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     

Stress relaxation behavior of starch powder‐epoxy resin composites

The purpose of the present study is to investigate the quasi‐static and the viscoelastic behavior of epoxy resin reinforced with starch powder. An increase in the elastic modulus on the order of 42% was achieved; a behavior that was predicted by the modulus prediction model (MPM). Next, the composite was subjected to flexural relaxation experiments, in order to determine the relaxation modulus, at different filler‐weight fractions and flexural deflections imposed. The viscoelastic models of the standard linear solid, the power law model and the residual property model (RPM) were applied in order to simulate/predict the stress relaxation curves. Predicted values derived from the application of the above models were compared to each‐other as well as to respective experimental findings. From the above comparison it was proved the superiority of the RPM model in predicting both the linear and the nonlinear viscoelastic response of the materials investigated. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41697.     

The coupled relaxation model for toner melt rheology

Process changes aimed at improving printer engine performance must take into consideration not only the process variables (such as nip temperature and pressure and process time t_o), but also the melt rheological variables (such as the characteristic time scale of the toner T_c). The melt rheology relevant to the electrophotographic toner fusing process is discussed. One criterion for toner quality can be conveniently measured through the Deborah number De, which is the ratio of T_c to t_o. Modification of the melt rheology by matrix polymer composition and carbon black size and concentration has previously been explored. Here, the melt rheology of toners with a range of gel content was studied using a step shear test. The coupled relaxation model was employed to fit the stress relaxation data. The viscoelastic properties were calculated from the melt data with this model. These properties were then used to estimate the strain deformation of the toner as it passes through the nip with arbitrary residence time and nip pressure as a function of gel content. This method can be used to match the toner melt properties with the processing conditions.     

The effect of molecular weight and weight distribution upon polymer melt rheology

A major objective in polymer rheology is to predict a fluid's response to a general deformation from molecular information. A method has been developed which allows one to predict the viscoelastic properties of polymer melts from a limited amount of rheological and molecular data for the polymer. The input parameters are: (a) zero-shear viscosity; (b) molecular weight distribution; (c) temperature and density; and (d) constants relating Graessley's relaxation time to the Rouse relaxation time. The technique then “simulates” a discrete relaxation spectrum using G′ and G″ data from the Rouse theory and finally requires that a continuum model of polymer viscoelasticity be fit to shear viscosity data predicted by Graessley's theory. Examples of the utility of the procedure are given to illustrate the role of molecular weight and weight distribution in determining rheological behavior.     

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     

Dichotomous behavior of polymer melts in isothermal melt spinning

Isothermal melt spinning experiments have been conducted using two polyethylene melts of low density (LDPE) and high density (HDPE) to produce steady state spinline profiles. The data revealed the threadline extensional viscosity exhibiting a contrasting picture : extension thickening behavior for LDPE and extension thinning one for HDPE. A White-Metzner model having a strain rate-dependent relaxation time was then found to be able to simulate this dichotomy in melt spinning fairly well: the fluids whose relaxation times have smaller strain rate-dependence can fit LDPE data with extension thickening extensional viscosity whereas the fluids whose relaxation times have larger strain rate-dependence can fit HDPE data with extension thinning extensional viscosity. This dichotomous nature of viscoelastic fluids is also believed to be able to explain other similar contrasting phenomena exhibited by polymer melts, such as vortex/no vortex in entry flows, cohesive/ductile fracture modes in extension, and more/less stable draw resonance than Newtonian fluids.     

Evaluation of typical rheological models fitting for polycarbonate squeeze flow

High viscous polycarbonate melt exhibits some special rheological characters different from generalized Newtonian fluid during squeezing. It is necessary to evaluate whether the typical rheological models are suitable for polycarbonate squeeze. To avoid the difficult of measuring the inner melt rheological behavior directly, this study presents a method of measuring the compressing force applied on the upper disc of the rheometer to reveal the melt rheology indirectly. The finite difference method (FDM) was employed to discretize the governing equations and constitutive equations established on cylinder coordinate system and to simulate the compressing force. The experiments were carried out under four temperatures and three compressing velocities to test the validations of Leonov, Phan‐Thien–Tanner (PTT), eXtended Pom‐Pom (XPP), and Cross Williams‐Landel‐Ferry (Cross‐WLF) models. The experimental results show the unique character of compressing force evolution as ‘steep—steady—steep—steady’ pattern. Comparison between experiments and simulations reveals that both viscoelastic and viscous models can predict the two steady regions correctly, but only viscoelastic models can simulate the steep increase and decrease of the compressing force. Among the evaluated viscoelastic models, XPP is the most suitable to describe polycarbonate melt compression flow. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42279.     

低密度聚乙烯熔体毛细管挤出的数值模拟

借助2种微分型黏弹性本构模型DCPP模型和S-MDCPP模型来描述支化高分子熔体的复杂流变行为,并采用离散的弹性黏性应力分裂方法(DEVSS)/迎风流线方法(SU)解决黏弹性流体流动过程中的对流占优问题以及缺少椭圆算子的问题,进而用基于有限增量微积分(FIC)方法的压力稳定型分步算法求解质量守恒方程、动量守恒方程,对低...     

The role of the interface in melt linear viscoelastic properties of LLDPE/LDPE blends: Effect of the molecular architecture of the matrix

The rheological properties of blends consisting of a long chain branched low‐density polyethylene (LDPE) and two linear low‐density polyethylenes (LLDPE) are studied in detail. The weight fractions of the LDPE used in the blends are 5 and 15%. The linear viscoelastic characterization is performed at different temperatures for all the blends to check thermorheological behavior and miscibility in the melt state. Blends containing metallocene LLDPE as the matrix display thermorheologically complex behavior and show evidences of immiscibility in the melt state. The linear viscoelastic response exhibits the typical additional relaxation ascribed to the form deformation mechanism of dispersed phase droplets (LDPE). The Palierne model satisfactorily describes the behavior of these blends in the whole frequency range explored. However, those blends with Ziegler‐Natta LLDPE as the matrix fulfill the time‐temperature superposition, but exhibit a broad linear viscoelastic response, further than the expected for an immiscible system with a sharp interface. The rheological analysis reveals that, in addition to the droplets form relaxation, another mechanism at lower frequencies exists. The broad linear response of the blends with the Ziegler‐Natta LLDPE can be explained by hypothesizing a strong interaction between the high molecular weight linear fraction of the LLDPE and the low molecular weight (almost linear) chains of the LDPE phase, forming a thick interface with its own viscoelastic properties. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

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     

Glass‐polymer melt hybrids. I: Viscoelastic properties of novel affordable organic‐inorganic polymer hybrids

A novel class of organic‐inorganic polymer hybrids was developed by melt‐blending up to 50 (v/v) % [about 83 (w/w) %] tin‐based polyphosphate glass (Pglass) and low‐density polyethylene (LDPE) in conventional plastics processing equipment. The liquid‐ and solid‐state rheology of the polymer hybrids was studied under oscillatory shear flow and deformation to understand the behavior of these materials and to accelerate efforts to melt process the Pglass with organic polymers. All the materials were found to be linearly viscoelastic in the range of temperature and frequencies examined and their viscoelastic functions increased with increasing Pglass concentration. The Pglass significantly enhanced the shear‐thinning characteristics of the Pglass‐LDPE hybrid, indicating the presence of nonlinear chemical and physical interactions between the hybrid components. Morphological examination of the materials by scanning electron microscopy revealed interesting evolution of microstructure of the Pglass phase from droplets (or round beads) to elongated and interpenetrating network structures as the glass concentration was increased in the Pglass‐LDPE hybrids. Melt viscosities of the materials were well described by a simple power‐law equation and a Maxwellian (Hookean) model with three relaxation times. Time‐temperature superpositioning (TTS) of the complex viscosity versus frequency data was excellent at 170°C < T < 220°C and the temperature dependencies of the shift factors conformed excellently well to predictions from an Arrhenius‐type relation, enabling calculation of the flow‐activation energies (25–285 kj/mol) for the materials. The beneficial function of the Pglass in the hybrid system was significantly enhanced by pre‐treating the glass with coupling agents prior to incorporating them into the Pglass‐LDPE hybrids.     

Opposing effects of nanoclay on viscoelastic response of reactive phenoxy/poly (trimethylene terephthalate) blends: Clay‐induced transreactions versus percolated network formation

The role of nanofillers in reactive blends, which are compatibilized via interchange/exchange reactions, in particular transesterification reactions, is still a challenge. In this study, effects of clay on viscoelastic response of reactive melt intercalated phenoxy/poly (trimethylene terephthalate) blends are investigated. Using rheological plots, it was found that at low clay contents, clay‐induced transreactions could cause an unexpectedly enhanced viscous response. But higher clay contents lead to an enhancement in elastic behavior by inducing the formation of a percolated network. The observed opposing effects of clay particles on viscoelastic response were further examined by stress relaxation analysis, which verified the enhanced viscous response at low clay contents. The effect of interaction between the silicate layers and the blend matrix is also probed by using two different organo‐modifiers. Viscoelastic behavior of samples was also studied by dynamic mechanical analysis, and the results corroborated our findings from rheological measurements. Based on loss modulus data, the improved dynamic homogeneity of nanocomposites is attributed to the enhanced transreactions and stronger hydrogen bonds between the blend components. POLYM. COMPOS., 2011. © 2010 Society of Plastics Engineers     

Polystyrene/polybutadiene blends: An analysis of the phase‐inversion region and cophase continuity and a comparison with theoretical predictions

Blends of polystyrene and polybutadiene were prepared by melt mixing. The melt rheology behavior of the blends was studied with a capillary rheometer. The morphology of the blends was examined with scanning electron microscopy. The levels of continuity and cocontinuity were studied by both morphology and dissolution techniques. The region of phase inversion was observed at 50 wt % polystyrene. Various theoretical models were applied to determine the region of cophase continuity and to locate the point of phase inversion. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 1007–1016, 2003     

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     

Role of the interface in the melt‐rheology properties of linear low‐density polyethylene/low‐density polyethylene blends: Effect of the molecular architecture of the dispersed phase

We studied the melt linear viscoelastic and elongational properties of blends consisting of a Ziegler–Natta linear low‐density polyethylene (LLDPE) and different LDPEs. The weight fraction of the LDPE used in the blends was 15%. The linear viscoelastic characterization was performed at different temperatures for all of the blends to determine the thermorheological behavior in the melt state. The blends fulfilled the time–temperature superposition but exhibited a broad linear viscoelastic response, which was further than that expected for miscible blends and even immiscible systems with a sharp interface. A rheological study of the application of the Palierne model revealed that in addition to the droplet shape relaxation, another mechanism was present at lower frequencies. We discuss the results by hypothesizing a strong interaction between the high‐molecular‐weight linear fraction of the LLDPE matrix and a fraction of molecules of the dispersed phase, which formed a thick interface with its own viscoelastic properties. A clear change in this additional mechanism was observed, depending on the dispersed minor‐phase properties, which produced an impact on the processing of the blends, and more precisely, on the values of the melt strength in the melt‐spinning experiments. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Modeling the stress‐relaxation behavior of wool fibers

The stress‐relaxation behavior of wool fibers after a pretreatment with a chemical solution is particularly important for evaluating the efficiency of the pretreatment. In this study, three viscoelastic models, including the Maxwell, two Maxwell unit, and modified two Maxwell unit models, were established first. To verify the feasibility of the models, stress‐relaxation experiments for wool fibers were performed. The wool fibers were pretreated with a sodium bisulfite solution (1 and 3%) at various temperatures (293, 298, 303, 308, 313, and 318 K). Then, the experimental values were fitted to the three models to obtain the rate constants of relaxation. The activation energy of the wool fibers was calculated with the Arrhenius equation. The results showed that the modified two Maxwell unit model provided the best fit for the experimental data of the wool fibers. The stress‐relaxation process of the wool fibers could be divided into two stages, a rapid stage followed by a slow stage. The rapid relaxation of stress was attributed to the weak bonds in the wool fibers, and the following slow relaxation stage was attributed to strong bonds. The Arrhenius equation could describe the stress‐relaxation process of the wool fibers very well. Furthermore, the activation energy decreased in the presence of sodium bisulfite. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Birefringence and interface in sequential co‐injection molding of amorphous polymers: Simulation and experiment

Modelings of the interface distribution and flow‐induced residual stresses and birefringence in the sequential co‐injection molding (CIM) of a center‐gated disk were carried out using a numerical scheme based on a hybrid finite element/finite difference/control volume method. A nonlinear viscoelastic constitutive equation and stress‐optical rule were used to model the frozen‐in flow stresses in disks. The compressibility of melts is included in modeling of the packing and cooling stages and not in the filling stage. The thermally induced residual birefringence was calculated using the linear viscoelastic and photoviscoelastic constitutive equations combined with the first‐order rate equation for volume relaxation and the master curves for the relaxation modulus and strain‐optical coefficient functions of each polymer. The influence of the processing variables including melt and mold temperatures and volume of skin melt on the birefringence and interface distribution was analyzed for multilayered PS‐PC‐PS, PS‐PMMA‐PS, and PMMA–PC–PMMA molded disks obtained by CIM. The interface distribution and residual birefringence in the molded disks were measured. The measured interface distributions and the gapwise birefringence distributions in CIM disks were found to be in a fair agreement with the predicted interface distributions and the total residual birefringence obtained by the summation of the predicted frozen‐in flow and thermal birefringence. POLYM. ENG. SCI., 55:88–106, 2015. © 2014 Society of Plastics Engineers     

Creep and stress relaxation modeling of vinyl ester nanocomposites reinforced by nanoclay and graphite platelets

This article discusses the viscoelastic behavior of a vinyl ester (Derakane 411‐350) reinforced with 1.25 and 2.5 wt % nanoclay and exfoliated graphite nanoplatelets during short‐term creep and relaxation tests with a dynamic mechanical analyzer. Linear viscoelastic models are generally composed of one or more elements such as dashpots and springs that represent the viscous and elastic properties. Stress relaxation data from the dynamic mechanical analyzer have been used to obtain the elastic parameters based on model constitutive equations. The standard linear solid model, which is a physical model, has been used for predicting the creep deformation behavior of the vinyl ester nanocomposites over a wide temperature range. Some correlations have been made with the mechanical model, such as the effect of temperature on the deformation behavior, which is well explained by the dashpot mechanism. At lower temperatures, higher creep compliance has been observed for the vinyl ester versus the nanocomposites, whereas at temperatures near the glass‐transition temperature of the vinyl ester, creep compliance in the nanocomposites is closer in magnitude to that for the vinyl ester. The creep response of the pure vinyl ester and its nanocomposites appears to be modeled reasonably well at temperatures lower than their glass‐transition temperatures. A comparison of the predictions and experimental data from the creep tests has demonstrated that this model can represent the long‐term deformation behavior of these nanoreinforced materials reasonably well. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Study of rheological behavior of calcium carbonate‐filled polypropylene in dynamic extrusion process

A novel rheological measuring apparatus was designed, which introduced an additional sinusoidal vibration in parallel on the extruding direction of melt polymer in this article. Melt rheology of polypropylene filled uncoated CaCO₃ particles in 3 and 20 %wt amounts of filler during capillary melt‐extrusion was investigated, respectively. A mathematical model of melt polymer under the action of vibration was set up. The effects of vibration parameters on rheological behaviors were studied. The apparent viscosity of filled system decreased remarkably with the increasing vibration frequency and amplitude. The apparent viscosity reached to minimum value when the vibration frequency was 8 Hz. POLYM. COMPOS., 36:630–634, 2015. © 2014 Society of Plastics Engineers