoidal vibration, the die swell ratio and the primary normal stress difference of polymer melt are all decreased obviously.

The characterization of the time-dependent nonlinear viscoelastic of an LDPE melt using a simple thixotropy model

A new simple thixotropy model was proposed in the present paper to characterize the thixotropy-loop experiments and the start-up experiment of an LDPE (PE-FSB-23D022/Q200) melt. The thixotropy model is a combination of a viscoelastic-component and a postulated kinetics process of structure change, which is constituted in terms of the indirect microstructural approach usually adopted in the characterization of thixotropy. The descriptions of the thixotropy model on both the thixotropy-loop tests and the start-up test show good agreement with the experimental values, indicating the good capability of the model in characterizing the time-dependent nonlinear viscoelastic. The stress overshoot phenomenon and the stress relaxation after cessation of the thixotropy loop test can be described well by the model, whereas both of the typical viscoelastic phenomena could not be described in our previous work with a variant Huang model.