Capillary study on geometrical dependence of shear viscosity of polymer melts

Geometrical dependence of viscosity of polymethylmethacrylate (PMMA) and high density polyethylene (HDPE) are studied by means of a twin‐bore capillary rheometer based on power‐law model. Contrary geometrical dependences of shear viscosity are observed for PMMA between 210 and 255°C, but similar geometrical dependences are revealed for HDPE between 190 and 260°C. The fact that wall slip can not successfully explain the irregular geometrical dependence of PMMA viscosity is found in this work. Then, pressure effect and dependence of fraction of free volume (FFV) on both pressure and temperature are proposed to be responsible for the geometrical dependence of capillary viscosity of polymers. The dependence of shear viscosity on applied pressure is first investigated based on the Barus equation. By introducing a shift factor, shear viscosity curves of PMMA measured under different pressures can be shifted onto a set of parallel plots by correcting the pressure effect and the less shear‐thinning then disappears, especially at high pressure. Meanwhile, the FFV and combining strength among molecular chains are evaluated for both samples based on molecular dynamics simulation, which implies that the irregular geometrical dependence of PMMA viscosity can not be attributed to the wall slip behavior. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2014 , 131, 39982.     

High shear strain rate rheometry of polymer melts

The rheology of a range of polymer melts has been measured at strain rates above those attained during conventional rheometry using an instrumented injection molding machine. Deviations from shear thinning behavior were observed at high rates, and previously unreported shear thickening behavior occurred for some of the polymers examined. Measured pressure and volumetric throughputs were used to calculate shear and extensional viscosity at wall shear strain rates up to 10⁷ s^?1. Parallel plate rheometry and twin bore capillary rheometry were used to provide comparative rheological data at low and medium shear strain rates, respectively. Commercial grades of polyethylene, polypropylene, polystyrene, and PMMA were studied. Measured shear viscosity was found to follow Newtonian behavior at low rates and shear thinning power law behavior at intermediate strain rates. At shear strain rates approaching or above 10⁶ s^?1, shear viscosity reached a rate‐independent plateau, and in some cases shear thickened with further increase in strain rate. A relationship between the measured high strain rate rheological behavior and molecular structure was noted, with polymers containing larger side groups reaching the rate‐independent plateau at lower strain rates than those with simpler structures. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Determination of the pressure dependence of polymer melt viscosity using a combination of oscillatory and capillary rheometer

For an accurate simulation of a high-pressure injection molding process by using the CAE software, it is important to understand the pressure sensitivity of a polymer's melt viscosity. The current work describes a method for the determination of the pressure dependence parameter D₃ of the Cross-WLF model. It uses a combined rheological technique using both dynamic and capillary rheometers. Three grades of polycarbonate homopolymers were studied in this work and their complex viscosities were measured using a dynamic shear rheometer. The dynamic data were used to obtain six out of the seven parameters of the Cross-WLF, except D₃. A capillary rheometer fitted with a counter pressure chamber was further used to characterize the pressure dependence of the zero shear viscosity and to determine the D₃ parameter. Finally, the derived parameters were validated by carrying out injection molding with a box tool and comparing the actual pressure profiles with simulation results using the Autodesk® MoldFlow® software. The validation results indicated that actual pressure profiles from the simulation were found to be less than 10% than that of injection molding. POLYM. ENG. SCI., 60:517–523, 2020. © 2019 Society of Plastics Engineers     

Measurement of pressure dependence on the shear viscosity of polymer melts

We built a rheometer which has a simple structure and can measure the pressure dependence of the viscosity consuming small amount of sample. Main part of the rheometer consists of two sample chambers connected through a slit channel in which two pressure transducers and a pressure adjusting valve are mounted. The double piston arrangement enables to use the materials over and over by the reciprocating flow of the polymer melts from one chamber to the other chamber. The viscosity of polymer melts can be measured at wide range of shear rate and pressure with only about 3 g sample. The pressure coefficients of various polymers are measured by the designed equipment. Measured values are compared to reported values and provide a good agreement.     

Geometrical dependence of viscosity of polymethylmethacrylate melt in capillary flow

The shear viscosity of polymethylmethacrylate (PMMA) melt is particularly investigated by using a twin‐bore capillary rheometer at four temperatures of 210, 225, 240, and 255°C with different capillary dies. Experimental results show that the geometrical dependence of shear viscosity is significantly dependent on melt pressure as well as melt temperature. The measured shear viscosity increases with the decrease of die diameter at lower temperatures (210 and 225°C) but decreases with the decrease of die diameter at higher temperatures (240 and 255°C). Based on the deviation of shear viscosity curves and Mooney method, negative slip velocity is obtained at low temperatures and positive slip velocity is obtained at high temperatures, respectively. Geometrical dependence and pressure sensitivity of shear viscosity as well as temperature effect are emphasized for this viscosity deviation. Moreover, shear viscosity curve at 210°C deviates from the power law model above a critical pressure and then becomes less thinning. Mechanisms of the negative slip velocity at low temperatures are explored through Doolittle viscosity model and Barus equation, in which the pressure drop is used to obtain the pressure coefficient by curve fitting. Dependence of pressure coefficient on melt temperature suggests that the pressure sensitivity of shear viscosity is significantly affected by temperature. Geometrical dependence of shear viscosity can be somewhat weakened by increasing melt temperature. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3384–3394, 2013     

Micro‐injection molding of thermoplastic polymers: Proposal of a constitutive law as function of the aspect ratios

Based on experimental measurements of the in situ conditions within polymer flow during micro‐injection molding, a new geometrical parameter is defined to predict realistic dimensions of micro‐parts (μparts). To this aim, thin‐walled parts of various aspect ratios “length/thickness” (L/h) were first molded, with two different polymers: (i) a polystyrene and (ii) a cyclo‐olefin copolymer. It is shown that pressure drops (ΔP_i), measured between the injection pressure and the various sensors present in the mold, are directly related to the square of the ratio of L/h. This approach has finally been successfully applied to the results of the literature, confirming its relevance. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45719.     

Measurement of dynamic capillary pressure and viscosity via the multi-sample micro-slit rheometer

We develop two direct methods to simultaneously measure the dynamic capillary pressure and the viscosity of fluids by application of differential forces during flow into micro-channels. In the first method, a series of external pressures is applied in conjunction with the dynamic capillary pressure and a “Bagley analysis” is applied to the flow front velocity, and in the second, we utilize differential gravitational forces. By explicitly measuring the dynamic capillary pressure, the measurement window of the recently developed multi-sample micro-slit rheometer is extended to the regime where capillary forces are significant. These measurement methods will be useful in understanding filling flows encountered in diverse areas such as microfluidics, oil recovery and biological transport.     

Measurement and numerical prediction of fiber‐reinforced thermoplastics' thermal conductivity in injection molded parts

Recent improvements in injection molding numerical simulation software have led to the possibility of computing fiber orientation in fiber reinforced materials during and at the end of the injection molding process. However, mechanical, thermal, and electrical properties of fiber reinforced materials are still largely measured experimentally. While theoretical models that consider fiber orientation for the prediction of those properties exist, estimating them numerically has not yet been practical. In the present study, two different models are used to estimate the thermal conductivity of fiber reinforced thermoplastics (FRT) using fiber orientation obtained by injection molding numerical simulation software. Experimental data were obtained by measuring fiber orientation in injection molded samples' micrographs by image processing methods. The results were then compared with the numerically obtained prediction and good agreement between numerical and experimental fiber orientation was found. Thermal conductivity for the same samples was computed by applying two different FRT thermal conductivity models using numerically obtained fiber orientation. In the case of thermal conductivity, predicted results were consistent with experimental data measurements, showing the validity of the models. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 39811.     

New extensional rheometer for elongational viscosity and flow birefringence measurements: some results on polystyrene melts

A new extensional rheometer allowing the simultaneous measurement of elongational viscosity and flow birefringence is described. Polystyrene melts have been tested at different temperatures and strain rates. It appears that the time-temperature superposition principle holds for elongational tests in the temperature range investigated, with the same shift factors as for linear shear experiments. It has been verified that the stress optical behaviour of the melts is linear for small values of the stress whereas significant deviations appear at higher stresses.     

On the non‐newtonian viscous behavior of polymer melts in terms of temperature and pressure‐dependent hole fraction

A new theoretical non‐Newtonian viscosity model is developed by taking the fractional series expansion of Eyring's shearing strain rate. A broad range of experimental rheological data of various polymer melts including polyethylenes, polypropylene, polystyrene, poly (methyl methacrylate), and polycarbonate are fitted well using the proposed model. From the model; zero shear, constant shear‐stress and constant shear‐rate viscosities are derived as a linear function of viscosity related quantity, Y_h, called “thermo‐occupancy function” and their coefficients are discussed in detail. The thermo‐occupancy function is expressed in terms of temperature and structural vacancies such as hole fraction computed from the Simha‐Somcynsky Hole Theory (SS). In addition, the derivative of the logarithm of viscosities with respect to the hole fraction, named as viscoholibility, is observed decreases with the increasing hole fraction. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40540.     

FEM calculations of capillary rheometer flow for carbon‐filled liquid crystal polymer composites

There is an emerging market for conductive resins for use in fuel cell bipolar plates. This research focuses on developing a finite element model of a capillary rheometer. Comsol Multiphysics 3.2b was used to model the flow of a remeltable thermoplastic matrix material, Vectra A950RX Liquid Crystal Polymer, with varying amounts of either a carbon black or synthetic graphite filler, to obtain the velocity profile and pressure drop of these composites within the capillary. Previous experimental results have shown that the molten composites obey a shear‐thinning power law behavior. When comparing the model predicted pressure drops from the model with the experimental data, very good agreement was obtained. This signifies that the rheological behavior of the composites can be described by a power law relationship, using parameters specific to each composite. When comparing the modeled velocity profile with the theoretical profile, it was found for all composite formulations that the velocity becomes fully developed within a length of 0.05 times the diameter of the tube, independent of the power law parameters n and m. This work is a necessary first step in developing 2D or 3D mold filling simulations for fuel cell bipolar plate applications. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Comparison of relative viscosity measurement of polyvinylpyrrolidone in water by glass capillary viscometer and differential dual‐capillary viscometer

The relative viscosity (RV) of polyvinylpyrrolidone (PVP) with different molecular weights was measured with a glass capillary viscometer and with a differential dual‐capillary viscometer in water at different concentrations. For the differential dual‐capillary viscometer, RV increases with a decreasing flow rate, especially for high molecular weight PVP at a 1% concentration. A good agreement in the RV between the two methods can be obtained for PVP with different molecular weights and at various concentrations if an appropriate flow rate is selected for the differential dual‐capillary viscometer. Special precaution is needed when using the differential dual‐capillary viscometer to measure the viscosity of a pure solvent. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 1312–1315, 2002     

Rheological behavior of polymer melts with natural fibers

Flow behavior of polymer liquids filled with short fibers (particulate fillers) was theoretically analyzed from the point of view of the free volume theory. Assuming that the filler addition changes the occupied volume, while the temperature variations cause mainly the free volume changes, a general expression describing the viscosity of the system as a function of the filter content, temperature variations, and rheological properties of the pure polymer liquid was derived. If the viscosity curve of the unfilled polymer is described by the Carreau equation, the corresponding viscosity curve of the filled polymer is also represented by an equation of Carreau type. However, this equation has other values of Newtonian viscosity and the power exponent in comparison with the initial equation. Both parameters depend on the filler content and temperature. The derived equation predicts a viscosity rise and a stronger non‐Newtonian behavior of the system with increasing filler content. The temperature rise exerts an opposite effect on the rheological behavior. The theoretical predictions are in good accordance with viscosity measurements for low‐density polyethylene and polystyrene melts filled with short cotton, flax, and hemp fibers. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1401–1409, 2005     

Shear viscosity,extensional viscosity,and die swell of polypropylene in capillary flow with pressure dependency

The shear and extensional viscosities of a polypropylene resin were studied using a capillary rheometer and capillary dies of 1‐mm diameter and length of 10, 20, and 30 mm. Melt temperatures at 190, 205, and 220°C and shear rates between 100 and 5000 s^?1 were used. At the highest shear rate a visible melt fracture was observed. An equation relating the pressure drop and die length was derived with consideration of pressure effects on melt viscosities and the end effect. After the correction for pressure effects the true wall shear stress and end effect at zero pressure were calculated. The end effect showed a critical stress of melt fracture around 10⁵ Pa, and increased rapidly when shear stress increased above the critical stress. From shear stress the shear viscosity was calculated, and a power law behavior was observed. Extensional viscosity was calculated from the end effect and showed a decreasing trend when strain rate increased. After time–temperature superposition shift shear viscosity data correlated well, but an upward trend was observed in extensional viscosity when melt fracture occurred. Die swell ratio at different temperatures can be plotted as a function of wall shear stress and was higher for shorter dies. © 2002 Wiley Perioodicals, Inc. J Appl Polym Sci 84: 1269–1276, 2002; DOI 10.1002/app.10466     

Impact of injection‐molding processing parameters on the electrical,mechanical, and thermal properties of thermoplastic/carbon nanotube nanocomposites

Thermoplastic nanocomposites, based on high‐density polyethylene, polyamide 6, polyamide 66, poly(butylene terephthalate), or polycarbonate and containing multiwalled carbon nanotubes (CNTs), were compounded with either neat CNTs or commercial CNT master batches and injection‐molded for the evaluation of their electrical, mechanical, and thermal properties. The nanocomposites reached a percolation threshold within CNT concentrations of 2–5 wt %; however, the mechanical properties of the host polymers were affected. For some nanocomposites, better properties were achieved with neat CNTs, whereas for others, master batches were better. Then, polycarbonate and poly(butylene terephthalate), both with a CNT concentration of 3 wt %, were injection‐molded with a screening design of experiments (DOE) to evaluate the effects of the processing parameters on the properties of the nanocomposites. Although only a 10‐run screening DOE was performed, such effects were clearly observed. The volume resistivity was significantly dependent on the working temperature and varied up to 4 orders of magnitude. Other properties were also dependent on the processing parameters, albeit in a less pronounced fashion. Transmission electron microscopy indicated that conductive samples formed a percolation network, whereas nonconductive samples did not. In conclusion, injection‐molding parameters have a significant impact on the properties of polymer/CNT nanocomposites, and these parameters should be optimized to yield the best results. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Short‐term flexural creep behavior and model analysis of a glass‐fiber‐reinforced thermoplastic composite leaf spring

Present work investigated the short‐term flexural creep performance of fiber reinforced thermoplastic injection molded leaf springs. Unreinforced polypropylene, 20 wt % short and 20 wt % long glass fiber reinforced polypropylene materials were injection‐molded into constant thickness varying width mono leaf spring. Short‐term flexural creep tests were performed on molded leaf springs at various stress levels with the aid of in‐house developed fixture integrated with the servo‐hydraulic fatigue machine. Spring rate reduction is reported as an index for the accumulated damage. Experimental creep performance of molded leaf springs for 2 h was utilized to predict the creep performance with the aid of four parameter HRZ model and compared with 24‐h experimental creep data. Test results revealed that HRZ model is sufficient enough to predict short‐time flexural creep performance of engineering products over wide range of stress. Test results also confirmed the suitability of long fiber reinforced thermoplastic material for creep application over other considered materials. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Measurement of the rheological properties of polymer melts with annular rheometer

An annular die has been designed having a very thin gap distance between two coaxial cylinders. The die was then used to measure wall normal stresses along the longitudinal direction of polymer melts flowing through the thin annulus. The materials investigated were high-density polyethylene, low-density polyethylene, polypropylene, and polystyrene. Also investigated were blends of polystyrene and polypropylene, and blends of polystyrene and high-density polyethylene The measurements of wall normal stresses were used to determine the rheological properties of the melts, namely, the melt viscosity from the slope of axial wall normal stress profiles and the melt elasticity from exit pressures. The interpretation of the experimental data was made possible by the fact that the narrow-gap annular die can be considered as a substitute for a thin slit die. It has been found that the results obtained in the present study are consistent with those reported earlier by the author, who at that time used both capillary and slit dies.     

A multiscale simulation of polymer processing using parameter-based bridging in melt rheology

To investigate the effect of molecular structure on macroscopic flow behavior of polymeric liquid, attempts have been made to embed the microscopic information into the flow simulation. Constitutive equation based on the theory of polymer dynamics is ideal but the theory is still under development. The CONNFFESSIT approach (where microscopic simulation is embedded into calculation grid in macroscopic simulation) is another promising direction but the computational cost is not practical yet. In this study, we propose another simple method using parameter-based bridging where the parameters for phenomenological constitutive equations in macroscopic flow simulation are obtained from coarse-grained molecular simulation. As an example, we performed a simulation of injection molding and examined the effect of molecular weight on warpage of the molded product. We used the primitive chain network simulation to calculate linear viscoelasticity of linear monodispersed polystyrenes from molecular weight. The obtained linear viscoelasticity was converted into the relaxation spectrum and into the flow curve to be used in the macroscopic simulations. From the flow curve, the parameters of an inelastic non-Newtonian constitutive equation were obtained and used for the simulation of filling process. The relaxation spectrum was used to calculate residual stress from the flow profile in the filling process. From the residual stress and thermal shrinkage, warpage of the product was obtained. For the examined thin plate product, significant change in the warpage direction was demonstrated according to the molecular weight of the material. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

New method for evaluating adhesive property of fabrics and TPU: The rigid‐body pendulum rheometer approach

Coating and laminating processes play an important role in textile industry. They are frequently used to produce fabric laminates during which the physical properties and appearance of textile fabrics are modified and enhanced. Currently, the adhesive property testing of a fabric laminate is done so by the use of pulling test machines such as Universal Tensile Tester, which measures the strength required to peel the tested materials apart. The adhesive test to date has not yet been performed using a newly developed machine, Rigid‐Body Pendulum Rheometer (RPR). This study was to establish a more effective method for fast‐evaluating adhesive properties of fabric laminates by assessing the performance of RPR. Specifically, RPR and Universal Tensile Tester were used to measure, respectively, the viscosity and peeling strength of PET/TPU (thermoplastic polyurethane) and nylon/TPU in response to UV exposure and water immersion. RPR can continuously observe and record viscosity behavior of tested samples in various temperature condition including from low temperature to high temperature, it not only measures viscosity speed, it also detects the differences in crosslinking and measures data generated during the softening process when the balanced time was achieved during the oscillations procedure. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2855–2863, 2007