Accepted Manuscript A novel online rheometer for elongational viscosity measurement of polymer melts Thomas Köpplmayr, Hans-Jürgen Luger, Ivana Burzic, Markus G. Battisti, Leonhard Perko, Walter Friesenbichler, Jürgen Miethlinger PII:
S0142-9418(15)30279-8
DOI:
10.1016/j.polymertesting.2016.01.012
Reference:
POTE 4572
To appear in:
Polymer Testing
Received Date: 14 December 2015 Accepted Date: 17 January 2016
Please cite this article as: T. Köpplmayr, H.-J. Luger, I. Burzic, M.G. Battisti, L. Perko, W. Friesenbichler, J. Miethlinger, A novel online rheometer for elongational viscosity measurement of polymer melts, Polymer Testing (2016), doi: 10.1016/j.polymertesting.2016.01.012. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Test Equipment
A novel online rheometer for elongational viscosity measurement of polymer melts Thomas Köpplmayr1,2*, Hans-Jürgen Luger1, Ivana Burzic1,3, Markus G. Battisti4,5, Leonhard
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Perko4,6, Walter Friesenbichler4, Jürgen Miethlinger1 1
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Institute of Polymer Extrusion and Compounding, Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria 2 Profactor GmbH, Im Stadtgut A2, 4407 Steyr-Gleink, Austria 3 Kompetenzzentrum Holz GmbH, Altenberger Str. 69, 4040 Linz, Austria 4 Chair of Injection Moulding of Polymers, Department Polymer Engineering and Science, Montanuniversität Leoben, Otto-Glöckel Str. 2, 8700 Leoben, Austria 5 Hirschmann Automotive GmbH, Oberer Paspelsweg 6-8, 6830 Rankweil, Austria 6 Woco Industrietechnik GmbH, Hanauer Landstr. 16, 63628 Bad Soden-Salmünster, Germany * corresponding author:
[email protected]
Abstract
This paper focuses on the measurement of elongational viscosity of polymer melts and filled compounds using a novel online rheometer. We developed a device with two slit sections
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and a hyperbolic contraction part in between, which allows for constant monitoring of both shear and elongational viscosity during an extrusion process. Due to the favorable design of the hyperbolic contraction, pressure transducers can be incorporated directly into the flow channels, which prevents material accumulation in pressure holes. The results of a pipe-
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grade polypropylene random copolymer melt are in good accordance with Sentmanat Extensional Rheometer (SER) measurements, in contrast to other methods such as Cogswell analysis of High Pressure Capillary Rheometer (HPCR) data or measurement on a
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wedge-shaped slit die, which fail to predict the true non-Newtonian behavior of the melt. In addition, we present the results of a polypropylene homopolymer intended for thermoformed packaging applications, a glass fiber and a talc compound, which could all be successfully characterized using our rheometer.
Introduction Processing of polymer melts often involves a significant amount of extensional flow, which has an impact on both the design of flow channels and on the final properties of the product. Extensional flows are not only dominant in melt spinning, film or bottle blowing and biaxial stretching of extruded sheets, but also occur in converging and squeezing flows during injection molding or profile extrusion. While shear viscosity is defined as the resistance to
ACCEPTED MANUSCRIPT flow due to a force which is perpendicular to the nodal of the plane on which the force acts, elongational viscosity is the resistance to flow due to a force which is parallel to the nodal of the plane on which the force acts. As a consequence, shear viscosity may be thought of as the resistance to fluid flow between layers, and elongational or extensional viscosity may be thought of as the resistance to stretching of the fluid. In general, the correlation of these fluid properties is quite complex and strongly depends on the macromolecular structure [1-3]. For
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axisymmetric contraction flows, the elongational viscosity of Newtonian fluids is three times their shear viscosity, as reported by Trouton in 1906 [4]. For polymeric fluids, the Trouton ratio is three only at low elongation rates within what is known as the Newtonian region of polymeric viscosity before shear thinning occurs. The ratio of elongational to shear viscosity
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for polymers at intermediate deformation rates is often much higher than its value for Newtonian fluids [5]. In typical polymer processing technologies, higher shear and elongation
at realistic processing conditions.
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rates are involved which emphasizes the importance of elongational viscosity measurements
There have been numerous approaches for measuring the extensional viscosity of polymer melts. Tensile rheometers ensure a truly uniform extensional deformation during uniaxial extension experiments. One of the first elongational rheometers was developed by Meissner [6], where a rectangular strip sample is extended in the horizontal direction by two rotary clamps in an oil bath. Münstedt [7] instead used samples which are fixed by two grips and
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stretched in the vertical direction, also supported by an oil bath. Various modified versions of the Meissner and Münstedt rheometers are described in more recent literature [8-10]. The Sentmanat Extensional Rheometer (SER) is a patented technology by Sentmanat [11] and involves a detachable fixture on commercially available rotational rheometer host systems. A
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rectangular sample fixed on two counter rotating drums enclosed in an air conditioned chamber is stretched by the rotation of the drums. The extensional viscosity is calculated
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from the measured torque considering the changing cross-section of the sample [11]. Another promising group of techniques proposed for measurement of extensional viscosity involves studying the fluid flow through contractions and determining the inlet pressure loss. Cogswell [12] presented a simplified analytical approach for the determination of the elongational viscosity from converging flows. Binding [13] performed a more accurate analysis of entrance flow using the energy principle. Using data from a High Pressure Capillary Rheometer (HPCR), the elongational viscosity is considered to be constant over the whole inlet area, which is not true due to transient elongational rates in an abrupt contraction. Improvements have been made by Obendrauf [14] and Perko et al. [15]. To alleviate the effect of shear at the walls of contractions, Shaw [16] proposed the use of a lubricating layer of low-viscosity fluid that is injected at the walls near the upstream entrance. In order to
ACCEPTED MANUSCRIPT provide a constant elongation rate, hyperbolically converging dies can be used and have been evaluated by means of numerical simulations by Feigl et al. [17]. In three-dimensional flow simulations, a generalized Newtonian fluid is defined by its dependence upon the second invariant of the rate of deformation tensor. Due to the assumed incompressibility, the first invariant is neglected. In pure shear flow, the third
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invariant also vanishes, but in extensional flow both the second and third invariant reach nonzero values. Debbaut and Crochet [18] extended this dependence of viscosity to the third invariant, and thus obtained arbitrary values of the Trouton ratio in uniaxial extension. They showed that a high Trouton ratio leads to vortex enhancement in an abrupt 4:1 circular contraction. However, these values are useless in plane flows since the third invariant
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vanishes. Sarkar and Gupta [19] proposed a model for strain rate dependence of elongational viscosity of a polymer, which can capture the initial strain thickening, followed by
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a descent in elongational viscosity as the elongation rate is further increased. Their model only depends on the second invariant of the rate of deformation tensor and can be used along with the Carreau model for shear viscosity in finite element simulations [20, 21]. In order to also account for viscoelasticity, plenty of constitutive equations exist with varying degrees of success and popularity. Hulsen and Van der Zanden [22] used a multi-mode Giesekus differential viscoelastic model to simulate vortex enhancements in contraction flows. However, this model does not show the maximum of steady elongation that is typical
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for LDPE melts, and other differential viscoelastic models, such as Phan-Thien Tanner [23] or eXtended Pom-Pom [24] can be used instead. Ansari et al. [25] used the integral-type KBKZ model to predict the entrance pressure loss of polyethylene melts in tapered dies. The K-BKZ model guarantees a good fit of many experimental data obtained from rheometry,
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such as shear viscosity, first normal stress difference and uniaxial elongational viscosity [26]. Subsequently, the other extensional viscosities in planar extension and in biaxial extension
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are predicted by the model [27]. Mitsoulis investigated the creeping entry flow of a wellcharacterized polymer melt (IUPAC-LDPE) in a 4:1 axisymmetric contraction. His numerical solutions show that in the axisymmetric contraction the vortex in the reservoir first increases with increasing flow rate, goes through a maximum and then decreases, following the behavior of uniaxial elongational viscosity [28]. Independent of the constitutive model used, accurate data on elongational viscosity at process-related conditions is essential for every type of numerical simulation. In industrial applications, it is often desired to monitor the polymer viscosity during processing, and existing online rheometers usually have a shear viscosity sensing capability and a bypass line integrated into the unit. Converging dies provide the advantage of using them in online process control by monitoring the extensional viscosity. Pabedinskas et al.
ACCEPTED MANUSCRIPT [29] presented an online extrusion rheometer based on the flow of polymer through a wedge (vertically tapered slit). The geometry of the converging section determines the elongation rate, which, in contrast to that of a hyperbolic die, is not constant along the converging section. However, since this section is very short, an averaged value is considered reasonable [29]. In some cases, the extensional flow behavior shows perceived differences better than the shear flow behavior. For example, elongational measurements provide an
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efficient method to characterize fiber-filled compounds since the extensional viscosity increases with increasing fiber length. In one of our previous studies, we showed that it is possible to distinguish between short- and long-fiber-filled polypropylene melts even if the same mass ratio is used and the samples cannot be distinguished by means of pure shear
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rheology [30]. Also, we improved the tensile modulus of polymer nanocomposites by using elongational flow generating devices for better intercalation and exfoliation of nanofillers in a polypropylene melt [31]. Stading and Bohlin [32] used a contraction nozzle to characterize
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viscoelastic materials such as fermented milk products, whose spreadability depends largely on extensional flow behavior. Collier developed a lubricated elongational rheometer based on hyperbolic or semihyperbolic dies where e.g. polypropylene is used as core and polyethylene as skin material [33]. Although it is possible to promote wall-slip in polymer melts, it is hard to achieve complete slip in a controllable fashion, especially for low-viscosity materials. A few years later Collier discovered that effects of developing orientation in the
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fluid during converging flow are so strong that the shear contribution becomes negligible, eliminating the need for lubricating during measurements [34]. In this contribution, we present a novel online-rheometer, which allows for shear viscosity measurements in two slit sections (γ ≈ 10 − 100 s and γ ≈ 100 − 1000 s ) and
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elongational viscosity measurements in a hyperbolic section at constant elongation rates (ε ≈ 1 − 15 s ) without the need for lubrication. Moreover, due to the favorable design of the
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hyperbolic contraction, pressure transducers (e.g. with 1/2 inch UNF thread) can be incorporated directly into the flow channels, which prevents material accumulation in pressure holes and allows for monitoring of polymer compounds, as shown in our study. The results of a pipe-grade polypropylene melt are in good accordance with SER measurements, in contrast to other methods such as Cogswell analysis of HPCR data or measurement on a wedge-shaped slit die, which fail to predict the true non-Newtonian behavior of the melt.
ACCEPTED MANUSCRIPT Experimental Materials: A Borealis RA130E polypropylene random copolymer intended for plumbing and heating applications was used as a base polymer, and compounds were prepared (24-wt% glass fibers or 60-wt% talc) by means of a Coperion ZSK 70 industrial twin-screw extruder with a
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length of 42 times the diameter and three venting units (two atmospheric and one under vacuum) in combination with underwater pelletizing. The melt flow rate (MFR) according to ISO 1133 of the base polymer was about 0.3 g/10 min (230°C/2.16 kg). In addition, a Borealis HC205TF polypropylene homopolymer intended for thermoformed packaging
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applications with a MFR of about 4 g/10 min (230°C/ 2.16 kg) was also used. Parallel plate rheometer (PPR):
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The shear viscosity was measured using a stress- and strain-controlled rheometer (AntonPaar MCR 302) equipped with an electrically heated thermostating unit. The experiments were carried out in parallel plate mode at 220°C or 240°C under nitrogen with a plate diameter of 25 mm. The materials were compression molded at 180°C into disc-shaped specimens with a diameter of 25 mm and a thickness of about 1 mm. Molding time was approximately 5 min. Strain sweeps were carried out in the strain range from 0.01 to 10% at
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a fixed frequency of 1 rad/s. All frequency sweep tests were conducted in the linear viscoelastic region, as confirmed by an independent strain sweep test, and the angular frequency range was 0.0628 – 628 rad/s. The Cox-Merz rule [35] was used to convert oscillatory data to steady shear data.
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High pressure capillary rheometer (HPCR):
The viscosity measurements were carried out on a Rheograph 25 (Goettfert Werkstoff
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Prüfmaschinen GmbH, Buchen, Germany) with 2 different circular dies (diameter = 1 mm; lengths = 1 mm and 20 mm). The shortest die was used as orifice die for a refinement of the measurements. The pressure loss of this die was used for the correction of shear viscosity and for the calculation of elongational viscosity according to Cogswell [12]. The reason for this approach was the strong scattering of the inlet pressure values derived from the Bagley plot [36]. The shear viscosity was measured at shear rates between 1 s-1 and 20,000 s-1 and at test temperatures of 220°C or 240°C. Sentmanat extensional rheometer (SER): The SER device was used on a MCR 501 rheometer (Anton Paar GmbH, Graz, Austria). The measurements were carried out at Hencky strain rates of 0.01 s-1, 0.1 s-1, 1 s-1 and 10 s-1.
ACCEPTED MANUSCRIPT The test temperatures were 190°C, 210°C and 230°C.
To prevent sagging of the samples,
relatively low temperatures have to be used compared to online rheometry in extrusion dies. Slit rheometer: All data were obtained using a Thermo Haake Rheomex system, which consists of a singlescrew extruder (screw diameter 19 mm, length 33 times the diameter) equipped with a melt
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pump (2.4 cm3) and a slit die of defined gap size (2 mm or 0.5 mm). This is a convenient and simple method for obtaining viscosity data, and consists of measuring the pressure drop along a die for different volume flow rates. The test temperatures were 220°C, 230°C and 240°C.
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The expressions commonly used to relate pressure drop ∆p to shear stress τ, and volume flow rate V to the apparent (Newtonian) shear rate γ . in a capillary slit of thickness H and
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length L are: τ=
and
∆∙
γ . = ∙ ,
(1)
(2)
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where W is the width of the gap and both τ and γ . apply at the capillary wall. In practice, Equation (2) requires a correction. The Weissenberg-Rabinowitsch correction,
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which allows for the fact that the material may be non-Newtonian, is given by:
γ = ! ∙ "2 +
%&'() *++. %&'(,
- ∙ γ . ,
(3)
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where γ is the true shear rate.
The shear viscosity is then given by: η = )
/ 0123
.
(4)
Elongational rheometer: The first elongational die used in this study consists of two slit sections (pure shear) and a converging section in between (elongation and shear). The gap size of the two slit sections is denoted as H1 or H2, respectively, and the width is W1 or W2, respectively. L denotes the length of the converging section. Each slit section is equipped with two pressure sensors. To ensure a nearly homogeneous temperature field, the die is combined with two separately
ACCEPTED MANUSCRIPT controlled heating zones. The geometry of the converging section determines the elongation rate which, in contrast to that of a hyperbolic die, is not constant along the converging section. However, since this section is very short, an averaged value can be considered reasonable:
∙
−
-. 5 ∙5
(5)
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4
ε = ∙ "
The pressure drop within the converging section is the sum of a shear and an elongational contribution. The viscous shear part can be calculated by: 9:5 ∙;<=>∙
⁄<
= ";8>∙;8>9: ∙?-
(6)
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∆673*1 8
with W(z) = W1-(W1-W2)/L·z and H(z) = H1-(H1-H2)/L·z. It should be noted that this equation is only valid for aspect ratios W/H ≥ 10 [37]. This equation is based on the assumption that the
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flowing material exhibits power-law behavior (fluidity Φ and flow index m).
According to Equation (7), the pressure drop consists of three contributions, the pressure drop ∆pshear due to viscous shear flow, the pressure drop ∆pelong. due to viscous elongational flow and the pressure drop ∆pelast. dedicated to the elasticity of the melt. C D
= ∆ACE
+ ∆A &'F(. + ∆A &C. GHHHHIHHHHJ
(7)
∆K
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∆AB
The elongational stress σ is equal to the entrance pressure drop ∆pE and can be obtained by knowing the shear part in the converging section with the assumption that elastic properties
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are neglected. The elongational viscosity is then given by: η
&'F(.
=
L M
=
∆K M
=
∆N3*6213O ∆673*1 . M
(8)
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The Hencky number εH is a characteristic measure of the elongation of material. In our case, it is defined by the ratio of the areas of both slit sections: ∙
εP = ln "5 ∙5 -.
(9)
As a starting point for developing a novel online rheometer, hyperbolic contractions used by Oliveira et al. [38] were studied numerically. The microgeometries used in this work are planar in character and are designed to have a hyperbolic contraction section followed by an abrupt expansion. For 0 ≤ z ≤ L, the contraction wall is shaped according to the following function: S;T> = U ⁄;V + T>,
(10)
ACCEPTED MANUSCRIPT where a = L·W2/(W1-W2) and C = L· W1·W2/[2·(W1-W2)]. The microfluidic channels were scaled up in order to use them for thermoplastic melts. Table 1 shows an overview of different dimensions of the contraction sections investigated in our study. Although the converging region leads to a uniform elongation rate, the deformation is always planar and the aspect ratio of the second slit section is very low (W2/H2 = 2.5),
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which makes the pressure drop difficult to measure and analyze. Therefore, we modified the channel width in the contraction part to: ∙
S;T> = =!8 ∙ U;T>
(11)
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where W = W1 = W2, C(z) = H1/H(z) and H(z) = H1-(H1-H2)/L·z. The shape of width and height along the contraction part is shown in Fig. 1. As a result, the aspect ratio (W/H2 = 20) is increased by a factor of 8 and the channel width W allows for direct measurement of the
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pressure drop by commonly used transducers.
The average elongation rate in the contraction part remains constant and can be calculated for each segment i by:
W = ∆8 ∙ X;8
Y:5 >∙;8Y:5 >
− ;8 >∙;8 >Z. Y
Y
(12)
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Compared to the wedge-shaped slit, our approach provides a uniform elongation rate along the contraction part. For a flow rate of 400 mm3/s and a division of the contraction part into 200 segments, the elongation rate varies between 3 s-1 and 188 s-1, which yields an average elongation rate of about 30 s-1. For the same flow rate, both the planar and the quasi-
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axisymmetric hyperbolic die give a constant elongation rate of 6 s-1, as shown in Fig. 2. The elongational viscosity is again determined by Equation (8). For our experimental studies, we used both the wedge-shaped slit die supplied by Thermo Scientific and the novel hyperbolic
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die in combination with four pressure transducers and one temperature sensor. A drawing of our online rheometer is shown in Fig. 3. Shear viscosities were determined by the pressure drops in the two slit sections and power law parameters were calculated pointwise. All measurements were conducted at a constant processing temperature, but our approach also accounts for viscous heating in the contraction part, as both slit sections were used for analyzing the shear contribution in the contraction part. The melt pump speed was varied from 2 rpm to 25 rpm, which yields elongation rates between 1.2 s-1 and 15 s-1.
ACCEPTED MANUSCRIPT Results and discussion Entrance pressure drop: A contraction flow causes an extra pressure drop due to the stretching of fluid elements. This entrance pressure drop is determined by comparing the measured pressure drop with the theoretical value if pure shear is assumed. Although viscoelastic effects such as secondary
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flows also influence the entrance pressure drop, it is mainly attributed to the elongational viscosity of the polymer melt [39]. Due to the limited accuracy of commonly used pressure transducers, the measured entrance pressure drop should be at least 1-2 bar depending on the full scale output of the sensor. The entrance pressure drops of all materials investigated
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with our online rheometer are listed in Table 2. High viscous polymer melts such as Borealis RA130E showed values between 20 and 32 bar within the measurement range, which was easy to detect even if 500 and 700 bar sensors were used. Polypropylene melts with lower
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viscosity, such as Borealis HC205TF or filled compounds, showed lower values between 4 and 21 bar, which still did not cause problems during the measurements. In general, the determined entrance pressure drops exceeded the values obtained by Cogswell analysis of HPCR data. Shear viscosity:
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The viscosity curves of all investigated materials are shown in Figs. 4-7. For the pure polypropylene melts and the glass fiber compound, shear viscosity was measured by three independent methods: parallel plate rheometry in oscillation mode, high-pressure capillary rheometry and slit rheometry using our online rheometer. The results show good correlation
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of the different methods in the viscosity curves (Figs. 4-6). For the talc compound parallel plate rheometry was not applicable due to the high amount of filler, but HPCR and slit rheometry data are mainly in good accordance. Only a slight deviation concerning the first slit
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section is observed (Fig. 7), which may be explained by low orientation of the filler particles in the flow direction in the larger slit and leads to higher viscosity values than expected. Elongational rheometry:
Although shear viscosity could be accurately measured by different characterization techniques and yields comparable results, measurement of elongational viscosity was more challenging and large deviations were obtained for some samples. The fact that elongational viscosity data largely varies depending on the method used, has already been reported by Sridhar in his review article [40]. Borealis RA130E was used as a model polymer, because its high viscosity and melt strength allow for the characterization using SER, which is commonly used for uniaxial extensional measurements. The transient elongational viscosity curves are
ACCEPTED MANUSCRIPT exemplarily illustrated in Fig. 8 at a test temperature of 210°C. For the comparison of the SER method with the HPCR and online measurements, a plot of elongational viscosity versus elongation rate is needed. We evaluated this steady state value from the peak of the tensile stress growth curves as a function of strain rate, such that ηE(W) = max[ηE+(W,t)]. Thus, the “evaluated points” in Fig. 8 were used for the generation of the SER curve in Fig. 9. Although an extensional viscosity can still be computed beyond this point using the
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measured tensile force, the imposed deformation rate and the (assumed) exponential variation in the cross-sectional area, previous stress relaxation experiments by Sentmanat et al. [41] coupled with theoretical and numerical stability considerations [42-43] suggest that, beyond the maximum, the elongating polymeric strip is in fact unstable to free surface
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perturbations that grow and result in necking of the sample, followed by complete rupture. The actual cross-sectional area and the local deformation rate in the neck will then not be the same as the nominal imposed values. Therefore, we do not use the measured data beyond
state extensional viscosity function.
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the maximum value of the transient extensional viscosity for representing the quasi steady-
The elongational viscosity curve determined by our online rheometer is in good agreement with the SER results as shown in Fig. 4. Other methods such as Cogswell analysis of HPCR data and entrance pressure loss from the wedge-shaped slit predict much lower values for ηE
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and a smaller gradient of the curve. In particular, the wedge-shaped slit method predicts an almost horizontal trend, while Cogswell analysis shows a more realistic gradient. The differences can be explained by the non-uniform elongation rates in both methods, which assign lower viscosity values to the assumed average elongation rate. Towards the end of the contraction part, high elongation rates are expected (Fig. 2); the entrance pressure drop,
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and thus the elongational viscosity, decrease. Due to the constant elongation rate and the quasi-axisymmetric character, our online rheometer provides results which are closer to the
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SER curve. However, it is worth noting that the elongational viscosity determined by SER corresponds to a total Hencky strain of εH = 3.2, while our measurement device provides only εH = 1.4. In contrast to shear viscosity which reaches constant values in steady-state, elongational viscosity will depend on strain (Fig. 8). In this case, lower values would be expected for our online rheometer, whereas SER measurements are not meaningful at Hencky strains around εH ≈ 1 due to the absence of strain hardening. This effect can be explained either by a measurement inaccuracy or by the presence of strain hardening at lower deformations in a channel flow compared to transient measurements on rectangular strips. In particular, the positions of the pressure transducers highly influence the results. Although pressure measurements made through pressure holes are essentially the same as those made with flush-mounted instruments, as reported by Han [44], the extrapolation length of the pressure gradients in the two slit sections towards the contraction part
ACCEPTED MANUSCRIPT decreases due to the size of the sensor tip. Extrapolation starting from the tip center produced non-evaluable results (negative entrance pressure values), and the tip edge was used as a starting point for further evaluation of the pressure drop in the contraction part. Fig. 3 shows the distances used for extrapolation of the two pressure drops ∆p1ex and ∆p2ex. Consequently, a higher share of the total pressure drop is attributed to elongation rather than shear. This increases the entrance pressure drop, and thus the measured elongational
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viscosity. In Fig. 10, the shear and elongational viscosity curves at temperatures of 220°C, 230°C and 240°C are plotted. Shear viscosity decrea ses with increasing temperature at low shear rates in the first slit section, while this effect vanishes at higher shear rates and is not visible in the elongational viscosity curves within the measurement range. The SER results in
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Fig. 9 show some temperature dependence, but large scattering of the data prevents further analysis of the temperature shift.
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For Borealis HC205TF, a similar trend can be observed: Using our hyperbolic slit die, higher values of the elongational viscosity are measured at well-defined elongation rates (Fig. 5). The wedge-shaped slit measurement produces similar results compared to our method only for the glass fiber compound (Fig. 6), which may be explained by a stabilizing effect of the glass fibers at the end of the contraction part. The stiff fibers are oriented in the flow direction and, during entry to the second (smaller) slit section, they prevent further elongation of the polymer melt at small time scales. Thus, high elongation rates towards the end of the
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contraction part have a lower effect on the final result than without the fibers. The highest elongation rates are expected in a HCPR. The outcome of this is that for both the glass fiber compound and HC205TF, the wedge-shaped slit results are between Cogswell data and our hyperbolic slit measurement. For the talc-filled compound, the Cogswell data again deviate
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from our results, providing lower elongational viscosity values (Fig. 7).
ACCEPTED MANUSCRIPT Conclusions We developed a novel online rheometer with two slit sections (γ ≈ 10 − 100 s and γ ≈ 100 − 1000 s ) and a hyperbolic contraction part (ε ≈ 1 − 15 s ) in between, which allows for constant monitoring of both shear and elongational viscosity during an extrusion process. The elongational properties of a pipe-grade polypropylene random copolymer melt could be
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measured successfully on both an SER device and our elongation die. Entrance pressure drops turned out to be high enough for detection using commonly available pressure transducers (e.g. with 1/2 inch UNF thread), which can be incorporated directly into the flow channels. Other methods, such as Cogswell analysis of High Pressure Capillary Rheometer (HPCR) data or measurement on a wedge-shaped slit die, failed to predict the true non-
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Newtonian behavior of the melt, mainly due to the non-uniform elongation rate in the measurement devices. If higher elongation rates occur towards the end of the contraction
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part, lower values of the elongational viscosity are assigned to the assumed average elongation rate and wrong results are produced. A similar trend could be observed using a polypropylene homopolymer intended for thermoformed packaging applications and a highly filled talc compound. The wedge-shaped slit measurement produced results close to our method only for a glass fiber compound, which may be explained by a stabilizing effect of the glass fibers at the end of the contraction part. The shear viscosity could be accurately
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measured by the different characterization techniques, and all methods yield comparable results. Future investigations will focus on long-time monitoring of polymer compound quality, data acquisition for parameter fitting of constitutive models as well as the implementation and consideration of elongational viscosity in numerical simulations.
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Acknowledgements
Financial support by the Austrian Research Promotion Agency (FFG) within a national
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research project (“Polymer-Compounds mit erhöhter Homogenität und Performance durch gezielten Einsatz von Dehnströmungen”, project number 843507) is kindly appreciated.
ACCEPTED MANUSCRIPT References [1] H. Münstedt. Dependence of the Elongational Behavior of Polystyrene Melts on Molecular Weight and Molecular Weight Distribution. J Rheol 1980;24(6):847. [2] W. Minoshima, James L. White, Joseph E. Spruiell. Experimental investigation of the influence of molecular weight distribution on the rheological properties of polypropylene
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melts. Polym Eng Sci 1980;20(17):1166. [3] H. Münstedt, H.M. Laun. Elongational properties and molecular structure of polyethylene melts. Rheol Acta 1981;20(3):211.
[4] F.T. Trouton. On the coefficient of viscous traction and its relation to that of viscosity, P
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Roy Soc A-Math Phy 1906;77(519):426.
[5] A. Bach, H. Koblitz Rasmussen, O. Hassager. Extensional viscosity for polymer melts
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[8] J. Meissner, J. Hostettler. A new elongational rheometer for polymer melts and other highly viscoelastic liquids. Rheol Acta 1994;33(1):1. [9] J.M. Maja, J.A. Covas, J.M. Nóbrega, T.F. Dias, F.E. Alves. Measuring uniaxial extensional viscosity using a modified rotational rheometer. J Non-Newtonian Fluid Mech
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ACCEPTED MANUSCRIPT List of Tables Table 1 Dimensions of different contraction sections investigated in our study. W1
W2
H1
H2
L
εH
wedge-shaped slit
20 mm
5 mm
2 mm
0.5 mm
5 mm
2.7
planar hyperbolic slit
20 mm
5 mm
2 mm
2 mm
5 mm
1.4
20 mm
20 mm
2 mm
0.5 mm
quasi-axisymmetric hyperbolic slit
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Type of contraction
5 mm
1.4
RA130E
HC205TF
PP 24-wt% GF
PP 60-wt% talc
mm3/s
bar
bar
bar
bar
80
20.6
6.1
5.1
4.3
104
21.9
7.1
6.4
5.5
140
23.4
8.2
8.0
7.4
184
24.7
9.3
10.5
9.0
244
25.6
10.4
12.5
11.1
324
26.7
11.5
15.1
13.5
432
28.7
12.9
16.6
15.9
572
30.3
14.5
18.8
18.8
756
31.7
16.0
20.9
20.8
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Table 2 Entrance pressure drops (∆pE) of different materials measured by our online rheometer.
ACCEPTED MANUSCRIPT List of Figures Fig. 1. Shape of the width function W(z) = 2·x(z) and the height function H(z) = 2·y(z) along the contraction part. Fig. 2. Distribution of elongation rates along the contraction part of the hyperbolic slit and the wedge-shaped slit for a flow rate of 400 mm3/s and a division of the contraction part into 200
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Fig. 3. Drawing of online rheometer developed in our study: (A) connection to melt pump, (B) first slit section with pressure drop ∆p1, (C) contraction part with pressure drops ∆pshear + ∆pE, (D) second slit section with pressure drop ∆p2, (P1) … (P4) pressure transducers, (T1)
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temperature sensor. The pressure transducer (P3) is part of the second slit section (D) and is only shown in (C) for illustration. ∆p1ex and ∆p2ex are the extrapolated pressure drops from
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Fig. 4. Comparison of shear and elongational viscosity curves at 220°C of Borealis RA130E using different characterization methods.
Fig. 5. Comparison of shear and elongational viscosity curves at 220°C of Borealis HC205TF using different characterization methods.
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Fig. 6. Comparison of shear and elongational viscosity curves at 240°C of polypropylene 24wt% glass fiber compound using different characterization methods. Fig. 7. Comparison of shear and elongational viscosity curves at 240°C of polypropylene 60-
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wt% talc compound using different characterization methods. Fig. 8. Transient elongational viscosity curve of Borealis RA130E at 210°C showing strain
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hardening at different Hencky strain rates. The double rule indicates the linear visco-elastic envelope (LVE) obtained by multiplying the PPR data with the Trouton ratio of 3 for axisymmetric flow.
Fig. 9. Steady elongational viscosity curves of Borealis RA130E at different temperatures obtained by using maxima of viscosity values in transient curve. Fig. 10. Shear and elongational viscosity curves of Borealis RA130E at different temperatures measured by our hyperbolic slit rheometer.
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