Properties Of Polymer Melts Research Articles

Inverse parameter estimation for the white–metzner equation using extrudate diameter measurements

Abstract This study presents a method to determine the elastic modulus of the White–Metzner (WM) viscoelastic model, which is used to describe polymer melt flow. In processes involving polymeric liquids, elastic effects are essential for accurate simulations. In particular, phenomena such as melt swelling after extrusion and upon gate passage in injection molding are critical to process simulation. However, systematic procedures for material characterization remain underdeveloped since implementation of an appropriate material model is challenging due difficulties inherent in parameter determination. In this work, to account for the shear thinning behavior, which is essential when handling polymeric liquids in current processes, while also incorporating elastic properties, the WM equation was employed. The method employs the post-extrusion swelling phenomenon where the diameter of the extruded material expands after exiting the capillary die. It integrates melt swell measurements with numerical simulations based on the WM equation and highlights the importance of considering gravity in the simulation. A laser scanning microscope is used to measure the extruded diameter while adaptive multi-objective optimization identifies unknown parameters in the model to align the simulation results with the measured diameter. This approach successfully determined the elastic modulus of the PET-PEN copolymer, establishing a system for determining the viscoelastic properties of polymer melts.

Simultaneous effects of temperature and backbone length on static and dynamic properties of high-density polyethylene-1-butene copolymer melt: Equilibrium molecular dynamics approach

Abstract Temperature and chain length play significant roles in determining the physical properties of polymer melts. In the current computational research, a molecular dynamics (MD) approach was implemented to describe the static and dynamic properties of (1) high-density polyethylene-1-butene with 120 beads in backbone (PE120) and (2) entangled high-density polyethylene-1-butene with 600 beads in the backbone (PE600). The transferable potentials for phase equilibria force fields were used for CH2 beads in a defined initial condition. First, the equilibrium phase of the designed systems was reported with total energy and density convergency at various initial temperatures (T 0 = 450, 470, and 490 K). Also, gyration radius (R g) and end-to-end distance (R) were calculated for the static behavior description of the two PEs. Zero-shear viscosity (η 0), mean square displacement, and diffusion coefficient (D) were estimated to define the dynamic behavior of PE120 and PE600 systems. MD outputs predicted that 10 ns is sufficient for equilibrium phase detection inside polymeric samples. After equilibrium phase detection, R g converged to 14.97 and 17.35 Å in PE120 and PE600, respectively (T 0 = 450 K). Furthermore, MD outputs show that temperature variation can considerably affect the time evolution of the system. Numerically, the η 0 of PE120 and PE600 converged to 49 and 168 cp at 450 K. These results of η 0 parameter as a function of temperature are an important output of MD simulations. The results predicted that η 0 decreases to 24 and 44 cp for PE120 and PE600 samples with an increase in temperature from 450 to 490 K. With the creation of the entanglements network, D reached the highest value of 2 × 10−9 m2·s−1 among the designed polymeric systems. The results are in good consistency with experimental reports. It is expected that the result of this study can be used in designing improved polymeric systems for real applications.

Two-relaxation-time lattice Boltzmann model of the velocity profiles and volumetric flow rate of generalized Newtonian fluids in a single-screw extruder

Single-screw extruders and injection molding machines are essential equipment in polymer processing. It is of great importance for the optimization of operating parameters and the design of extrusion screw to predict the throughput of an extruder and the metering time of an injection molding machine according to the geometric parameters of the screw, operating parameters, and the rheological behavior of materials. Most polymer melts exhibit non-Newtonian behavior. The lattice Boltzmann method has many advantages in simulating the flow of non-Newtonian fluids. Herein, the dimensionless velocity profiles and dimensionless volumetric flow rate of generalized Newtonian fluids in a screw channel have been studied using the two-relaxation-time lattice Boltzmann method (TRT–LBM). The numerical results of power-law fluids are in good agreement with the analytical solutions, which verifies the validity of TRT–LBM. Through research, the change rule of the dimensionless volumetric flow rate of Bingham fluids with dimensionless pressure gradient has been obtained. It was found that the rheological properties of polymer melts and the dimensionless pressure gradient significantly affect the dimensionless velocity profiles and dimensionless volumetric flow rate. The dimensionless volume flow rate has some unexpected changes with the increase of the dimensionless pressure gradient. This study can provide theoretical guidance for the optimization of operating parameters and the design of extrusion screws.

Thermodynamic Insights into Variation in Thermomechanical and Physical Properties of Isotactic Polypropylene: Effect of Shear and Cooling Rates.

In order to elucidate the effect of shear and cooling process on structural, thermomechanical, and physical properties of polymer melt, excess entropy, a thermodynamic quantity is calculated from radial distribution function generated from equilibrated parts of the molecular simulation trajectories. The structural properties are calculated, which includes the density of polypropylene melt, end to end distance, radius of gyration of the polypropylene polymer chain, and monomer-monomer radial distribution function. Non-equilibrium molecular dynamics simulation was employed to investigate the role of the applied shear rate on the properties of polypropylene. Furthermore, a range of cooling rates were employed to cool the melt. Thermomechanical properties, such as Young's modulus, and physical properties, such as glass transition temperature, were determined for different cases. Results showed that slow cooling and high shear substantially improved the Young's modulus and glass transition temperature of the i-PP. Furthermore, a two-body contribution to the excess entropy was used to elucidate the structure-property relationships in the polymer melt as well as the glassy state and the dependence of shear and cooling rate on these properties. We have used the Rosenfeld excess entropy-viscosity relationship to calculate the viscous behavior of the polymer under a steady shear condition.

Influence of fly ash on thermo-mechanical and mechanical behavior of injection molded polypropylene matrix composites

Polypropylene composites find widespread application in industries, including packaging, plastic parts, automotive, textiles, and specialized devices like living hinges known for their remarkable flexibility. This study focuses on the manufacturing of polypropylene composite specimens by incorporating varying weight percentages of fly ash particles with polypropylene using a twin-screw extruder and injection molding machine. The composites were comprehensively tested, evaluating tensile, compressive, and flexural strength, solid-state and polymer melt properties, modulus, damping, and thermal response. The findings reveal that the compressive strength of polypropylene increases up to 2 wt% of added fly ash particles and subsequently exhibits a slight decline. Tensile strength demonstrates an increase up to 1 wt% of fly ash, followed by a decrease with a 2 wt% addition, and then a subsequent increase. Flexural strength shows improvement up to 3 wt% fly ash addition before declining. The storage modulus curve is categorized into three regions: the glassy region (up to 0 °C), the glass transition region (0–50 °C), and the glass transition region of polypropylene (>50 °C), each corresponding to different molecular motions. Weight loss curves exhibit similar trends, indicating uniform pyrolysis behavior attributed to consistent chemical bonds. Plastic degradation commences around 440 °C and concludes near 550 °C. Additionally, elemental mapping of fly ash composition identified various elements such as O, Si, K, Mg, Ca, Cl, Na, P, Al, Fe, S, Cu, Ti, and Ni. These findings offer valuable insights into the mechanical and thermal properties of polypropylene composites reinforced with fly ash, rendering them suitable for a wide range of industrial applications necessitating strength and durability across temperature variations.

Slip-Spring Hybrid Particle-Field Molecular Dynamics for Coarse-Graining Branched Polymer Melts: Polystyrene Melts as an Example.

The topology of chains significantly modifies the dynamical properties of polymer melts. Here, we extend a recently developed efficient simulation method, namely the slip-spring hybrid particle-field (SS-hPF) model, to study the structural and dynamical properties of branched polymer melts over large spatial-temporal scales. In the coarse-grained SS-hPF simulation of polymers, the bonded potentials are derived by iterative Boltzmann inversion from the underlying fine-grained model. The nonbonded potentials are computed from a density functional field instead of pairwise interactions used in standard molecular dynamics simulations, which increases the computational efficiency by a factor of 10-20. The entangled dynamics is lost due to the soft-core nature of density functional field interactions. It is recovered by a multichain slip-spring model that is rigorously parametrized from existing experimental or simulation data. To quantitatively predict the relaxation and diffusion of branched polymers, which are dominated by arm retraction rather than chain reptation, the slip-spring algorithm is augmented to improve the polymer dynamics near the branch point. Multiple dynamical observables, e.g., diffusion coefficients, arm relaxations, and tube survival probabilities, are characterized in an example coarse-grained model of symmetric and asymmetric star-shaped polystyrene melts. Consistent dynamical behaviors are identified and compared with theoretical predictions. With a single rescaling factor, the prediction of diffusion coefficients agrees well with the available experimental measurements. In this work, an efficient approach is provided to build chemistry-specific coarse-grained models for predicting the dynamics of branched polymers.

Equilibrium and non-equilibrium molecular dynamics approaches for the linear viscoelasticity of polymer melts

Viscoelastic properties of polymer melts are particularly challenging to compute due to the intrinsic stress fluctuations in molecular dynamics (MD). We compared equilibrium and non-equilibrium MD approaches for extracting the storage (G′) and loss moduli (G″) over a wide frequency range from a bead-spring chain model in both unentangled and entangled regimes. We found that, with properly chosen data processing and noise reduction procedures, different methods render quantitatively equivalent results. In equilibrium MD (EMD), applying the Green−Kubo relation with a multi-tau correlator method for noise filtering generates smooth stress relaxation modulus profiles from which accurate G′ and G″ can be obtained. For unentangled chains, combining the Rouse model with a short-time correction provides a convenient option that circumvents the stress fluctuation challenge altogether. For non-equilibrium MD (NEMD), we found that combining a stress pre-averaging treatment with discrete Fourier transform analysis reliably computes G′ and G″ with a much shorter simulation length than previously reported. Comparing the efficiency and statistical accuracy of these methods, we concluded that EMD is both reliable and efficient, and is suitable when the whole spectrum of linear viscoelastic properties is desired, whereas NEMD offers flexibility only when some frequency ranges are of interest.

Shear Modification of Polyolefines and its Integration in Polymer Processing

Abstract The viscous and especially the elastic properties of polymer melts can be altered by a previously imposed deformation history. This phenomenon, usually termed as shear modification, is caused by the reversible physical disentanglement of the polymer molecule chains. The shearing unit presented in this paper was used to systematically investigate the processing parameters governing shear modification. A set of rheological tests was carried out with the shear modified sample material and the expected changes in the rheological behaviour were detected. The relative change of the storage modulus G’, measured using a Rheometrics On-line Rheometer system, was taken as a measure for the degree of modification and was found to correlate with the specific energy dissipated during sample preparation. The effects of shear modification on product properties were investigated for the tubular film-blowing process. Changes in the optical and mechanical properties of films which can be attributed to the previously imposed shear modification process were found.

Dynamic Processes and Mechanisms Involved in Relaxations of Single-Chain Nano-Particle Melts.

We present a combined study by quasielastic neutron scattering (QENS), dielectric and mechanical spectroscopy, calorimetry and wide-angle X-ray diffraction on single-chain nano-particles (SCNPs), using the corresponding linear precursor chains as reference, to elucidate the impact of internal bonds involving bulky cross-links on the properties of polymer melts. Internal cross-links do not appreciably alter local properties and fast dynamics. This is the case of the average inter-molecular distances, the β-relaxation and the extent of the atomic displacements at timescales faster than some picoseconds. Contrarily, the α-relaxation is slowed down with respect to the linear precursor, as detected by DSC, dielectric spectroscopy and QENS. QENS has also resolved broader response functions and stronger deviations from Gaussian behavior in the SCNPs melt, hinting at additional heterogeneities. The rheological properties are also clearly affected by internal cross-links. We discuss these results together with those previously reported on the deuterated counterpart samples and on SCNPs obtained through a different synthesis route to discern the effect of the nature of the cross-links on the modification of the diverse properties of the melts.

Molecular configuration evolution model and simulation for polymer melts using a non-equilibrium irreversible thermodynamics method

Almost all flows of polymers are accompanied by evolution of the molecular configuration, which has a great influence on material properties. However, the existing molecular configuration evolution models are mainly limited to the configuration evolution of a single molecular chain in a dilute solution ignoring intermolecular forces; it is impossible to predict the evolution of the molecular configuration of polymer melt with a complex entanglement network. Thus, we propose a non-isothermal compressible viscoelastic molecular configuration evolution model for polymer melt using non-equilibrium irreversible thermodynamic methods. The proposed model can more accurately describe the rheological properties of polymer melts compared with the commonly used XPP model, especially at high shear rates. The predicted molecular configuration in rotary Couette flow agrees well with the measured dielectric anisotropy results. Finally, the present model and a simulation method are successfully applied to predict the evolution of polymer molecular configuration and birefringence in three-dimensional injection compression molding, and the predicted birefringence is consistent with the measured results. A typical skin-core structure, resulting from the competition of the flow field and the molecular Brownian thermal motion in the injection molding, is investigated.

Scaling Characteristics of Rotational Dynamics and Rheology of Linear Polymer Melts in Shear Flow

Rheological properties of polymer melts under weak flow reflect the orientational anisotropy of the chains, which is established experimentally as the validity of the stress-optical rule (SOR). In ...

Influence of hydrostatic pressure on rheological properties of polymer melts—A review

Rheological properties of polymer melts are significantly dependent on molecular structure and external parameters. While numerous experimental data of the dependence of the rheological behavior on stress, shear rate, and temperature are available in the literature, much less is known on the effect of hydrostatic pressure. This article reviews the knowledge about the pressure dependence of rheological properties of polymer melts. The different experimental devices for measurements under pressure are described, and the methods of determining the pressure coefficients of viscosity are critically analyzed. Very few investigations of the pressure dependence of viscoelastic properties are addressed. A comparison of the pressure coefficients of commercial polymers obtained by various authors from viscosity measurements with different methods shows the deficits in getting exact data. It can be said, however, that the pressure coefficients increase in the order of high density polyethylene, linear low-density polyethylene, low-density polyethylene, polypropylene, and polystyrene. For amorphous polymers and, particularly, for polystyrene, it is shown how the pressure coefficients decrease with growing temperature. For polyolefins, this dependency is less significant. The free volume concept is discussed with respect to an interpretation of the experimental findings. Results of using the hole fraction theory for describing the pressure dependence of viscosity are presented and critically assessed.

Modeling and simulation of weld line location and properties during injection molding based on viscoelastic constitutive equation

Weld lines are one of the typical quality issues of injection molded parts. They are unavoidable even for moderate complex products. To explore the formation of weld lines in injection molding, a flow model based on viscoelastic constitutive equation is presented in this article to predict and evaluate of weld lines location and properties, in which Rolie-Poly constitutive equation is used to describe the viscoelastic properties of polymer melts and level set method is used to capture melt front. Furthermore, the formation and evolution processes of weld lines are investigated by co-injection molding technique in simulation, since the processes are determined by the flow front and rheological history of the melt streams. Numerical results show that weld lines can be predicted accurately, and the formation and evolution processes of weld line can be shown more clearly by co-injection molding technique. In addition, properties of polymer melt such as velocity, pressure, principal stress difference, and molecular orientation in the weld line regions are investigated and presented.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts.

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius , packing length p, pair correlation function , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

Molecular Dynamics Simulations of Surface and Interfacial Tension of Graft Polymer Melts.

Understanding the surface properties of polymer melts is crucial for designing new polymeric coatings, adhesives, and composites. Here, we study the effect of molecular architecture on surface and interfacial tension of melts of graft and linear polymers by molecular dynamics simulations. In particular, we elucidate the effect of the degree of polymerization of the side chains nsc and their grafting density 1/ ng on the surface tension of the graft polymer/vacuum interface, γG, and the interfacial tension of the interface between graft and linear polymer melts, γGL. For the case of the graft polymer/vacuum interface, our simulations confirm that the surface tension is a linear function of the fraction of the backbone ends fbe and side chain ends fse, γG = γ∞ - γbe fbe - Δγ fse, where γ∞ is the surface tension of the system of graft polymers with infinite molecular weight and γbe and Δγ are surface tension contributions from backbone ends and difference between contributions coming from the side chain ends and grafting points, respectively. This dependence of the surface tension highlights the entropic origin of the surface tension corrections associated with the redistribution of the grafting points and ends at the interface. However, the interfacial tension of the interface between graft and linear polymer melts does not show any significant dependence on the molecular structure of the graft polymers, thus pointing out the dominance of enthalpic contribution to the interfacial tension.

A comparative study of thermodynamic, conformational, and structural properties of bottlebrush with star and ring polymer melts.

Thermodynamic, conformational, and structural properties of bottlebrush polymer melts are investigated with molecular dynamics simulations and compared to linear, regular star, and unknotted ring polymer melts to gauge the influence of molecular topology on polymer melt properties. We focus on the variation of the backbone chain length, the grafting density along the backbone, and the length of the side chains at different temperatures above the melt glass transition temperature. Based on these comparisons, we find that the segmental density, isothermal compressibility, and isobaric thermal expansion of bottlebrush melts are quantitatively similar to unknotted ring polymer melts and star polymer melts having a moderate number ( f = 5 to 6) of arms. These similarities extend to the mass scaling of the chain radius of gyration. Our results together indicate that the configurational properties of bottlebrush polymers in their melt state are more similar to randomly branched polymers than linear polymer chains. We also find that the average shape of bottlebrush polymers having short backbone chains with respect to the side chain length is also rather similar to the unknotted ring and moderately branched star polymers in their melt state. As a general trend, the molecular shape of bottlebrush polymers becomes more spherically symmetric when the length of the side chains has a commensurate length as the backbone chain. Finally, we calculate the partial static structure factor of the backbone segments and we find the emergence of a peak at the length scales that characterizes the average distance between the backbone chains. This peak is absent when we calculate the full static structure factor. We characterize the scaling of this peak with parameters characterizing the bottlebrush molecular architecture to aid in the experimental characterization of these molecules by neutron scattering.

Diffusion and Relaxation Dynamics of Supercooled Polymer Melts

The dynamic properties of polymer melts are investigated in the range of normal liquid regime to the supercooled liquid regime. The polymer is modeled as a coarse-grained bead-spring model with chain length ranging from 5 to 160. The mean squared displacement and non-Gaussian parameter are used to describe the self diffusion of polymer beads. We find slow dynamics with decreasing temperature and increasing chain length. The time evolution of non-Gaussian parameters shows two peaks (or one peak one shoulder) in the α-relaxation time, τα, regime and sub-diffusion time regime, respectively, where the first primary peak indicates the dynamic heterogeneity stemmed from the motion of beads, and the secondary peak is the result of correlated motion along a polymer chain. Moreover, the relaxation of polymer beads shows clear two-step decay in supercooled melts and the dynamics shows growing heterogeneity with decreasing temperature. As chain length is increased, a peak of the dynamic susceptibility occurs, and the peak height, χ*4, increases and then reaches a plateau. The curves of the height of the first peak of α2α*2, versus τα and the curves of χ*4 versus ταfollow two master curves for different chain lengths. Our results indicate the similarity of dynamic heterogeneity dominated by the motion of single bead even the chain length is different. It is interesting to find that the Stokes-Einstein (SE) relation between τα and diffusion coefficient D, D~τ −1 , is highly length-scale dependent. The SE relation breaks down in both normal melts regime and supercooled regime at large magnitude of wave vectors, attributed to the non-Brownian motion arising from the chain connectivity and growing heterogeneity due to supercooling. However, the SE relation is reconstructed when the probing length scale is large (at small magnitude of wave vectors). Our results show a hierarchical physical picture of the supercooled polymeric dynamics.

Multiscale modeling of poly(lactic acid) production: From reaction conditions to rheology of polymer melt

Poly(l-lactic acid) (PLLA) is a fully biodegradable bioplastic with promising market potential. The paper deals with systematic development and analysis of the modeling framework allowing direct mapping between PLLA production process conditions and rheological properties of the polymer melt. To achieve this, the framework builds upon three distinct elements that approach the production process from different scales: (i) macroscopic deterministic model of l,l-lactide ring opening polymerization taken from the literature, (ii) microscopic stochastic simulation of the polymerization process based on hybrid Monte Carlo approach, and (iii) mesoscopic public domain model of polymer chain reptation dynamics. Based on the input reaction conditions, the macro-scale model predicts l,l-lactide conversion and averaged molar mass of PLLA, while the micro-scale and meso-scale simulations allow prediction of full molar mass distribution and melt viscosity of the product. The developed predictive tool is validated by literature data, i.e. experimentally measured rheological characteristics of three commercial PLLA samples with different molecular architecture. Moreover, comprehensive global sensitivity analysis has been carried out to support exploration of the process conditions space in relation to target polymer melt properties. Computational efficiency of the developed model achieved so far foreshadows its potential use as soft sensor for molar mass distribution and melt viscosity in the optimization and control of PLLA production.

Monitoring and dynamic control of quality stability for injection molding process

Stability control of production is an important aspect of injection molding. However, challenges continue to exist with respect to improving product quality stability to achieve a faster forming speed and a higher automation for injection molding because the injection process is usually disturbed by several inevitable variations. The difficulty in overcoming the fore-mentioned inevitable disturbances and achieving dynamic control of product quality is related to establishing a quantitative relationship between product quality and process variables. In this study, a quality prediction model based on polymer melt properties is established to monitor product weight variation online. A pressure integral (PI) based on the prediction model is proposed as an effective process variable to predict product weight variation. Additionally, a dynamic control method is proposed to improve product quality stability. The experimental results indicate that PI presents advantages of consistency and stability in monitoring product weight variation when compared with models proposed by extant studies. The proposed control method results in a decrease in product weight variation from 0.16% to 0.02% in the case of varying mold temperature and the number of cycles to return stability decreases from 11 to 5 in with respect to variations in the melt temperature.