Long chain branched impact copolymer of polypropylene: Microstructure and rheology

A biphasic impact copolymer of polypropylene (ICP) was modified with peroxide by reactive extrusion process resulting in reduced melt flow index, improved melt strength, and higher die swell. The polymers were for the first time subjected to systematic rheological and microstructural characterization in an effort to understand their structure‐property relations. In shear rheological tests, the modified ICP displayed higher flow activation energy, reduced values of loss tangent and nearly equal frequency dependence of storage and loss modulli. The modified ICP also showed strain hardening behaviour in uniaxial extensional rheology and higher crystallization temperature in differential scanning calorimetry (DSC). All these are definitive indications of the presence of long chain branches (LCB). Fitting the rheological data of modified ICPs with the eXtended Pom Pom (XPP) model indicated the presence of LCB on the higher molecular weight fraction in the polymer, a result which was corroborated with multi‐detector high temperature gel permeation chromatography (HT‐GPC). More importantly, the matrix and rubber phases of the ICP were separately characterized for presence of long chain branching by rheology, DSC and HT‐GPC. The results indicate that while LCB existed in the matrix phase, microgels were present in both phases indicating that the reaction with peroxide occurred in both phases. POLYM. ENG. SCI., 55:1463–1474, 2015. © 2014 Society of Plastics Engineers     

System identification and modeling of viscoelastic behavior from capillary melt rheological data

An investigation was conducted to identify and characterize the relaxation spectrum of polymer melts from transient capillary rheological data. System identification techniques using an iterative prediction‐error minimization (PEM) method were applied to isolate the viscoelastic melt response from the apparatus dynamics. Parameters for linear time invariant (LTI) models of varying complexity were estimated using capillary rheology data across a range of temperatures and shear rates using the principle of time‐temperature superposition. Melt capillary rheology data for polystyrene was found to exhibit viscoleastic behavior. Subsequently, three viscoelastic constitutive models were then implemented and their model coefficients directly fit using optimization techniques. The implemented methods provided useful relaxation behavior from melt capillary rheology data while also explaining much of the residual error in the purely viscous response as traditionally fit to the Cross‐WLF model. POLYM. ENG. SCI., 54:2824–2838, 2014. © 2014 Society of Plastics Engineers     

Using multiple‐mode models for fitting and predicting the rheological properties of polymeric melts. II. Single and double step‐strain flows

Several classes of multiple‐mode rheological constitutive equations are examined for predicting the viscoelastic flow properties of a typical polymer melt in single and double step‐strain flows. The phenomenological parameters appearing in these models have been obtained by the fitting of experimental data taken in small‐amplitude oscillatory shear and steady shear flows. The performance of the models for predicting the experimental data in the step‐strain experiments is examined in detail. Specifically, we examine whether or not mode coupling is necessary to describe the experimental behavior under step‐strain flows. Furthermore, it is demonstrated that the reversing double step‐strain experiment is a very powerful tool for testing viscoelastic constitutive equations. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Extrusion film casting of long chain branched polypropylene

Extrusion film casting (EFC) is an important melt processing operation which is extensively used to make polypropylene (PP) films. Linear PP shows significant amount of necking and draw resonance during EFC. One of the ways to reduce necking is to introduce long chain branches (LCB) on the polymer backbone. The long branches impart extensional strain hardening behavior thereby stabilizing the melt flow. In this work, we investigate the influence of long chain branching in polypropylene on the extent of necking in the EFC process. Laboratory scale EFC experiments were performed on homopolymer PP of linear and long chain branched architectures. Simulations of the EFC process were carried out using the one‐dimensional flow model of Silagy et al., Polym. Eng. Sci., 36 , 2614 (1996) into which we incorporate two different multi‐mode molecular constitutive equations namely, the ‘eXtended Pom‐Pom’ equation (XPP, for long chain branched PP) and the ‘Rolie‐Poly’ equation (RP‐S, for linear PP). Our experimental data confirm that presence of long chain branching in PP reduces the extent of necking and our numerical predictions show qualitative agreement with experimental data, thereby elucidating the role of chain architecture on the extent of necking. POLYM. ENG. SCI., 55:1977–1987, 2015. © 2014 Society of Plastics Engineers     

Peroxide induced cross‐linking by reactive melt processing of two biopolyesters: Poly(3‐hydroxybutyrate) and poly(l‐lactic acid) to improve their melting processability

Poly(3‐hydroxybutyrate) (PHB) and poly(l ‐lactic acid) (PLLA) were individually cross‐linked with dicumyl peroxide (DCP) (0.25–1 wt %) by reactive melt processing. The cross‐linked structures of the polymer gel were investigated by nuclear magnetic resonance (NMR) and Fourier transform infrared (FTIR) spectroscopies. The size of the polymer crystal spherulites, glass transition temperature (T_g), melting transition temperature (T_m), and crystallinity were all decreased as a result of cross‐linking. Cross‐linking density (ν_e) was shown to increase with DCP concentration. Based on parallel plate rheological study (dynamic and steady shear), elastic and viscous modulus (G″ and G′), complex viscosity (η^*) and steady shear viscosity (η) were all shown to increase with cross‐linking. Cross‐linked PHB and PLLA showed broader molar mass distribution and formation of long chain branching (LCB) as estimated by RheoMWD. Improvements in melt strength offer bioplastic processors improved material properties and processing options, such as foaming and thermoforming, for new applications. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41724.     

Numerical simulation of viscoelastic two-phase flows using openFOAM

In this work a new solver is developed for the OpenFOAM^® CFD toolbox, which handles viscoelastic two-phase flows. A derivative of the volume-of-fluid (VoF) methodology is used to describe the interface. Established constitutive equations derived from kinetic theory, such as Oldroyd-B, Giesekus, FENE-P and FENE-CR, from network theory of concentrated solutions and melts, such as linear and exponential Phan-Thien–Tanner (PTT), and from reptation theory, such as Pom–Pom and XPP models, as well as multi-mode formulations are implemented in OpenFOAM. Validation of the numerical technique is performed by comparing detailed simulation predictions to data from several experimental studies, numerical studies and analytical models found in the literature. Two well-known viscoelastic free-surface effects, namely the Weissenberg and the Die Swell effect, are simulated. Furthermore, transient and steady-state droplet flow in shear and elongational flows is examined.     

Characterization of liquid crystalline polyester polycarbonate blends

Mechanical and rheological properties of blends of a thermotropic liquid crystalline polyester with a polycarbonate have been investigated. The blends are fibrillar in character and exhibit great hardness and toughness due to high degree of molecular orientation which develops during the melt blending and processing steps. Increases of the Young modulus by 100 percent are observed for blends containing only 10 percent of liquid crystalline polymer, LCP. Time-dependent behavior of the blends was investigated by performing solid state relaxation measurements and the relaxation modulus was also found to increase by the addition of LCP. The effect is relatively small in the glassy zone of viscoelastic response, but increases through the transition and viscous flow regions. The melt viscosity of the polycarbonate is slightly shear thinning whereas that of the unblended LCP increases rapidly with decreasing shear rate at low shear rate. This suggests the presence of yield stresses as confirmed by measurements on the Rheometics RSR in the stress sweep mode. The melt viscosity of the blends was found to be similar to that of the unblended polycarbonate, but more shear-thinning and less viscous. Preliminary results of scanning electron microscopy (SEM) and differential scanning calorimetry (DSC) are also presented.     

高弹态耐冲击聚苯乙烯本构模型分析

应用旋转流变仪开展高抗冲聚苯乙烯（PS?HI）在不同温度下的流变实验，分析常用黏性模型描述高弹态PS?HI的精度，并基于黏弹性Phan?Thien Tanner （PTT）模型建立PS?HI流动理论模型和数值算法，研究高弹态PS?HI的黏弹性特征。理论分析和实验结果表明，黏性模型中Cross模型和Carreau?Yasuda模型较好地描述了PS?HI的流变特征，而黏弹性PTT模型的精度明显高于黏性模型，显示高弹态PS?HI具有一定的弹性特征。     

Transient modeling of viscosity

Capillary and parallel plate rheological characterization was conducted for a low‐density polyethylene. In contrast with conventional rheological analysis, steady conditions were not assumed. Transient data, with time steps between 0.0001 and 0.2 s, were analyzed with a nonlinear, viscoelastic constitutive model in which the relaxation time was modeled as a function of the applied stress. The fit model explained more than 99% of the observed transient variation in the capillary and parallel plate rheometers. The model coefficients for the capillary and parallel plate were compared directly to conventional linear viscoelastic analysis of the same parallel plate data. The results indicate that the described constitutive model closely predicts the observed viscoelastic behavior of the polymer melt tested in the parallel plate rheometer. Furthermore, the results indicate that the relaxation spectrum modeled with the transient analysis of the capillary rheological data correlate closely to the results predicted by the same transient analysis of parallel plate rheological data. The conclusion is that described constitutive modeling describes the viscoelastic behavior in both capillary and parallel plate rheometers. Moreover, the analysis and results suggest that the viscoelastic behavior of the polymer melt is a significant factor during the rheological characterization and the modeling of the transient response should be taken into consideration during rheological analysis to provide high fidelity models. POLYM. ENG. SCI., 57:1110–1118, 2017. © 2017 Society of Plastics Engineers     

Pressure drop estimation for polyamide 6 flow through spinnerets and filters

The pressure drop resulting from polyamide 6 flow through industrial spinnerets and wire‐mesh filters was examined as a possible parameter for improving spinning process constancy with experimental techniques and a numerical approach. The rheological characterization of the polymer melt was performed with a capillary rheometer and a controlled‐stress rotational rheometer equipped with a high‐temperature oven cell. Measurements in a nitrogen atmosphere were carried out at different temperatures and at various moisture contents to determine the effect of the postcondensation process on the rheological properties of the polymer melt. These experiments were used to collect all basic material information necessary to fit the data with the purely viscous Cross model and the viscoelastic Kaye, Bernstein, Kearsley, Zappas (K‐BKZ) model. A spinning pilot plant (consisting of an extruder, a gear pump, a pressure sensor, and a spin beam with several spin packs installed) was used to measure pressure drop values through industrial spinnerets and through two types of filters: (1) Dutch twilled weave filters and (2) sintered filters. Pilot plant tests on filters showed that in the examined range of melt throughputs, the pressure drop increased linearly with an increase in the melt flow rate for all the filters considered. The results with respect to the spinneret geometry led to the conclusion that the numerical simulations gave satisfactory predictions even for experimental data coming from complex systems such as spinning plants, as long as extensional properties were accounted for by the model. On the contrary, pressure drop predictions obtained from the Cross model underestimated the pilot plant values by approximately 20% because of the inability of the model to consider the extensional component of the flow. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 1577–1587, 2006     

Entropically‐driven ring‐opening polymerization of cyclic butylene terephthalate: Rheology and kinetics

Cyclic butylene terephthalate oligomers (CBT) with ultra‐low melt viscosity can be polymerized into poly (butylene terephthalate) (pCBT) via entropically‐driven ring‐opening polymerization (ED‐ROP) in a short time (ranging from several seconds to 10 min) with no chemical emission and no heat generation during the polymerization process. Due to no heat generation, dynamic rheological measurements were used to monitor the polymerization of CBT from 220 to 250°C. The polymerization was accompanied by a steep increase of the melt viscosity and modulus in isothermal rheological tests, and much faster at higher temperature. With rheological results, reptation theory and Double reptation model were adopted to determine the variation of the molecular weight and concentration with time for pCBT. According to the ED‐ROP mechanism of CBT, kinetics equations were also established to simulate the polymerization process. Furthermore, using the results of variation of molecular weight with time for pCBT and kinetics equations, the polymerization rate constants for initiation and propagation steps were evaluated, and the activation energy was also obtained. It was proved that rheological method is a convenient and reliable way to investigate the kinetics of ED‐ROP of CBT. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

Effect of high molecular weight acrylic copolymers on the viscoelastic properties of engineering resins

In this work, the viscoelastic properties of acrylic‐based copolymer blends with poly(methyl methacrylate) (PMMA) and polycarbonate were investigated in the molten and solid states. High molecular weight copolymers of methyl methacrylate with butyl acrylate (MMA‐co‐BA) having varying molecular weight and composition were used to enhance the rheological properties in shear and extension. Blends containing up to 15 wt% of copolymer were prepared at 200°C and 150 rpm by using a DSM micro‐compounder. The samples were characterized by size exclusion chromatography (SEC), dynamic mechanical analysis (DMA), and rheology. The rheological properties were determined by using small amplitude oscillatory measurements (SAOM) in shear and a Rheotens? device for melt strength determination. For PMMA, the effects of high molecular weight PMMA copolymer on the matrix were related to the molecular weight, the tacticity of the copolymer, and the individual components. The rheological properties in shear showed enhanced storage and loss moduli at low frequency, while no change was observed at high frequency. In addition, extensional viscosity measurements made by using the filament stretching technique showed a significant increase in melt strength compared to that of the base PMMA with the blend containing the highest molecular weight copolymer showing the maximum force and a reduced drawdown ratio. For polycarbonate, its blends with acrylic copolymer were found to be immiscible. Similar enhancement in the moduli at low frequencies was observed, but a significant increase in the viscosity was obtained as well, resulting from the response of the two‐phase system. This change in the rheological properties was further increased at 15 wt% loading. Owing to the formation of a phase‐separated morphology, the melt strength was found to increase only slightly. J. VINYL. ADDIT. TECHNOL., 12:143–150, 2006. © 2006 Society of Plastics Engineers     

Dynamic and capillary rheology of LDPE‐EVA–based thermoplastic elastomer: Effect of silica nanofiller

The effect of pristine silica nanoparticles on the dynamic and capillary rheology of a model LDPE‐EVA thermoplastic elastomeric system is explored in this paper. The pristine silica nanoparticles were melt‐blended with the LDPE‐EVA system at 1.5, 3, and 5 wt% loadings, respectively, by varying the sequence of addition. In one of the compositions, coupling agent bis‐[3‐(triethoxysilyl)propyl] tetrasulphide (Si‐69) was used to improve the interaction of hydrophilic silica particles with polymer matrix. Results obtained reveal that the viscoelastic behavior of such composites is influenced remarkably by loadings of silica, variation of sequence, and addition of Si‐69. Upon addition of coupling agent, G′ value increases especially at higher strain levels due to increased polymer‐filler interactions. All systems with various loading of nanosilica represent an increase in elastic response with increasing frequency. Both the unfilled and filled blends exhibit rheological behavior of non‐Newtonian fluids. But interestingly, the viscoelastic response varies markedly with the temperature. The dynamic and steady shear rheological properties register a good correlation in regard to the viscous vs. elastic response of such systems. Finally, the rheological behavior is correlated with morphology of the present system processed at various shear rates. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers     

Capillary flow of low‐density polyethylene

The capillary flow of a commercial low‐density polyethylene (LDPE) melt was studied both experimentally and numerically. The excess pressure drop due to entry (Bagley correction), the compressibility, the effect of pressure on viscosity, and the possible slip effects on the capillary data analysis have been examined. Using a series of capillary dies having different diameters, D, and length‐to‐diameter L/D ratios, a full rheological characterization has been carried out, and the experimental data have been fitted both with a viscous model (Carreau‐Yasuda) and a viscoelastic one (the Kaye—Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko, or K‐BKZ/PSM model). Particular emphasis has been given on the pressure‐dependence of viscosity, with a pressure‐dependent coefficient β_p. For the viscous model, the viscosity is a function of both temperature and pressure. For the viscoelastic K‐BKZ model, the time‐temperature shifting concept has been used for the non‐isothermal calculations, while the time–pressure shifting concept has been used to shift the relaxation moduli for the pressure‐dependence effect. It was found that only the viscoelastic simulations were capable of reproducing the experimental data well, while any viscous modeling always underestimates the pressures, especially at the higher apparent shear rates and L/D ratios. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Decomposition of three-dimensional linearized equations for Maxwell and Oldroyd viscoelastic fluids and their generalizations

A new exact method of solving general three-dimensional nonstationary linearized equations for viscoelastic fluids is described based on breaking these equations down into several simpler equations. Formulas are given that make it possible to express the solution in the respective systems (consisting of four connected equations) by solving two independent equations. The most widespread rheological models of viscoelastic fluids are considered to illustrate the powerful capabilities of the proposed method. A new differential-difference model for a viscous fluid with a constant relaxation time is proposed that gives a finite disturbance propagation rate and is in good agreement with the Maxwell and Oldroyd differential models of viscoelastic fluids. The axial flows of viscoelastic fluids are studied, and solutions to certain hydrodynamic problems are given.     

Rheology of 1‐butyl‐3‐methylimidazolium chloride cellulose solutions. I. Shear rheology

In this article, shear rheology of solutions of different concentrations obtained by dissolution of cellulose in the ionic liquid (IL) solvent 1‐butyl‐3‐methylimidazolium chloride ([Bmim]Cl) was studied by measuring the complex viscosity and dynamic moduli at different temperatures. The obtained viscosity curves were compared with those of lyocell solutions and melt blowing grade polypropylene melts of different melt flow rates (MFR). Master curves were generated for complex viscosity and dynamic moduli by using Carreau and Cross viscosity models to fit experimental data. From the Arrhenius plots of the shift factors with respect to temperature, the activation energies for shear flow were determined. These varied between 18.99 and 24.09 kCal/mol, and were compared with values for lyocell solutions and different polymeric melts, such as polyolefins, polystyrene, and polycarbonate. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Linear viscoelastic and morphological description of multiphase systems affected by processing parameters

Influence of processing methods, in terms of comparing compression and injection moldings, on the rheological behavior of polycarbonate (PC)/acrylonitrile‐butadiene‐styrene (ABS) blends and PC/ABS/glass fibers composites is presented. Blend compositions and fiber content are considered as material variables. For blends, the effect of the processing route on the viscoelastic functions is evident only for low shearing frequencies. Injection molding created morphology with cocontinuous character, while compression molded blends have “relaxed” structure, where dispersed phase domains are several times larger than in injection molded ones. The glass fiber reinforcement led to the significant differences in viscoelastic properties of composites processed by injection and compression molding. Injected composites have both moduli always higher than compression molded. Also, fiber lengths are reduced more for compressing molding. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Simulations of a full three‐dimensional packing process and flow‐induced stresses in injection molding

Numerical investigations of a full three‐dimensional (3D) packing process and flow‐induced stresses are presented. The model was constructed on the basis of a 3D nonisothermal weakly compressible viscoelastic flow model combined with extended pom‐pom (XPP) constitutive and Tait state equations. A hybrid finite element method (FEM)–finite volume method (FVM) is proposed for solving this model. The momentum equations were solved by the FEM, in which a discrete elastic viscous stress split scheme was used to overcome the elastic stress instability, and an implicit scheme of iterative weakly compressible Crank–Nicolson‐based split scheme was used to avoid the Ladyshenskaya–Babu?ka–Brezzi condition. The energy and XPP equations were solved by the FVM, in which an upwind scheme was used for the strongly convection‐dominated problem of the energy equation. Subsequently, the validity of the proposed method was verified by the benchmark problem, and a full 3D packing process and flow‐induced stresses were simulated. The pressure and stresses distributions were studied in the packing process and were in agreement with the results of the literature and experiments in tendency. We particularly focused on the effects of the elasticity and pressure on the flow‐induced stresses. The numerical results show that normal stress differences decreased with incremental Weissenberg number and increased with incremental holding pressure. The research results had a certain reference value for improving the properties of products in actual production processes. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Equal Low-Order Finite Element Simulation of the Planar Contraction Flow for Branched Polymer Melts

The rheological characteristics of branched polymer melts is described by the modified XPP model, which is discretized by inconsistent streamline-upwind method. A finite increment calculus procedure is introduced to reformulate the mass equation and to overcome oscillations of the pressure field. Moreover, the governing equations are discretized and solved by the iterative fractional step algorithm. Thus the equal low-order finite elements for velocity-pressure-stress variables are adopted to calculate the planar contraction viscoelastic flows. The influences of the Weissenberg number and the amount of branched-arms on the rheological behavior of the Pom-Pom molecule are discussed. Results demonstrate good agreement with those given in the literatures.