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Rheology and processing of molten poly(methyl methacrylate) resins Stamboulides, Christos 2005

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RHEOLOGY AND PROCESSING OF MOLTEN POLY(METHYL METHACRYLATE) RESINS by C H R I S T O S S T A M B O U L I D E S Diploma, Chemical Engineering, Aristotle University of Thessaloniki, Greece, 2002 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in the Faculty of Graduate Studies Chemical and Biological Engineering T H E U N I V E R S I T Y O F BRITISH C O L U M B I A February 2005 © Christos Stamboulides, 2005 AB S T R A C T ABSTRACT The rate of production in many commercial polymer processing operations is limited by the appearance of flow instabilities. Flow instabilities might manifest themselves as fine and periodic distortions on the extrudate surface (sharkskin or surface melt fracture) or in the form of helix and/or chaotic distortions (gross melt fracture). To postpone such phenomena to higher shear rates processing aids are used. External processing aids, such as fluoropolymers and waxes, have been found to be effective in eliminating sharkskin. Internal processing aids, such as boron nitride and clays, have been found effective in postponing the onset of gross melt fracture. In addition, different polymers have also been used as processing aids in the processing of other polymers with both polymers to be immiscible. In many of these cases melt fracture phenomena have been eliminated. The first objective of this present work was to study the rheological behavior of poly(methyl methacrylate) resins under shear and extension. Several frequency sweep experiments were carried out using the concentric parallel plate rheometer at various temperatures. By applying time temperature superposition, master curves for the linear viscoelastic moduli were obtained and the activation energy of flow was found to be independent of molecular weight. Following, extensional measurements using the Sentmanat Extensional RJieometer (SER) were attempted. It was found that poly(methyl methacrylate) resins exhibit shear thickening effects only at high shear rates. The main objective of this work was to identify suitable processing aids for the extrusion of poly(methyl methacrylate). Three different molecular weight poly(methyl methacrylate)s were tested together with various processing aids through capillary rheometer studies. ii ABSTRACT First, it was found that poly(methyl methacrylate) polymers exhibit spiral/helical type of distortions at a critical shear stress value (0.35 ± 0.03 MPa) independent of temperature and molecular weight. "Traditional" processing aids used mainly in the extrusion of polyolefins and some other commercial polymers were found ineffective in eliminating instabilities in the case of poly(methyl methacrylate) processing. On the other hand, mixing of poly(methyl methacrylate) with a proprietary blend of synthetic resins and fatty glycerides with modified organic fatty acids, MoldWiz® INT-35UDH, was able to reduce the extrusion pressure and postpone the onset of gross melt fracture to higher shear rates. Also, the addition of different polyethylenes (LLDPE, LDPE and HDPE) resulted into a significant pressure reduction along with significant postponement of gross melt fracture to higher shear rates. iii T A B L E OF CONTENTS T A B L E O F C O N T E N T S Page ABSTRACT ii LIST OF FIGURES v i LIST OF TABLES ix ACKNOWLEDGEMENTS x 1 INTRODUCTION 1 2 LITERATURE REVIEW 7 2.1 Rheological Measurements 7 2.1.1 Rotational Concentric Rheometer and Linear Viscoelasticity 7 2.1.2 Extensional Rheometer 16 2.1.3 Capillary Rheometer 19 2.2 Time Temperature Superposition 25 2.3 Melt Fracture 28 2.4 Mechanisms To Explain Melt Fracture 31 2.4.1 Die exit effects: Surface Melt Fracture (SMF) 31 2.4.2 Wall Slip Effects: Stick-slip 34 2.4.3 Die Entry Effects: Gross Melt Fracture (GMF) 35 2.5 Processing Aids (PAs) 38 2.5.1 External PAs 38 2.5.2 Internal PAs 40 2.5.3 Polymer Blends and the Mechanism of Processing Aid Action 41 2.5.4 Filters 42 2.5.5 Comments on Processing Aids for PMMA Resins 43 2.6 Miscibility Studies 44 3 OBJECTIVES 47 4 MATERIALS AND METHODOLOGY. 48 4.1 Polymers 48 iv TABLE OF CONTENTS 4.2 Processing Aids (PAs) 49 4.3 Blends Preparation 52 4.4 Experimental Methodology 54 4.4.1 Rotational Concentric Rheometry 55 4.4.2 Extensional Rheometry 56 4.4.3 Capillary Rheometry 57 4.5 Sample Inspection 59 5 RESULTS AND DISCUSSION 60 5.1 Introduction 60 5.2 Linear Viscoelasticity Studies : 60 5.2.1 Pure Poly(methyl methacrylate) Resins 60 5.2.2 Poly(methyl methacrylate) Blends with Processing Aids 69 5.2.3 Polymeric Processing Aids 74 5.3 Extensional Rheometer Studies 78 5.4 Capillary Rheometer Studies 82 5.4.1 Pure Poly(methyl methacrylate) Resins 82 5.4.2 Poly(methyl methacrylate) Blends with Processing Aids 86 5.5 Conclusion 97 6 RECOMMENDATIONS 99 REFERENCES 100 APPENDIX A - LINEAR VISCOELASTICITY OF PMMA RESINS 106 APPENDIX B - LINEAR VISCOELASTICITY OF VARIOUS POLYMERS. 110 APPENDIX C - CAPILLARY RHEOMETER STUDIES 115 NOMENCLATURE 126 v LIST OF FIGURES LIST OF FIGURES Page Figure 1.1 Aery late monomer 1 Figure 1.2 a-methacrylate monomer 2 Figure 1.3 Free radical vinyl polymerization of methyl methacrylate 2 Figure 1.4 Pictures of typical PMMA extrudates. Shear rate increases from left to right: (a) smooth, (b) helical, (c) severe helical and (d) indications of gross melt fracture 5 Figure 2.1 Schematic of a parallel plate rheometer 8 Figure 2.2 Small amplitude oscillatory shear response of a purely elastic solid and a purely viscous liquid 10 Figure 2.3 Indicative plot of G'(GJ) for three samples of a linear polymer 12 Figure 2.4 Indicative plot of G'(co) and G " (co) for PMMA 13 Figure 2.5 Mechanical analog of the generalized Maxwell model 13 Figure 2.6 Schematic of Sentmanat Extensional Rheometer 17 Figure 2.7 Capillary rheometer fitted with a capillary die 20 Figure 2.8 Pressure profile for a flow in a capillary 24 Figure 2.9 Typical Bagley plot 25 Figure 2.10 Typical apparent flow curve of a linear polymer 29 Figure 2.11 Apparent flow curve of PMMA(l) at 210°C 31 Figure 2.12 Time-temperature superposition failure 45 Figure 2.13 Sudden change in slope of storage modulus G ' and tan5 46 Figure 5.1 Storage modulus of PMMA(l) at various temperatures 61 Figure 5.2 Loss modulus of PMMA(l) at various temperatures 62 Figure 5.3 Complex viscosity data for PMMA(l) at various temperatures 62 Figure 5.4 The master curves of linear viscoelastic moduli of PMMA(l) at the reference temperature 170°C 63 Figure 5.5 The master curves of linear viscoelastic moduli of PMMA(2) at the reference temperature 170°C 64 Figure 5.6 The master curves of linear viscoelastic moduli of PMMA(3) at the reference temperature 170°C 64 Figure 5.7 The horizontal shift factors of all PMMA resins showing that the Arrhenius equation is closely followed 66 LIST OF FIGURES Figure 5.8 Overall fit of all horizontal shift factors of all PMMA resins showing that they follow the Arrhenius equation 67 Figure 5.9 Complex viscosity master curves of all PMMA resins at the reference temperature of 170°C 68 Figure 5.10 Linear viscoelastic moduli of PMMA(2) with and without 0.2%BN (blend prepared by compounding) 69 Figure 5.11 Linear viscoelastic moduli of PMMA(2) with and without 0.2%Nanomer I.44PA (blend prepared by compounding) 70 Figure 5.12 Linear viscoelastic moduli of PMMA(2) with and without 0.2%Atmer 1759 (blend prepared by compounding) 70 Figure 5.13 Linear viscoelastic moduli of PMMA(2) with and without 0.2%INT-35UDH (blend prepared by compounding) 71 Figure 5.14 Linear viscoelastic moduli of PMMA(2) with and without 0.2%PVDF 6010 (blend prepared by compounding) 71 Figure 5.15 Linear viscoelastic moduli of PMMA(2) with and without 2% BN (blend prepared by compounding) 72 Figure 5.16 Linear viscoelastic moduli of PMMA(2) with and without 2% Nanomer I.44PA (blend prepared by compounding) 73 Figure 5.17 Linear viscoelastic moduli of PMMA(2) with and without 2% INT-35UDH (blend prepared by compounding) 73 Figure 5.18 Linear viscoelastic moduli of PMMA(2) with and without 2% Atmer 1759 (blend prepared by compounding) 74 Figure 5.19 Complex viscosities of PMMA(l) and various other polymers used as processing aids 76 Figure 5.20 Complex viscosities of PMMA(2) and various other polymers used as processing aids 76 Figure 5.21 Complex viscosities of PMMA(3) and polyethylenes used as processing aids 77 Figure 5.22 Complex viscosities of PMMA(3) and various other polymers used as processing aids 77 Figure 5.23 Complex viscosities of all PMMA resins and LLDPE used as processing aid 78 Figure 5.24 The tensile stress growth coefficient of PMMA(l) for various Hencky strain rates at 170°C 79 Figure 5.25 The tensile stress growth coefficient of PMMA(2) for various Hencky strain rates at 170°C 80 Figure 5.26 The tensile stress growth coefficient of PMMA(3) for various Hencky strain rates at 170°C 80 Figure 5.27 Comparison of the tensile stress growth coefficient of all resins at = 22.6s"1 8 1 LIST OF FIGURES Figure 5.28 Maxwell model fit of linear viscoelastic moduli for all resins at temperature 170°C 82 Figure 5.29 Apparent flow curves of PMMA(l) at several temperatures 84 Figure 5.30 Apparent flow curves of PMMA(2) at several temperatures 84 Figure 5.31 Apparent flow curves of PMMA(3) at several temperatures 85 Figure 5.32 Pictures of typical PMMA extrudates at different shear rates 85 Figure 5.33 Apparent flow curves of PMMA(2) with and without Dynamar 591IX (blend prepared by dry mixing) 88 Figure 5.34 Apparent flow curves of PMMA(l) with and without Viton Z-200 free flow (blend prepared by dry mixing) 88 Figure 5.35 Apparent flow curves of PMMA(3) with and without PVDF 6010 (blend prepared by dry mixing) 89 Figure 5.36 Apparent flow curves of PMMA(2) with and without BN (blend prepared by compounding) 90 Figure 5.37 Apparent flow curve of PMMA(2) with and without Nanomer I.44PA (0.2% blend prepared by compounding) 91 Figure 5.38 Apparent flow curve of PMMA(2) with and without Nanomer I.44PA (0.5% blend prepared by compounding) 91 Figure 5.39 Apparent flow curve of PMMA(2) with and without Atmer 1759 (blend prepared by compounding) 93 Figure 5.40 Apparent flow curves of PMMA(2) with and without INT-35UDH (blend prepared by dry mixing) 93 Figure 5.41 Apparent flow curves of PMMA(l) with and without LLDPE (blend prepared by dry mixing) 95 Figure 5.41 Apparent flow curves of PMMA(l) with and without LDPE (blend prepared by dry mixing) 95 Figure 5.42 Apparent flow curves of PMMA(3) with and without HDPE (blend prepared by dry mixing) 96 Figure 5.43 Apparent flow curves of PMMA(2) with and without LLDPE & Dynamar 9613X (blend prepared by dry mixing) 96 Figure 5.44 Apparent flow curves of PMMA(2) with and without ABS (blend prepared by dry mixing) 97 LIST OF TABLES LIST O F T A B L E S Page Table 4.1 Typical properties of poly(methyl methacrylate) 48 Table 4.1 List of processing aids and their manufacturers 53 Table 4.1 List of average particle size of processing aids 54 Table 5.1 Horizontal and vertical shift factor values for PMMA(l), PMMA(2) and PMMA(3) 65 Table 5.2 Zero shear viscosity values obtained by fitting the Cross model on complex viscosity data 68 Table 5.3 Critical apparent shear rates and shear stresses for the onset of helical flow of all PMMA resins at various temperatures 86 ix ACKNOWLEDGEMENTS ACKNOWLEDGEMENTS I am grateful to my supervisor, Prof. Savvas G. Hatzikiriakos, for his skillful guidance and constructive criticism throughout the course of this work. I thank him for helping me become a better professional. I thank my parents, my sister and friends in Greece, and all my friends in Vancouver for all the support they have provided me all this time. They have all contributed in their own special ways. I would also like to thank all the members of the Rheology group of the University of British Columbia for their friendship, help and support. My extra gratitude goes to Edward Budi Muliawan for his help with the extensional rheometer experiments and the constant exchange of ideas. Above all I want to thank God for keeping me strong and healthy throughout this work. x C H A P T E R 1 - INTRODUCTION 1 I N T R O D U C T I O N Polymers either natural, such as wood, leather and wool, or synthetic such as polyolefins, fluoropolymers and acrylics have become part of our lives after the development of rubber technology in the 18th century. Polymers are the materials from which plastics, rubbers, fibers, surface coatings, and adhesives are made. They are classified as thermosets or thermoplastics according to their response to temperature, as addition or condensation polymers according to their mode of synthesis, or as linear, branched, or cross-linked according to their molecular structure. One of the most widely manufactured polymer families is the one of vinyl polymers family. It includes a group that chemists call "acrylates", but the rest of the world calls acrylics. Acrylics are made from acrylate monomers; the chemical structure of a typical acrylate monomer is shown in Figure 1.1. Acrylate monomers are esters which contain vinyl groups, that is, two carbon atoms double bonded to each other, directly attached to the carbonyl carbon. Some acrylates have an extra methyl group attached to the alpha carbon, and these are called methacrylates. The chemical structure of a typical a-methacrylate monomer is shown in Figure 1.2. \ Or carbon atom carbonyl carbon atom / Q R Figure 1.1 Acrylate monomer (http://www.psrc.usm.edu/macrog/acrylate.htm) 1 CHAPTER 1 - INTRODUCTION H / C H 3 F=<\ H C = 0 a methacrylate Figure 1.2 a-methacrylate monomer (http://www.psrc.usm.edu/macrog/acrylate.htm) This family of plastics includes a range of polyacrylates, poly(methyl methacrylate) (PMMA) and the important fiber-forming polymer, polyacrylonitrile. One of the most common methacrylate polymers is poly(methyl methacrylate) and it is being produced by the free radical vinyl polymerization of methyl methacrylate. The reaction can be seen in Figure 1.3. The most important acrylic plastics are based on PMMA. H CHT free radical \ / 3 v inyl polymerization / 3 C = C * + C H 2 — C + -/ \ \ n H C = 0 C = 0 0 0 C H 3 C H 3 methyl methacrylate poly(methyl methacrylate) Figure 1.3 Free radical vinyl polymerization of methyl methacrylate (http://www.psrc. usm. edu/macrog/images/pmma02.gij) Poly(methyl methacrylate) (PMMA) is an amorphous polymer known for its high hardness and stiffness. It is scratch-resistant and has high gloss surface capable of being polished. It exhibits good electrical and dielectrical properties, resistance to weak acids 2 CHAPTER 1 - INTRODUCTION and alkaline solutions as well as to non-polar solvents, grease, oils and water. It also exhibits good processability and machinability. Outstanding properties of PMMA are optical clarity, lack of color and unusually good resistance to outdoor weathering. The three basic types of PMMA resins available are cast sheet powder (used in glazing), standard moulding powder (used for making lenses and dials), and high-impact powder, which gives less transparency but takes higher shock loads. PMMA is the only industrial product based on acrylic resins that has found rigid applications. The production started at Darmstadt in Germany in 1927, under the leadership of Otto Rohm, cofounder of Rohm & Haas. The first application of PMMA was as an intermediate sheet in safety glass, followed during the Second World War in vacuum formed aircraft canopies. PMMA is made industrially by four different processes, i.e. bulk casting, bulk polymerization, suspension polymerization and emulsion polymerization, all based on free-radical chemistry. The worldwide capacity of PMMA stands of about 1.8 million tones (Blass and Wolf, 1998). The PMMA homopolymer is brittle. High impact molding compounds can be produced by co- and graft-polymerization with butadiene or other elastomers with low glass transition temperature. Such polymer blends or graft polymers are opaque. Crystal-clear copolymers are obtained with styrene or ct-styrene. PMMAs and their copolymers with acrylonitrile are of importance in industrial applications. Copolymerization with acrylonitrile increases resistance to solvents. PMMA is used in fittings, rear lights, housings, covers, vases, signs, dials, drawing instruments, watch glasses, lenses, light 3 CHAPTER 1 - INTRODUCTION shaded, aircraft cockpits, models, optical fibers, lighting, costume jewelry, sanitary fittings, artificial eyes, dental articles, corrugated sheets, tubes, sheet, steering wheel bosses, windshields, cisterns and pick-ups. There are different commercial polymer processing operations that are used to transform PMMA into a useful commercial product, such as fiber spinning, film blowing, profile extrusion, and various coating flows. The most important polymer processing operations are extrusion and injection molding (Vlachopoulos, 2000). In extrusion processes a limiting factor exists in the rate of production. At a given temperature, when the shear rate exceeds a given value, extrudate distortions are observed that render the product commercially unattractive. The severity of the distortions (amplitude and irregularity) usually increases with increasing flow rate. Thus, the production rate of commercially acceptable products is limited to the ones below these critical values (Achilleos et al, 2002). These phenomena of extrudate distortion/irregularities collectively are known as melt fracture phenomena. As the shear rate increases, small amplitude periodic distortions first appear on the surface of the extrudate, a phenomenon known as sharkskin melt fracture. As the shear rate increases further and depending on the molecular structure, the extrudate might be exhibiting alternating smooth and distorted portions. This phenomenon is called stick-slip melt fracture. Finally, at even higher shear rates, melt fracture takes the form of wavy or chaotic distortions phenomena, which are collectively known as gross (or volume) melt fracture. 4 C H A P T E R 1 - INTRODUCTION In the case of PMMA what is most frequently observed is a phenomenon called "helical extrudate from swirling entrance flow" (Dealy and Kim, 2004). This phenomenon at higher shear rates is followed by gross melt fracture. Figure 1.4 shows typical pictures of extrudates exhibiting these kinds of distortions at increasing values of shear rate. In order to overcome these difficulties and to render the processes economically feasible, processing aids (PAs) are frequently used. Processing aids eliminate flow instabilities or postpone them to higher flow rates. The end result is an increase of the productivity as well as an energy cost reduction, while high product quality is maintained. Processing a) b) c) d) Figure 1.4 Pictures of typical PMMA extrudates. Shear rate increases from left to right: (a) smooth, (b) helical, (c) severe helical and (d) indications of gross melt fracture aids (PAs) are used in small quantities of the order of 1000 ppm (Hatzikiriakos, 2004a). The most commonly used PAs are fluoropolymers, stearates and certain waxes. These have been used traditionally for surface melt fracture elimination in the case of CHAPTER 1 - INTRODUCTION polyethylenes. New processing aids, namely boron nitride (a solid inorganic compound) and nanoclays, have been recently found to be effective in delaying significantly gross melt fracture to higher shear rate values. To the author's knowledge, no processing aids have been developed to eliminate/postpone melt fracture phenomena in the extrusion of PMMA resins. The objective of this present work is to first study in general the rheology and processing of PMMA resins. It is another objective to study the processability of PMMA resins in capillary flow and study the instability occurring during capillary flow of PMMA resins. Finally and most importantly, it is another objective to identify possible processing aids for the extrusion of PMMA resins which are capable in eliminating and/or postponing melt fracture phenomena to higher shear rates while at the same time cause a reduction in the extrusion pressure (slip promotion). Different type of processing aids will be tested, including fluoropolymers, solid inorganic lubricants, polyethylenes, polyamides, fatty acids and others which will be discussed later. Pure polymer and polymer blends including various processing aids (PAs) will be tested, analyzed and fully characterized by means of rheological techniques. 6 CHAPTER 2 - LITERATURE REVIEW 2 L I T E R A T U R E R E V I E W This chapter presents a number of important concepts and terminologies, useful for gaining a better understanding of the analysis and interpretation of experimental results which will be presented in the subsequent chapters. The topics covered in this section include: rheological techniques and measurements of the polymers used; melt fracture phenomena; and the use of polymer processing aids to eliminate these phenomena for polymers such as polyolefins. 2.1 Rheological Measurements Rheology is defined as the science of material behavior under deformation, due to the application of external forces (Dealy and Wissbrun, 1990). It attempts to understand why a material behaves in a certain way when a force is applied. There are certain techniques that can be used to determine the rheological behavior of various fluids. Some of these are discussed below, especially those used in the present study. The equations which underline the operation of the rheological equipment and data analysis obtained from these rheological techniques are also discussed to a certain detail. 2.1.1 Rotational Concentric Rheometer and Linear Viscoelasticity An important aspect of polymer rheology is the study of the viscoelastic behavior of the molten polymer. Most polymeric materials are said to be Theologically viscoelastic, i.e. possess rheological properties similar to viscous liquids (dissipate energy) and similar to 7 C H A P T E R 2 - L I T E R A T U R E REVIEW elastic solids (store energy) components which depend on the time scale of the deformation. Concentric plate rheometers are commonly used to study the viscoelastic properties of polymers (Dealy and Wissbrun, 1990). Typically, these rheometers are also used extensively in industry for quality control purposes because experimental data from these rheometers are relatively fast to collect and able to reveal structural information (Dealy and Wissbrun, 1990). A schematic of the parallel plate rheometer is shown in Figure 2.1. In this rheometer, two circular plates are mounted on a common axis of symmetry, and the sample is inserted in the space between them. The upper plate is rotated at a specified angular velocity <y(t) and as a result the sample is subjected to shear. In general the motion of the upper plate can be programmed to generate ant type of deformation, and the resulting torque, M, is measured (strain controlled rheometer). Another mode of operation is fixing the torque and measuring the displacement (stress controlled rheometer). i c ^ca(t) .y 1 A / H i zi u \ Fluid * sample Pressure ^ ^ 3r transducer Figure 2.1 Schematic of a parallel plate rheometer. 8 CHAPTER 2 - LITERATURE REVIEW The real power of this instrument lies in its ability to apply very small amount of deformations in dynamic or oscillatory fashion, without breaking the elastic structure of the sample. This is known as linear viscoelastic characterization of the material and provides very useful information about the molecular structure of the material. The most common type of deformation used to characterize Theologically molten polymer is the imposition of sinusoidal strain deformation. This is also known as small amplitude oscillatory shear and a brief overview of this test is presented here. As discussed above, a very small shear strain is applied to the sample sinusoidally - this is similar to vibrating the sample within its linear elastic range, and the stress response of the sample is observed. Since a viscoelastic material possesses properties of combined viscous and elastic character it is expected that: the elastic contribution/component to the stress response will follow Hook's law, where stress is directly proportional to strain - leading to stress responses "in phase" with the applied sinusoidal strain; on the other hand the viscous or liquid contribution/component will follow Newton's law, where stress is directly proportional to shear rate - leading to stress responses completely "out of phase" to the applied strain. This is shown schematically in Figure 2.2. Applied Sinusoidal Strain Time ^ ' ~ ~* -. Purely Elastic Stress Response of Solid (0 0 phase lag) Time Purely Viscous Stress Response of Liquid (90 0 phase lag) s~ — - - ' Time Figure 2.2 Small amplitude oscillatory shear response of a purely elastic solid ana a purely viscous liquid 9 CHAPTER 2 - LITERATURE REVIEW In practice, most polymeric materials are a combination of viscous and elastic components and so the measured phase angle (S) will be somewhere between 0° and 90°. Since in this test, stress and strain are constantly changing, the viscoelastic properties are described in terms of elastic (storage) modulus (G') and viscous (loss) modulus (G") defined below. Applied sinusoidal strain can be represented as: y(t) = y0 sin(flrf) (2.1) where yo is the strain amplitude and co is the frequency. The stress response can be shown to be also sinusoidal and written as: o~(t) = cr0 sin(cot + S) (2.2) where <TQ is the stress amplitude and S is a phase angle shift in the response. Using a trigonometric identity, one can rewrite Equation 2.2 in the following form: °(t) = Yo CT—cos( S)sm( cot) + — sin(5)cos( cot) r0 (2.3) From Equation 2.3, one can define the dynamic moduli as G'= Yo -cos(S) and ^ s i n ( J ) Yo 10 CHAPTER 2 - LITERATURE REVIEW There are two other parameters that are frequently used to present the test results. These are the complex modulus (G*) and the complex viscosity (7*), defined as: G'=G' + iG" (2.4) V =" ~ i n (2.5) G' G'' where, 77' = — and 7 " = - — co co As mentioned earlier, the oscillatory tests are very sensitive to the molecular structure of the polymer sample. Figure 2.3 (Dealy and Wissbrun, 1990) shows a typical plot of storage modulus for different molecular weight (MW) linear polymer samples of the same homologous series. It may be observed that at high frequencies, glassy behaviour is exhibited and the behavior is independent of MW. At smaller frequencies, molecular rearrangement becomes possible and that leads to a transition zone. For the low molecular weight materials (A) such transition zone does not exist and the terminal zone is obtained directly. For the higher MW sample (B), a plateaue zone is obtained. The plateaue zone is not clear for polydisperse material (C). 11 CHAPTER 2 - LITERATURE REVIEW co (log scale) Figure 2.3 Indicative plot of G'(co) for three samples of a linear polymer. ( A ) is monodisperse with low MW, (B) is monodisperse with high MW, and (c) is polydisperse with high MW (Dealy and Wissbrun, 1990). Figure 2.4 depicts linear viscoelastic moduli for a linear polymer. It may be observed that at small frequencies (terminal zone) G' becomes proportional to co2 (slope of 2), whereas G" proportional to co (slope of 1). It may also be noted that at low frequencies, G" > G', implying a rubbery or liquid like behaviour. At higher frequency, a crossover exists indicating a rigid, glassy or solid like behaviour. The linear viscoelastic response of a molten polymer under any kind of deformation can be predicted if the relaxation modulus G(t), is determined . It is convenient to have a general form for G(t) that contains sufficient parameters to fit experimental data, such as G' and G ". The most popular approach to establish such a functional form is based on the . use of the Maxwell element analogy, that is a linear spring in series with a dashpot. Greater flexibility can be obtained by use of the "generalized Maxwell model", which is 12 CHAPTER 2 - LITERATURE REVIEW the rheological constitutive equation analogous to the mechanical assembly shown in Figure 2.5 (Dealy and Wissbrun, 1990). Frequency (log scale) Figure 2.4 Indicative plot of G'(co) and G" (co) for PMMA. The forces in the various elements are additive, and the general Maxwell constitutive equation model can be written as: r9 (') = j l Gk {exp[- (t - t')l Xk ]};>. (t')dt' (2-6) where Gk and Xk. are the modulus and relaxation time corresponding to each Maxwell element. Figure 2.5 Mechanical analog of the generalized Maxwell model 13 CHAPTER 2 - LITERATURE REVIEW The relaxation modulus for an assemply of N Maxwell elements is: G{t) = fjGl[cxp(-t/Ai)] (2.7) By using a sufficient number of elements, this equation can be made to describe almost any experimental G(t) behavior. Between five and ten (Gi - A,-) pairs are usually sufficient to fit experimental data reasonably well. Such a set of values is called a "discrete relaxation spectrum" of the material. Since linear viscoelasticity is governed by the Boltzmann supeposition principle, which is based on the relaxation modulus, G(t), it is possible to predict the response of a material to any kind of deformation. In the case of small amplitude oscillatory shear, it can be shown that G'(co) and G"(a>) are the Fourier sine and cosine transforms, respectively, of the relaxation modulus (Dealy and Wissbrun, 1990): G'(co) = co \G(s)sm(o)s)ds (2-8) 0 m (2 9) G"{co) - co JG(s)cos(cos)ds 0 If a generalized Maxwell model is used to represent the relaxation modulus (Equation 2.7), the resulting functions are: 14 CHAPTER 2 - LITERATURE REVIEW GW = £ f ^ £ l (2-10) R „ ( \ T?_G _ (2.11) Apart from the small oscillatory shear experiment another useful test in linear visocelasticity is the start up of steady shear experiment. In such an experiment, a sample initially in an equilibrium state is subjected to a constant strain rate starting at time t = 0. The data are reported in terms of the "shear stress growth coefficient" defined as follows: n+(t) = <r(t)/r (2.12) where a(t) is the instanteneous shear stress and y is the shear rate. The Boltzamann superposition principle can be used to show how the shear stress growth coefficient is related to the relaxation modulus. If we set s = t-t'; n+(t) can be written as: rj+(t)='\G(s)dS (2"13) 0 The coefficient t]+(t) at long times becomes the viscocity of the material at the shear rate, y. The viscosity of molten thermoplastics decreases sharply as the shear rate is increased. At sufficiently low shear rates, the viscosity normally becomes independent of shear rate. The constant viscosity that prevails at very low shear rates is called the "zero 15 CHAPTER 2 - LITERATURE REVIEW shear voscosity" and is denoted by the symbol n0. A number of generalized power law equations has been proposed that predict an approach to a constant viscosity at low shear rates (Dealy and Wissbrun, 1990). Cross (1968) proposed the following relationship to exhibit shear thinning: At low shear rates the viscosity approaches rj0, while at high shear rates ( | / l ^ | » l ) power law behavior is predicted. 2.1.2 Extensional Rheometer Another important method in characterizing polymeric material is to study its behavior under extensional deformation. In this kind of experiment, the ends of a polymer sample are stretched, often under relatively high extensional rates. This high extensional rate subjects the polymer to non-linear deformation, which helps to understand and reveal structural information that is otherwise impossible to obtain from linear viscoelastic data. For example, the molecular weight distribution and the degree of long branching may have the same effect on the linear viscoelastic properties of a polymer. However, these effects can be separated by studying the sample under extensional flow (Munstedt, 1980). A schematic of an extensional rheometer which has been used in this study is shown in Figure 2.6. (2.14) 16 CHAPTER 2 - LITERATURE REVIEW A = Master windup drum B = Slave windup drum C = Bearings D = intermeshing gears E = Chassis F = Drive shaft G = Torque shaft H = Polymer sample I = Securing clamps Figure 2.6 Schematic of a Sentmanat Extensional Rheometer (Sentmanat, 2003a). This extensional rheometer is designed for use as a detachable fixture on commercially available rotational rheometer host systems whose main function was described in the previous section. As such, this rheometer is able to fit within the host oven chamber, thus allows temperature-controlled testing. The extensional rheometer consists of master and slave windup drums. Rotation of the master drum with an angular speed, fl, results in an equal but opposite rotation of the slave drum. This causes the ends of the affixed sample to be wound up onto the drums resulting in the sample being stretched over an unsupported length, L 0 . For a constant drive shaft rotation rate. fl, the Hencky strain rate applied to the sample specimen can be expressed as (Sentmanat, 2003b) 17 CHAPTER 2 - LITERATURE REVIEW where R is the radius of the windup drums, and L 0 is the fixed, unsupported length of the specimen sample being stretched which is equal to the centerline distance between the master and slave drums. The material's resistance to stretch is observed as a tangential force, F, acting on the drums which is then translated as a torque upon the chassis housing the assembly. The resultant torque transmitted through the chassis to the torque shaft is determined from the summation of moments about the axis of the torque shaft. This yields (Sentmanat, 2003b) T = 2{F + FF)R (2.16) where T is the resultant torque measured by the torque transducer, and FF is the frictional contribution from the bearings and intermeshing gears. With precision bearings and gears, the frictional term is typically quite small (< 2% of the measured torque signal) and can be neglected such that equation 2.16 may be simplified to (Sentmanat, 2003b) T = 2FR (2.17). For polymer melts, if there is no deviation between the nominal and actual strain rates, the instantaneous cross-sectional area, A(t), on the stretched material changes exponentially with time for a constant Hencky strain rate experiment and can be expressed as (Sentmanat, 2003b) 18 CHAPTER 2 - LITERATURE REVIEW A(t) = A0exp[-eHt] (2.18) where A 0 is the initial cross-sectional area of the unstretched specimen. For a constant Hencky strain rate, the tensile stress growth coefficient, n*(t), of the stretched sample can then be expressed as (Sentmanat, 2003b) where F(t) is the instantaneous extensional force at time t exerted by the sample as it resists stretch. 2.1.3 Capillary Rheometer Flow of molten polymer through a tube or a channel under pressure is commonly encountered in polymer processing, for example in an extrusion die or in the runner feeding of an injection mold. A capillary rheometer simulates this type of flow behavior. Capillary rheometers are also used widely to determine the viscosities in the shear rate range from 5 to 5000 s"1 (Dealy and Wissbrun, 1990). Reproducibility of capillary rheometer experiments is typically ± 5%. In the present research work, capillary rheometer is primarily used to extrude pure PMMA and blends of PMMA mixed with different polymer processing aids in order to study the effect of these polymer processing aids in eliminating/postponing the appearance of melt fracture at a given shear rate. _ Fit) (2.19) sHA{t) 19 CHAPTER 2 - LITERATURE REVIEW The capillary rheometer consists of a melt reservoir or barrel in which the polymer is melted and a plunger or piston that forces the melt to flow through a die of known measurements (e.g diameter, D, or length, L). The quantities normally measured are the volumetric flow rate, Q and the driving pressure, P<j. A schematic diagram of the rheometer and the capillary die is shown in Figure 2.7. I Constant force or X constant rate Figure 2.7 A schematic diagram of ROSAND Capillary Rheometer fitted with a capillary die. For this particular flow, simple equations can be derived to determine shear viscosity as far as Newtonian and power law fluid is concerned. For other types of fluid, where no specific constitutive equation is known to be valid, special computational techniques are required to calculate the shear stress, shear rate and viscosity. 20 CHAPTER 2 - LITERATURE REVIEW For a steady and fully developed flow of an incompressible fluid in a tube of radius R, a force balance can be performed to yield the absolute value of shear stress at the tube wall, o~w: AP R where APW is the pressure drop over the length of the tube, L. For a Newtonian fluid, shear stress is related to deformation by: a = r/y (2.21) where the viscosity rj, is constant at a given temperature. Combining Equations 2.20 and 2.21, the fully developed parabolic velocity profile of Newtonian fluid can be obtained. Knowing the velocity profile, the shear rate at the tube wall can be calculated by differentiating the velocity profile with respect to the radius of the tube to yield: • x dV /(Newtonian) = — dr r=R ^ (2-22) where Q is the volumetric flow rate. For non-Newtonian fluids, the velocity profile differs compared to that for a Newtonian fluid. In addition, a constitutive equation is also needed to represent the viscosity of the 21 CHAPTER 2 - LITERATURE REVIEW fluid which depends on the shear rate. If a power law model is assumed, the constitutive equation is given by: o- = Ky" (2.23) where K and n are the consistency index and the power law exponent, respectively. Note that the special case of Newtonian flow behavior is recovered for n=l. It can be shown that the wall shear rate for a power law fluid is given by (Dealy and Wissbrun, 1990): y. 3» + l An (2.24) It is noted that the term in bracket in the above equation is the wall shear rate for a Newtonian fluid (Equation 2.22). This term itself has no significance in the non-Newtonian case and it is, referred to as the "apparent shear rate", yA . Using Equation 2.23 and 2.24, it can be shown that a ^ K { - ^ r ) ^ (2-25) The constants K and n can be determined from the intercept and the slope of the straight-line plot of the above equation in a double log scale. 22 CHAPTER 2 - LITERATURE REVIEW If no specific constitutive equation is assumed, it is then not possible to calculate the true shear rate at the wall directly, knowing onlyyA. A special technique which requires pressure drop data for a number of flow rates is needed. This technique makes use of the plot of log(crw) versus log(fA).T\is true wall shear rate is then given by: fA (2-26) V * J where b is the Rabinowitsch correction given by This correction term measures the fluids deviation from Newtonian behavior. It equals unity for a Newtonian fluid and 1/n for a power-law fluid. A large number of data is needed for this technique since differentiation is required to determine b. In a capillary rheometer, the shear stress is determined by monitoring the driving pressure, Pd, in the barrel and assuming that the pressure at the outlet of the capillary is equal to the ambient pressure, Pa. Pd can be related to the force that is driving the piston (plunger), Fd, as: (2.28) 23 CHAPTER 2 - LITERATURE REVIEW where Rb is the radius of the barrel. The pressure drop (-APW) in Equation 2.20 is then given by (Pd-Pa) or, since for melts Pd is nearly always much larger than Pa, the pressure drop can simply be replaced by Pd. However, this is not the actual pressure drop that is observed for a fully developed flow in a capillary of length L. End correction is needed to take into account the large pressure drop at the entrance of the capillary and the small residual pressure at the exit. Figure 2.8 shows the pressure profile for a flow in a capillary. B A R R E L Figure 2.8 Pressure profile for a flow in a capillary. The pressure end correction can be determined as outlined by Bagley (1931) in which the driving pressure, Pd is plotted versus the length to diameter (L/D) ratio of capillaries of fixed diameter for each value of wall shear rate. This plot is also referred to as the "Bagley plot". A typical Bagley plot is shown in Figure 2.9. The end correction is obtained by extrapolating the plot to L/D=0 (another way of determining Pend is by making use of an orifice die with L=0). Using the corrected pressure drop, the wall shear stress can then be calculated as 24 CHAPTER 2 - LITERATURE REVIEW 4(L/D) (2.29). In general, the Bagley plot may include some curvature at high L/D ratio. This is due to the dependence of viscosity on pressure, slip at wall or viscous heating (Hatzikiriakos andDealy, 1992). 2.2 Time Temperature Superposition Rheological properties of molten polymers such as those obtained from parallel plate or capillary rheometer are usually highly dependent on temperature. This means that to obtain a complete picture of the behavior of the polymer, experiments must be carried out at several temperatures. It is often found that rheological data measured at several temperatures can be brought together on a single master curve by means of "time-temperature superposition" (Dealy and Wissbrun, 1990). This greatly simplifies the P 0 Figure 2.9 A typical Bagley plot. 25 CHAPTER 2 - LITERATURE REVIEW description of the effect of temperature. Furthermore, it makes possible the display on a single curve of material behavior covering a much broader range of time or frequency than can ever be measured at a single temperature. Materials whose behavior can be displayed in this way are said to be "thermorheologically simple" (Dealy and Wissbrun, 1990). It is found that data for different temperatures can often be superposed by introducing a shift factor, aT, determined empirically. Thus, if one makes a plot of a rheological property versus a quantity with a time unit, ar is obtained from the horizontal shift necessary to bring the data corresponding to a specific temperature T onto the same curve as data corresponding to another temperature TQ. For example, to superpose flow curves (shear stress versus shear rate) obtained from different temperatures, the curves have to be plotted on a shear stress versus (shear ratex« 7 . ) scale. Note that no shift factor is required for quantities containing no units of time. This implies that a plot of such a quantity versus another, both containing no units of time, will be temperature independent. The shift factor is a function of temperature, and the WLF equation has been found to be a useful correlation for ar (Ferry, 1980): . . , - C ? ( T - T 0 ) logM=cJ7^T7) (2-30) 26 C H A P T E R 2 - LITERATURE REVIEW where C,° and C2° are constants determined at 7b for each material. This equation holds at temperatures very close to glass transition temperature, Tg. At temperatures at least 100 K above Tg, an empirical relationship, the Arrhenius equation, has been found to be valid (Dealy and Wissbrun, 1990): where Ea is the flow activation energy, R is the gas constant, and Tref is the reference temperature. Since the processing temperatures of PMMA are much higher than Tg (about 100°C), equation 2.31 is chosen to be used in this present work. There are some cases where rheological data might need both horizontal and vertical shifting in order to generate the master curve, as in the case of the linear viscoelastic data obtained for PMMA. Even though this case is still under investigation by many researchers in order to come up with models that perfectly predict the polymers behavior, the modified Rouse model (Gurp and Palmen, 1998) is capable of predicting both horizontal and vertical shift factors. The shift factors are defined as: log(ar)=- (2.31) r,(T) (2.32) r,(T0) bT = G,(T) (2.33) G,{T.) 27 C H A P T E R 2 - LITERATURE REVIEW where ar and bj are called horizontal and vertical shift factor respectively, and T, is the relaxation time and G, is the relaxation modulus. When both horizontal and vertical shifting exist, the modified Rouse theory predicts that the product of the horizontal and vertical shift factors equals the shift factor determined from the zero shear viscosity: aTbT = (2.34) which is consistent with the above discussion and references. 2.3 Melt Fracture Melt fracture is a term, used collectively for the appearance of instabilities that occur beyond a critical shear rate in a capillary, slit or annular dies during the extrusion of polymers. The term melt fracture was introduced by Tordella (1956) because of the audible tearing noises which accompanied the distortion of the extrudate. Melt fracture is a major problem in the extrusion of linear low-density polyethylenes (LLDPEs) and many other commercial polymeric materials such as PMMA studied in this thesis. In addition to shear rate or processing speed, melt fracture depends on a number of factors which include the polymer structure and its molecular characteristics, die geometrical characteristics and the process temperature. There are various types of flow instabilities observed in the flow of polymeric liquids through capillary, slit and annular dies. These are also sometimes reflected in the 28 CHAPTER 2 - LITERATURE REVIEW apparent flow curve, determined by means of a capillary rheometer. An apparent flow curve is basically a log-log plot of the wall shear stress as a function of the apparent shear rate. Depending on the die geometry and the type of polymer tested, the flow curve may exhibit different flow regions. A typical apparent flow curve for a linear polymer such as high-density polyethylene (HDPE) and linear low-density polyethylene (LLDPE) is shown in Figure 2.10. One can easily identify the five different flow regions in the flow curve. Initially, there is a stable region where the extrudate appears smooth and glossy (region 1). In this region, the behavior of the melt resembles that of a Newtonian fluid and the no slip boundary condition can be assumed to be valid. Figure 2.10 A typical apparent flow curve of a linear polymer Beyond some critical wall shear stress, <JC\, the first visual manifestation of flow instability appears. The extrudate beyond this critical value exhibits high-frequency, small-amplitude periodic distortion on its surface, a phenomena known as sharkskin 29 CHAPTER 2 - LITERATURE REVIEW (region 2). The onset of sharkskin appears to coincide with a change in the slope of the apparent flow curve (Achilleos et al, 2002; Hatzikiriakos et al, 1995; Kalika and Denn, 1987). At a second critical wall shear stress value, <JCI and within a certain range of apparent shear rates, the flow ceases to be stable (region 3). This is the region of oscillating or stick-slip melt fracture, where the extrudate exhibits alternating smooth and distorted portions. In this region, the extrusion pressure oscillates between two extreme values. The periodic variations of the pressure define a hysteresis loop that connects the two branches of the apparent flow curve. At higher throughputs, there is sometimes a transition to a second stable flow regime in which the extrudate again becomes smooth. This is called the super extrusion region (region 4). Finally, at still higher shear rates, melt fracture takes the form of a wavy chaotic distortion, commonly called gross melt fracture. Gross melt fracture gradually becomes more severe with an increase in the apparent shear rate, yA (region 5). Figure 2.11, represents a typical example of an apparent flow curve of PMMA. As it can be seen in this case, no sharkskin and stick-slip instabilities are observed which are in contrast with the behavior of a LLDPE or a HDPE. This behavior rather resembles those obtained for a low-density polyethylene or that of a polypropylene (Achilleos et al, 2002). 30 C H A P T E R 2 - LITERATURE REVIEW Q. w v> 2 4-1 CO u . CO 0) J= to 4-1 c a Q. < 0.1 PMMA(1), T = 210°C Capillary Die: L/D = 16, D = 1mm 101 102 103 Apparent Shear Rate (s~1) Figure 2.11 Apparent Flow Curve of PMMA(l) at 210°C. Arrows indicate the onset of helical flow and severe gross melt fracture respectively. 2.4 Mechanisms To Explain Melt Fracture As a result of the large number of research work and the use of sophisticated flow visualization techniques, there is a general agreement among the researchers about the causes of the two types of melt fracture - gross melt fracture and surface melt fracture. 2.4.1 Die exit effects: Surface Melt Fracture (SMF) There is general agreement about the site of initiation of melt fracture, which is located at the die exit. The first theory about surface melt fracture was proposed by Howells and Benbow (1962) and later by Cogswell (1977). They hypothesized that the polymer 31 CHAPTER 2 - LITERATURE REVIEW fractures due to high stretching rates and to high stresses as a result of the abrupt change (shear to free surface flow) in the boundary condition at the exit of the die. The melt leaving the die in the neighborhood of the wall experiences a large, rapid, tensile deformation as the velocity field adjusts from the no-slip boundary condition to a free-surface condition. Polymer chains are stretched during the tensile deformation, which causes the highly entangled polymer to respond like a rubber. The large stresses on the free surface cause the cracks to open up giving them the appearance of sharkskin. Therefore, as the melt is extruded out of the die, it experiences a sudden jump in velocity near the die exit leading to large extensional stresses on the polymer surface, which results in the surface distortion (or sharkskin). In short, the absence of lubrication at the die exit is considered as the main cause of sharkskin. The findings by Howells and Benbow (1962) are also supported by other researchers. Bergem (1976) carried out capillary experiments for different polymers, using a tracer technique. He found that sharkskin arose from a tearing of the melt at the exit of the capillary. Piau et al (1988) has shown that cracks on the surface of extrudate always originate at the exit of the die. It should be noted that the existence of localized stresses at the die exit is also confirmed by birefringence photographs (Vinogradov and Malkin, 1980). Tremblay (1991) simulated the flow of a linear polydimethylsiloxane melt and showed that high stresses at the die exit produce negative hydrostatic pressure. He suggested that cavitation should occur very close to the die lip, thus leading to surface effects. 32 CHAPTER 2 - LITERATURE REVIEW Kurtz (1992) suggested that two critical conditions are required for sharkskin. First, a critical value of the wall shear stress must be exceeded and, second, the extrudate must be stretched for a sufficient period of time as it leaves the die. Moynihan et al (1990) added to this conclusion that the melt should be first "pre-stressed" critically at the entry region of the die. Ramamurthy (1986) suggested that the onset of sharkskin was accompanied by the occurrence of wall slip in the capillary. This suggestion is supported by a noticeable slope change in the flow curve at the onset of sharkskin (Kurtz, 1984) which can be interpreted as slip. However, Piau and El Kissi (1992) argued that slip in the die cannot explain the origin of the sharkskin. Hatzikiriakos (1994) carried out numerical simulations of the flow of high density and linear low density polyethylenes under slip conditions and showed that slip is not a necessary condition for the occurrence of the sharkskin phenomenon, although it may affect it. Instead, a critical extension rate at the capillary exit and a critical pre-stress of the polymer at the land region of the die provide the necessary conditions for its occurrence. Wang et al (1996) speculated that the slope change in the flow curve arises from a combination of interfacial slip and cohesive failure due to chain disentanglement initiated on the die wall in the exit region. Since the disentanglement state is unstable for the adsorbed chains, it is followed by a consequent re-entanglement, thus producing entanglement-disentanglement fluctuations that cause the sharkskin phenomenon. However, perhaps the most significant finding made by Wang et al (1996) was that the 33 CHAPTER 2 - LITERATURE REVIEW sharkskin dynamics is in good correlation with chain relaxation process. They used capillaries of different diameter and measured the period of surface distortions. Regardless of the capillary geometry, the period of surface distortions was found to be directly proportional to a polymer characteristic relaxation time, which was determined as an inverse of the crossover frequency of the storage and loss moduli. Sharkskin does not occur for all polymers (Denn, 1990), and for those for which it does occur, the onset condition has been found to depend on various operational and geometric factors which include die design and geometry, the structure of the polymer and its molecular characteristics and the process temperature. Melt fracture is most easily observed during extrusion at high throughputs through a long die (Moynihan et al, 1990). Usually, the critical shear rate or shear stress decreases with an increase in process temperature (Kurtz 1992). 2.4.2 Wall Slip Effects: Stick-Slip There is a second critical stress at which periodic pressure pulsations are frequently observed. The extrudate surface alternately shows relatively smooth and sharkskin regions. This is known as stick-slip, or spurt flow. In this region, the average stress remains approximately constant in the stick-slip region. Although this phenomenon has been reported by several authors (Tordella, 1963; Myerholtz, 1967), the mechanism of the initiation of this oscillation has not been explained thoroughly. 34 CHAPTER 2 - LITERATURE REVIEW Both Lin (1985) and Myerholtz (1967) who performed studies on the oscillating flow in different polyethylene samples, reported that oscillating melt fracture occurs more prominently in polymers that have narrower molecular weight distribution or higher molecular weight, or if the experiments were done at lower operating temperature or using longer dies. Tordella, (1963) suggested that this oscillating phenomenon is precipitated by slippage of the melt at the capillary wall. This explanation was further justified by experiments done by Lupton andRegester (1965). Probably the best explanation for stick-slip melt fracture was given by Leonov (1984). He explained that as polymer is extruded through a die, the shear stress increases up to a certain level (upper extreme value of shear stress) above which the polymer starts to slip. This slippage instantaneously reduces the stress level to a lower value (lower extreme value of shear stress) that causes the shear stress to increase again. This process repeats itself, thus resulting in an oscillating flow where the stress level varies between two extreme values. This oscillating flow occurs until the shear rate is increased to a value that is large enough to promote total wall slip. This explanation also helps in understanding the occurrence of stick-slip only in linear polymers. In non-linear polymer, such as low-density polyethylene (LDPE), there is significant branching that allows the polymer to stick to the die wall, thus preventing wall slip. 2.4.3 Die Entry Effects: Gross Melt Fracture (GMF) Most authors agree in claiming that above a certain extrusion rate, the flow upstream of the die contraction becomes unstable. These instabilities occur in the form of sudden 35 CHAPTER 2 - LITERATURE REVIEW pulsations or cavitation which were confirmed by visualization (Piau et al, 1990; Kazatchkov et al, 2000; Son and Migler, 2002) and birefringence measurements (Tordella, 1969). They showed that such instabilities started along the upstream flow axis owing to the high elongation stresses that develop in this area. These instabilities trigger the phenomenon of gross melt fracture, which is often seen in the form of a regular helix oscillating at the same frequency as that of the pulsations of the upstream elongational flow (Piau et al, 1990). It is then generally accepted that gross melt fracture is a die entrance phenomenon. This phenomenon affects the entire cross sectional area of the extrudate and is therefore sometimes called volume melt fracture to distinguish it from sharkskin, which affects only the surface of the extrudate and is often called surface melt fracture (Dealy and Kim, 2004). However, volume melt fracture also includes the helical extrudate that is caused by a swirling motion of the melt as it enters the converging section of the die. Smooth, helical extrudates, which are noticed in the case of PMMA extrusion, from a capillary were first noticed by Tordella (1956), who associated them with a swirling flow at the entrance. It has been clearly demonstrated, as been reported by Oyanagi (1973) and Bergem (1976), that such extrudates do indeed result from an entrance flow instability that causes the spiraling of the flow as it enters a capillary from a larger reservoir. When a given polymer exhibits both helical extrudate and gross melt fracture (i.e. poly(methyl methacrylate), the spiral flow occurs first as the flow rate is increased (Dealy and Kim, 2004). 36 CHAPTER 2 - LITERATURE REVIEW Oyanagi (1973) used birefringence to visualize swirling entrance flow and hypothesized that it involved slow, localized slip along a conical surface that rotated along with the streamlines. On the other hand, McKinley et al (1991) did not see any evidence of slip in their thorough experimental study of hydroelastic entrance flow instabilities in abrupt contractions, and McKinley et al (1996) later reported a theoretical framework for analyzing the swirling flow as a hydroelastic instability with no slip surface. Oyanagi (1973) also observed two additional types of unstable flow in his studies of high-density polyethylene (HDPE). At flow rates above those where swirling flow occurred, he observed a "switching" motion in which the angle of the center streamline oscillated periodically between two limiting values, producing a "zig-zag" or "wavy" extrudate. This is a type of flow observed in slit flow under conditions that would produce swirling flow in a capillary, i.e., the extrudate is smooth and there is a periodic oscillation of the angle of the center surface of the flow about the center plane of the die (McKinley et al, (1996). Further evidence that may suggest that gross melt fracture is initiated at the die entrance is presented by Kalika and Denn (1987) and Piau et al (1990). Their studies show that gross melt fracture occurs when the wall shear stress reaches a critical condition that seems to depend only on the polymeric fluid and little or not at all on the characteristics of the die (diameter, length, and the material of construction). 37 CHAPTER 2 - LITERATURE REVIEW 2.5 Processing Aids (PAs) As discussed earlier, both surface and gross melt fracture pose an undesirable constraint on the rate of production. It is necessary to eliminate melt fracture or postpone it to higher rates in order to increase the rate of production. Processing aids used for melt fracture and gross melt fracture elimination include different additives, surface coatings and solids. Some of them target a slip promotion at the die exit, thereby eliminating surface melt fracture and they are called "external" PAs. This in turn also reduces the extrusion pressure. On the other hand, there are the "internal" PAs and their presence results into a more "organized" flow, thus eliminating gross melt fracture. Typically, polymer processing aids are fluoropolymers, stearates and certain waxes, which have been used traditionally for surface melt fracture elimination. Processing aids are usually used in small quantities of the order of 1000 ppm (Hatzikiriakos, 2004a). They have a good affinity with the wall and create a fine coating on the die wall during extrusion. 2.5.1 External PAs External processing aids, like fluoropolymers, create a fine coating on the die wall during extrusion of polyethylenes. The extruding polymer then slips along the smooth coating on the die, thus eliminating the surface melt fracture (Rudin et al 1985; Anastasiadis and Hatzikiriakos, 1998; Denn, 2001; Migler et al, 2001; Achilleos et al, 2002). This in turn reduces the extrusion pressure. Rrtester and Stewart (1992) suggested that the factors that may affect the performance of the processing aid include the level of additive, dispersion quality and the interaction with 38 CHAPTER 2 - LITERATURE REVIEW other ingredients (antioxidants and stabilizers) in the resin. They have also mentioned that a large number of small particles of the additive can result into a better polymer processing effect than a small number of large particles. It was also reported that a masterbatching step was required in order to provide a good quality of dispersion of additives into the resin. This view, however, has recently changed through the work of Oriani and Chapman (2003). It was demonstrated that large fluoropolymer particles dispersed into the polymer, coat the die easier and faster. This allows melt fracture to be eliminated faster. In general, fluoropolymer based processing aids reduce the pressure required to extrude the resin at a particular flow rate and eliminate or postpone surface melt fracture to higher extrusion rates. It should be noted that these additives can eliminate only sharkskin and the so-called stick-slip (oscillating or cyclic) melt fracture. They do not appear to have an effect on the extrudate appearance in the gross melt fracture region (Rosenbaum et al, 1998). In typical industrial usage, fluoropolymers are added to the polymer in small quantities (less than 0.1% of mass fraction of PA in polymer) (Hatzikiriakos, 2004a). To be effective, fluoropolymer based PAs must do two things. First, they must coat the die wall and in particular the exit. Second, they must induce slippage of the primary polymer over the die wall. 39 CHAPTER 2 - LITERATURE REVIEW 2.5.2 Internal PAs It has been reported that certain Boron Nitride (BN) based compositions may act as effective processing aids in the extrusion of a number of fluoropolymers and polyolefins (Buckmaster et al, 1997; Yip et al, 1999; Rosenbaum et al, 2000; Lee et al, 2000; Hatzikiriakos, 2004b). It has also been reported that BN can successfully be used as a processing aid to eliminate not only sharkskin melt fracture but also substantially postpone gross melt fracture to significantly higher shear rates well within the gross melt fracture region. Since gross melt fracture is a bulk phenomenon, it appears that BN acts as an internal lubricant, such as plasticizers do. Yip et al (1999) reported that BN is an effective processing aid when it possesses the following characteristics: (i) average particle size of up to about 10pm, (ii) no agglomerations, (iii) absence of boron oxides in its structure and (iv) good dispersion into the resin under process. Also, BN must be used at its optimal concentration depending on the type of polymer and the extrusion temperature. It has also been observed that the presence of BN does not alter the linear viscoelastic behavior (for BN loadings < 0.5 wt. %) as well as the flow curve during extrusion of m-LLDPE. However, it was found to have a significant effect on extrudate appearance (Rosenbaum et al, 1998a; Yip et al, 1999; Kazatchkov et al, 2000). Lee et al (2000) have reported that the critical apparent shear rate for onset of melt fracture and the shape of extrudate are highly dependent on processing temperature, length of die and content of the BN. They found that the addition of 0.5 wt. % of BN in 40 CHAPTER 2 - LITERATURE REVIEW m-LLDPE eliminate or delay sharkskin, stick-slip melt fracture and gross melt fracture to much higher rates, even though there is no difference in the linear viscoelastic and mechanical properties between the virgin polymer and the one containing BN. In addition, effects of BN on the processability of polyolefins on other processes such as blow molding (Yip et al, 2000; Seth et al, 2000), film blowing (Pruss et al, 2002), and fiber spinning (Vogel et al, 2003) has been tested. In general, the presence of BN is beneficial in these operations. 2.5.3 Polymer Blends and the Mechanism of Processing Aid Action Hydrocarbons blended with the process polymer can also act as processing aids. This technique might involve not only a small quantity of PA dispersed into a process polymer, but also polymer blending to ratios of the same order of magnitude. Although the notion of processing aid has a meaning at small concentrations (typically less than 1% PA mass fraction in resin), blending at higher concentrations might also improve processing (Shih, 1976). Blending of two incompatible polymers, as shown by Shih (1976) in the case of blending a fluoropolymer and EPDM, improved the performance of the extrudate and reduced the shear stress. It was experimentally determined that, during the extrusion of blends, the polymer used in small concentration created a buildup layer on the die wall, indicating that a phase separation occurred, in which the polymer used as additive accumulated on the wall. 41 CHAPTER 2 - LITERATURE REVIEW Examination of a broad range of fluorocarbon/hydrocarbon blends (Achilleos et al, 2002) had led to the following general observations. Firstly, for the one component of the blend to act as a processing aid the blend should be immiscible; secondly, to be effective, the minor component must be at a finely divided state of particle diameter less than about 0.2 pm and must be at a very low concentration of less than about 1% by weight. For optimum performance, the viscosities of the two polymers should be approximately equal. The relative work of adhesion between the two polymers and the metal surface and between the polymers themselves determines the final performance. For example, fluoropolymers will displace nonpolar hydrocarbons with low work of adhesion, but will not displace polar polymers such as nylon, polyesters or poly (methyl methacrylate) from metal surfaces because of the very high value for the work of adhesion of these polymers to metal (Achilleos et al, 2002). 2.5.4 Filters Done et al (1983) has first underlined the influence of porous media on the flow of polymer melts in capillaries. Similar studies have been driven by Piau et al, (2000) to examine the effect of porous media of different filtering rates on the processability of polymer melts. Their conclusion was that the addition of porous media in the entrance of a die allows delaying the onset of gross melt fracture to higher shear rates. Done et al (1983) have attributed these results to chain disentanglement of the polymer through the porous medium, which temporary changes the rheological properties of the melt. Goutille and Guillet (2002) reported that it is possible to significantly reduce the severity of gross melt fracture by setting filters in the die entrance region. Capillary rheometer and two-42 CHAPTER 2 - LITERATURE REVIEW dimensional flow experiments enabled them to study and characterize gross melt fracture. By using flow visualization techniques to study the flow behaviour of the linear SBR copolymer, as it is processed through a transparent slit die with and without filters, they concluded that the filters allow to stabilize the stream lines and reduce the amplitude of gross melt fracture. Therefore, by enhancing the shear deformations with respect to elongation deformations, it is possible to reduce the severity of gross melt fracture. 2.5.5 Comments on Processing Aids for P M M A Resins To the author's knowledge, processing aids for the processing of poly(methyl methacrylate) and other acrylic polymers have not been developed or reported in the literature. Therefore, at the beginning of this work, "traditional" PAs, widely used for the processing of the majority of the commercial polymers, will be tested. Suggested PAs for the processing of PMMA by different chemical companies will also be tested. The general theory of immiscible blends will be utilized in an attempt to identify processing aids for the extrusion of PMMA. By saying "theory of immiscible blends", it is meant that a possible effective processing aid of polymeric nature, has to be immiscible with PMMA. A general discussion on the methodology used to study miscibility between polymers follows. 43 CHAPTER 2 - LITERATURE REVIEW 2.6 Miscibility Studies Rheological techniques to study miscibility of a polymer blend are discussed here. The methods for detecting phase separation in polymer blends make use of a rheological device such as a rotational concentric rheometer (parallel plate and cone and plate). As discussed above this is useful in trying to identify possible processing aids. As stressed above, the first requirement is immiscibility with the processing polymer. One method to study the phase separation behavior of two polymers is the use of time temperature superposition principle of linear viscoelastic moduli. It has been reported (Ajii et al, 1988; Ajii et al, 1991) that the WLF superposition principle was applicable only at temperatures below the phase-separation, i.e. for a LOST in the miscible and homogeneous temperature regime. In addition the relationship of loss modulus, G" vs. storage modulus, G', was found to be temperature independent and varied with composition in the miscible regime; however it was found to be temperature and composition dependent in the immiscible regime. The principle of time-temperature superposition is valid for both G' and G" in the temperatures of the homogeneous regime. The data in the two-phase region do not superpose and a shoulder appears at small frequencies. This observation indicates that the polymer blend has undergone phase separation. This is shown in Figure 2.12 where characteristic master curves of G' and G" for a SMA(14)/PMMA blend, showing failure of time temperature superposition at a certain temperature (Chopra et al, 2002a). The change in slope of storage modulus, G' and the corresponding peak in tand in temperature sweep experiments can also be used to detect the onset of phase separation. 44 CHAPTER 2 - LITERATURE REVIEW Chopra et al (2002a) have performed dynamic temperature sweeps on different concentration SMA(14)/PMMA blends and the results are depicted in Figure 2.13. This Figure represents a typical example of sudden change in the slope of G' and tand. This sudden change in the slopes signifies that the blends have undergone phase separation. In addition, the presence of two peaks in the Cole-Cole plot indicates that the polymer mixture has undergone phase separation (Chopra et al, 2002a). By applying steady shear measurements to detect phase separation temperatures, it has been found (Chopra et al, 2002b) that as the temperature of the polymer blend is reduced from the miscible region to the phase separation region below the UCST, a change in the slope of the stress vs. temperature graph is observed. The results reported by Chopra et al (2002a and 2002b) were confirmed by turbidity measurements. a l ..„.,. I, i li.uut- 1 i • ' i IJJJ '—• i • '"il I—I_I t -IIJ '—'—i 10* 1Cr2 10 s 10° 101 10* 1Q3 o*aT> rad/s Figure 2.12 Time-temperature superposition failure, (Chopra at al, 2002a) 45 CHAPTER 2 - LITERATURE REVIEW 220 240 260 280 T, °C Figure 2.13 Sudden change in slope of storage modulus G' and tan8 which depicts phase separation (Chopra et al, 2002a) 46 CHAPTER 3 - OBJECTIVES 3 OBJECTIVES The main objective of the present work is to identify suitable processing aids for the extrusion of PMMA. This will be accomplished primarily by testing various processing aids through capillary rheometer studies. The various materials will also be Theologically characterized by performing linear viscoelasticity and extensional rheological measurements. The various processing aid to be tested are internal and external processing aids as well as various polymers which are immiscible with the PMMA resins under examination. It is expected for the identified PAs to: • Improve the processability of PMMA during extrusion • Increase the critical shear rate at which instabilities first occur, therefore increase the production rate • Improve the extrudate appearance by increasing the critical shear rate for the onset of instabilities • Cause pressure reduction in the extrusion process, therefore contribute to an operating cost reduction 47 CHAPTER 4 - MATERIALS AND METHODOLOGY 4 M A T E R I A L S A N D M E T H O D O L O G Y This chapter describes the various poly(methyl methacrylate) and the other polymeric resins as well as the processing aids (PAs) used in this study. Blend preparation methods and the experimental methodology used to assess the efficiency of the various processing aids tested are also discussed in this chapter. 4.1 Polymers Three different poly(methyl methacrylate) resins were used as base resins, labeled as PMMA(l), PMMA(2) and PMMA(3). PMMA(l) was provided by ICI Acrylics and PMMA(2) and PMMA(3) by Lucite International. Particular information about the molecular weight and its distribution is not known. Physical, mechanical and other properties of PMMA resins are summarized in Table 4.1. Table 4.1 Typical properties of poly(methyl methacrylate) Density -1.18 g/cm3 Tensile Strength 55 - 80 MN/m 2 Tensile Modulus 2-3 GN/m 2 Elongation at Break <10% Specific Heat 1.25 - 1.7kJ/kg/°C Glass Transition Temperature 105-115°C Heat Deflection Temperature <100°C Coefficient of Thermal Expansion 5- 10 x 1 0 5 / ° C Specific Gravity 1.0 to 1.2 Water Absorption 0.1 -0.5% (50% rh) Transparency Transparent 48 CHAPTER 4 - MATERIALS AND METHODOLOGY 4.2 Processing Aids (PAs) The polymer processing aids that were used in this study are summarized in Table 4.2. These processing aids are of various types, including fluoropolymers (Dynamar® and Viton®), stearates, solid inorganic lubricants (boron nitride and clay), different polyethylene polymers (LLDPE, LDPE and HDPE), surlyn polymers, polymers known to be immiscible with PMMA such as polystyrene (PS), acrylonitrile-butadiene-styrene (ABS) styrene-acrylonitrile (SAN) copolymer and polyvinylidene fluoride (PVDF), different blends of polyamides and fatty acids (Atmer 1759, Struktol TR016 and INT-35UDH) and a mixture of fluoropolymer with boron nitride (Cerflon). More specifically the following polymers and other known "traditional" processing aids were used: • L L D P E , LDPE and HDPE: It is well known that PMMA/PE blends are immiscible (Choi et al, 2002; Utracki, 1989). Therefore, the objective was to investigate the possible effects of polyethylenes on the processing of PMMA resins when added at small concentrations. • Surlyn: It is a PE based ionomer of high surface energy. It is hoped that Surlyn will coat the die wall so that PMMA can slip over this layer. • PS, ABS, SAN: ABS and SAN are polystyrene based polymers. Utracki (1989) has reported that these polymers are immiscible with PMMA and as in the case of the polyethylenes the objective was to investigate the possible effects of these polymers on the processing of PMMA when added at small concentrations. • PVDF: It has been reported that PVDF/PMMA blends are immiscible (Utracki 1989). Therefore, as a fluoropolymer, it is expected to have an effect on the processing of PMMA. 49 CHAPTER 4 - MATERIALS AND METHODOLOGY • Dynamar*, Viton®: Fluoropolymers have been well proved for their effectiveness to postponing melt fracture phenomena in the extrusion of polyolefins. They usually migrate towards the polymer surface and coat the surface of the die. Therefore, they promote slip and a significant pressure reduction is usually observed (Achilleos et al, 2002). Therefore it becomes interesting to test them to see whether or not they act as processing aids for PMMA extrusion. • Boron Nitride (BN): Boron nitride (BN) is a white solid lubricant. It has a high thermal conductivity, low dielectric loss modulus, low thermal expansion and high lubricity over a wide temperature range. BN has one of the highest thermal conductivity of any commercial electrical insulator in the polymer system. BN powder has been shown to be an excellent additive for coatings and release agents, as well as for oils, potting compounds, friction plates and other applications (Hatzikiriakos, 2004b). • Cerflon - A Reinforced Fluoroadditive: It is fluoropolymer-boron nitride combination. Thus, it is mainly an internal-external processing aid combination. It has been used as a processing aid in the extrusion of fluoropolymers and polyolefins. • Nanomer 1.44 PA: It is an inorganic solid lubricant, proven to be effective as an internal lubricant that postpones gross melt fracture in the extrusion of polyolefins (Hatzikiriakos et al, 2005). It is organically modified and its morphology is similar to boron nitride as both exhibit a platelike structure. It belongs to the family of montmorilonites which are high purity aluminosilicate minerals sometimes referred to as phyllosilicates. 50 CHAPTER 4 - MATERIALS AND METHODOLOGY • Stearates: Stearates, such as calcium and zinc stearates, are present in several commercial resins of both linear and long-chain branched polyethylenes. There is strong evidence that they promote slip and aid in the reduction of instabilities in the case of metallocene low-density polyethylene copolymers with long chain branching. • Struktol®TR 016: It is a blend of fatty acid metal soap and an amide. Used for better flow at processing temperatures and for a better surface appearance. It has been reported that amides have been used quite effectively as processing aids in the extrusion of PMMA. For more details see (http://www.struktol.com/TechReports.asp) • Atmer SA 1759: It is an oligoamide - a primary long chain fatty acid amide which, due to its high purity and thermostability, is recommended as slip agent for polyolefin films and as mold release agent for injection molding. It is a highly effective slip agent for polyethylene and polypropylene films. The use of Atmer SA 1759 is recommended when a decrease in friction, both film-to-film friction and that between the film and production equipment, is needed in order to increase the output of the film line and to improve packaging line operations. Use of Atmer SA 1759 decreases the internal friction during the production process. For more details see (http://www.cibasc.com/index/ind-index/ind-pla/ind-pla-effectsweoffe^ processingefficiency/ind-pla-eff-pro-slipeffect. htm). • INT-35 UDH: It is an internal lubricant/process aid with anti-static properties. It can eliminate the need for an external mold release agent. It generally improves resin flow, dispersion of other resin additives (reinforcements, fillers, and pigments), shortens cycle times, reduces temperatures and pressures of molding machines, and reduces or eliminates weld/knit lines (http://www.axelplastics.com/thermoPA.html). 51 CHAPTER 4 - MATERIALS AND METHODOLOGY 4.3 Preparation of Blends In the present work blends of PMMA with the different processing aids were prepared in two ways; (1) dry mixed; (2) compounded. Dry mixing consists of weighing the exact amount of processing aid need to be added to the pure resin, carefully adding it and then stirring it for about 15 minutes. The polymers used as processing aids were first grinded in order to attain a better dispersion when dry mixed with the host PMMA resin. Compounding was carried out in two steps. Firstly, a concentrate was prepared, usually 2% by means of a single screw extruder. The second step includes dilution of the concentrate to the final desirable concentration by passing the blend a second time through the single screw extruder. It should be noted that a uniform dispersion is a necessary condition for obtaining a good performance of processing aids and this is why grinding and preparation of concentrates was used (Yip, 1999; Rosenbaum et al, 2000). Table 4.3 lists the typical particle sizes of all processing aid used in this study. 52 CHAPTER 4 - MATERIALS AND METHODOLOGY Table 4.2 List of processing aids and their manufacturers Processing Aid Manufacturer LLDPE (Exact® 3128) Exxon Mobil LDPE (EF 606) Westlake Polymers HDPE Nova Chemicals Surlyn® Ionomers Dupont PS, ABS, SAN Dow Chemicals PVDF Dyneon Dynamar™: FX 9613, FX 5914X and FX 5911 Dyneon Viton® Z-200 free flow DuPont Dow Elastomers L. L. C Boron Nitride, Carbotherm™ CTF5 Saint-Gobain Advanced Ceramics Corporation Cerflon® Micropowder Saint-Gobain Advanced Ceramics Corporation Nanomer® I.44PA Nanocor, Inc Zinc and Calcium Stearate St. Lawrence Chemical Inc Struktol® TR016 Struktol Company of America Atmer SA 1759 Ciba Specialty Chemicals INT-35UDH Axel Plastics Research Laboratories, Inc 53 CHAPTER 4 - MATERIALS AND METHODOLOGY Table 4.3 List of average particle size of processing aids used in this study Processing Aid Particle size LLDPE, LDPE, HDPE, Surlyn Ionomers, PS, ABS, SAN, PVDF ~ 1-2 mm pellets Dynamar™ FX 5911 98% less than 2400 microns Dynamar™ FX 5914X Powder form Dynamar™ FX 9613 Approximately 25 mesh Viton Z-200 free flow Powder form Boron Nitride, Carbotherm™ CTF5 6-13 pm Cerflon Micropowder 2-4 pm Nanomer I.44PA ~ 13 pm Zinc and Calcium Stearate 99.8% passing 325 mesh Struktol® TR016 Powder form Atmer SA 1759 Powder form INT-35UDH Powder form 4.4 Experimental Methodology In this study, a rotational equipped with a parallel plate geometry, an extensional and a capillary rheometer were used to assess the rheological properties of the various materials and the performance of the various processing aids on the processability of the PMMA blends respectively. This section provides an overview of the experimental procedure and the methodology employed in this study. 54 CHAPTER 4 - MATERIALS AND METHODOLOGY Prior to any type of rheological and processing characterization, PMMA resins were dried under vacuum for 24 hrs at 80-90°C. The purpose of this was to remove humidity that could cause the generation of air voids in the samples and/or degradation. 4.4.1 Rotational Parallel Plate Rheometry In this work, a Rheometrics System IV rheometer utilizing the parallel plate geometry was used to study the linear viscoelasticity of the various poly(methyl methacrylate) samples, their blends with the various processing aids and the polymeric processing aids. The concentric plates used were both flat disks with a diameter of 25 mm. The rheometer comes with software that allows data to be logged and processed automatically into relevant rheological quantities. Before the rotational concentric test was carried out, round polymer sample of 25 mm in diameter and 1.5 mm in thickness were prepared. This was done by heating the polymer pellets to about 200°C and compressing them using a Carver laboratory press to achieve samples free of voids and of specified thickness. The sample was left compressed for about 10 minutes before it was cooled. Sample preparation is critical in this procedure since it is important to ensure that the samples contain no air voids. Circular samples were then cut from the film. Linear viscoelastic tests began by heating the concentric plates to the desired temperature. After zeroing the gap between the two plates at the desired temperature, the polymer sample was inserted into the gap. Consequently, the gap was reduced to about 55 CHAPTER 4 - MATERIALS AND METHODOLOGY 1.2 mm. Excess polymer on the sides was trimmed before the gap was reduced further to 1 mm. Settings for the experiment (e.g. strain % and frequency range) were input into the software and the experiment was then started. Data was logged and processed automatically by the software. The file created by the software contains all of the necessary viscoelastic properties such as G', G" and t|* as functions of frequency. After the experiment, the plates were separated and the sample was scraped off the plates before it solidified. 4.4.2 Extensional Rheometry Xpansion Instruments Sentmanat Extensional Rheometer (SER) was used in this study. The SER is hosted by a Bohlin VOR rotational rheometer. Extensional melt rheology specimens were prepared by compression molding polymer sample between polyester films to a gage of 0.5-1 mm using a Carver laboratory hydraulic press. Long polymer strips approximately 15-17 mm in width were then cut from the molded polymer sheets. From these long strips, individual polymer specimens were then cut to a width of 6.4-12.7 mm using a dual blade cutter with adjustable gap spacing. Prior to any type of test, the SER unit was allowed to soak at operating temperature for about 15 minutes. Extensional rheology tests began by loading the polymer sample onto the drums after heating the SER unit to the desired temperature. Settings for the experiment (e.g. strain rate and frequency of data collection) were input into the software that comes with the rotational rheometer. Raw torque data was logged and processed 56 CHAPTER 4 - MATERIALS AND METHODOLOGY manually as explained in Chapter 2 in order to obtain the extensional properties of the polymer sample. After the experiment, the sample was scraped off the drums before it solidified. 4.4.3 Capillary Rheometry In this work, the ROSAND RH-2000 capillary rheometer was used. The barrel is equipped with a three zone electric heater and an adaptive PID temperature controller with an accuracy of ± 0.1 oC. The barrel is 190 mm in length and 15 mm in diameter. A stepper motor is used to drive the piston from a speed of 0.1 mm per minute to a maximum speed of 600 mm per minute. A pressure transducer installed on top of the piston driver measures the extrusion pressure. The rheometer also comes with data analysis software. Only one type of capillary die was used in this study. The capillary die is made of tungsten carbide, with a diameter of 1 mm, length to diameter ratio of 16 and entrance angle of 180°. In this study, no Bagley correction was applied to the extrusion pressure. Due to the fact that the length of the die is considered to be long, the end pressure correction, known as Bagley correction, is taken to be insignificant. Before any extrusion both the barrel and the die of the capillary rheometer were cleaned thoroughly. Consequently, extrusion of one full barrel with pure PMMA at a constant piston speed (constant shear rate) was performed in order to remove possible 57 CHAPTER 4 - MATERIALS AND METHODOLOGY contaminants or residues in both barrel and die. At the same time the obtained shear stress value was compared with the one that corresponds to the extrusion of pure PMMA. After assuring that the barrel and die are free of any contamination, the extrusion process started. The experimental procedure and the data collection consist of the following steps: • The blend with the processing aid was extruded two times at a constant shear rate. • After observing a steady shear stress/pressure value the actual runs started. • The extrusion runs were carried out under increasing shear rate, decreasing shear rate and random shear rate order. • The values needed to construct/plot the flow curve are average values of all apparent shear stresses values obtained for each shear rate. • Finally, in order to be certain about the effectiveness of the processing aid, one last extrusion is carried out under constant critical shear rate, and at the same time both extrudate appearance and shear stress value are observed to assure that they are determined as before. Before the extrusion experiments, the PMMA resins and their blends are left into the barrel for about 5-10 minutes to attain an equilibrium temperature. Consequently they are compressed twice for 2 min each time, at 2 MPa and 3 MPa respectively. Again, this is done to remove air voids generated in the samples. About six to ten barrels (beyond the first two preliminary constant rate extrusions) are extruded in order to determine the effectiveness of a processing aid. The intention of this procedure is to minimize possible statistical errors. 58 CHAPTER 4 - MATERIALS AND METHODOLOGY No Bagley and Rabinowitch corrections were applied to the data obtained for all the resins and their blends. Hence, the obtained experimental data yield the apparent flow curves of the resins and their blends; that is the relationship between the apparent shear stress and apparent shear rate. 4.5 Sample Inspection After all extrusion experiments were completed, extrudates were inspected using a digital camera and a digital microscope in order to detect the onset of melt fracture, that is the critical shear rate and/or stress at which distortions first appear. In summary: • A Sony DSC-F505V digital camera was used in order to capture and inspect closer images of the extrudates' waviness, and • An Olympus MIC-D digital microscope was used to detect any possible distortions on the extrudates' surface not easily seen with the Sony camera. 59 CHAPTER 5 - RESULTS AND DISCUSSION 5 RESULTS AND DISCUSSION 5.1 Introduction This chapter is divided into three parts. In the first part, the linear viscoelastic properties of the three poly(methyl methacrylate) (PMMA) resins, their blends with some of the processing aids (including those of polymeric nature) and the polymeric processing aids are presented. The second part presents the extensional rheological characterization of the three pure PMMA resins. Finally, the third part focuses on the testing of various processing aids in the capillary extrusion of PMMA resins. The processability of pure PMMA resins is first presented followed by the effects of the different processing aids on their processability. 5.2 Linear Viscoelasticity Studies 5.2.1 Pure Poly(methyl methacrylate) Resins The linear viscoelastic-rheological characterization of the three PMMA samples was carried out by using a Rheometrics System IV rheometer equipped with 25mm in diameter parallel plates. Possible effects of the processing aids on the linear viscoelastic properties of the host polymer were also examined. Linear rheological characterization of the processing aids of polymeric nature was also performed. The linear rheological characterization experiments included frequency sweep experiments in the frequency range of 0.01 rad/s to 500 rad/s. The tests were performed at multiple temperatures in the range of 150°C to 250°C. The viscoelastic data at all temperatures of PMMA(l) are 60 CHAPTER 5 - RESULTS AND DISCUSSION presented in Figures 5.1-5.3. The corresponding data for PMMA(2) and PMMA(3) are presented in Appendix A. Specifically, Figures 5.1, 5.2 and 5.3 depict the storage, loss moduli and the complex viscosity of PMMA(l) respectively at various temperatures. CO T3 O 0) O) re tm o CO 10s 105 o to 104 103 102 101 i i i i I I i i | i - r — r ! PMMA(1) v • • v • • Y V • • • • v • • V fl • -. • • V • • 17O°C ; o 190°C B • • 210°C i • • . i . i • . . v 230°C : • 250°C 10-1 10° 101 Frequency co (rad/s) 102 103 Figure 5.1 Storage modulus of PMMA(l) at various temperatures 61 CHAPTER 5 - RESULTS AND DISCUSSION 10s (0 Q. O CO •§ 104 u o (0 (A O 103 102 Pli/IMA(i) 8888.--:::;::::::;5:::::::::^ _ I I 1 1Cr1 10° 101 Frequency co (rad/s) 102 • 170°C o 190°C • 210°C v 230°C • 250°C —I 1—1 I ' ' • ' 103 Figure 5.2 Loss modulus of PMMA(l) at various temperatures 106 S. 10= 8 io< > x o a o 102 PMMA(1) • Y , F V ? V W V V ° 8 8 • 170°C o , 190°C • 210°C -7 230°C • 250°C • 2 v v • 2 • 2, 101 10° 101 Frequency co (rad/s) 102 103 Figure 5.3 Complex viscosity data for PMMA(l) at various temperatures 62 CHAPTER 5 - RESULTS AND DISCUSSION Time-temperature superposition was applied to the linear viscoelastic data of the three P M M A resins in order to produce their master curves. This will result rheological data over a wide range of frequencies for a given temperature. The chosen reference temperature was 170°C for all resins, and the obtained master curves are shown in Figures 5.4, 5.5 and 5.6 for PMMA(l) , PMMA(2) and PMMA(3) respectively. As it can be seen from these Figures, 5.4-5.6, the time-temperature superposition applies well for all P M M A resins. Thus, it can be concluded that all P M M A resins are thermorheologically simple fluids. It can also be seen that the Newtonian plateau viscosity region has been reached, where the zero-shear viscosity of all resins can be determined. re Q. 1 0 8 re Q_ 1 0 6 t -Q b • 1 0 S 3 O u E re c >» a £ 1 0 4 (0 o u g 1 0 3 X Q. 102 E o O 1Q1 1 0 ° PMMA(1) Tref=170°C 11r11j 1—i—r i 11ii| 1—i—i n i T I | i—i i 11T i i ] 1—r "r i r i i i j™ D Oooo6 B B8ooooooo880 • 8 0 ° ° 8B„ " ° ° ° o ° 170°C ° 190°C A 210°C o 230°C * 250°C J -Ll i i I • • I l—d-l I i > i ml i - . i i 11 ml 10" 4 10" 3 10 - 2 10" 1 1 0 ° 1 0 1 Frequency co.aT (rad/s) 1 0 2 1 0 3 Figure 5.4 The master curves of linear viscoelastic moduli of PMMA(l) at the reference temperature of 1 7 0 ° C 63 CHAPTER 5 - RESULTS AND DISCUSSION 10 7 S. % 106 ^ Q. i - ' ' -a i— - • re O "T- 10 5 ^ .a P- * ' • ° . P" 4 3 .-^ 10 4 — (0 3 O T3 O o .52 § > 10 3 U X . - fl) re i->, o 10 2 Q O I I I I 111 I I—I I I I M | 1 | " T - I I PMMA(2) Tre,= 170°C I T T TT"| 1 1—I I I I 111 1—I—I I I I IL • 150°C * 170°C o 190°C • 210°C o 230°C "| Q 1 I ' • i •«• I i i • * i 1111 i i » i i i > 11 i i «I I i • i i m | q • i • i • M I • ' I 1 0 - 2 1 Q - 1 1 Q 0 1 Q 1 1 Q 2 Frequency co.aT (rad/s) 10 3 10 4 Figure 5.5 The master curves of linear viscoelastic moduli of PMMA(2) at the reference temperature of 170°C 10 7 E re Q. b 3 T5 O O E re c >. Q to re o_ re 10 6 10 5 & 10 4 to o o to > 10 3 X «t Q. I 10 2 o 10 1 TTTTT 1—I—I I I I I 11 1 1—1 r I I I 11 1 1—I I I I I 11 1 1—I I I I I 11 1 1 — I T I T r i f Tref=170°C i f t a n o o D " ' ' ' G" 8 8 « ° t * .8° G' " 170°C ° 190°C o 210°C • 230°C • t i l l I I 1 • • • • »»•••• • • ' t • • • • I | | « • • • i • I | | * I ' 10"1 lO"3 lO"2 10° 10 1 10 2 10 3 Frequency co.aT (rad/s) Figure 5.6 The master curves of linear viscoelastic moduli of PMMA(3) at the reference temperature of 170°C 64 CHAPTER 5 - RESULTS AND DISCUSSION As discussed in section 2.2, it has been found that rheological data over a wide range of temperatures (usually for amorphous polymers) can be brought together on a single master curve by applying both a horizontal and vertical shift factor. For semi crystalline polymers such as polyolefins there is a narrow window of temperatures over which rheological data can be obtained and a horizontal shift is sufficient to produce master curves. In the present study, both horizontal and vertical shift factors had to be applied for all three PMMA resins in order to generate the master curves. These horizontal and vertical shift factor values listed in Table 5.1. Table 5.1 Horizontal and vertical shift factor values for PMMA(l), PMMA(2) and PMMA(3) Temperature Horizontal shift factor Vertical shift factor T(°C) aT bx 170 1.0000 1.0000 190 0.0987 0.4816 PMMA(l) 210 0.011264 0.7600 230 0.00259 0.6317 250 0.000976 0.72 150 10.614 0.95 170 1.0000 1.0000 PMMA(2) 190 0.1587 0.6303 210 0.03165 1.1576 230 0.00251 1.2705 150 13.1820 0.8145 170 1.0000 1.0000 PMMA(3) 190 0.1000 0.9224 210 0.0192 0.7144 230 3.0000e-3 0.9100 65 CHAPTER 5 - RESULTS AND DISCUSSION The horizontal shift factors are plotted in Figure 5.7 as a function of the reciprocal temperature (T in K) in order to check if they follow an Arrhenius Equation: K 1 1 \ T Tref J (5.1) where E a is the activation energy for flow, R is the universal constant of the ideal gas law and T r e f is the reference temperature. It can be seen that all shift factors for all PMMAs follow this equation. Fit of this equation to the individual data, gave Ea/R values of 20443, 19333 and 22107 K"1 for resins (1), (2) and (3) respectively. These values are close enough to imply consistency of the experimental data obtained. 0.0018 0.0020 0.0022 0.0024 Reciprocal Temperature 1/T (T in K) Figure 5.7 The horizontal shift factors of all PMMA resins showing that the Arrhenius equation (5.1) is closely followed 66 CHAPTER 5 - RESULTS AND DISCUSSION Fitting a single straight line results in an average E a /R value of 21098 K"1; These results essentially show that the activation energy of flow is molecular weight independent. 0.0018 0.0019 0.0020 0.0021 0.0022 0.0023 0.0024 0.0025 Reciprocal Temperature 1/T (T in K) Figure 5.8 Overall fit of all horizontal shift factors of all PMMA resins showing that they follow the Arrhenius equation (5.1) The zero shear viscosities for the three resins were also calculated by fitting the data to the Cross model as discussed in section 2.1.1. The results are listed in Table 5.2. It can be seen that they exhibit significant different values indicating that they have a quite different molecular weight. Figure 5.9 presents the complex viscosity master curves of all resins at the reference temperature of 170°C. The observation that viscosity becomes 67 CHAPTER 5 - RESULTS AND DISCUSSION molecular weight independent at higher shear rates/frequencies is well documented in literature (Dealy and Wissbrun, 1990) 10"4 10-3 10-2 10-1 10° 101 102 1 0 3 1 0 4 Frequency co.aT (rad/s) Figure 5.9 Complex viscosity master curves of all PMMA resins at the reference temperature of 170°C Table 5.2 Zero shear viscosity values obtained by fitting the Cross model on complex viscosity data plotted in Figure 5.9 Resin T | 0 * (Pa*s) PMMA(l) 4.226* 106 PMMA(2) 2.388*105 PMMA(3) 1.007* 106 68 C H A P T E R 5 - RESULTS A N D DISCUSSION 5.2.2 Poly(methyl methacrylate) Blends with Processing Aids The same experimental procedure was followed to investigate any possible effects of the processing aids on the rheological properties of PMMA. It should be mentioned here that rheological characterization was done only to the PMMA blends that were prepared by means of a compounding process. The results are depicted in Figures 5.10-5.14. These Figures represent the comparison of linear viscoelastic properties of PMMA with and without processing aids. The temperature of 190°C was chosen as reference to perform the comparison. It can easily be seen that the presence of 0.2% processing aid such as BN, clay, Atmer 1759, INT-35UDH and PVDF into PMMA results into practically no change in the linear viscoelastic properties of PMMA. i i i i i | i—i—i i i i | FT = 190 OC o i o +0 .2%BN • PMMA(2) Frequency co (rad/s) Figure 5.10 The linear viscoelastic moduli of PMMA(2) with and without PA (BN) at 190°C 69 CHAPTER 5 - RESULTS AND DISCUSSION 10 6 FT = 190°C 1o *M Q. CO 10 5 '—' Q. b *_ 3 O 10" •o o o <*> 5 > o x 6 °-g E lO 3 >» o o o 10 2 . . . . . . . . . , HI;;-' i l l ! a i f l G . • O • 1 O • © + 0.2% I.44PA • PMMA(2) i ' i i 1 i 10"1 10° 10 1 Frequency co (rad/s) 10 2 10 3 Figure 5.11 The linear viscoelastic moduli of PMMA(2) with and without PA (Nanomer I.44PA) at 190°C 10 s CO * Q. CO 10 s '—' Q. ©v 3 o 10 4 rs o o <o S > O X .- a> S E lO 3 >. o a o 10 2 tT = 190°C ullSSlii"" 1 1 1 B 8 B 8888 8 8 8 8 ' o o i 8 i « » B . , l l _ s i 2 8 l • • b : , | | 8 _ B 8 „ a 8 s G 88, o + 0.2% Atmer 1759 • PMMA(2) 10"1 10° 10 1 Frequency co (rad/s) 10 2 10 3 Figure 5.12 The linear viscoelastic moduli of PMMA(2) with and without PA (Atmer 1759) at 190°C 70 CHAPTER 5 - RESULTS A N D DISCUSSION 10 6 w ' Q. b *_ 3 O 1 0 4 •o o o w s > O X . - 0) 2 £ 103 5* O Q O 10 2 n - n j 1—i— i :T = 190°C o f i 0 B § M 0 I a • S § • „ ° B : ° o 1 9 - . ; 8 B , 8 I i K « « " , , M , , ° ° B -® • o ° 8 Q -• © • PMMA(2) © +0.2% INT-35UDH 1—i— 11 • 10-1 10° 101 10 2 10 3 Frequency co (rad/s) Figure 5.13 The linear viscoelastic moduli of P M M A ( 2 ) with and without P A (INT-35UDH) at 190°C 10 6 0. re 10 5 "—' Q_ b *_ 3 o 10 4 •o o o w 2 > U X .- a) S E 103 >, o Q U 10 2 E O Q T= 190°C . ° © • £ § • • 8 •B, o o , ' g o , • PMMA(2) © +0.2% PVDF 6010 10"1 10° 10 3 101 10 2 Frequency co (rad/s) Figure 5.14 The linear viscoelastic moduli of P M M A ( 2 ) with and without P A ( P V D F 6010) at 190°C 71 CHAPTER 5 - RESULTS AND DISCUSSION Similar results were found for the linear viscoelastic moduli of the PMMA blends filled with 2% processing aid. The results are shown in Figures 5.15-5.18. This implies that the compounding of PMMA with the processing aids does not significantly affect the rheological properties of PMMA resins up to loadings of about 2%. A small measurable effect (reduction of the complex viscosity) can only be seen in the cases of rNT-35UDH and Atmer 1759. Both these act as effective lubricants and possibly induce slip at the interface. 106 "re," '—' Q_ ID V 3 o 104 TJ O O O S > U X . - 0) m °-c E i o 3 >. o Q O 102 rr-n "f ' — 1 — ' " 1 1 ' ' i ~ — ' 1 — ' — 1 ' Tf~ T= 190°C n 1 1—i— [ 1 1—i— • 9 . R H H H 8 _" a H -_ n u : . H Q H • A * " • - m Hp. H H B l H l '*>. • A _i_tj 1 1 1— 1 1 1 1— • P M M A ( 2 ) ^ + 2% B N - i • — i — 10-' 10° 101 102 Frequency co (rad/s) 103 Figure 5.15 The linear viscoelastic moduli of PMMA(2) with and without PA (BN) at 190°C 72 CHAPTER 5 - RESULTS AND DISCUSSION 106 CO * Q. co 105 — » „„„ 3 O 104 •a o o <f> E > u x c JJ § E 103 >. o Q O 102 _ • • m - B B g | o O " Hisn»« '88 "8 "8 8 8 , G5-o « °"5. O + 2% I.44PA • PMMA(2) 10"1 10° 101 102 103 Frequency co (rad/s) Figure 5.16 The linear viscoelastic moduli of PMMA(2) with and without PA (Nanomer I.44PA) at 190°C 10s CL co i o 5 3 o 104 •o o o w s > o x c « 2 E 103 >. o Q O 102 fr = 190°C A A A A A A A ' A - A a " " • - • A a A • A A I " A • A A a A • PMMA(2) A + 2% INT-35UDH —I I I I 10 1 10° 101 Frequency co (rad/s) 102 103 Figure 5.17 The linear viscoelastic moduli of PMMA(2) with and without PA (INT-35UDH) at 190°C 73 CHAPTER 5 - RESULTS AND DISCUSSION 106 g « 10= b * = to „„, 3 O 10" T3 O O W S > O X • - fl) 2 E 103 >» o Q O 102 T H 2 1 '—' " i q 1 1 1—i—r-T = 1 9 0 ° C T l ^ 1 1 1 1 l l | | | 1 1 1 1 l l l l . _ ' A ' A : • • T A " A A " A . A " A • A • A • A . , " A Hp. A 8 : • A ' • ' • PMMA(2) ^ +2% Atmer 1759 -^->— 10"1 10° 101 102 103 Frequency a (rad/s) Figure 5.18 The linear viscoelastic moduli of P M M A ( 2 ) with and without P A (Atmer 1759) at 1 9 0 ° C 5.2.3 Polymeric Processing Aids Rheological characterization of the processing aids (PAs) of polymeric nature was also performed in order to obtain their linear viscoelastic data and compare them to those of the pure PMMA resins. This will be useful in drawing conclusions on the mechanism by which these processing aids affect the processability of PMMA resins. In this section, only the complex viscosities are plotted and compared. Figures of the loss and storage moduli of all PAs of polymeric nature can be found in Appendix B. Figures 5.19-5.23 compare the complex viscosities of PMMA resins with that of the various processing aids of polymeric nature at 210°C. It can be observed from Figures 5.19 and 5.21 that all polyethylenes have significantly lower viscosity values than 74 CHAPTER 5 - RESULTS AND DISCUSSION PMMA(l) and PMMA(3) at low shear rates/frequencies. As the shear rate increases and due to the high shear thinning of PMMA the picture changes and the viscosity of PMMA becomes smaller than that of the various polyethylenes in many cases. For example Figure 5.23 shows that the viscosity of LLDPE (Exact 3128) is much higher than that of all PMMA resins at shear rates/frequencies higher than about 100s"1. On the other hand, Figure 5.23 shows that PMMA(2) has slightly lower viscosity than LLDPE, which becomes even smaller at higher shear rates. PVDF 6010 and 1010 possess about the same viscosity values with that of PMMA(3), while PVDF 60512 exhibits significantly higher viscosity (see Figure 5.22). Most of these polymers, as will be presented later in this chapter (capillary rheometer studies) did not act effectively as processing aids. It should be mentioned here that the comparison of viscosities was performed at 210°C to be the same with the capillary extrusion temperature. 75 CHAPTER 5 - RESULTS AND DISCUSSION 105 * 10" p -S> 103 102 H T = 2l6°c' A A A A A * A , A PMMA(1) • LLDPE (Exact 3128) • LDPE (EF 606) o HDPE G J A 10"1 10° 101 Frequency co (rad/s) 102 103 Figure 5.19 The complex viscosities of PMMA(l) and various other polymers used as processing aidsat210°C S 1 0 3 102 -n r — ' ' • I • " 1 1 1 1 . 1—r :T = 210°C A 1 I 1 • 1 1 1—1—1 1 1 11 PMMA(2) • PS (Styron 685D) V LLDPE (Exact 3128) • SAN (Tyril 990) • -LJ 1 1 1—I—I i I I 1 1 I I i • • • • ' • • • • : • 10"1 10° 101 102 Frequency co (rad/s) 103 Figure 5.20 The complex viscosities of PMMA(2) and various other polymers used as processing aidsat210°C 76 CHAPTER 5 - RESULTS AND DISCUSSION 105 in * co Q. in o o in x a. E o o 104 103 102 T T T T 1 T =210°C 1—I—I I I I 1 1 1 1—I I I I I * PMMA(3) o HDPE a LLDPE (Exact 3128) o LDPE (EF 606) o o , 2 ° D 0 ® S • , 60 D D D 2 A ° O D ° o _  A 9 10- 10° 101 Frequency co (rad/s) 102 103 Figure 5.21 The complex viscosities of PMMA(3) and several polyethylenes used as processing aidsat210°C 106 in D_ 8 to" o > X a. E 103 o o 102 T = 210°C ~ i r i l * PMMA(3) • PVDF 6010 • PVDF 1010 o PVDF 60512 A ABS (Magnum 9035) 10"1 10° 101 10 2 103 Frequency co (rad/s) Figure 5.22 The complex viscosities of PMMA(3) and various other polymers used as processing aids at 210°C 77 CHAPTER 5 - RESULTS AND DISCUSSION 105 T = 210°C (0 * ra w o o w X 0) a E o o A PMMA(1) • PMMA(2) • PMMA(3) o LLDPE (Exact 3128) 10" ~ A A 103 A ° o * . A A ° ° 0 102 1 1 1 1 • • • 1 10-' 10° 101 Frequency co (rad/s) 102 103 Figure 5.23 The complex viscosities of all PMMA resins compared to that of LLDPE (Exact 3128) 5.3 Extensional Rheometer Studies Extensional rheological measurements for the three pure PMMA resins were carried out by using the SER rheometer as described in Chapter 4. All experiments were performed at 170°C and at Hencky strain rates varying from 0.113s"1 to 22.6s"1. The characterization temperature was chosen to be 170°C so that the results could be correlated to the ones obtained from the time-temperature superposition on all pure resins. The low temperature is also necessary to avoid sagging of the polymer samples during their stretching in the oven. 78 CHAPTER 5 - RESULTS AND DISCUSSION Figures 5.24-26 plot the tensile stress growth coefficient at various Hencky strain rates for the three pure PMMA resins. It can be seen that these resins exhibit behavior typical for linear polymers with a small degree of strain hardening at high Hencky strain rates. One common characteristic of the extensional behavior of all resins is that small strain hardening effect is present only at high rates. In each of these cases, the tensile stress growth coefficient tends to plateau before it suddenly decreases due to rupture. Superposed with the tensile stress growth curves is the fitted Maxwell model for the linear viscoelastic data of each pure resin. As can be observed from these figures, the experimental data are in a very good agreement with the model prediction, especially for the case of PMMA(l) and PMMA(3). PMMA(2) has considerably lower viscosity than the other two resins, and this probably has been the reason for not having such a good agreement between experimental data and model prediction. Figure 5.27 compares the tensile stress growth coefficient rjl of the three resins at the Hencky strain rate sH of 22.6s"1. It can be seen that n*E. scales with the molecular weight of the three resins as indicated by the shear rheological data of these resins, that is PMMA(l), PMMA(3) and PMMA(2). Similar observations can be derived from Figure 5.28 where the Maxwell model predictions for all three resins are plotted. 79 CHAPTER 5 - RESULTS AND DISCUSSION 107 M * co a. U l 1—i—i—i—i • 111 PMMA(1) T = 1 7 0 ° C -i 1—i— i —i—i—i i 111 0.45s1 10° time (s) LVE: Maxwell Model Fit 102 Figure 5.24 The tensile stress growth coefficient of PMMA(l) for various Hencky strain rates at 170°C PMMA(2) | -T = 170 o C 10 s (fl * ra Q. LU > i i 1111 -i—i—i i i 111 11.3s 1 4.5s" 0.45s"1 e „ = 22.6s"1 1.13s"1 0.113s -1 LVE: Maxwell Model Fit 10 2 Figure 5.25 The tensile stress growth coefficient of PMMA(2) for various Hencky strain rates at 170°C 80 CHAPTER 5 - RESULTS AND DISCUSSION 107 PMMA(3) t T = 170°C 106 * ro Q. UJ P" - i 1 1 i i i i i | 1 1 I 1 1 ! ' LVE: Maxwell Model Fit 22.6s 102 Figure 5.26 The tensile stress growth coefficient of PMMA(3 for various Hencky strain rates at 170°C 107 106 n a. UJ p-105 104 T = 170°C £ H = 22.6s 1 0.01 PMMA(1) PMMA(2) PMMA(3) 0.1 time (s) Figure 5.27 Comparison of the tensile stress growth coefficient of all resins at £ H - 22.6s"1 CHAPTER 5 - RESULTS AND DISCUSSION : ' ' ' i i 1111 1 1—i i i i 111 1 1—i i i 1111 • 1—i i i i 111 : T = 170°C : LVE: Maxwell Model Fit time (s) Figure 5.28 Maxwell model fit of linear viscoelastic moduli for all resins at temperature 170°C 5.4 Capillary Rheometer Studies The performance of the various processing aids used in this study was assessed by determining the critical shear rate for the onset of "helical flow" (gross melt fracture) and by comparing it with that obtained for the pure poly(methyl methacrylate). 5.4.1 Pure Poly(methyl methacrylate) Resins The extrusion experiments were carried out at 190°C, 210°C, 230°C and 250°C for PMMA(l), 190°C, 210°C and 230°C for PMMA(2) and PMMA(3) over a shear rate range from 5 s"1 to 1500 s"1 depending on how easily the polymer under examination 82 CHAPTER 5 - RESULTS AND DISCUSSION exhibited melt fracture. Figures 5.29-5.31 depict the apparent flow curves of PMMA(l), (2) and (3) at all temperatures at which experiments were performed. It can be seen form Figures 5.29-5.31 and Table 5.3 that the critical shear stresses for the onset of helical to be about the same value for the three resins and independent of the extrusion temperature. This observation implies that the critical stress is temperature and molecular weight independent for the case of poly(methyl methacrylate) resins. The value is 0.35±0.03 MPa. This value agrees well with other reported values in the literature for the onset of melt fracture (Dealy and Kim, 2004). Most of these values are between 0.3-0.4 MPa. Typical extrudate photos from the extrusion of PMMA(2) at 190°C appear in Figure 5.32. At small shear rates the extrudate looks smooth and glossy (Figure 5.32a). At higher apparent shear flow rates, helical flow starts, which reflects on the extrudate appearance (Figure 5.32b). Helical appearance becomes more severe (Figure 5.33c) which becomes gross melt fracture at even higher shear rates (Figure 5.32d). 83 CHAPTER 5 - RESULTS AND DISCUSSION |_PMMA(1) Capillary Die: L/D = 16, D = 1mm ra Q. to (0 a *-CO I— ra a> £ CO § 0.1 n o. Q. < A 190°C • 210°C • 230°C • 250°C 10 1 10 2 Apparent Shear Rate (s1) 10 3 Figure 5.29 The apparent flow curves of PMMA(l) at several temperatures. Arrows indicate the onset of extrudate distortion in terms of helical appearance PMMA(2) L Capillary Die: L/D = 16, D = 1mm ra Q. E (0 (0 £ CO im n CD CO +-c £ ra a 0.1 < A 230°C • 210°C • 190°C 10 1 10 2 10 3 Apparent Shear Rate (s~) Figure 5.30 The apparent flow curves of PMMA(2) at several temperatures. Arrows indicate the onset of extrudate distortion in terms of helical appearance 84 CHAPTER 5 - RESULTS AND DISCUSSION PMMA(3)' ' Capillary Die: L/D = 16, D = 1mm 0.1 • 190°C o 210°C • 230°C 101 10 2 Apparent Shear Rate (s"1) 103 Figure 5.31 The apparent flow curves of PMMA(3) at several temperatures. Arrows indicate the onset of extrudate distortion in terms of helical appearance 85 CHAPTER 5 - RESULTS AND DISCUSSION Table 5.3 Critical apparent shear rates and shear stresses for the onset of helical flow of all PMMA resins at various temperatures j Sample Temperature (°C) Critical Shear Rate (s"1) for the Onset of Helical Flow Critical Shear Stress (MPa) 190 10 0.3601 PMMA(l) 210 50 0.3178 230 350 0.3230 250 >1500 190 50 0.3756 PMMA(2) 210 350 0.3280 230 1750 0.3654 190 25 0.3715 PMMA(3) 210 200 0.3508 230 1000 0.3462 Average Critical Shear Stress 0 .35±0 .03 5.4.2 Poly(methyl methacrylate) Blends with Processing Aids The extrusion of pure PMMA was followed by the extrusion of all PMMA blends with processing aids. The objective of this work was to identify any changes in the critical shear rate or the critical shear stress in the presence of processing aids. For this purpose all extrudates were inspected thoroughly. In this section, the most significant results will be presented, together with some representative from each "group" of processing aids. Results obtained from processing aids that exhibited no effect in the extrusion of PMMA are presented in Appendix C. Fluoropolymers The first attempt to identify suitable processing aids for PMMA was testing traditional processing aids used for the extrusion of polyolefins; namely fluoropolymers such as Dynamar and Viton, discussed in detail in Chapter 4. Polyvinylidene fluoride (PVDF) 86 CHAPTER 5 - RESULTS AND DISCUSSION was also used as a possible processing aid. In summary, the addition of all these fluoropolymers into PMMA had no effect in its processability. It is known that fluoropolymers have the tendency to coat the surface of the die wall, thus promoting slip. Apparently, this is not true for the case of PMMA. This is illustrated in Figures 5.32-34, where the addition of Dynamar, Viton free flow and PVDF into PMMA(2), (1) and (3) respectively, has shown no improvement on their processability. It should be mentioned that these plots are only representative from each fluoropolymer "group". Other flow curves showing no effect of fluoropolymer in the extrusion of PMMA can be found in Appendix C (Figures Ci-Ce). A possible explanation for this behavior would be that these additives cannot coat the die wall due to the high surface energy of PMMA. Thus, once PMMA being at the die wall surface it is very difficult to be displaced by fluoropolymer particles. 87 CHAPTER 5 - RESULTS AND DISCUSSION re w w £ CO ra co JC CO c a> re Q. a < 0.1 1 1 1 1 1—r—| T = 210°C Capillary Die: L/D = 16, D = 1mm * + 0.3% Dynamar 5911X • PMMA(2) 10 2 10 3 Apparent Shear Rate (s'1) Figure 5.32 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by dry mixing) 1 re Q. il) W 2 CO re .c CO c 0) k . re a. a. < 1 i 1 r — I 1 1—j T =210°C 1 I I I i I — T — Capillary Die: L/D = 16, D = 1mm • * • • • • * • • • A + 0.3% VITON Z-200 free flow i • PMMA(1) 10 2 10 3 Apparent Shear Rate (s1) Figure 5.33 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) 88 CHAPTER 5 - RESULTS AND DISCUSSION T = 210°C Capillary Die: L/D = 16, D = 1mm t t — J t 1 * +0.3% PVDF 1010 • PMMA(3) - i i i i 102 103 Apparent Shear Rate ( s 1 ) Figure 5.34 Apparent flow curve o f P M M A ( l ) with and without processing aid (blend prepared by dry mixing) Inorganic Solid Lubricants The addition of another traditional processing aid (boron nitride) used for polyethylenes by compounding, also resulted in no improvement on the processability of PMMA. These results are plotted in Figure 5.35 where it can be seen that the addition of boron nitride has no effect in both the flow curve and the critical shear rate for the onset of melt fracture. Boron nitride usually acts as an internal lubricant, which means that it promotes slip of polymer layers in the bulk. Therefore, in this case pressure reduction was not expected, but only a postponement of the onset of helical flow. However, this was not observed and therefore it can be concluded that boron nitride is not a suitable processing aid for the extrusion of PMMA. 89 re Q. S W (0 0) CO co CO c L _ re a a. < C H A P T E R 5 - RESULTS A N D DISCUSSION T = 210°C Capillary Die: L/D = 16, D = 1mm * + 0.2%BN • PMMA(2) 10 2 10 3 Apparent Shear Rate (s1) Figure 5.35 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by compounding) On the other hand, the addition of 0.2% Nanomer I.44PA by compounding resulted into an improvement of the processability of PMMA. This can be observed in Figures 5.36 and 5.37 where a slight decrease of the extrusion pressure is observed, which is accompanied by an increase of the critical shear rate for the onset of melt fracture. 90 CHAPTER 5 - RESULTS AND DISCUSSION ra o. in in o L _ 4-* CO ra CD £ CO c ra Q. Q. < 0.1 T = 210°C Capillary Die: L/D =16, D =1mm A + 0.2% I.44 PA • PMMA(2) 10 2 10 3 Apparent Shear Rate (s*1) Figure 5.36 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by compounding) ra m in a> mm CO mm ra a> CO *ml c 0) L _ ra a. a < 0.1 T = 210°C Capillary Die: L/D = 16, D = 1mm A A + 0.5% I.44 PA • PMMA(2) 102 10 3 Apparent Shear Rate (s~1) Figure 5.37 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by compounding) 91 CHAPTER 5 - RESULTS AND DISCUSSION Fatty Acids-Amides Blends These types of processing aids generally decrease polymer-to-wall friction; therefore they have been used in this study to examine if they could promote slip between the die surface and the polymer flowing through it. In such case a significant pressure reduction is expected in extrusion. In the case of Atmer-1759, addition of 0.2% by compounding resulted into a small reduction in pressure and a slight improvement on the processability. This can de seen in Figure 5.38. Atmer 1759 was also added in dry mixed form into PMMA. The apparent flow curves of the dry mixed blends are presented in Appendix C (Figures C 6 - C 9 ) . In all the cases a small reduction in extrusion pressure is observed. The addition of Struktol TR 016PD resulted into no improvement of the processability, and these flow curves are also presented in Appendix C (Figures Cio-Cn). Finally, the addition of INT-35UDH resulted into a significant pressure reduction and at the same time the onset of "helical flow" was shifted to higher shear rate values. Figure 5.39 is an indicative flow curve of the blend prepared by compounding. Flow curves of the blends prepared by dry mixing along with those prepared by compounding but processed at different temperatures are all presented in Appendix C (Figures C12-C14). 92 CHAPTER 5 - RESULTS AND DISCUSSION re Q. s (0 co CD tm CO L _ co CD f CO +-c £ CO Q. a. < 0.1 LT= 190°C [Capillary Die: L/D = 16, D = 1mm • A A A A A +0.2% ATMER 1759 • PMMA(2) 101 102 103 Apparent Shear Rate (s1) Figure 5.38 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by compounding) 1 co Q. (0 co £ CO re a> .C CO c £ re Q. a < 0.1 T=190 °C Capillary Die: L/D = 16, D = 1mm A • A A — A + 0.2% INT-35UDH • PMMA(2) 101 102 Apparent Shear Rate (s"1) Figure 5.39 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by compounding) 93 CHAPTER 5 - RESULTS AND DISCUSSION Other Polymeric Processing Aids The influence of immiscibility of various polymers on the processability of PMMA was investigated by using different polymers as processing aids. Polyethylenes (LLDPE, LDPE and HDPE), polystyrene (PS), acrylonitrile-butadiene-styrene (ABS) and styrene-acrylonitrile (SAN) copolymer are all polymers that exhibit immiscible blends with PMMA (Utracki, 1989). As can be seen from Figures 5.40-43 using polyethylenes as processing aids leads to a significant pressure reduction. At the same time, the onset of helical flow is postponed to the next measured shear rate. In these series of experiments it was observed that the surface of the extrudate was turning slightly opaque which indicates the presence of the polyethylene. The presence of polyethylene at the polymer-wall interface also explains the pressure reduction by the mechanism of PMMA slippage over a PE layer. This is a true slip and not due to the lower viscosity of the fluid on the interface. As can be seen from Figures 5.19 and 5.21, the viscosity of PE is higher than that of PMMA at shear rates relevant to the capillary extrusion tests presented in Figures 5.40-43. Amongst several polystyrene based polymers examined, ABS was the only one that has shown a slight effect on the PMMA processability. As been depicted in Figure 5.44, a pressure reduction was observed, although no effect on the critical shear rate for the onset of melt fracture was observed. 94 CHAPTER 5 - RESULTS AND DISCUSSION ro a S ID in 2 co k_ n co £ CO c CO re Q. CL < 0.1 T = 210°C Capillary Die: LVD = 16, D = 1mm A * + 0.2% LLDPE (Exact 3128) • PMMA(1) 102 103 Apparent Shear Rate (s'1) Figure 5.40 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) re Q. in m 2 CO lm re CO JC CO c CO re ct a < 0.1 T = 230°C Capillary Die: L/D = 16, D = 1mm - +0.1% LDPE (EF606) • PMMA(1) 102 103 Apparent Shear Rate (s1) Figure 5.41 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) 95 C H A P T E R 5 - RESULTS A N D DISCUSSION a. co a> L_ +-co mm re a> sz CO re a. a. < 0.1 T = 210°C Capillary Die: L/D = 16, D = 1mm A • A A +0.3% HDPE • PMMA(3) 102 1 03 Apparent Shear Rate (s1) Figure 5.42 Apparent flow curve of P M M A ( 3 ) with and without processing aid (blend prepared by dry mixing) re 0L (0 w S *-* (O re d) si CO re o. o. < 0.1 T = 210°C papillary Die: L/D = 16, D = 1mm A * +0.3% LLDPE (Exact 3128) +0.1% Dynamar FX 9613 • PMMA(2) 102 103 Apparent Shear Rate (s1) Figure 5.43 Apparent flow curve of P M M A ( 3 ) with and without processing aid (blend prepared by dry mixing) 96 CHAPTER 5 - RESULTS AND DISCUSSION re Q. 0) co CO I — re CO c CO re CL CL < 0.1 |.T = 210°C Capillary Die: L/D = 16, D = 1mm A A A A A * +0.3% ABS (Magnum 9035 ] • PMMA(3) 1 0 2 1 0 3 Apparent Shear Rate (s1) Figure 5.44 Apparent flow curve of PMMA(3) with and without processing aid (blend prepared by dry mixing) 5.5 Conclusion In this study, the rheology and processing of three poly(methyl methacrylate) resins were studied thoroughly by means: (i) of a concentric plate and extensional rheometers in order to fully characterize rheologically the three resins and (ii) capillary rheometer in order to investigate the performance of the various processing aids and their effect on PMMA processability. From the experiments that have been performed it can be concluded that first the time-temperature superposition applies very well on the linear rheological viscoelastic data showing that the PMMA resins are thermorheologically simple fluids. The addition of processing aids by means of compounding does not alter 97 CHAPTER 5 - RESULTS AND DISCUSSION the rheological properties of the pure resins. It was also found that there is a good agreement between the data obtained from the extensional and concentric parallel plate rheometers. Extensional rheological data have shown that a small degree of strain hardening is present at high Hencky strain rates. The onset of melt fracture was found to occur at a critical shear stress value (0.35±0.03 MPa), independent of molecular weight and temperature. Identifying processing aids for the extrusion of PMMA resins was proven to be a difficult task. This is mostly due to the fact that the polar nature of PMMA results into a good affinity with the die wall. Hence it makes it difficult for the used processing aid to displace PMMA from the die wall. Polymers immiscible with PMMA were found to cause a moderate pressure reduction and at the same time to increase the shear rate for the onset of melt fracture. These included mostly polyethylenes (HDPE, LLDPE and LDPE). The mechanism by which pressure is caused is slip and this is "true" slip as all PEs used have a higher viscosity at the shear rate of processing. In all, performance of several processing aids was tested. As discussed above, the most significant results were found for the polyethylenes, a proprietary blend of fatty acids-polyamides (INT 35-UDH) and an inorganic solid lubricant (Nanomer I.44PA). 98 CHAPTER 6 - RECOMMENDATIONS 6 RECOMMENDATIONS Based on the experience gained throughout this work, the following recommendations for future work can be made: • Identify more polymers that are incompatible with PMMA and investigate their performance as processing aids. Apart from the polymers used in this study as processing aids, literature shows that polymers such as PMA, PLA, PP, PEAM, PVAc, PA-6 and others are incompatible with PMMA. • Measure the surface energy of all polymers used as processing aids and relate it to their performance as processing aids. Based on the fact that PMMA is a polar polymer with high surface energy, it would be interesting to see how different surface energies of polymers used as processing aids would affect the processing of PMMA. Based on the fact that polyethylenes improved the processability of PMMA extrusion and other polymers did not (PS, SAN, ABS and fluoropolymers), this could probably lead to useful conclusions. • Quantify the relationship between wave lengths of the helical flow as a function of temperature and shear rate. This would help as understand the phenomenon under study. 99 REFERENCES REFERENCES Achilleos, E.C., Georgiou, G., Hatzikiriakos, S.G., Role of processing aids in the extrusion of molten polymers. J.Vinyl Addit. Technol., 8 (1), 7-24 (2002) Aelmans, J.J.N., Reid, C.M.V., Higgins, Change of phase behavior of SMA PMMA blends during processing at high deformation rates S. J., Polymer. 40, 5051-5062(1999) Ajii, A., Choplin, L. , Prud'Homme, R.E., Rheology and phase separation in polystyrene/poly(vinyl methyl ether) blends. J. Polym. Sci. 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Papers, 1223-1227 (1999) 105 APPENDIX A APPENDIX A - Linear Viscoelasticity of PMMA Resins Linear viscoelastic moduli along with complex viscosity plots obtained at various temperatures for PMMA(2) and PMMA(3) are presented in this section. re a. 107 106 105 o V) 3 •O 10" o s Q) o CO 102 101 PMMA(2) 10"1 10° 101 102 Frequency co (rad/s) • 1 5 0 ° C o 1 7 0 ° C • 1 9 0 ° C v 2 1 0 ° C • 2 3 0 ° C 103 Figure A j Storage modulus of P M M A ( 2 ) at various temperatures 106 APPENDIX A 107 106 PMMA(2) 0_ O 105 CO 3 10" (0 CO o 103 t 102 I I I I I I 1— 2 s : : : : : ! ! ! « 8 8 8 M ' " * 9 9 ^ •::::^" ! ,^.-:::::- : : s s , : L v v v • 150°C o 170°C • 190°C v 210°C • 230°C 10'1 10° 101 Frequency co (rad/s) 102 103 Figure A 2 Loss modulus of P M M A ( 2 ) at various temperatures 106 105 10" 103 102 P M M A ( 2 ) 0 0 o ° 0 o • • 150°C o 170°C • 190°C v 210°C • 230°C • o • 10 102 10° 101 Frequency co (rad/s) Figure A 3 Complex viscosity of P M M A ( 2 ) at various temperatures 103 107 APPENDIX A 107 10 6 10 s 10" 10 3 10 2 101 PMMA(3) — I — I I I I I. • ••• O ° _ • „ v v _ • • • 1 5 0 ° C o 1 7 0 ° C • 1 9 0 ° C , v 2 1 0 ° C ; • 2 3 0 ° C : 10-1 10° 101 10 2 103 Frequency co (rad/s) Figure A 4 Storage modulus o f PMMA (3 ) at va r ious temperatures tn * re Q. 107 10s 10 5 o tn 3 3 O 10" tn tn o 10 3 10 2 - I - T T 1 PMMA(3) n 1 1 — j o 0 o ° • 1 5 0 ° C o 1 7 0 ° C T 1 9 0 ° C v 2 1 0 ° C • 2 3 0 ° C 10"1 10° 101 Frequency co (rad/s) 102 103 Figure A 5 L o s s m o d u l u s o f PMMA (3 ) at va r ious temperatures 108 APPENDIX A 107 <n 106 cu n. ^ 10s itr '35 o o cn > 10" x 0) Q. E o 103 102 PMMA(3) t o, 1 i 1 i i i I J ° ° o , • 150°C o 170°C • 190°C v 210°C • 230°C 1 _ j — i • • • • < I i _ 102 10"1 10° 101 Frequency co (rad/s) Figure A 6 Complex viscosity of PMMA(3) at various temperatures • • • • 103 109 APPENDIX B APPENDIX B - Linear Viscoelasticity of Various Polymers Linear viscoelastic moduli of all polymeric processing aids obtained at 210°C are presented here. 10 6 tn 10 5 CD * Q. CO — 0. ET = 210°C b & 10 4 n ^ O r> ° _ G ct° ~ © - © „ 0 0 © ° 0 © ° ° i ° © o o g 8 e ,0@ 0o © © o o o g o 8 = (0 3 O •o o O « S > 10 3 O X .- a, 2 E goOoooooSooo, ©o° o u o ©o, 10 1 1 • ' ' 1 I— © L L D P E (Exact 3128) a i i 10"' 10° 10 1 10 2 Frequency co (rad/s) 10 3 Figure B, The linear viscoelastic moduli of LLDPE at 210°C 110 APPENDIX B 106 ~ « > 10= Q_ CO w Q. 104 b * = (0 3 O •D O O M S > 103 o x .- a> 2 E cT<S ™2 101 TI J1 I 1 f • fr = 2io°c n 1 — i — i i i i 111 o 0 o 0 ° ° o 0 „ « o ° ° o ° S88 88 9 0 ° ' 888 8 8 SSo o § 8 ° V o o ° G o' G G G ° G , w o , ' G 0 , o LDPE (EF606) • • I I— —I I I ' ' • ' 1 10-1 10° 101 Frequency co (rad/s) 102 103 Figure B2 T h e l inear v i scoe las t ic m o d u l i o f L D P E at 210°C CO * Q. re '—' Q. b * = ID 3 O T3 O O M S > O X c a> > o a o 106 105 104 103 102 p - T - —II I I I I | 210°C • HDPE 1 1 1 I I • • • • 1 10"1 10° 101 102 Frequency co (rad/s) Figure B3 T h e l inear v i scoe las t ic m o d u l i o f H D P E at 210°C 103 111 APPENDIX B 10 s ~<0 10^ Q. CO '—1 Q. 10" b * 3 O •a o O !2 5 > 10 3 U X . - a, 2 E it 8 i ° 2 10 1 T = 210°C o ° o o o o o 8 o 8 o o 8 8 o o o g 8 8 6 0o88SioooOoo G G ° o G ° ° ° o , ©o o o o o © o © Tyril 100 (SAN) _ l I • • ' • 1 10"1 10° 10 1 10 2 Frequency co (rad/s) Figure B 4 The linear viscoelastic moduli of SANat210 ° C 10 3 10 6 p-n .—, :T = 210°C £*co 1 0 S £L br b & •- "55 i o 4 3 O •a o O <0 2 > 0 X 1 g - 10 3 >, o Q U 10 2 n 1 — r -i © © o © 8 8 o e 888oooooo©oo© o © ( 0 0© _ O O ° O r, © © 0 © o o ° o ° © © o o o O o © o© o PS (ST 685D) -1.1.1 1 I • • ' ' » I I • 1 ' • 1 10"1 10 2 10° 10 1 Frequency co (rad/s) Figure B5 The linear viscoelastic moduli of PS at 210°C 10 3 112 APPENDIX B 106 0. co 105 — ' pt_ e> ^ 3 O 104 "O o o <» E > O X .- 0) S E 103 >» o Q O 102 cT-n 1 r-A B S (Magnum 9035) CT = 2 1 0 ° C i i — i — i — r n | • • • • • , | « , , A • m r~\ 1 1 1—i—r—n A A A • • - i 10"1 10° 10' 102 Frequency CD (rad/s) Figure B6 The linear viscoelastic moduli of A B S at 210°C 103 1 10 Frequency co (rad/s) 1000 Figure B7 The linear viscoelastic moduli of PVDF 1010 at 210°C 113 APPENDIX B 107 — Q. PVDF 6010 FT = 210°C O *_ (D & := tn 3 O -a o o w 2 > o x c i> 2 E > O Q O 105 104 103 102 • • A A A * . • 1 101 102 10° 101 Frequency co (rad/s) Figure B8 The linear viscoelastic moduli of PVDF 1010 at 210°C 103 114 APPENDIX C A P P E N D I X C - Capillary Rheometer Studies Apparent flow curves that depict little or no improvement on the extrusion of all PMMA resins are presented here. — 1 r 1 1 r 1 — i — | T = 210°C Capillary Die: L/D = 16, D = 1mm -1 1 r 1 1 1—r - | -0.1 A + 0.3% Dynamar FX 5914X • PMMA(1) 102 103 Apparent Shear Rate (s1) Figure C i Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) 115 APPENDIX C ro 0. co co a CO ro a> CO CO CL CL < 0.1 T = 210°C Capillary Die: LVD = 16, D = 1mm A + 0.3% Dynamar 5911X • PMMA(2) 102 lO 3 Apparent Shear Rate (s1) co 0_ CO CO CO L _ *-CO ro co CO co ro a CL < Figure C 2 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by dry mixing) 0.1 T = 210°C Capillary Die: L/D = 16, D = 1mm A +0.2% PVDF 6010 • PMMA(3) 102 Apparent Shear Rate (s1) 103 Figure C 3 Apparent flow curve of PMMA(3) with and without processing aid (blend prepared by compounding) 116 APPENDIX C ra Q. £ CO n CO *< c 0) L _ ra a a. < 0.1 T = 210°C Capillary Die: L/D = 16, D = 1mm A +0.3% PVDF 60512 • PMMA(3) _j i i i_ 10 2 Apparent Shear Rate (s1) 10 3 ra Q. W Oi 0) 4 - * CO ra a> .c CO c 0) k . ra o. a < Figure C 4 Apparent flow curve of PMMA(3) with and without processing aid (blend prepared by dry mixing) T=210 °C .Capillary Die: L/D = 16, D = 1mm 0.1 A +0.3% PVDF 1010 • PMMA(3) 102 103 Apparent Shear Rate (s1) Figure C 5 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) 117 APPENDIX C ro Q. CO CO CO k_ •+-• CO k-ro co _c CO 4-* c CO k_ ro a a < 1 1 1 1 1 1 — 1 T = 190°C .Capillary Die: L/D = 16, D = 1mm ' ' ' • t • t A • A 1 • • * • A • • A > . . . . A +0 .1% ATMER 1759 • PMMA(1) . . . i . . . 101 102 Apparent Shear Rate (s1) Figure C 6 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) - i — i 1 1 1—i—i—i—i—i—i 1 1 T = 190°C Capillary Die: L/D = 16, D = 1mm ro Q. CO CO CO k-CO k_ ro CO c CO k-ro a a . < 1 1 t I t t t I A A + 0 . 3 % ATMER 1759 • PMMA(1) 101 102 Apparent Shear Rate (s1) Figure C 7 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) 118 APPENDIX C ra OL in in a to mm ra CO c d> mm n a Q. < 0.1 n in in a *m CO >_ n 0) CO *m C £ n a OL < 1 , , r r i — i — | 1 T = 210°C Capillary Die: L/D = 16, D = 1mm • A • t 1 * t m t I A A + 0.1%ATMER 1759 • PMMA(1) 102 103 Apparent Shear Rate (s1) Figure C g Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) 1 0.1 T = 210°C . . i I i i i i i ! Capillary Die: L/D = 16, D = 1mm -1 A t t t 8 t t • • A A + 0.3% ATMER 1759 . i • PMMA(1) 102 103 Apparent Shear Rate (s1) Figure C 9 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) 119 APPENDIX C co OL (0 in CD mm CO mm CO CD CO c CD L _ co a a < 0.1 —i 1 1 1 1 i T = 210°C Capillary Die: L/D = 16, D = 1mm A +0.3%Struktol TR 016PD • PMMA(1) 10 2 10 3 Apparent Shear Rate (s1) Figure C i 0 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) co Q. E in in CD mm *-CO mm CO <D .C CO c CD mm co a Q. < 0.1 T = 230°C Capillary Die: L/D = i i i i 16, D = 1mm 1 1 1 1 1 1—1—1—1 A • * • A • • * • * "T* • A +0.3%Struktol TR 016PD • PMMA(1) 10 2 10 3 Apparent Shear Rate (s1) Figure C n Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) 120 APPENDIX C Q. tn tn £ *-CO k-ra co AZ CO c CO n a CL < 0.1 T = 210°C Capillary Die: L/D = 16, D = 1mm i i • i | • = * " » • A • A • • A A -« 1 : A . . . i A +0.3% INT-35UDH • PMMA(1) 102 103 Apparent Shear Rate (s'1) Figure C i 2 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) • A A A + 0.3%INT-35UDH • PMMA(1) • 102 103 Apparent Shear Rate (s"1) Figure C 1 3 Apparent flow curve of PMMA(l) with and without processing aid (blend prepared by dry mixing) 121 APPENDIX C ro CL ID lli CD 4-» CO b _ ro o> f CO c S> ro a CL < 0.1 1 1 I I I T = 2 1 0 ° C 1 I I I i i — i — i .Capillary Die: L/D = 16, D = 1mm -• • • 4 • A • • A i • • A A • A A + 0.2% INT-35UDH • PMMA(2) 102 103 Apparent Shear Rate (s1) Figure C M Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by compounding) ro 0. V) ID CD CO L_ ro o> CO c £ re Q. CL < 0.1 T = 2 1 0 ° C Capillary Die: L/D = 16, D = 1mm - i — i — i — j -A + 0.2%Cerflon PMMA(2) 102 103 Apparent Shear Rate (s1) Figure C] 5 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by dry mixing) 122 APPENDIX C 1.0 A 0. V) (0 £ CO mm ra a> JC CO £ ra a. a. < 0.1 T = 210°C Capillary Die: L/D = 16, D = 1mm • + 0.3% PS (Styron 685 D) • PMMA(2) 102 Apparent Shear Rate (s1) 103 Figure C16 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by dry mixing) ra QL S V) W CD mm «-» CO mm ra CD £ CO 4-1 c £ ra o. a < 0.1 T = 2 1 0 ° C Capillary Die: L/D = 16, D = 1mm • A + o.5% SAN (Tyril 990) • PMMA(2) — i 1—i i i i i 102 103 Apparent Shear Rate (s1) Figure C i 7 Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by dry mixing) 123 APPENDIX C ra o_ S v> 0) a> b. *J CO ra a> co ra OL a < T = 210°C I Capillary Die: UD = 16, D = 1mm 0.1 —I 1 1 1— ± +0.2% Zinc Stearate • PMMA(3) 102 103 Apparent Shear Rate (s~1) Figure C l g Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by compounding) ra o. w w CO mm n CO ra a a . < 0.1 T = 210°C Capillary Die: U D = 16, D = 1mm A + 0.3% Calcium Stearate • PMMA(3) 10 2 Apparent Shear Rate (s1) 10 3 Figure C19 Apparent flow curve of PMMA(3) with and without processing aid (blend prepared by dry mixing) 124 APPENDIX C Q. CO CO £ CO k_ ro cu £ CO c v-ro a. cu < 0.1 T = 210°C Capillary Die: L/D = 16, D = 1mm 1 » I I 1_ +0.2% Zinc Stearate PMMA(3) i i i i i i 10 2 10 3 Apparent Shear Rate (s1) Figure C 2 0 Apparent flow curve of PMMA(3) with and without processing aid (blend prepared by compounding) ffl CL CO CO £ co k_ re CD CO tz 01 l _ re cu a < 0.1 T = 210 °C .Capillary Die: L/D = . | 1 I F 16, D = 1mm • • • A A • A • • A • t : A + 0 .3% P V C A • PMMA(2) 102 103 Apparent Shear Rate (s) Figure C 2 J Apparent flow curve of PMMA(2) with and without processing aid (blend prepared by dry mixing) 125 N O M E N C L A T U R E A cross sectional area horizontal shift factor b Rabinowitsch correction bj vertical shift factor D capillary diameter Ea activation energy for flow • e Bagley end correction or F tangential force FF frictional force Fd piston force G shear modulus, Pa G' storage modulus, Pa G" loss modulus, Pa G* complex modulus, Pa Gd amplitude ratio in oscillatory shear h gap between plates K power-law consistency index, MPa* L,L0 capillary length; sample length M power-law exponent n power-law exponent P absolute pressure, Pa Pa ambient pressure, Pa Pa driving pressure, Pa ^end Bagley correction, Pa Went entrance pressure drop, Pa &Pex exit pressure drop, Pa Q volumetric flow rate, m3/s r capillary radius, m R radius of SER windup drums Rb radius of barrel, in T torque; absolute temperature K t time u melt velocity, m/s slip velocity, m/s Ax plate displacement, m Greek Letters P geometrical parameter for shear stress distribution m shear strain f shear rate, s"1 YA apparent shear rate, s"1 Y A,s apparent shear rate, corrected for slip, s"1 K wall shear rate, s"1 Yo strain amplitude in oscillatory shear 8 mechanical loss angle £H Hencky strain rate, s"1 V viscosity, Pa*s no zero-shear viscosity, Pa*s dynamic viscosity, Pa*s V" out-of-phase component of complex viscosity, Pa*s n* complex viscosity, Pa*s rtE tensile stress growth coefficient NOMENCLATURE X relaxation time, s Xc critical relaxation time, s p density critical shear stress for the onset of melt fracture, Pa principal stretching stress, Pa <yn normal stress, Pa aw wall shear stress, Pa ° " o stress amplitude in oscillatory shear, Pa r stress tensor, Pa CO frequency, rad/s or specific volume, cm3/g Q angular speed 128 

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