Improved measurement and analysis techniques for melt extensional rheometry

Table of contents

Abstract

Nomenclature
1.1 Background
1.2 Objectives

2. Materials and equipment
2.1 Materials
2.1.1 Polystyrene
2.1.2 Polypropylene
2.1.3 PPNC
2.2.1 ARES rotational rheometer
2.2.2 CEAST Modular Melt Indexer
2.2.3 RME extensional rheometer
2.2.4 MDSC 2920 calorimeter

3.1 Introduction to rheology
3.2 Shear rheology
3.2.1 Sample preparation
3.2.2 Steady shear measurement
3.2.3 Dynamic measurement
3.3 Melt Density
3.4 Extensional rheology
3.4.1 Sample preparation
3.4.2 Measurement
3.4.3 Visual analysis
3.5 DSC

4. Results & discussion
4.1 shear testing
4.2 DSC
4.3 Extensional testing
4.2.1 Error analysis
4.2.2 Error calculation for video analysis
4.2.3 Comparison of PP and PPNC

5. conclusions

References

Appendix

Nomenclature

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1. Introduction

1.1 Background

Characterising the deformation of a polymer melt is an important task to model its processing behaviour. Knowing only shear flow properties is not sufficient to explain processing behaviour of polymers in many processes such as blown film extrusion, thermoforming, fibre spinning or blow moulding that involve stretching. As Meissner (1979) realised on different LDPE resins using only shear data can not always sufficiently explain the deformation behaviour and therefore the processing behaviour of polymers.

Since the 1980s the extensional or elongational viscosity has been recognised as a very important property for processes like blown film extrusion, thermoforming or fibre spinning (Baird 1999, Wagner et al. 2002, Bhattacharya 2004). Obtained results show that the elongational viscosity is also a very sensitive indicator for long-chain branching.

Measuring the extensional viscosity means getting a value for the materials resistance to stretching flow or elongational deformation. Since the first theoretical works have been made on this topic by Trouton in 1906, different measuring methods have been developed. Apart from simple methods which are not well defined and perform only indirect measurements (like the melt strength test or capillary rheometry), some more complex and precise methods have been established. The widely accepted and commercial available and therefore the most important ones are the Munstedt-type and the Meissner-type, both introduced in the 1970’s. The Munstedt-type rheometer operates via translating clamps suspended in an oil bath (Munstedt 1979) and the Meissner-type uses counter rotating belts (Meissner 1981). Both have been commercialised by Rheometrics, the Munstedt-type as the Rheometrics Extensional Rheometer (RER) in 1981 and a modified Meissner-type as the Rheometrics Melt Extensional Rheometer (RME) in 1994.

The RME technique was used for various experiments such as Meissner et al. (1981, 1982), Meissner (1985), Meissner and Hostettler (1994), Levitt and Macosko (1997), Wagner et al. (1998, 2000, 2002), Schulze at al. (2001).¹

Nevertheless there are different problems occurring with the RME device discussed in various papers e.g. by Meissner (1994), Schweizer (2000), Schulze at al. (2001) and Barroso et al. (2002). For some of the problems solutions and/or correction methods have been developed, others still affect the results of the RME. Problems occurring in testing devices preceding the commercialised RME used for the experiments in this study will not be mentioned but can be read in earlier works by Meissner (1981, 1994) so will aspects of the sample preparation. Discussing the reasons, the effects and the solutions of inaccurate results are therefore the major task of this work.

1.2 Objectives

The overall objective of this study is to establish the factors that influence the measurements of the extensional viscosity and provide the techniques that improve the accuracy of these measurements using RME rheometer. A review of previous works will therefore be followed by a series of experiments and analysis. As mentioned in other works on extensional rheology (Schulze et al. 2001, Meissner 1994, etc.) the measurement is quite sensitive to different parameters and therefore not easy to perform with adequate accuracy. The objectives in particular are to analyse the possible errors resulting from the instrumentation and experimental conditions while influences of the sample preparation will not be discussed. Furthermore, the aim is to apply the acquired knowledge to producing the most accurate extensional rheology data for selected polymer grades and composites. For this task different measurement methods e.g. visual and instrumented are used on samples of different cross-sectional areas and different materials. By comparing the different methods and obtaining the true strain and strain rates and relating them to the set values the performance of the RME testing should be assessable. The materials used in this thesis are polystyrene, as a rheologically simple material, polypropylene, and polypropylene nanocomposite (PPNC) as a more complex material. Additionally a comparison of PP and PPNC elongational data will be performed.

2. Materials and equipment

2.1 Materials

2.1.1 Polystyrene

Polystyrene is an most important packaging material with a worldwide production capacity of about 16 million tonnes. About half of the amount is the common transparent GPPS (general purpose PS) which is a rigid, inflexible and brittle polymer. The other half is HIPS (high impact PS), which is modified with rubber and therefore impact resistant and opaque. Furthermore a common form is the foamed form used as an insulating material. Polystyrene is little heat resistant with a maximum working temperature of about 70°C . The polystyrene used for this work is Polystyrene Australia’s Austrex 555, a general purpose grade GPPS. It is an atactic polystyrene and therefore it is totally amorphous. Structural reasons for this are its disorientation and its randomly arranged site chains (Figure 1).

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Figure 1: Polystyrene

Further properties for extrusion on the material are shown in Figure 2 while properties for moulding processes are expected to be slightly lower. The reason for choosing PS to examine these tests is that this polymer is an easy to handle one because of having a relatively easy structure but still being amorphous. That means it is easy to produce samples with constant properties because of no crystallisation and a very little effect of thermal and mechanical preload. The complete datasheet can be seen in the appendix.

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Figure 2: Polystyrene properties²

2.1.2 Polypropylene

To give a comparison between different types of polymers Polypropylene is used as the second sample material. It is one of the most common used polymers since the early 1970’s. The tacticity of this polymer, in this case the orientation of the methyl groups as shown in Figure 3, has a big effect on its properties. Randomly ordered methyl groups provide an amorphous PP with poor mechanical properties because the so called atactic PP (aPP) is not able to form any crystals. In contrast to this the regular syndiotactic (sPP) or even isotactic PP (iPP) allows crystallinity up to 85% which provide generally good mechanical properties.

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Figure 3: Polypropylene

All these modifications are made possible through different catalysts make PP a polymer which can be used for a broad range of applications, from packaging to construction. Further modifications can be achieved by copolymerisation of different sorts of PP or PP and other polymers. The density of PP ranges from 0.895 to 0.92 g/cm³ while the i-PP used here has a density of 0.9 g/cm³. The service temperature can be up to 110°C while the melting temperature of crystalline PP is up to about 160°C. The properties of the Polypropylene PP homopolymer Moplen HP400H (used in this study) give a tensile modulus of 1400 MPa and a tensile strength of 34 MPa while the MFR at 230°C and 2.16kg load is about 2g/ 10min. These and further properties in Figure 4 and the appended datasheet characterise the polymer as a commodity, suitable for most mass applications with undemanding requirements like blister packs and small blow moulded bottles.

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Figure 4: Polypropylene properties³

2.1.3 PPNC

The used PPNC is a composite of the PP mentioned above modified with 3% Bentone 109 organo-modified clay which has a density of 1.7 g/cm³. The addition level is within the range of 1-5% recommended for plastic systems. It is compatibilised with maleic anhydride grafted PP (MAgPP).

2.2 Equipment

2.2.1 ARES rotational rheometer

The ARES Advanced Rheometric Expansion System is a variable rotational rheometer manufactured by Rheometric Scientific. It can be either mounted as a coneplate-measuring system or as a plate-plate-measuring system. There are generally two different modes which can be run on the ARES rheometer: steady shear measurement and oscillatory measurement. To provide a wide range of testing temperatures the ARES is furthermore equipped with a temperature chamber which can be used either to cool or to heat the measuring system.

By rotating either the cone or the plate in the cone-plate geometry or one of the plates in the parallel plate geometry a shear is applied to the sample. The measurement of the resulting moment on the other, fixed, plate or cone gives the shear stress and hence the viscosity can be obtained. Furthermore the normal stress can be measured in addition to the torque.

The transducer in the ARES is the 200/2000 FRT which allows torque measurement in the range of 0.01 to 2000 g/cm. The measuring range for the normal force is ranged from 2 to 2000 g. The thermal drift is about 0.002% per °C maximum and the maximum operating frequency is 100 rad/s (15.92 Hz). Further information on the device can be taken from the Rheometric Scientific manual (2000). The diameter of the plates used is 25mm and the angle of the cone used for the cone- plate configuration is 0.1 radians. The gap between the cone tip and the plate while running the test is about 0.05 mm.

2.2.2 CEAST Modular Melt Indexer

The Ceast Melt Indexer consists of a thermostatically controlled cylinder sealed by a round die at the lower end. The cylinder is filled with polymer which will be pushed through the die by a steel piston after being melted at a certain temperature. To adjust the speed of the extrusion there are three weights to apply to the piston: 2.16 kg, 5.0 kg and 21.6 kg. To perform an automatic cut-off there is a flag of a discrete length attached to the piston. By passing a light barrier it forces an automatic spatula to cut off the extruded strand after a certain throughput of polymer melt through the die.

To assure constant conditions the melting time after filling the cylinder is set to 6 minutes. The dimensions of the die used to perform the testing are a length of 8mm and a die diameter of 2.0955mm (0.0825”).

The scale used to weight the strands is a Mettler Toledo PB403-S allowing a precision of ± 0.001g. This is used for melt density measurement as described later in chapter 3.3.

2.2.3 RME extensional rheometer

The Rheometric Scientific Polymer Melt Elongational Rheometer (RME) consists of a heat-insulated housing containing a stretching device to process the testing. Attached to the RME is a water-cooling circulation to prevent the force transducer from heat related incorrect measurement. To stretch the sample the stretching device consists of four counter-rotating belts while an air table is used to achieve an even state of stress. The air table supports the sample through a cushion of either air or nitrogen preventing it from sticking to the table. The stretching device with the elements mentioned above can be seen in Figure 5. The measurement range provided by the RME allows strain rates from 0.001-1.0 s-¹ while the maximum Hencky strain is limited to 7 by the lengths of the belt, resulting in a stretch ratio, , of about 1100. The measurable tensile force is ranged from 0.001 to 2 N with a resolution of 0.001 N. The maximum temperature for the heating chamber is about 350°C with an accuracy of ± 0.2°C.

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Figure 5: stretching device⁴

The principle of measurement and the calculation steps for the data obtained by the RME are described in chapter 3.4. Further information on the rheometer can be obtained from the introduction of this testing device by Meissner and Hostettler (1994) and from the instrument manual by Rheometric Scientific (2001).

2.2.4 MDSC 2920 calorimeter

The differential scanning colorimetry tests were performed using a modulated TA Instruments DSC 2920. It allows standard mode operation as well as modulated scans (TA Instruments 1997). Temperatures at which the device can be operated range from -70 to 400°C with scan rates from 0.01 - 10°C/min with modulation or 0.01 - 20°C/min without modulation. Purging gas can either be helium or nitrogen. Data analyses were done using the TA Universal Analysis Software. The thermal response calibration was done using pure indium. Figure 6 shows the device used for the DSC tests.

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Figure 6: TA Instruments DSC 2920

3. Experiments

3.1 Introduction to rheology

The expression rheology as a new subject, proposed to describe “the study of the flow and deformation of all forms of matter” was introduced in 1929 by M. Reiner and E. C. Bingham on the establishment of The Society of Rheology. The naming occurred in imitation to Heraclites’ quote “panta rhei” meaning “everything flows”. The common definition nowadays is the study of “the deformation and flow of a material when under the influence of an applied stress” (Bhattacharya 2004). A measurement for the material’s resistance to the applied stress is its viscosity, which can be measured with a viscometer or a rheometer whereas a rheometer is also suitable for other measurements then only viscosity (Reiner 1964).

To describe this flow behaviour mathematically various Models have been introduced after Newton developed his equation for fluids where the viscosity is constant at different shear rates as;

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These fluids are called Newtonian fluids. The viscosity of Non-Newtonian fluids is in contrast to those which are shear rate depended. Most common behaviours are shearthinning and shear-thickening where the viscosity decreases or increases respectively with higher shear rates. Behaviours of different fluids are shown in Figure 7.

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Figure 7: viscosities of different fluids⁵

The basic mathematical model to describe the Non-Newtonian behaviour is the so called Power law model with the Newtonian fluid as a special case of it (when n = 1) (Bhattacharya 2004).

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A further developed model for shear thinning behaviour is the Cross Model (Cross 1965) where zero shear viscosity and infinite shear viscosity are considered:

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Apart from these two models various other models such as the Bingham, the Herschel-Bulkley or the Carreau model. They have additional parameters or/and describe special behaviours and are described for example by Fried (2003) or Bhattacharya (2004).

In this thesis two different kinds of deformation are analysed which are shear and extension. A third deformation which is not relevant at this point is compression. The shear deformation can be shown as a deformation of rectangular bars. Applying a shear deformation the upper surface is displaced at į,while the lower bar is stationary as is shown in Figure 8. The angular displacement, , which is called strain, is correlated to į and the gap between the bars, h, by:

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For small Ȗ the angle tan γ can be regarded as Ȗ yielding

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Figure 8: shear deformation applied on a rectangular bar

In general the viscosity, Ș, defined for Newtonian fluids in shear deformation referring to Newton’s law from 1687 is described in eq. 3. 1

The shear stress, τ, is defined as the quotient of Force, F, per Area, A, written

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The derivative dv/dy can be substituted by the derivative of strain over time which results in the shear rate, γ & ,

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Using equations 3. 6 and 3. 7 on Newton’s law (eq 3. 1) and solving it for the viscosity yields

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This is the common definition of the shear viscosity. Extensional deformation is different to this, and a simple elongation of a rectangular bar as shown in Figure 9.

Figure 9: extensional deformation applied on a rectangular bar

In this case the strain can be calculated from the initial length, L0, and the final length, L, which is

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Due to the fact that the final length can be significantly larger than the initial length,

H, rather than the Cauchy strain as

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The tensile stress ı FDQ EH FDOFXODWHG VLPLODUO\ WR WKH VKHDU stress (eq 3. 6) as

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the strain is usually calculated as Hencky strain, İ and divided by the Hencky strain (eq. 3. 10) to define ηE which is called either extensional, elongational or Trouton viscosity:

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The Trouton ratio describes the ratio between shear viscosity and extensional viscosity. For Newtonian liquids or low shear rates the Trouton ratio is 3 and allows comparison between both viscosities. For non-Newtonian liquids at high shear rates the ratio is greater than 3 as described by Wisniak (2001) and other authors.

3.2 Shear rheology

3.2.1 Sample preparation

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For the execution of the shear rheology tests disc shaped samples are necessary. In the ARES rotational rheometer two diameters, 25mm and 50mm samples can be used. For this study samples of 25mm diameter and 2mm thickness where used. The preparation of the samples is similar to the strip samples for the extensional rheology tests mentioned in chapter 3.4.1.

3.2.2 Steady shear measurement

For the shear viscosity measurement with a steady shear rate there are 2 major configurations, the plate/plate and the cone/plate configuration. Both have advantages and disadvantages for certain tasks:

a.) The cone/plate configuration

The cone/plate configuration has a rotating plate at the bottom and a cone on top to which a force and torque measurement device is attached. The main advantage of the cone/plate configuration is that the shear rate is the same at every distance from the centre of the device. A diagram of the device is shown in Figure 10.

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Figure 10: cone/plate configuration⁶

The shear rate, γ & , for this configuration is given as the quotient of the constant angular velocity, ȍ DQG WKH FRQH DQJOH ȕ

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[...]

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¹ Taken from Mechbal and Bosmina, 2004.

² adapted from Austrex 555 datasheet (s. appendix)

³ adapted from Moplen HP400H datasheet (s. appendix)

⁴ adapted from Ivanov 2003

⁵ adapted from Steffe, 1996

⁶ adapted from Hochstein, 1997