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Paste extrusion of polytetrafluoroethylene (PTFE) fine powder resin : the effects of processing aid physical… Ochoa, Isaias 2006

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Paste extrusion of Polytetrafluoroethylene (PTFE) fine powder resin: The effects of processing aid physical properties by Isaias Ochoa Master of Material and Polymers Science, University of Sonora, 1997 Bachelor of Chemical Engineer, University of Sonora, 1991 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Chemical and Biological Engineering) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A A pr i l 2006 © Isaias Ochoa, 2006 Abstract The rheological properties of a number of polytetrafluoroethylene (PTFE) pastes were studied relevant to paste extrusion process. The effects of the physical properties of lubricants and the geometrical characteristics of the extrusion die on the preforming, extrusion pressure and mechanical properties of the final extrudates were studied. A number of lubricants were identified as suitable for the paste extrusion of polytetrafluoroethylene (PTFE). They were characterized in terms of both flow and surface properties. It was found that it is possible to alter the flow and surface properties of these lubricants independently and thus it became possible to study their relative effects on preforming and extrusion of P T F E paste. Based on this study, it was concluded that preforming quality increases with increase of lubricant viscosity and with improvement in the wetting characteristics of the lubricant with P T F E . The effects of the lubricant physical properties on the processing of polytetrafluoroethylene (PTFE) fine powder resins were also studied by using dies of various geometrical characteristics and resins having a variety of molecular architecture. It was found that the wettability (surface tension) of the lubricant strongly affects the pressure needed to extrude the P T F E pastes. The viscosity of the lubricant was also found to play a significant role in the process since a lubricant with a low viscosity causes the paste to be extruded at a lower pressure. These effects significantly influence the mechanical properties of the final extrudates. The latter are functions of the degree of fibrillation which is significantly influenced by the wettability and viscosity of lubricants. The effects of die geometry on extrusion pressure and mechanical properties of extrudates were assessed in order to determine the geometrical characteristics and operation conditions for the optimization of the process. A rheological equation was developed and proposed for flow simulations of the paste extrusion of P T F E pastes, aiming at optimizing this process. Finally, various additives were tested in order to determine possible processing aids for the paste extrusion of P T F E . It was found that moderate amount of boron nitride and organically modified clays can have beneficial effects on mechanical properties of the final extrudates. i i Table of contents Abstract i i Table of contents i i i List of tables v i List of figures v i i List of symbols xv i i Acknowledgements xx 1 The Physics and Chemistry of Polytetrafluoroethylene 1.1. Introduction 1 1.2. Tetrafluoroethylene (TFE) polymerization techniques: types o f resins 2 1.3. Chemical and physical properties of P T F E 3 1.4. P T F E fine powder resin processing and applications 6 2 P T F E Paste Extrusion: General review 2.1. Introduction 13 2.2. Paste preparation, preforming and extrusion 2.2.1. Paste formulation 14 2.2.2. Preform ing 15 2.2.3. Phase migration and extrusion 16 2.2.4. Sintering 17 2.3. Constitutive equations proposed to predict pressure drop in capillary die flows 18 2.4. Basic equations governing the principle of operation of the experimental equipment 2.4.1. Capillary flow 20 2.4.2. Flow in a rectangular channel 22 2.4.3. Parallel plate flow 22 2.4.4. Extensional rheometer 24 2.5. Stress-strain curves 26 3 Scope of Work 29 3.1. Introduction 29 3.2. Thesis objectives 30 3.3. Thesis organization 4 Experimental Equipment, Materials and Procedures 4.1. Introduction 32 4.2. Material 4.2.1. PTFE fine powder resins 32 4.2.2. Lubricants 33 4.2.3. Other lubricants 34 i i i 4.3. Experimental equipment 4.3.1. Preforming and extrusion 36 4.3.2. Mechanical and viscoelastic properties measurement 38 4.3.3. Other equipment 39 4.4. Experimental procedure 4.4.1. Paste preparation 40 4.4.2. Capillary and sessile drop experiments 41 4.4.3. Effect of surfactant on lubricant surface tension & wettability 49 4.4.4. Preform ing 5 2 4.4.5. Extrusion 54 4.4.6. Extrudate analysis 54 5 P T F E Paste Preforming 5.1. Introduction 55 5.2. Densification studies 55 5.3. Liquid migration 5.3.1. Axial liquid migration 58 5.3.2. Radial liquid migration 60 5.3.3. Effect of high preforming pressure and its duration on liquid migration 67 5.4. Liquid migration during extrusion 69 5.5. Summary 74 6 P T F E Paste Extrusion 6.1. Introduction 76 6.2. Pressure transient in P T F E extrusion 77 6.3. The effect of the physical properties of lubricants on P T F E paste extrusion 6.3.1. The effect of surface tension 82 6.3.2. The effect of viscosity 86 6.4. The effect of geometrical characteristics of die on extrusion pressure 6.4.1. Reduction ratio 88 6.4.2. Length-to-diameter ratio (L/D) 89 6.4.3. Entrance angle 91 6.4.4. Molecular structure of the resin 93 6.5. Effect of temperature on P T F E paste extrusion 95 6.6. Appearance of P T F E extrudates 98 6.7. Mechanical properties of P T F E extrudates 106 6.8. Interpretation of P T F E paste extrusion 109 6.9. Summary 111 7 Rheology of Preformed and Extruded P T F E Pastes 7.1. Introduction 112 7.2. Rheology of dry P T F E powders and preformed pastes 113 7.3. Y i e l d stress of P T F E pastes 119 7.4. Extensional rheology of extrudates obtained from slit die extrusion 134 7.5. Yielding and deformation behaviour in extrusion 142 7.6. Modell ing the extensional behaviour through the strain-energy function 145 7.7. Summary ; 153 iv 8 Extrusion of P T F E Blends and Effects of Various Additives 8.1. Introduction 8.2. P T F E blend extrusion 8.3. The effect o f lubricant blend on P T F E paste extrusion 8.4. Effects of additives on paste extrusion 8.5. Summary 9 Conclusions, Recommendations and Contribution to Knowledge 9.1. Conclusions 9.2. Contribution to knowledge 9.3. Recommendations for future work Bibliography Appendix v List of tables Table 4.1 Physical properties of P T F E fine powder resin studied in this work, as provided by the supplier. 33 Table 4.2 Physical Properties of Isopar® and HFE-7500 lubricants. 34 Table 4.3 Physical properties of Isopar® G - A O T solutions at 25°C. 35 Table 4.4 Physical properties of Isopar® G & Isopar® V solutions at 25°C. 35 Table 4.5 Comparison of contact angles of various lubricants with a P T F E substrate obtained by the Young-Dupre equation, the capillary rise and sessile drop methods. 49 Table 4.6 Contact Angle o f Isopar® G - A O T solutions on a P T F E substrate at 25°C. 52 Table 4.7 Physical properties of Isopar® G - A O T solutions. 52 Table 5.1 Liquid concentration during four extrusion experiments at the conditions listed in Figure 5.20. 70 Table 5.2 Mechanical properties of the extrudates obtained in different flow zones. 71 Table 6.1 Mechanical properties of P T F E resins extruded under different conditions. 108 Table 6.2 Heat of melting and melting point of P T F E resins extruded at different conditions. 110 Table 7.1 Y i e l d stress of P T F E resins. 122 Table 7.2 Y i e l d stress of various pastes determined by means of fitting viscoplastic models to the experimental data depicted in Figures 7.23 to 7.26. 131 Table 7.3 The yield stress and strain of P T F E extrudates at room temperature. 143 Table 7.4 Ogden's parameters for P T F E samples subjected to different Hencky strain rates. 149 Table 8.1 Mechanical properties of PTFE-additive blends + Isopar® G extruded at different conditions. 166 VI List of figures Figure 1.1 Schematic diagram of a chain segment of P T F E molecule 3 Figure 1.2 Partial phase diagram of P T F E (Sperati, 1989). 5 Figure 1.3 Tube extrusion equipment of P T F E fine powder (Daikin technical bulletin). 9 Figure 1.4 Electric wire insulation extrusion process of P T F E fine powder (Daikin technical bulletin). 10 Figure 1.5 Cross section of electric wire insulation extruder die (Daikin technical bulletin). 11 Figure 1.6 Production of unsintered tape from P T F E fine powder (Daikin technical bulletin). ' 12 Figure 2.1 Schematic diagram of capillary rheometer. 21 Figure 2.2 Parallel plate rheometer. 23 Figure 2.3 Schematic of Sentmanat Extensional Rheometer (SER). 24 Figure 2.4 A typical stress-strain curve of a material subjected to tension. 26 Figure 2.5 Classification of material based on the shape of the stress-strain curves: (a) soft & weak; (b) hard & brittle; (c) hard & strong; (d) soft & tough; and (e) hard & tough. 27 Figure 4.1 S E M image of F104 H M W fine powder resin. 33 Figure 4.2 Molecular structure of dioctyl sulfosuccinate sodium salt (AOT) . 35 Figure 4.3 Set-up of the Instron tensile tester machine for paste performing and extrusion. 37 Figure 4.4 Schematic diagram of a typical cylindrical capillary die along with the definition of the design parameters. 37 Figure 4.5 Schematic diagram of the tapered slit die showing its contraction and the land zones. 38 Figure 4.6 Set-up of C O M - T E N tester to measure the mechanical properties of extrudates 39 Figure 4.7 Max imum packing of the solid phase in P T F E paste. 41 vn Figure 4.8 Variation of density of a compacted P T F E resin as a function of pressure. 42 Figure 4.9 Variation of porosity, s, of a compacted P T F E resin as a function of pressure. 43 Figure 4.10 Capillary rise method to determine the surface energy of a powder or a liquid. 44 Figure 4.11 Capillary rise experiment of Isopar® G through a tube filled with P T F E powder at 25°C. 46 Figure 4.12 Capillary rise experiment of H F E 7500 through a tube filled with P T F E powder at 25°C. 46 Figure 4.13 Drops of liquid placed on P T F E substrate, (a) Water, (b) Isopar® V . 47 Figure 4.14 Capillary rise experiment of Isopar® G - A O T solutions through a tube filled with P T F E resin at 25°C. 51 Figure 4.15 (a) Preform paste slicing for determination of the axial density variation and liquid migration, (b) Preform paste slicing for determination of radial liquid migration, (c) Top view of the preform sliced for radial liquid migration. 53 Figure 5.1 Variation of preform density in axial direction resulting from an applied pressure of 1 M P a for 30 s on F104 L M W resin +18 wt% of lubricant. 56 Figure 5.2 Variation of preform density in axial direction resulting from an applied pressure o f 2 M P a for 30 s on F104 L M W resin + 18 wt% of lubricant. 57 Figure 5.3 Variation of preform density in axial direction resulting from an applied pressure of 3 M P a for 30 s on F104 L M W resin + 18 wt% of lubricant. 57 Figure 5.4 L iquid migration in axial direction of Isopar® G , M and V through one-sided preformed F303 paste when a 2 M P a pressure was applied for 30 s at 25°C. 59 Figure 5.5 A x i a l liquid migration for Isopar® G , M and V for a two-sided F303 paste preformed by applying a pressure of 2 M P a for 30 s at 25°C. 60 Figure 5.6 A x i a l and radial liquid distribution of Isopar® G for a one-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 61 Figure 5.7 A x i a l and radial liquid distribution of Isopar® G for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 61 Figure 5.8 A x i a l and radial liquid distribution of Isopar® M for a one-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 62 Vll l Figure 5.9 A x i a l and radial liquid distribution of Isopar® M for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. Figure 5.10 A x i a l and radial liquid distribution of Isopar® V for a one-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. Figure 5.11 A x i a l and radial liquid distribution of Isopar® V for a two-sided preformed sample by applying a pressure o f 2 M P a for 30 s at 25°C. Figure 5.12 Contour plot of axial and radial liquid distribution o f Isopar® G for a one-sided preformed sample by applying a pressure o f 2 M P a for 30 s at 25°C. Figure 5.13 Contour plot of axial and radial liquid distribution of Isopar® G for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. Figure 5.14 Contour plot of axial and radial liquid distribution of Isopar® M for a one-sided preformed sample by applying a pressure o f 2 M P a for 30 s at 25°C. Figure 5.15 Contour plot of axial and radial liquid distribution of Isopar® M for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. Figure 5.16 Contour plot of axial and radial liquid distribution of Isopar® V for a one-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. Figure 5.17 Contour plot of axial and radial liquid distribution of Isopar® V for a two-sided preformed sample by applying a pressure o f 2 M P a for 30 s at 25°C. Figure 5.18 Effect of preforming pressure and duration on the axial lubricant migration at 25°C on paste prepared with F301 and 38.8 V % of lubricant. Figure 5.19 A x i a l lubricant distribution in a one-sided preformed paste preparedwith F301 and various Isopar® G - A O T solutions preformed at 2 M P a for 30 s at 25°C. Figure 5.20 Typical start up of pressure transient during extrusion o f paste(F301 + 18 wt% of Isopar® M ) using a die having 2a = 60°, L / D = 20 and R R = 352:1 at yA =2812 5 _ ' a n d 3 5 ° C . 62 63 63 64 65 65 66 66 67 68 68 70 Figure 5.21 Stress vs. strain plot for extrudates obtained during flow zone 1 from Test 2 (see Table 5.2). Figure 5.22 Stress vs. Strain plot for extrudates obtained during flow zone II from Test 3 (see Table 5.2). Figure 5.23 Stress vs. strain plot for extrudates obtained during flow zone III from Test 1 (see Table 5.2). 72 72 73 ix Figure 5.24 Stress vs. Strain plot for extrudates obtained during flow zone IV from Test 4 (see Table 5.2). 74 Figure 6.1 Typical start up of pressure transient obtained in P T F E paste extrusion. 77 Figure 6.2 Extrusion of F104 H M W + 38.8 V % of Isopar® M . The extrusion was stopped and restarted after (a) 1.5 minutes, (b) 10 minutes, (c) 45 minutes, (d) 40 hours. 79 Figure 6.3 Pressure transients during extrusion of P T F E paste prepared with F104 H M W and Isopar G at different apparent shear rate values. 80 Figure 6.4 Pressure transients during extrusion of P T F E paste prepared with F104 H M W and different lubricants at different apparent shear rate values. 81 Figure 6.5 Pressure transients during extrusion of P T F E paste prepared with different resins and Isopar G . 81 Figure 6.6 Pressure transients during extrusion o f P T F E paste prepared with F104 H M W and Isopar G at different conditions and dies. 82 Figure 6.7 The effect of lubricant wettability on the extrusion pressure of paste prepared with resin F-104 H M W and two different lubricants having about the same viscosity and different wettability properties at 35°C. 83 Figure 6.8 The effect of lubricant wettability on the extrusion pressure of paste prepared with resin F-104 H M W and two different lubricants having about the same viscosity and different wettability properties at 35°C. 84 Figure 6.9 Tensile strength of extrudates obtained from paste prepared with resin F104 H M W and two different lubricants having about the same viscosity and different wettability properties with F104 H M W at 35°C. 85 Figure 6.10 Tensile strength o f extrudates obtained from paste prepared with resin F-301 and two different lubricants having about the same viscosity and different wettability properties with F301 at 35°C. 86 Figure 6.11 Effect of shear rate on extrusion pressure of F104 H M W . 87 Figure 6.12 Tensile strength of the dried extrudates of pastes prepared with F-104 H M W and different lubricants having different viscosities and about the same wettability properties. 87 Figure 6.13 Effect of die reduction ratio on extrusion pressure of F104 H M W resin. 88 Figure 6.14 Effect of die reduction ratio on the tensile strength of dried and sintered extrudates obtained from paste prepared with homopolymer F104 H M W and various lubricants at 35°C. 89 9 Figure 6.15 Effect of length-to-diameter ratio (L/D) on Extrusion Pressure of pastes prepared with F301 and various lubricants at 35°C. 90 Figure 6.16 Effect of L / D ratio on the tensile strength of dried (lower plot) and sintered (upper plot) extrudates of paste prepared with copolymer F301 and different lubricants. 91 Figure 6.17 Effect of die entrance angle on extrusion pressure of F301 resin. 92 Figure 6.18 Effect of die entrance angle on tensile strength of dried (lower plot) and sintered (upper plot) extrudates obtained from pastes prepared with copolymer F301 and different lubricants at 35°C. 93 Figure 6.19 Effect of the molecular structure of the resin on the extrusion pressure. 94 Figure 6.20 Effect of the molecular structure of the resin on the tensile strength of dried (lower plot) and sintered (upper plot) extrudates. 94 Figure 6.21 Effect of temperature on extrusion pressure. 96 Figure 6.22 Effect of temperature on tensile strength. 96 Figure 6.23 Effect of temperature on extrusion pressure. Contour plot of the results plotted in Figure 6.21. 97 Figure 6.24 Effect of temperature on tensile strength. Contour plot of the results plotted in Figure 6.22. 97 Figure 6.25 F104 H M W + Isopar® M at 38.8 vo l%. 2a = 15°, L / D = 20, R R = 352, yA = 5859 s"1. Extrusion Pressure: 59.3 M P a . Tensile Strength: 4.4 M P a . 98 Figure 6.26 F104 H M W + Isopar® M at 38.8 vol%. 2a = 30°, L / D = 20 R R = 352, yA = 5859 s"1. Extrusion Pressure: 53.8 M P a , Tensile Strength: 3.9 M P a . 99 Figure 6.27 F104 H M W + Isopar® M at 38.8 vo l%. 2a = 60°, L / D = 20, R R = 352, yA = 5859 s"1. Extrusion Pressure: 73.8 M P a , Tensile Strength: 2.3 M P a . 99 Figure 6.28 F104 H M W + Isopar® M at 38.8 vo l%. 2a = 90°, L / D = 20, R R = 352, yA = 5859 s'1. Extrusion Pressure: 81.0 M P a , Tensile Strength: 3.2 M P a . 100 Figure 6.29 F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 90°, L /D = 0, R R = 352, yA = 5859 s"1. Extrusion Pressure: 73.0 M P a , Tensile Strength: 0.7 M P a . 101 Figure 6.30 F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 90°, L /D = 10, R R = 352, yA = 5859 s"1. Extrusion Pressure: 77.6 M P a , Tensile Strength: 3.2 M P a . 101 XI Figure 6.31 F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 90°, L /D = 40, R R = 352, fA = 5859 s"1. Extrusion Pressure: 93.0 M P a , Tensile Strength: 2.8 M P a . 102 Figure 6.32 F104 H M W + Isopar® M at 38.8 vo l%. 2a = 60°, L / D = 20, R R = 352, fA = 5859 s"1. Extrusion Pressure: 73.8 M P a , Tensile Strength: 2.3 M P a . 102 Figure 6.33 F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 60°, L / D = 20 R R =156, yA = 5859 s"1. Extrusion Pressure: 24.9 M P a , Tensile Strength: 2.4 M P a . 103 Figure 6.34 F104 H M W + Isopar® M at 38.8 vo l%. 2a = 60°, L / D = 20, RR = 56, yA = 5859 s"1. Extrusion Pressure: 9.8 M P a , Tensile Strength: 1.2 M P a . 103 Figure 6.35 F104 H M W + Isopar® M at 38.8 vo l%. 2a = 30°, L / D = 20, R R = 352, yA = 5859 s"1, T = 15°C. Extrusion Pressure: 39.0 M P a , Tensile Strength: 2.2 M P a . 104 Figure 6.36 F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 30°, L / D = 20, R R = 352, fA = 5859 s"1, T = 22°C. Extrusion Pressure: 55.9 M P a , Tensile Strength: 3.6 M P a . 105 Figure 6.37 F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 30°, L / D = 20, R R = 352, fA = 5859 s"1, T = 35°C. Extrusion Pressure: 53.8 M P a , Tensile Strength: 3.9 M P a . 105 Figure 6.38 F104 H M W + Isopar® M at 38.8 vo l%. 2a = 30°, L / D = 20, R R = 352, yA = 5859 s"1, T = 65°C. Extrusion Pressure: 53.2 M P a , Tensile Strength: 7.0 M P a . 106 Figure 7.1 Strain sweep test of F104 L M W powder at 1.5 H z and 35°C. 113 Figure 7.2 Frequency sweep test of different resins (1% of strain and 35°C). 114 Figure 7.3 Preparation of sample for parallel plate rheological test. 115 Figure 7.4 Strain sweep of F104 H M W resin (frequency of 1.5 H z and 35°C). 115 Figure 7.5 Strain sweep test of F104 H M W preformed at different pressures (frequency of 1.5 H z and 35°C). 116 Figure 7.6 Frequency sweep of F104 H M W resin preformed at 0.5 M P a and tested at different temperatures. 116 Figure 7.7 Frequency sweep of F104 H M W resin preformed at 2 M P a and tested at different temperatures. 117 x i i Figure 7.8 Frequency sweep of F104 H M W resin preformed at 10 M P a and tested at different temperatures. 117 Figure 7.9 Frequency sweep tests of different P T F E resins preformed at0.5 M P a (1% 118 strain and 35°C). Figure 7.10 Frequency sweep tests of paste prepared with different resins and Isopar® M at 38.8vol% and preformed at 0.5 M P a (1% strain and 35°C). 119 Figure 7.11 Y i e l d stress measurements for F104 H M W resin at 35°C. 120 Figure 7.12 Y i e l d stress measurements for F104 L M W at 35°C. 121 Figure 7.13 Y i e l d stress measurements for F301 at 35°C. 121 Figure 7.14 Y i e l d stress measurements for F303 at 35°C. 122 Figure 7.15 Creep test for F104 H M W fine powder resin at 35°C (cr= 600 Pa, t = 100 s). 123 Figure 7.16 Creep test for F104 L M W fine powder resin at 35°C (cr= 600 Pa, t = 100 s). 124 Figure 7.17 Creep test for F301 fine powder resin at 35°C (a = 600 Pa, t = 100 s). 124 Figure 7.18 Creep test for F303 fine powder resin at 35°C (cr= 600 Pa, t = 100 s). 125 Figure 7.19 Creep test for F104 H M W resin at different levels of stress. 126 Figure 7.20 Creep test for F104 L M W resin at different levels of stress. 126 Figure 7.21 Creep test for F301 resin at different levels of stress. 127 Figure 7.22 Creep test for F303 resin at different levels o f stress. 127 Figure 7.23 Step stress test for F104 H M W fine powder resin preformed at 0.5 M P a . 128 Figure 7.24 Step stress test for F l 04 L M W fine powder resin preformed at 0.5 M P a . 129 Figure 7.25 Step stress test for F301 fine powder resin preformed at 0.5 M P a . 129 Figure 7.26 Step stress test for F303 fine powder resin preformed at 0.5 M P a . 130 Figure 7.27 Fitting viscoplastic models to the rheological data of F104 H M W fine powder resin. 132 Figure 7.28 Fitting viscoplastic models to the rheological data of F104 L M W fine powder resin. 132 Figure 7.29 Fitting viscoplastic models to the rheological data of F301 fine powder 133 resin. x i i i Figure 7.30 Fitting viscoplastic models to the rheological data of F303 fine powder resin. Figure 7.37 Comparison of extensional behaviour of slit die extrudates obtained at yA =3750 s"1 and subjected to an extension at tH = 0.0113 s"1. 133 Figure 7.31 The extrusion pressure of various paste extruded with a slit die as function of the apparent shear rate at 35°C. 134 Figure 7.32 Tensile strength of extrudates obtained from slit die at 35°C as a function of the apparent shear rate. 135 Figure 7.33 Engineering tensile stress response o f F104 H M W extrudates ateH =0.01135"'. 137 Figure 7.34 Engineering tensile stress o f F301 extrudates at £ H = 0.0113-s~'. 137 Figure 7.35 Stress growth coefficient of F104 H M W extrudates obtained from a slit die with L / H = 20 and different apparent shear rates at 35°C. 138 Figure 7.36 Stress growth coefficient of F301 extrudates obtained from a slit die with L / H = 20 and different apparent shear rates at 35°C. 139 139 Figure 7.38 Stress growth coefficient for F104 H M W at different Hencky strain rates. Samples used were produced by extruding the resin atyA = 3750 s~]. 14Q Figure 7.39 Stress growth coefficient for F301 at different Hencky strain rates. Samples used were produced by extruding the resin at^^ = 3750 s~*. Figure 7.40 Stress growth coefficient for F104 L M W at different Hencky strain rates. Samples used were produced by extruding the resin at^^ = 3750 s~]. 14^ Figure 7.41 Stress growth coefficient for F303 at different Hencky strain rates. Samples used were produced by extruding the resin at yA =3750 s'x. 142 Figure 7.42 Engineering tensile stress-strain curves for F104 H M W as a function ofsH . 143 Figure 7.43 Engineering tensile stress-strain curves for F104 L M W as a function of sH . 144 Figure 7.44 Engineering tensile stress-strain curves for F301 as a function o£sH. 144 Figure 7.45 Engineering tensile stress-strain curves for F303 as a function of sH. 145 xiv Figure 7.46 Uniaxial extension of F104 H M W samples stretched at different Hencky strain rates. Continuous lines represent the model fittings. 151 Figure 7.47 Uniaxial extension of F104 L M W samples stretched at different Hencky strain rates. Continuous lines represent the model fittings. 151 Figure 7.48 Uniaxial extension of F301 samples stretched at different Hencky strain rates. Continuous lines represent the model fittings. 152 Figure 7.49 Uniaxial extension of F303 samples stretched at different Hencky strain rates. Continuous lines represent the model fittings. 152 Figure 8.1 The extrusion pressure o f a blend o f a homopolymer (F104 H M W ) and a copolymer (F301) extruded at various apparent shear rates at 35°C. 155 Figure 8.2 The tensile strength of a blend of a homopolymer (F104 H M W ) and a copolymer (F301) extruded at various apparent shear rates at 35°C. 156 Figure 8.3 The extrusion pressure of a blend of two copolymers (F301 and F303) extruded at various apparent shear rates at 35°C. 156 Figure 8.4 The tensile strength of a blend of two copolymers (F301 and F303) extruded at various apparent shear rates at 35°C. 157 Figure 8.5 The density of mixtures of Isopar® G and Isopar® V as a function of composition at 25°C. 158 Figure 8.6 The viscosity o f mixtures o f Isopar® G and Isopar® V as a function o f composition at 25°C. 158 Figure 8.7 The surface tension of mixtures of Isopar® G and Isopar® V as a function of composition at 25°C. 159 Figure 8.8 Steady state extrusion pressure of a paste prepared with homopolymer F104 H M W and a mixture of Isopar G & V at 35°C. 159 Figure 8.9 Tensile strength o f a paste prepared with homopolymer F104 H M W and a mixture of Isopar G & V at 35°C. 160 Figure 8.10 Extrusion pressure of F104 H M W + B N blends extruded at 35°C. 161 Figure 8.11 Tensile strength of F104 H M W + B N blends extruded at 35°C. 161 Figure 8.12 Extrusion pressure of F104 H M W + Nanomer® I.44P blends extruded at 35°C. 162 Figure 8.13 Tensile strength of F104 H M W + Nanomer® I.44P blends extruded at 35°C. 163 xv Figure 8.14 Extrusion pressure of F104 H M W + Nanomer® P G V blends extruded at 35°C. 163 Figure 8.15 Extrusion pressure of F104 H M W + Nanomer® P G V blends extruded at 35°C. 164 Figure 8.16 The effect of B N and clay addition on the extrusion pressure of F104 H M W pastes. 164 Figure 8.17 The effect o f B N and clay addition on the tensile strength o f F104 H M W pastes. 165 Figure 8.18 Extrusion pressure of blends of F104 H M W + Isopar® G and Boron Nitride. 166 Figure 8.19 Tensile strength of blends of F104 H M W + Isopar® G and Boron Nitride. 167 xvi List of symbols Chapter 1 A7 Number average molecular weight. Chapter 2 C Proportionality constant for the viscous term in mathematical model D Die exit diameter Db Die entrance diameter. Also refer to the diameter of the barrel Fd Piston force in capillary flow L Length o f the die capillary land m Power law index for the viscous term in mathematical model. n Power law index for the elastic term in mathematical model. Pd Driving pressure in capillary flow. AP Pressure drop in capillary flow. Q Volumetric flow rate. RR Reduction ratio defined as the ratio of the die entrance to exit cross sectional area. v Velocity distribution in capillary flow. a Die entrance angle, a = 90° refers to a flat die. y Critical strain value at yielding. f Recovarble strain tensor in mathematical model. y Shear rate at the wall in capillary flow. n Proportionality constant for the viscous term in mathematical model. Also refers to the viscosity coefficient in Newton's law for viscoua flow. ow W a l l shear rate. a0 Y i e l d stress extrapolated at zero velocity. Chapter 4 a Constant that groups the physical properties of a liquid in capillary rise. Constant for a specific liquid. at Constant that groups the physical properties of liquid i in capillary rise. c Constant that account for a packed column. Db Die entry diameter also the die of the barrel. D Die exit diameter. / Correction facto for du Notiy ring tensiometer. FR Force to detach the ring from a liquid surface. g Gravity. h Height reached by a liquid in a capillary rise. k Tortuosity of the porous in a packed column. L Length o f the die capillary land. m Slope of the Aw1 vs. t plot. nii Slope of the Aw2 vs. t plot for liquid i. rc Mean radius of the capillary in a packed column. rp Radius of the spherical particle. R, Inner radius of a tube used for capillary rise. RR Radius of the ring. Rr Radius of the ring's wire. xvn RR Reduction ratio defined as the ratio of the die entrance to exit cross sectional area. / Time. Vc Volume of the cubic unit in close packing. Vp Volume occupied by the particles in the unit cell. V\ Volume occupied by the lubricant in the unit cell. Vh Volume of the porous. Vhs Volume of the porous material. VR Volume of liquid rise above the flat level of the liquid surface. vol% Volume percentage of lubricant in the paste. w, Weight of preform before drying. Wf Weight of preform after drying. wt% Weight percentage of lubricant in the paste. Ws Work of spreading. Wt Work of immersion. a Die entrance angle, a = 90° refers to a flat die. y Surface tension of a liquid. yD Non-polar component of a liquid surface tension. Polar component of a liquid surface tension. Surface energy of a solid. y t> Non-polar component of a solid surface energy. yND Polar component of a solid surface energy. n Viscosity of a liquid. 6 Contact angle. Aw Mass of a liquid that has penetrated the packed column in a capillary rise. pi Density of the lubricant. ps Density of the solid material. phs Density o f a porous material. pa Density of air. e Porosity of a porous material. Chapter 6 Db Die entrance diameter. Also refer to the dimeter of the barrel. D Die exit diameter. L Length of the die capillary land. Q Volumetric flow rate. R R Reduction ratio defined as the ratio of the die entrance to exit cross sectional area. T Temperature. vol% Volume percentage of lubricant in the paste. wt% Weight percentage of lubricant in the paste, a Die entrance angle, a = 90° refers to a flat die. A / / Second heat of recrystallization. A / / Heat of melting. AH R Heat of melting of the reference. AH_C Heat of melting of the sample. xv i i i y Apparent shear rate. £ h Hencky strain. £ h Hencky strain rate. Chapter 7 Dt, Die entry diameter also the die of the barrel. D Die exit diameter. E Young's modulus. G * Complex shear modulus. G' Shear storage modulus. G" Shear loss modulus. J(t) Shear creep compliance. L Length o f the die capillary land. RR Reduction ratio defined as the ratio of the die entrance to exit cross sectional area. a Die entrance angle, a = 90° refers to a flat die. y Shear strain. y Shear rate. e Linear strain. EH Hencky strain. sH Hencky strain rate. n Viscosity. rji Instantaneous viscosity. rj+E Tensile stress growth function. n * Complex viscosity. a Shear stress. OE True tensile stress. as Engineering tensile stress. a0 Y i e l d stress in shear. <7V Y i e l d stress in extensional. xix Acknowledgements I wish to express my sincere gratitude to my supervisor, Dr. Savvas G . Hatzikiriakos, for his truthful guidance and support during the course of my studies and his patience throughout all these years. Thanks to Daikin Industries Ltd for the financial support and the supply of the polymer samples. Special thanks to Daikin personnel for the comments, suggestions and technical information provided during their visit to our laboratory. Thanks to my colleagues and ex-colleagues from RheoLab at U B C for their helpful discussions and exchange of ideas. I would like to extend a special note of thanks to my parents, brothers, sisters, nieces and nephews for their love and continuing support. Finally, I thank to the National Council o f Science and Technology of Mexico for its financial support that allowed me to continue my education. xx CHAPTER 1 The Physics and Chemistry of Polytetrafluoroethylene 1.1 Introduction The era o f fluoropolymers began with the important discovery made by Dr. Roy Plunkett on Apr i l , 1938 while experimenting with tetrafluoroehtylene (TFE) in the synthesis of a new safe, non-flammable, non-toxic, colorless and odourless fluorinated refrigerant (CCIF2-CHF2). Polytetrafluoroethylene (PTFE) was synthesized for the first time by accident, but once its physical and chemical properties were disclosed, a wide gamut of applications was envisioned. Those outstanding properties include a high melting point, exceedingly high molecular weight and melt viscosity, and very limited solubility. Thanks to its unique properties, P T F E has transformed the plastic industry and enhanced the application of plastic where it was never thought possible. However,' these exceptional properties also constituted an obstacle for processing. The development of innovative fabrication processes resembling those used with metal powders was a crucial step in the emergence of P T F E products. Processes currently in use include coating from aqueous dispersions, compression molding and ram extrusion of granular powders and paste extrusion o f lubricated fine powder (Mazur, 1995). It is the last process of paste extrusion that is being studied in this work. The rheology of P T F E paste relevant to the paste extrusion of P T F E is studied. During the process of extrusion, the paste starts as a two phase system (lubricant and solid P T F E fine particles) and ends as a solid phase. It is known that many structural changes take place during the flow and thus rheological changes are significant. Therefore, in order to completely understand the process of paste extrusion, a more fundamental understanding of the rheological changes that occur during extrusion is needed. In particular, several questions should be considered: what is the influence of the resin structure on the rheological changes taking place during extrusion; what is the influence of the lubricant concentration on these rheological properties; how is the process influenced by the physical properties of the lubricant; and what are the effects of the geometric characteristics o f the extrusion die used on the overall process as wel l as on the mechanical properties of the final extrudates. These questions define the scope of the present work and they are discussed in more detail in chapter 3. 1 This chapter presents a general overview of the main object of this work, namely polytetrafluoroethylene (PTFE). The types o f resins produced, the chemistry o f P T F E and its various physical properties are discussed. A n overview of the various applications of P T F E is also covered. Emphasis is placed on the industrial processes used to synthesize P T F E and in particular on the paste extrusion process. 1.2 Tetrafluoroethylene (TFE) polymerization techniques: types of resins Tetrafluoroethylene (TFE), the monomer for polytetrafluoroethylene (PTFE), is polymerized in a highly exothermic reaction. Two different regimes of polymerization are common for production of different types of P T F E . Both of them are carried out in an aqueous medium involving an initiator, a surfactant, other additives and agitation at a high temperature and pressure. The main differences are the amount of surfactant added to the polymerization reactor and the shear rate applied during the reaction. The first method is known as suspension polymerization. This is the route to produce granular resins which are processed as molding powder. In this method, little or no dispersing agent is used along with an initiator in a medium which is subjected to vigorous agitation. This initially causes a stable dispersion of P T F E for a brief period of time. The dispersing agent is rapidly consumed causing the polymer to precipitate. A pressure between 0.03 and 3.5 M P a is kept constant to control the molecular weight and its distribution whereas the temperature is held between 40-90°C (Ebnesajjad, 2000). The resulting dried polymer is 'stringy, irregular, and variable in shape' and is known as granular resin. The particle sizes of granular resin and its powder flow property can be varied, depending on the end product requirements, by size reduction (cutting), or by mixing different grades (Gangal, 1994). The second technique of polymerization is called emulsion or dispersion polymerization. Using this method, dispersion and fine powder P T F E products are manufactured. M i l d agitation, ample dispersant along with an emulsifying agent and an initiator are involved in this method. The pressure is set around 2.4 M P a , while the temperature is about 95°C. Gentle stirring is usually employed to ensure dispersion stability. The extent of the dispersion stability is crucial at this stage since the P T F E particles should not coagulate prematurely and yet should be stable enough for transportation, storage and handling. The dispersion recovered from the reactor is finished by two different series of processes depending on whether a dispersion or a fine powder is the desired final product. In the case of the former, the diluted dispersion is brought up to 40-65% polymer solids by weight in water. In the latter, the agglomerates are isolated by skimming 2 or filtration and then dried by vacuum, radio frequency or heated air such that the wet powder is not excessively fluidized to avoid premature mechanical damage by shearing between particles (Gangal, 1994; Ebnesajjad, 2000). 1.3 Chemical and physical properties of PTFE Fluoropolymer or perfluoropolymer are the names given to designate those polymers whose molecules mainly consist of carbon (C) and fluorine (F) atoms. These names let us distinguish them from other polymers that are just partially fluorinated. A n example of a linear fluoropolymer is polytetrafluoroethylene (PTFE) whose chemical formula is [(-CF2-CF2-)n]. It can be compared with polyethylene [(-CH 2 -CH2-) n ] where all the hydrogen atoms have been substituted by fluorine atoms. O f course, polyethylene and P T F E are prepared in completely different ways. The basic properties of fluoropolymers arise from the atomic structure of fluorine and carbon and their covalent bonding in specific chemical structures. Figure 1.1 depicts the straight chain molecular configuration of P T F E . The fluorine atoms, in cyan color, are placed helically around the carbon backbone (in grey color) providing a protective shield from virtually any chemical attack thus imparting chemical inertness and stability to the molecule (Gangal, 1994; Ebnesajjad, 2000). The helical conformation o f the fluorine atoms assures that the hysteric repulsion is minimized. The two types of covalent bonds present in the P T F E molecule, C-F and C - C , are extremely strong (Cottrell, 1958; Sheppard and Sharts, 1969) causing P T F E to have excellent mechanical strength and resistance to heat. Figure 1.1: Schematic diagram o f a chain segment of P T F E molecule. 3 The fluorine shield is also responsible for the low surface energy (18 dynes/cm) causing P T F E to have a low coefficient of friction (0.05-0.8, static) and non-stick properties (Gangal, 1994). P T F E , with its thermal and chemical stability, makes an excellent electrical insulator. The slippery P T F E can not be dissolved in any solvent, acid, or base and upon melting forms a stiff clear gel without flow. Consequently, its molecular weight cannot be determined by conventional techniques. In practice, the number average molecular weight ( M n ) is usually estimated from the standard specific gravity (SSG) of the polymer. Higher S S G implies greater crystallinity and hence, lower molecular weight (Gangal, 1994; DuPont, 2001; Suwa, 1973). Due to the linearity of P T F E molecules, the crystallinity of a virgin P T F E resin may be as high as 92-98% (Gangal, 1989). A s a result, the S S G of P T F E is high for a polymer, typically ranging from 2.1 to 2.3. Following the determination of S S G using the standard procedure ( A S T M D4895), the number average molecular weight, Mn, can be estimated from Mn = (0.597 x l O 6 f A 1 £-7 \ l , , 0.157 2.306 - SSG [1.1] Equation 1.1 applies to 100% homopolymer resins with S S G > 2.18 (DuPont technical information, 2001). The calculated molecular weights for P T F E with S S G < 2.18 are quite large (probably unrealistic), due to the asymptotic behavior o f Equation 1.1 in this range. The number average molecular weight of a 100% homopolymer has also been correlated to the second heat of recrystallization (AHC). The second heat of recrystallization is obtained by melting and crystallizing a sample of P T F E twice by Differential Scanning Calorimetry (DSC) (DuPont technical information, 2001). It was found that Mn = 2 . 1 x l 0 1 0 ( A # c ) - 5 1 6 [1.2] where AHC is in cal/g. The applicable cooling rate is 4-32°C/min, over which the heat of crystallization remained constant for a given polymer. Typically, M n is in the 10 6 to 10 7 range (Gangal, 1994). Comparison of P T F E molecular weights, regardless of whether or not the resins contain other comonomers, can be made by considering the resin melt creep viscosity instead. The melt creep viscosity, as detailed in U S Patent 3,819,594 (Holmes et al, 1974), is higher for a higher molecular weight P T F E resin (DuPont, 2001). The melting point of virgin P T F E (first melting temperature) is 342°C (Sperati, 1989), which is high for a thermoplastic polymer. The second melting temperature is 327°C 4 (Ebnesajjad, 2000), which is the value often reported in the literature. It means that a previously melted P T F E does not recover its original crystallinity; making the resin less crystalline (Gangal, 1994). During melting, a volume increase of 30% is typical (Sperati, 1989). The melt is stable, since even at 380°C, the melt viscosity is relatively high at approximately 10 GPa.s (Gangal, 1994). Besides the melting point, P T F E has other transition temperatures, two of which are particularly important due to their proximity to the ambient temperature. These are shown in the partial phase diagram of P T F E in Figure 1.2 (Sperati, 1989). Under ambient pressure conditions, the first transition occurs at 19°C. At this temperature, the P T F E molecule chain segments change from a perfect three-dimensional order to a less ordered one undergoing a slight untwisting. Above 37°C, the second transition temperature, the extent of disorder of the rotational orientation of molecules about their long axis is increased. In other words, below 19°C P T F E resin is strong enough to withstand premature mechanical damage. Above 19°C, the molecules are packed more loosely and become highly deformable. Figure 1.2: Partial phase diagram of P T F E (Sperati, 1989). 5 1.4 PTFE fine powder resin processing and applications The following is a brief description of the most important steps in the P T F E extrusion process indicating the most significant variables involved in each step (Daikin technical bulletin). i. Care and handling of the raw material. P T F E fine powder resins must be in a completely powdered form, so as to enable even pouring when it is blended with an extrusion aid. Strong vibrations and shock should be avoided as much as possible during transport, because this may cause the powder to form lumps. If the powder is to be stored, the ideal storage conditions are a dry place with a temperature range of 5-20°C. In this way, the powder w i l l be less susceptible to lumping, and even i f it occurs, it is easy to restore the resin to its powdered form. If lumps exist in the powder prior to blending with the extrusion aid, the powder should be sieved using a No . 4 mesh sieve. Care should be taken not to apply too much force to the powder while sieving. A n y lumps that do not pass through the sieve should be carefully removed, placed in a different container and, once the container has been filled up to 1/3 of its capacity, shaken to break the lumps apart so that the powder can be sieved again. It is also important not to contaminate the powder during sieving since this may affect the quality of the final product. i7. Extrusion aid. In the extrusion process for P T F E fine powder, an extrusion aid is used. This acts as a lubricant to enable smooth, even extrusion. The extrusion aid must be able to completely saturate the resin, and must be easily and rapidly removable from the product after extrusion without leaving any residue that would provide odour and/or colour. If the product is to be sintered, the extrusion aid must have a volatizing temperature lower than the sintering temperature thus ensuring that it w i l l not color the product. The extrusion aids ordinarily used are typically clear, light, aliphatic hydrocarbon liquids. Liquids with viscosity o f 0.0005 to 0.005 Pa s are preferred. The amount of extrusion aid to be added to the resin varies accordingly to the application and the processing conditions. Ordinarily 15-25% in weight of extrusion aid is used. iii. Extrusion aid blending. The mixing of the powder and the liquid is crucial in ensuring a uniform flow of the paste. To prevent shear damaging of the resin, the blending operation must be performed with the resin temperature remaining below the transition temperature. The blending area should also provide controls for relative humidity, cleanliness, and safety. For blending, a clean, dry, wide-mouth container is filled with the powder (previously sifted) up to 2/3 of its capacity. The prescribed amount of processing aid is then 6 added and the container is covered and sealed so the processing aid does not volatilize. The container is then agitated, for example, by placing it horizontally on a two-roller jar mi l l for approximately 10-20 minutes at 30-45 rpm. iv. Aging. Before blending and prior to preforming, it is suggested that the container be left sealed for approximately 5-15 hours at room temperature (23°C) or above in order to allow the extrusion aid to completely permeate the surface of any powder not sufficiently permeated by the blending process. v. Preforming. The next step after blending the powder/extrusion aid mixture is preforming. The object of preforming is to remove most of the air from the powder after it has been blended with the extrusion aid, and to mould it into a shape which can be inserted into the cylinder of the extruder. It is beneficial to preform with the resin at the aging temperature. For preforming, the PTFE-lubricant mixture is poured in to the preforming mould and compressed until the volume of the paste is reduced to approximately 1/3 of its original volume to produce the preform. The pressure used in preforming should be 1.0-4.9 M P a , and the pressing speed should be 50 mm/min or less. Excessive shearing stress must not be applied, and no air should remain in the material after preforming. The powder is maintained in this pressed condition for 5-10 minutes, and then the pressure is gently released. For easy insertion, the diameter of the preform must be 0.5-2 mm smaller than the diameter of the extruder. The specific gravity of the preform prepared in this way is about 1.3-1.6 g/ml. After preforming, the powder is removed from the preforming mould and inserted into the extruder. Extreme care must be taken at this time, to avoid mixing any foreign matter into the preform. vi. Extrusion. In the extrusion step, the individual P T F E agglomerate particles in the preform are greatly deformed and forced together to create a continuous part such as tubing, rod, or tape. The extruder is capped with a die and the resin and lubricant are compressed and forced out of the die opening. The function of the die is to change the shape of the preform into a moulded product o f the specified shape. The construction o f the die greatly influences the extrusion pressure and hence the quality of the final product. The die angle varies inversely with the reduction ratio but 20-60° is suitable. The length of the die land is ordinarily 3-10 times its diameter. It is important for this process to occur above the transition temperature of the resin, which wi l l be greater than 19°C when under pressure. Room temperature is suitable for extrusion, but the die is usually heated to 50-60°C. More than one preform can be loaded into a ram extruder, which is basically a cylindrical press. In this case, prior to extrusion, an extra 7 preforming is carried out within the extrusion cylinder to merge the preforms. From here, the process steps and conditions change accordingly to the desired final product. vii. Drying. In order to remove the extrusion aid contained in the product, the product is placed in an oven and heated to a temperature high enough to evaporate the extrusion aid. Inside the drying oven, the extrusion aid must reach the surface of the product, and then be evaporated. The speed of this process depends on. the temperature of the oven, but it must be appropriately controlled in order to prevent blistering. The temperature of the drying oven varies accordingly to the thickness and diameter of the product, the extrusion speed, and the type of extrusion aid used. Ordinarily, however, the temperatures at the entrance and the exit of the oven are approximately 100°C and 250°C, respectively. The temperature of the drying oven is adjusted by controlling the temperature of the oven's heat source, and by varying the air current inside the oven. Because the extrusion aid is flammable, care must be taken to avoid fire, and sufficient ventilation must be provided. In practice, the drying oven must be 2-3 times longer than the sintering one. If the drying oven is too short, deformities w i l l occur due to inadequate drying. viii. Sintering. Immediately after the extrusion aid has been removed from the product, the temperature is raised to 360-390°C and the product is sintered. A s in the drying oven, the sintering temperature depends on the extrusion speed and it must be increased i f the extrusion speed increases. However, care must be taken to avoid degradation. The purpose of sintering is to coalesce the resin and eliminate porosity. A change in the volume of the product occurs during the latter part of the drying process and continues through the sintering process, shrinking the volume of the final product by 25-30%. There is a directional nature to this shrinkage. The most significant shrinking occurs in the direction of extrusion. This shrinkage is restricted to a large degree by the sintering equipment itself. Typical extrusion processes include tube extrusion, wire coating and calendering. For tube extrusion, the basic equipment is illustrated in Figure 1.3. The extruder consists of a cylinder, a ram, a driving mechanism (hydraulic or screw type), a die, a mandrel, etc. The cylinders generally used in extruders range from 50-200 mm in diameter, and from 500-1800 mm in length. The processing for electric wire insulation (Figures 1.4 and 1.5) is similar to that of tubes. The main difference is that in the former a clearance must be provided between the guide tube and the guide tip (x in Figure 1.5). If this clearance is too small, the flow section o f the resin is reduced causing the extrusion pressure to rise and the insulation to vary in thickness. If 8 the clearance is too large the flow speed of the resin w i l l decrease and an excessive shearing force wi l l be exerted on the resin particles in contact with the core wire. This w i l l cause a loss of resin fluidity, resulting in the cutting of the core wire or producing defects in the insulation. The resin which is extruded from the die enters the drying and sintering zone together with the core die. Since wire insulation and spaghetti tubes can be curved, the drying and sintering ovens used differ from those used for tubes. A multiple-turn type can be used, which greatly increases the moulding speed. Counter-•Gotitf6l;pane1' pjTl . — - Exhaust o j ' ° ( o ; i I" 1 :*3. I: •6: in CO « C°> 1 Wife pay-off r Take-up^ -Sp'ark.tester -Wire haul-off Wire Figure 1.3: Tube extrusion equipment of P T F E fine powder (Daikin technical bulletin). 9 Exhaust Tube extrusion die Cylinder Ram head Seal ring*-(Oh 30 - 60") Core """-Dfe:.Temp. (5Q~6CC) (-122-140°F) KT-Banci heater (50-~60r'C) (122-140'F) "'Oie orifice R,R. Molded product . PC*-Dm2 do ' -dp * Dc: Cylinder inside diameter Dm: Mandrel outside diameter do: Die orifice inside diameter dp: Core pin outside diameter Figure 1.4: Electric wire insulation extrusion process of P T F E fine powder (Daikin technical bulletin). P T F E fine powder can also be processed into unsintered tape by calendering. The process for ordinary unsintered tape is illustrated in Figure 1.6. The extrusion of unsintered rod (cylindrical or square shape) is done in the same way as in tube extrusion. However, because calendering is done in an unsintered state, the lubricating properties of the extrusion aid become more important than anything else. Generally, an extrusion cylinder 100-250 mm in diameter and a round die of 10-30 mm in diameter (or a rectangular die 15x6 mm or 20x10 mm) are used. For a single step process, a roll of 300-500 mm is used. The roll has a polished surface with no eccentricity and it is heated to 50-80°C and spins at 5-30 m/min. After these steps, the processing aid contained in the tape is removed by drying it in the calender roller and in a hot air furnace. Tape made in this way is called unsintered tape. It is generally a slit of 13 mm in width, and wound in fixed lengths onto reels (see Figure 1.6 for details). 10 Figure 1.5: Cross section of electric wire insulation extruder die (Daikin technical bulletin). In this work the paste extrusion of P T F E through circular and slit dies having various geometrical characteristics is studied. In particular the rheological properties relevant to the processing of paste are identified and an appropriate constitutive equation is formulated. This can be used to model several of the processes described above. The effect of the physical properties of the lubricant such as viscosity and surface tension on the rheology and extrusion pressure is also studied systematically. A n essential part o f this study is the effect o f the lubricant type and resin as well as the die geometry on the mechanical properties of the final 11 extrudates. The tensile strength of the unsintered and sintered dried extrudates is taken as a measure of their mechanical properties. Exhaust, or recovery Take-up. roll Take-up roll .Extrusion aid extraction:and:drawing Heating rolh.''00 ?5cc: Figure 1.6: Production of unsintered tape from P T F E fine powder (Daikin technical bulletin). 12 CHAPTER 2 PTFE Paste Extrusion: General Review 2.1 Introduction Paste extrusion is a widely used process in many different industries, including the chemical, food and pharmaceutical industries. Less common, but not less important products include ceramic components, catalyst supports, bricks, and many others. The increasing demand of these products has attracted the attention of researchers around the world and greatly increased interest in studying the paste extrusion process. Many complicated structures, such as thin-walled honeycomb catalytic supports, rely on the uniformity o f the extrudate to provide certain "high performance" properties. Ram extrusion has made possible the characterization of the rheological properties of pastes when other techniques can not be used. Among the most important factors to be considered in ram extrusion of pastes are paste formulation, paste densification, extrusion rate and die geometry. A l l these factors together w i l l allow a complete understanding of paste extrusion for determining the optimum processing conditions for a given extruded product. So far, most of the work on paste extrusion has been done with alumina pastes due to their importance in the catalyst and electronics industries. However, P T F E prepared by emulsion polymerization uses paste extrusion as a good alternative for product manufacturing. Thanks to paste extrusion it is possible to process thin hoses, thick tubes (liners), wire insulation and unsintered tapes of P T F E but, like for other materials, P T F E paste extrusion is still under study and development. In this chapter, literature related to the subject of P T F E rheology and its relation to the process of paste extrusion is reviewed. The discussion is subdivided into paste flow and extrusion, and the modelling of paste flow. In addition, some definitions used in other chapters are introduced and the fundamentals of the operation of the equipment used to study the rheology of P T F E paste extrudates are also included. 13 2.2 Paste preparation, preforming and extrusion 2.2.1 Paste formulation In simple terms, paste is a mixture o f solid and liquid, the relative amounts being such that the resulting material can be moulded readily (Benbow and Bridgwater, 1993). In other words, the composition o f the paste is that to render a material soft and plastic, but the object so formed should be able to retain its shape to allow further processing. However, this definition is not definitive and other definitions, based on the perceived mechanical response, have been put forward (Khan, 2001). Fine powders of polytetrafluoroethylene (PTFE) are also processed by paste extrusion. Here, P T F E resin is combined with a minimal quantity of lubricant (an inert liquid hydrocarbon) and then extruded at modest temperature (typically 30-35°C) into preforms of various shapes and dimensions with substantial mechanical integrity (Mazur, 1995). In paste extrusion, the liquid used as a processing aid has two purposes: to protect the solid particles from mechanical damage and to act as a lubricant. Thus, the particles that in the absence of lubricant were susceptible to shear damage, are now covered with a thin layer of lubricant that makes the paste become resistant to compressive load without increasing the inter-particle contact area. A s a lubricant, the liquid separates the particles and lubricates both the relative particle movement and the motion along the wall o f the die land or other surfaces in the flow path during extrusion (Benbow and Bridgwater, 1993). Even though the liquid imparts plasticity to the solid phase; it does not act like plasticizer and is removed from the extrudate right after extrusion (Mazur, 1995). The amount of lubricant and its properties critically affect the extrusion process and, hence, the quality of the final product. The concentration of the processing aid in the mixture depends on the type of the product, equipment design and the desired extrusion pressure. Its content should be as low as possible but not so low that the extrusion pressure would be excessively high. The optimum range of lubricant content was found to be between 15 and 25% of the total weight of the compound, which typically corresponds to a volume fraction between 0.34 and 0.45 (Mazur, 1995; Ebnesajjad 2000). As the amount o f liquid added to the powder increases above a critical value, the pressure required to extrude the mixture falls dramatically (Benbow, 1998; Ariawan, 2002). For a typical commercial fine powder, a 2% increase in lubricant causes a 40% decrease in extrusion pressure (Daikin technical bulletin). A s more 14 liquid is added, the material soon becomes too soft to retain its shape. On the other hand, i f an inadequate amount o f lubricant is used, the extrudate tends to be rough and irregular (Mazur, 1995). Regarding the properties of the processing aid, any difference in density and/or viscosity implies different rheological properties. The viscosity of the lubricant has a large effect on the quality of the paste. For example, the use of a more viscous liquid as a lubricant results in a less uniform mixture (Ochoa and Hatzikiriakos, 2004). Consequently the paste would not extrude as a continuous body, and many microcracks are developed during the drying process after extrusion (Ebnesajjad, 2000). In addition, the extrusion pressure exhibits higher values when a processing aid with a higher viscosity is used (Benbow, 1998; Ochoa and Hatzikiriakos, 2005). Ideally, the lubricant should have a lower surface tension than the critical surface tension of P T F E . The critical surface tension is the value of surface tension of a liquid below which the liquid w i l l spread on a solid. That increases the wettability of the lubricant with the resin particles (Ebnesajjad, 2000; Ochoa and Hatzikiriakos, 2005). The extrusion aid must be easily removable from the extrudate without leaving a residue, which could alter the colour of the final product. Other requirements of lubricants include high purity, low odour, low polar components, high auto-ignition temperature, and low skin irritation. 2.2.2 Preforming Another aspect related to paste extrusion is preforming. During this step, the paste is placed in a cylindrical billet and, by means of a piston, the pressure is gradually increased to remove the air voids that would otherwise render a final product mechanically weak. In this way a cylindrical rod that is fitted into the extruder's barrel is formed. In P T F E paste processing, the preforming stage is carried out at room temperature although it is not temperature sensitive (Mazur, 1995). However, the application o f stress introduces another problem since it may cause the liquid component of a paste to move through the solid matrix in the radial and axial directions causing a liquid maldistribution throughout the paste (Yu , 1998). The level of the preforming pressure and its duration significantly affect the quality of the preform. In addition, the magnitude of the pressure needed to produce a preform of uniform density depends on the molecular weight (standard specific gravity) of the resin (Ariawan, 2001). A lack of adequate pressure wi l l result in a preform of non-uniform density which w i l l extrude unsteadily, resulting in an unacceptable final product. During preforming, the applied pressure compacts the particles making those adjacent to the wall of the preforming unit undergo plastic deformation that results 15 in a smooth film of deformed powder surrounding the preform. Thanks to this layer, the rest of the resin particles remain spherical even after high preforming pressure (Mazur, 1995). 2.2.3 Phase migration and extrusion Phase migration is a phenomenon that occurs not only during preforming but also during extrusion (Yu, 1998). It is caused by relative motion of the liquid through the voids between the solid-phase particles. This migration eventually results in a non-uniform distribution of lubricant in the mixture. This effect is enhanced with time, especially in the presence of high extrusion pressures. A s the paste becomes drier, the extrusion pressure rises and the liquid loss increases consequentially. Eventually, high frictional forces may occur due to direct contact between particles, and between the particles and containing walls (Benbow et al., 1998; Blackburn, 1993). The packing characteristics of the paste depend on the particle size, shape and size distribution and there is a direct correlation between the permeability of a consolidated paste and its porosity (Rough, 2002). Thus, since the solid and liquid phases move at significantly different rates under the application o f a pressure gradient, part o f the liquid escapes from the paste. If the permeability through the packed particles is high and the liquid viscosity is low, conditions for the liquid to move faster than the solid w i l l be promoted. The result w i l l be that the paste becomes effectively drier, the extrusion pressure rises, and the extrusion process may have to be halted in extreme case (Benbow and Bridgwater, 1993). After extrusion, the extrudates can exhibit surface fracture depending on the processing conditions. Benbow and Bridgwater (1993) have reported the effect of die shape, operating conditions, and paste formulation on the surface defects in the final products. Domanti and Bridgwater (2000) studied extensively the effect of die land length, extrusion rate, die entry angle, extrusion ratio and water content on the surface fracture in the extrusion of a-alumina paste mixed with Bentonite clay and carbohydrates. To reduce the severity of the extrudate distortion several options are available such as decreasing the extrusion rate, increasing the lubricant concentration in the paste mixture, using an extrusion dies with long length to diameter ratio and a small entrance angle (Benbow et al., 1987; Benbow and Bridgwater, 1993), altering the viscosity and yield properties of the liquid phase, and blending fine and coarse powders in order to decrease the average pore size (Blackburn and Bohm, 1993). These alternatives have advantages and disadvantages, or may not work for some pastes. A s far as P T F E paste processing is concerned, there is an optimum value for the entrance angle and length to diameter 16 ratio of the die as well as lubricant and viscosity concentration (Ariawan, 2001; Ochoa and Hatizikiriakos, 2005). A very interesting phenomenon that occurs during P T F E paste extrusion is fibrillation. It is the formation of fibrils that interconnect the particles, and these essentially give the dimensional stability to the final product. Lewis and Winchester (1953) first reported that fibrillation occurs during paste flow through the contraction area of the die. Later, Ariawan (2001) found the same through S E M analysis of paste in the die entry region. Mazur (1995) explained this phenomenon by making reference to particles that reorganize themselves to pass through the die during the initial stage of extrusion. After passing that region, the particles are deformed due the shear/extensional stresses, resulting in the formation o f fibrils which contribute to the mechanical strength of the extrudates. 2.2.4 Sintering Sintering is the process during which a granular material, such as a polymer powder of ultra-high molecular weight polyethylene ( U H M W P E ) or P T F E , is heated to a temperature near its melting point (Hooper, 2000). In this process the particles of the loose powder or pressed compact material weld together to form an interconnected solid (Mackenzie, 1949). A s a result, the density of the compact changes. The coalescence of contacting polymer particles is important to provide the final product with suitable and improved mechanical properties. Previous studies of sintering revealed that the surface tension was the driving force for this phenomenon to occur. However, more recent reports have shown that the degree of sintering is governed by the particle size, viscosity, interfacial tension, molecular architecture and molecular weight distribution (Hooper, 2000). In P T F E paste processing, the elastic phenomena dominate the sintering process (Mazur, 1995). During P T F E sintering, the net volume o f the material changes but these changes in linear dimensions is highly anisotropic. During the heating cycle, the sample contracts in the axial direction and expands in the radial direction yielding a net shrinkage of about 4% (Mazur, 1995). In fact, axial contraction is the resultant of a contraction and expansion occurring simultaneously. Apparently, the axial contraction is driven by molecular orientation while the expansion is the response to release the stress accumulating during the former (Mazur, 1995). The resultant sintered extrudate exhibits a higher tensile strength than the unsintered sample, indicating improvement in its mechanical properties. 17 2.3 Constitutive equations proposed to predict pressure drop in capillary die flows Assuming steady state flow through an orifice die (length to diameter ratio, L/D = 0) o f conical entry angle 2a, and using the following rheological model: T = Cy" +T] dt [2.1] Snelling and Lontz (1960) derived the following relationship for the total pressure drop during extrusion: 12Qsin 3 a A P = - ^ - [ 3 i „ ( ™ , r + ^ 3(« + l) 3m [2.2] n(\- cos a)D3 where C, n, TJ, and m are constants to be evaluated experimentally, R R is the reduction ratio defined as (D//D) , and Q is the volumetric flow rate. To arrive at Equation 2.2 through Equation 2.1, the authors used the radial flow hypothesis. This hypothesis assumes that paste particles at the same radial distance from the virtual apex of the conical zone o f the die, move towards the die apex at the same velocity. This has been proven experimentally (Sneeling and Lontz, 1960; Ariawan et al., 2002b). Thus, the velocity of a point on a spherical surface at distance r from the apex is: - = ^ [2.3] dt 2tt(1 - cos a)r Doraiswamy et al. (1991) have developed a non-linear rheological model for concentrated pastes. This model considers the elastic, viscous, and yielding behaviour of the material by introducing a recoverable strain term, y . In addition, this model has the advantage of using data easily accessible by means of a parallel plate rheometer. Thus, they suggested the following constitutive equation for a material that exhibits yield stress: \?\<Yc [2.4] • + K\yr] y \y\=yc [2.5] J \?\<Yc t 2 - 6 ] 191= 7c < r [ 2 - 7 l T - Gy T = (Gy dy = Y ~dt dy ~dt = 0 18 where G is the elastic modulus, yc is the critical strain value at yielding, y is the recoverable strain tensor, and K and n are power law constants. Note that the viscosity, evaluated as the term in brackets, approaches a Newtonian viscosity at low shear rates and a power law viscosity at high shear rates. Based on the above model, the pressure drop for an orifice die can be found to be: f ~n + \ 4Q~ „ + . Gyc K n 7iD2 _ " i K D V J [2.8] A simple equation for paste flow through dies of various entry angles, cross-sectional shapes and L / D ratios have been derived analytically by Benbow and Bridgwater (1993). Particularly, for a steady state flow through a capillary die of entry angle 2a, and performing separate force balances on the entry region of the die and on the actual die land, the following relationship for the total pressure drop was derived: where a0, £ m, r0, /?/ and n are parameters to be determined experimentally, VsQ/nD2 and Db is the barrel diameter. The first term accounts for the change in cross sectional area in the conical entry {extensional and shear term), while the second term for the pressure drop in the die land {shear term). The rheological model used to obtain Equation 2.9 was cr = a0+a-V [2.10] where <J0 is the yield stress extrapolated to zero velocity and V is the paste velocity in the die land and a is a factor characterizing the effect of velocity. The term a- V is, thus, analogous to the product r/ • y in liquid shear flow. Using the radial flow hypothesis proposed by Snelling and Lontz (1960), Ariawan et al. (2002b) developed a one-dimensional mathematical model to describe the effect of extrusion conditions and geometric characteristic of the die in the extrusion pressure of P T F E paste. This model considers the paste as an elasto-viscoplastic material that exhibits both strain hardening and viscous resistance effects during flow. Thus, by using a power-law modified Kelvin 's stress-strain relationship, Ariawan (2002) suggested the following constitutive equation: ^-^r = CrL+w:m [ 2 . i i ] AP = \2(a0 +ZV" +TO cot a ' I D i - f — T 19 where ae and ar are the principal stresses in the 0 and r directions respectively and ynm and v are the maximum values of the strain and strain rate, respectively. The extrusion pressure in / max the conical zone was found to be: P . =<j. = C r RRB +2(1 + B)\ extrusion rb ra \ / f c V 12Qsin3 a (3m + 2 5 ) ^ ( 1 - cos a)D3 b J [2.12] where ar„ is the stress at the die exit, RR is the reduction ratio defined as (Dt/D)2, and C, 77, n, m and/are material constants that have to be determined experimentally. This model was found to describe adequately most experimental observations. Specifically, it was found to predict quantitatively and qualitatively the effects of die entrance angle, reduction ratio, pressure, L / D ratio of the die, and P T F E properties. However, it preassumes the velocity distribution by using the radial flow hypothesis. 2.4 Basic equations governing the principle of operation of the experimental equipment 2.4.1 Capillary flow The simplest and most popular type of rheometer is the capillary rheometer shown in Figure 2.1 (Dealy, 1990). In its simplest configuration, the capillary rheometer consists o f a small tube through which paste is made to flow, either by means of an imposed pressure or a piston moving at a fixed speed. The quantities normally measured are the flow rate Q, and the driving pressure, P^. If the flow is generated by a moving piston, it is usually the piston force, Fd, that is measured, and this is related to Pd as follows: 4F P d = - ^ [2.13] where Dt, is the diameter of the barrel or reservoir (Dealy and Wissbrun, 1990). It can be shown that the absolute value of the shear stress at the wal l , a w , is related to the pressure drop, AP, over a length of tube, L, as follows: • p .14] 2L 20 The pressure drop, AP, is always a negative quantity, because the flow is in the direction of the axial coordinate, z. A s this is a partially controllable flow, the velocity profile depends on the rheological properties of the fluid under study, and a general expression relating the volumetric flow rate, Q, to the wall shear rate cannot be derived. It is known that for a Newtonian fluid, the velocity distribution is given by the familiar parabolic law: Q v = 2-TlR' 1- [2.15] This is the velocity profile for "fully developed flow" in which the effects of the entrance and exit are assumed negligible and there is thus no velocity component in the radial direction. The absolute magnitude of the shear rate at the wall , yw, can be determined from Equation 2.15, as follows: y w \dr)r=R 4Q TZR3 [2.16] 21 For non-Newtonian fluids, Equation 2.16 no longer represents the true wall shear rate, instead it yields the apparent shear rate, yA . The total pressure drop for flow from the reservoir, through the capillary and out to the ambient pressure (Equation 2.13) can be thought to consist of three components: AP = AP ,+AP + AP=AP,+AP [2.171 ent cop exit end cap I J where APenl is the excess pressure drop due to entrance flow, APcnp is the pressure drop for fully developed flow in the capillary, and APexu is the excess pressure drop due to exit flow. The end correction, APen<i, can be determined by using a technique outlined by Bagley. In this correction, the driving pressure, Pj, is measured for various values o f the flow rate using a variety o f dies with different length-to-diameter ratios. The value of the driving pressure, Pa, for a length-to-diameter value equal to zero is then obtained by extrapolation. This correction is known as the Bagley correction and Equation 2.14 can be modified to estimate the true wall shear stress as: W - A P e , „ ) [2.18] 4(L/D) 2.4.2 Flow in a rectangular channel Equations 2.14 and 2.16 apply for a fluid flowing in a cylindrical channel. When a fluid flows through a rectangular channel in which the width, W,\s much larger than the thickness, H, the edges make a negligible contribution to the pressure drop and this geometry can effectively be used for rheological measurements. For the steady flow of an incompressible fluid in such a channel, the absolute value of the shear stress at the wal l , <jw, is given by (Dealy and Wissbrun, 1990): --^ where A P is the pressure drop over a length of channel, L. The apparent shear rate in a slit, which is the true wall shear rate for a Newtonian fluid is given by: r A = - ^ - [2.20] 2.4.3 Parallel plate flow Measurements of rheological properties at low shear rates and deformations (linear viscoelasticity) are usually carried out in rotational rheometers such as parallel-plate rheometers (Figure 2.2). The two plates are mounted on a common axis of symmetry, and the sample is 22 placed between them. The upper plate is rotated at a specified angular velocity co(t) and as a result the sample is subjected to shear. The shear rate in parallel plate rheometer experiments is given by the following expression (Dealy and Wessbrun, 1990) r • co Y=- H [2.21] where co is a rotational speed, r is the distance from the center of the plate, and H is the gap size between plates. The shear rate in the gap is not uniform which makes it impossible to calculate values of material functions on the basis of a single experiment, and differentiation data is required as indicated by the following equations, which are obtained by performing a force balance (Dealy and Wessbrun, 1990) 2F KR' 1 + 1 d\nF 2 d\nyR 3T = N](yR)-N2(yR) 1 + 1 d\nT 3 d In yR [2.22] [2.23] 2nR'yR where R is the radius of the plates, F and T are the force and the torque needed to rotate the upper plate, respectively, N/ and N2 are the forces exerted by the material perpendicular and along the upper plate, respectively, and T](YR) is the viscosity at the shear rate value calculated at r = R. en H Fluid " | sampk Pressure transducer R Figure 2.2: , Parallel plate rheometer. However, in determining the linear viscoelastic properties of a material (small amplitude oscillating experiments), the storage modulus, G\ and the loss modulus, G", can be calculated as follows (Dealy 1990): 23 G'= 2HM0 cos 5 2HM0 sin 8 [2.24] [2.25] where Ma is the torque oscillating amplitude, <p0 is an angular amplitude, and 8 is the loss angle. The complex viscosity, rj*, which approximately equals the real viscosity under small deformation, can be calculated as: ( G'~) 2 + V I ® J [co J [2.26] where co is the frequency of oscillations. 2.4.4 Extensional Rheometer The Sentmanat Extensional Rheometer (SER) is suitable to perform extensional rehology studies of strip-shape samples. A schematic of this rheometer is shown in Figure 2.3. This rheometer is attached to the concentric disks rheometer described in section 2.4.3. The rheometer consists of paired master and slave wind up drums mechanically coupled by a gear (Figure 2.3). The rotational motion o f the Bohl in V O R motor results in a rotation o f the master drum and an equal but opposite rotation of the slave drum. A s a result, the sample, which is secured on the drums by means of a pair of clamps, is subjected to a uniform extensional deformation. A data acquisition system allows collecting data at a rate of up to 5000 point per seconds. Lo Master Drum Clips Slave Drum Sample Intermejshing Gears Figure 2.3: Schematic of Sentmanat Extensional Rheometer (SER). 24 The Hencky strain, sH, in an extensional flow is defined as: sH = In KLoJ [2.27] where L is the length of the specimen at any time and L0 is the initial sample length. The Hencky strain rate is then obtained by taking the derivative of the Hencky strain with respect to time . de^^dL [ 2 2 g ] dt L dt For small deformations, the length remians approximately constant at the initial length and Equation 2.28 becomes * * = - — [2-29] " L0 dt Since the change of length with respect to time is essentially the linear velocity at which the sample is been stretched, it can be converted into angular velocity taking into account the drive shaft rotation rate, Q, and the radius of the drums, R. Thus, Equation 2.29 becomes 2Q7? £n = [2.30] The instantaneous torque reading, T(t), acquired from the instrument can be converted into instantaneous force, F(t), by: T(ty=2RF(t) [2.31] The instantaneous cross-sectional area, A(t), o f the stretched specimen changes with respect to the initial cross-sectional area, A0, in an exponential fashion as follows: A(t) = A0exp(-eHt) [2.32] The tensile stress, O~E, can be then estimated as c r . - g a . F ( , ) [2-33] A(t) Aa e x p ( - £ „ 0 Finally, for a constant Hencky strain rate, the tensile stress growth function, r/+E (t), of the stretched sample can be expressed as , ; ( 0 = - Q i L = I _ f W [2.34] A(t)sH Ao exp(-eHt)eH 25 2.5 Stress-strain curves Stress-strain curves are extremely important and useful representations of the mechanical properties of a material. Included in the information that can be obtained from these plots are the elastic modulus, the elongation at yield, the yield stress, the elongation at break, the modulus of resilience and the modulus of toughness. Figure 2.4 shows a generalized tensile stress-strain curve for nearly any plastic material provided that: 1) the curve is obtained by a constant rate-of-strain test, and 2) the rupture of the test specimen may occur at any point on the curve (Carswell, 1944). Elongation at break Elongation Strain, s Figure 2.4: A typical stress-strain curve of a material subjected to tension. A ductile material subjected to tension, w i l l display a plot similar to Figure 2.4 whereas a non-ductile material w i l l show just the initial portion of the curve in this figure. From this, figure, the following mechanical properties o f a material can be defined: a. The highest stress at which the stress is still directly proportional to the strain is called the proportional limit. The ratio of the stress to strain in this straight portion is known as the modulus of elasticity or Young's modulus. This is usually a measure of the stiffness of the material 26 b. The maximum stress the material can sustain without any permanent strain remaining upon the full release o f load is called the elastic limit. c. The stress at the first knee in the curve is known as the yield point and it is an indication o f the strength o f the material and o f its resistance to permanent deformation. Before this point is reached, any deformation the material undergoes is reversible and thus is a measure o f the elastic deformation. After this point, any elongation the material experiences is not easily recovered and, hence, is a measure o f the plastic deformation. d. The area under the stress-strain curve up to the elastic limit is the amount o f energy absorbed by the material in the elastic range and is called the modulus of resilience. Material with a high yield stress and a low modulus o f elasticity w i l l have good resilience. e. The area under the stress-strain curve, which represents the work required to fracture the test specimen, is a rough measure of toughness and is known as modulus of toughness. f. The stress at the breaking point is known as the ultimate strength and it is a measure of the force required to break the material completely. The parameters mentioned above influence the shape of the plot and allow us to classify the material based on its mechanical properties as shown in Figure 2.5. Figure 2.5: Classification of material based on the shape of the stress-strain curves: (a) soft & weak; (b) hard & brittle; (c) hard & strong; (d) soft & tough; and (e) hard & tough. 27 In general, soft, weak materials show a low modulus, a low yield point and a low elongation at rupture. Hard, brittle materials have a high modulus, no wel l defined yield point and a low elongation at break. Soft, tough materials are chracaterized by a low modulus, a low yield point, a high elongation and a high stress at break. Hard, strong materials have a high modulus, a high yield point, a high elongation, and a high breaking stress. 28 CHAPTER 3 Scope of Work 3.1 Introduction P T F E is a technologically important material that has become essential to our lives. Because of its outstanding properties, it is employed in a wide variety o f applications ranging from wire insulation to body part replacement. It is undeniable that the processing techniques by which P T F E is manufactured have been improved since their introduction. However there are still several issues to be understood in order to further optimize these techniques. Because it is a thermoplastic, initial attempts were made to melt process P T F E as is done for normal polymers. However, due to its high melting point and high viscosity, such techniques are generally unsuccesful. The second possibility is to treat P T F E as paste. Techniques for processing pastes are known for other materials such as ceramic pastes, food stuffs and metallic powders (Chevalier et al., 1997; Steffe et al., 1996; Rough, 2000). Since the P T F E manufacturing process involves the production of powders, it is not surprising that P T F E is processed using techniques such as pressing, paste extrusion and sintering. While paste extrusion has been studied for other materials to a great extent, it is only recently that P T F E paste extrusion has been the subject of scientific studies (e.g. Huang et al., 2005; Ariawan et al., 2002b). The present work intends to contribute to our understanding of several aspects of P T F E paste rheology and its role in extrusion. The various objectives of this work are discussed in detail in the next section. 3.2 Thesis objectives The objectives of this work can be summarized as follows: 1. To study the preform behavior of several types of P T F E fine powder pastes using two barrels of different size and a variety of lubricants having different physical properties, namely viscosity and surface tension. 2. To study the rheology o f several types o f P T F E fine powder pastes using a variety of rheometers including parallel plates, capillary and extensional (SER) rheometers. 29 3. To assess the processability of P T F E fine powder pastes by means of capillary rheometry that closely simulates the ram extrusion process. 4. To determine the effects o f die design, resin molecular structure, and processing conditions on the rheology of P T F E pastes and the mechanical properties of P T F E paste extrudates. 5. To study the shear/extensional-induced morphological changes during processing by means o f Scanning Electron Microscopy (SEM) and relate them to the rheology o f the pastes. 6. To develop a constitutive equation that accurately describes the rheological data derived from the paste extrusion process and rheological studies. 3.3 Thesis organization The first chapter of the thesis discusses basic information related to tetrafluoroethylene (TFE) polymerization techniques as well as the basic physical and chemical properties of P T F E that arise from its molecular conformation. The industrial processes relevant to P T F E are also discussed with particular attention to fine powder P T F E processes. Chapter 2 includes literature related to paste extrusion. The basic equations that underline the principles o f the operation o f the various pieces o f equipment used to Theologically characterize the materials under study are presented. Definitions related to shear and extensional rheology are also included in order to familiarize the reader with the terminology used in the rest of this work. Chapter 3 includes the objectives of the present work as well as the organization of the thesis. In Chapter 4 the experimental procedure followed to achieve the objectives is described in detail. The physical properties of the materials used for this study as wel l as the experimental equipment and procedure are also included here. Chapter 5 presents the performing aspect o f P T F E pastes. L iqu id migration and in general the effects of physical properties on P T F E performing are examined. This chapter is based on a journal paper that has already been published (Ochoa I. and S. G . Hatzikiriakos, " P T F E Paste Preforming: Viscosity and Surface Tension Effects," Powder Technology, 146, 73-83 (2004)). Chapter 6 focuses on P T F E paste processing, namely paste extrusion. The effects of various operating variables and physical properties of lubricants are discussed. The quality of the extrudates are examined and studied in terms of their mechanical properties and the 30 quantity/quality o f the fibrils formed during extrusion. This chapter is also based on a journal paper that has already been published (Ochoa I. and S. G . Hatzikiriakos, "Paste Extrusion of P T F E : Viscosity and Surface Tension Effects," Powder Technology, 153, 108-118 (2005)). Chapter 7 discusses the rheology of unprocessed paste and the extensional rheology of the final produced extrudates. A constitutive equation that is aimed at describing the rheology of paste before and after the extrusion is also presented. Chapter 8 examines the extrusion of various P T F E blends using different types of fine powders and processing aids that have been found useful in the processing of molten polymers. The effects of blending pastes made from different resins on the mechanical properties of the extrudates are also discussed. Finally, the conclusions and contributions to knowledge are discussed in Chapter 9. A general summary o f the most significant experimental findings resulting from this work and some recommendations for future work are also presented. 31 CHAPTER 4 Experimental Equipment, Materials and Procedures 4.1 Introduction This chapter discusses the experimental equipment and materials used to study and characterise the rheological and processing properties of P T F E pastes. It also describes in detail the conditions at which the different stages of P T F E processing are conducted. The measurements o f the physical properties such as surface tension, density and viscosity of the different materials used in this work are also explained in detail. The process of paste extrusion is explained briefly. The various dies used to extrude the P T F E pastes as wel l as their detailed geometric characteristics are also presented. The slit die is a new device introduced in this work to prepare samples in order to study the extensional rheology of the extrudates with the help of a new extensional rheometer. Finally, the various instruments used to characterize the P T F E extrudates are mentioned. The properties measured with these pieces of equipment are correlated with the mechanical properties of the P T F E extrudates. 4.2 Material 4.2.1 PTFE fine powder resins Four different P T F E fine powder resins were used in this work. A l l the resins were supplied by Daikin Industries Ltd. The primary particles which form the basis of these P T F E fine powder resins are extremely small, measuring approximately 0.2-0.4 urn (Daikin technical bulletin). They are almost spherical in shape and their properties are summarized in Table 4.1. In appearance, a large number o f these tiny particles aggregate to form secondary particles o f approximately 500 urn as shown in Figure 4.1. A s shown in Table 4.1, two resins have homopolymer structures and the other two have modified structures (copolymers). The resins have been classified according to A S T M D-1457-92, D-4895-98 standards and the physical properties were determined according to A S T M D-4895. 32 Figure 4.1: S E M image of F104 H M W fine powder resin. Table 4.1 Physical properties of P T F E fine powder resin studied in this work, as provided by the supplier. Resin Type Particle Diameter (urn) Apparent Density (g/ml) Specific Gravity F104 H M W Homopolymer 400-650 0.45 2.17-2.20 F104 L M W Homopolymer 400-650 0.45 2.16-2.18 F301 Modified 400-650 0.45 2.15-2.18 F303 Modified 400-700 0.45 2.14-2.16 4.2.2 Lubricants A n extrusion aid is added to P T F E fine powder as a lubricant to enable smooth, uniform paste extrusion. The extrusion aid must be able to completely wet the resin particles, and must be easily removable from the product after extrusion. If a sintering stage is present in the process, the extrusion aid must not color the product. In other words, the volatilizing temperature of the extrusion aid must be lower than the sintering temperature. The types and amounts of the extrusion aid ordinarily used depend on the application of the final product. Different lubricants were used as processing aid in this work in order to examine the effects of their physical properties on the extrusion process. First, several isoparafinnic liquids under the trade name of ISOPAR® were supplied by ExxonMobi l Chemicals. These lubricants are colorless, synthetically produced solvents with uniform composition, low reactivity, excellent stability and narrow boiling point ranges. The 33 odour of ISOPAR® ranges from almost undetectable to very mi ld depending on the grade. Perhaps the most important property of these lubricants is their low surface tension which promotes good spreadability of the lubricant between the resin particles. The other liquid used as a lubricant in this work was a perfluorinated liquid with the chemical name 2-trifluoromethyl-3-ethoxydodecafluorohexane, and referred to as HFE-7500. This is also a clear, colorless liquid with a viscosity and surface tension even lower than those of the Isopar® lubricants. A l l the lubricants were used as they were received. Their most important physical properties relevant to this work are listed in Table 4.2. Table 4.2: Physical Properties of Isopar® and HFE-7500 lubricants. Property Isopar H F E -C E G M V 7500 Density, g/cm J 25°C 0.70 0.72 0.74 0.79 0.82 1.61 Surface Tension, dynes/cm 25°C 21.2 22.5 23.5 26.6 30.8 16.2 Vapour Pressure, mmHg, 38°C 98.0 52.0 14.0 3.1 0.3 15.7( I ) Viscosity, mPa s 25°C 0.51 0.62 1.00 2.70 7.50 1.24 a{2) (g 2 s"1 cm"5) 2031.1 1886.5 1305.4 608.8 272.6 3386.5 (1) Value of vapour pressure reported at 25°C. (2) Group of physical properties given by a = pfyJ7) " s e d i n Equation 4.12 4.2.3 Other lubricants Dioctyl sulfosuccinate sodium salt (AOT) was used as a surfactant to alter the surface tension of Isopar®G due its ability to create reverse micelles in nonpolar solvents. A O T is an anionic surfactant with the structure shown in Figure 4.2. The longest portion of the molecule is the hydrocarbon (hydrophobic) part; whereas the other end is the hydrophilic part (polar). The main idea of the incorporation of this surfactant into Isopar®G is to modify the surface tension (wettability with P T F E ) o f the lubricant while maintaining the viscosity or viceversa. Solutions at different concentrations were prepared by dissolving known amounts of A O T in Isopar G . The surface properties of the mixture obtained in this way were measured by using the capillary rise method (Laskowski, 2001; Seth et al., 2001; Siebold et al., 1997), direct contact angle 34 measurements (Rathod, 2004; Anastasiadis and Hatzikiriakos, 1998; Huh and Reed, 1983) and the D u Nouy ring method. Their viscosities were measured by using a Cannon-Fenske Opaque (Reverse-Flow) viscometer and their densities where measured with a 10 ml picnometer. These values are listed in Table 4.3. It can be seen that the viscosity varies significantly while the surface tension remains almost constant. Figure 4.2: Molecular structure of dioctyl sulfosuccinate sodium salt (AOT) Table 4.3: Physical Properties of Isopar® G - A O T solutions at 25°C. Concentration (wt %) Density (g/cm3) Viscosity (mPa*s) Surface Tension (dynes/cm) 0.0 0.75 1.00 23.5 10.0 0.77 1.22 23.6 20.2 0.80 1.67 23.6 30.3 0.82 2.33 23.3 39.4 0.86 4.48 23.4 56.5 0.90 10.05 23.9 Additional to the mixtures of Isopar® G + A O T , mixtures of Isopar G + Isopar V at different weight concentrations were prepared. The physical properties of these mixtures were also measured and they are listed in Table 4.4. Table 4.4: Physical Properties of Isopar® G & Isopar® V solutions at 25°C. Concentration ofIsopar® V (wt %) Density (g/cm3) Viscosity (mPa*s) Surface Tension (dynes/cm) 0 0.74 1.00 23.5 20 0.76 1.54 26.0 40 0.77 2.17 27.3 60 0.79 3.36 : . 28.4 80 0.80 5.43 29.6 100 0.82 7.50 30.8 35 4.3 Experimental equipment 4.3.1 Preforming and extrusion As previously discussed, paste extrusion is a two-step process: preforming followed by extrusion. During preforming, important phenomena such as liquid migration and densification occur and these are investigated in the present thesis. Preforming and extrusion were performed by using an Instron tensile tester machine model 1123. A s shown in Figure 4.3, the instrument consists of a barrel, a motor drive, a load cell and a data acquisition system. Two interchangeable barrels o f 9.525 mm and 25.4 mm inner diameter were available. The smaller barrel was used for the paste extrusion study while both barrels were used in the liquid migration study. Both barrels have heating bands and temperature controllers. A load cell o f 2270 kg with a plunger attached to it is mounted on a mobile stage. The motor drive allows moving the stage at the specific speed entered into the control panel. The load cell senses the resistance to flow applied by the paste contained in the barrel through the plunger and sends it to the data acquisition system. The data acquisition board allows the experimental results to be recorded automatically and stored in the computer. The dies were attached at the lower end of the barrel as shown in Figure 4.3. For preforming and liquid migration studies, a blind die was used. For extrusion purposes, different tapered dies made of stainless steel were utilized. For these dies, the design variables of interest were the die entrance angle, 2a, the die reduction ratio, RR, and the die length-to-diameter ratio, L/D, as shown in Figure 4.4. The die reduction ratio is defined as the square of the ratio of the diameter o f the barrel, Db, to the diameter of the capillary, D, that is, the ratio o f the cross-sectional areas before and after the contraction zone. RR = [4.1] D X s To prepare samples suitable for extensional rheological studies, a tapered slit die was used. Like the cylindrical dies, this die also has a conical zone which gradually turns from a round shape to a rectangular one, thereby merging into the slit-shaped land o f the die. Figure 4.5 depicts this transition and the geometrical characteristics o f the slit die. This die produces a rectangular shaped sample o f high aspect ratio that can be easily loaded onto the S E R extensional rheometer. 36-Load Cel l Temperature Controllers Thermocounle Data Acquisition System r 1 l l ^ IBM Compatible Figure 4.3: Set-up of the Instron tensile tester machine for paste preforming and extrusion. Barrel diameter D b T Contraction zone Capillary zone L Capillary diameter D Figure 4.4: Schematic diagram of a typical cylindrical capillary die along with the definition of the design parameters. 37 Figure 4.5: Schematic diagram of the tapered slit die showing its contraction and the land zones. 4.3.2 Mechanical and viscoelasticproperties measurement V O R and C V O R parallel-plates Bohl in rheometers were used to characterize the rheology of the fine powder resins by measuring their viscoelastic properties. The former is a strain-controlled rheometer while the latter is a stress-controlled rheometer. A Sentmanat extensional rheometer (SER) was also attached to the V O R Bohlin rheometer in order to measure the extensional properties of the extrudates obtained from the slit die. A schematic diagram of the S E R rheometer has been shown previously in Figure 2.3. The principles and the details of loading the sample and operation were discussed in Chapter 2. The mechanical properties of the extrudates produced from the capillary dies were measured using a C O M - T E N (Compression & Tensile Strength) apparatus whose set-up is shown in Figure 4.6. This instrument comprises a motor drive with adjustable speed, two interchangeable load cells of 20 N and 200 N , a digital monitor controller ( D M C ) and the data acquisition system (DAS) . The sample is placed and held with two clamps, the upper clamp being fixed at the shaft activated by the motor. The sample is then stretched at a constant speed until it fails. The load cell senses the force applied by the sample and sends it to the D A S via the D M C . 38 4.3.3 Other equipment After extrusion and prior to measuring the mechanical properties of the extrudates, the lubricant had to be removed from the samples. In order to do this, the samples were dried in a vacuum oven for at least 16 hours at 120°C. The mechanical properties of the sintered extrudates were also determined as mentioned before. After removing the lubricant from the extrudates, the samples were sintered at 370°C for about 60 s. For the sintering process, a vertical tubular furnace of 2.54 cm inner diameter and 35 cm in length was used. The furnace consists of a single heater zone built o f two ceramic circular brick halves that contain the heater elements and a single temperature control with a J type thermocouple. A differential scanning calorimeter (DSC) was also used to determine the thermal properties of the fine powder resins before and after extrusion. In this way changes in the crystallinity of the samples can be detected and correlated with the extent of fibrillation during extrusion. Motor Load Sample Figures 4.6: Set-up of C O M - T E N tester to measure the mechanical properties of extrudates. 39 4.4 Experimental procedure 4.4.1 Paste preparation Paste preparation is the first step in P T F E paste extrusion. The fine powder is mixed with the processing aid (lubricant) at the proper concentration. Even though this step sounds simple to perform, it is very important that the lubricant wets the particle resin properly. A typical lubricant concentration varies from 16 wt% to 25 wt% (Daikin technical bulletin; Ebnesajad, 2000). In a previous study it was found that a higher lubricant concentration produces preforms with less density variation although it does increase the extent of lubricant migration, i.e., the preform w i l l have a larger lubricant concentration gradient (Ariawan et al., 2002a). Benbow and Brigwater (1993) have reported typical lubricant concentration o f 35 v o l % to 50 vo l%, depending on the physical properties of the solid component, such as the particle shape and size distribution. However, the physical properties of the lubricant play an important role in paste preparation and the effects are addressed in the present study. Assuming particles of spherical shape in a cubic arrangement, as shown in Figure 4.7, the volume of the void space that can be occupied by the lubricant can be calculated as follows. First, the volume of the cubic unit cell, Vc, (see Figure 4.7) is: where rp is the radius of the spherical particle. Thus, the volume occupied by the particles, Vp, is: where Vi is the volume occupied by the lubricant. This shows that 47.6% of the volume is void and it could be occupied by lubricant i f used in the right proportion. However, the amount o f lubricant used is less and this leaves voids inside the paste that must be removed during the preforming step. The amount of lubricant in wt.% can be estimated as follow: [4.2] V =-7V r\ P 3 P [4.3] Then the volume fraction that can be occupied by the lubricant is: V V n _ j p_ _ j _ _ K K ~ 6 c c [4.4] wt% _ p, vol% [4.5] l-wt% ps l - v o / % 40 Mixtures of various powders and lubricants were blended in a jar mi l l at a speed of 15 rpm for about 20 minutes. The resulting paste was then aged for at least 16 hours at room or lower temperature depending on the vapour pressure of the lubricant. Aging the paste is important to allow uniform wetting of the resin particles by the lubricant. It should be pointed out that the paste was prepared in a wide container made of either glass or P E T in order to avoid changes in the lubricant concentration. After aging, the concentration of the lubricant in the paste was measured by taking samples at different depths. These were weighed, dried and weighed again. The difference in weigh before and after drying was attributed to the presence of the lubricant. Figure 4.7: Maximum packing of the solid phase in P T F E paste. 4.4.2 Capillary and sessile drop experiments To determine the surface properties of the various lubricants used in the experimental work as well as their individual wetting characteristics with P T F E , (i) the capillary rise of a liquid through a tube containing a compacted P T F E powder was measured and (ii) direct contact angle measurements of the liquids on P T F E substrates were used. Prior to the capillary rise experiment, it was necessary to determine how the density and the porosity of the material change with pressure. This could help to determine the conditions at which the P T F E powder resin should be packed. For this purpose, 5 g of resin were poured into a copper tube (open from both ends) of 14.1 mm inner diameter and 100 mm length and 41 compacted at different pressures by using the Instron capillary rheometer (Figure 4.3). The pressure was applied for 30 minutes. After that, the compacted powder was removed from the tube, weighed and the bulk density was estimated by using Archimedes' principle. The porosity of the material is defined as: Vh e = -^- [4.6] hs where Vh and Vf,s are the volume of the pores and the porous material, respectively. Equation 4.6 can also be written as: s = \ ^- [4.7] where ps and phs are the densities of the solids and the porous material, respectively. Figure 4.8 shows how the bulk density of the compacted powder changes with applied pressure. Figure 4.9 depicts the change of porosity with pressure. It can be seen from Figures 4.8 and 4.9 that the bulk density and porosity change less significantly at pressures greater than about 20 M P a . 1.2 0 5 10 15 20 25 30 35 40 45 Pressure (MPa) Figure 4.8: Variation of density of a compacted P T F E resin as a function of pressure. 42 Even though the results shown in Figures 4.8 and 4.9 seem quite reproducible, a pressure of 3 M P a was used to pack the powder. Thus, a copper tube was filled with 5 g of P T F E fine powder and then compressed at a pressure of 3 M P a for 30 minutes. The filled tube was hung from the bottom of an analytical balance and its lower end was then placed in a reservoir containing the liquid whose wetting characteristics with P T F E were to be examined (see Figure 4.10). Depending on the surface properties of the liquid, it permeated up into the powder at a different rate. The weight of the column was recorded as a function of time by means of the electronic balance from which the tube was hung. The data acquisition system can be programmed to record data at a minimum rate of 10 points per second. This modified technique was developed and used successfully in the past by Laskowski et.al. (1996; 2001) for mineral systems. 0.5 0.4 'to 0.3 (A O o Q_ 0.2 h 0.1 k 0.0 "—>• 0 5 10 i | T — 1 — r ->—r 15 20 25 30 Pressure (MPa) 35 40 45 Figure 4.9: Variation of porosity, 8, of a compacted P T F E resin as a function of pressure. The data analysis of the capillary rise method is based on Washburn's equation: h2 = krcyL cos6 2^ . [4.8] where h is the rise height of the liquid front in the capillary tube, rc is the mean radius of the capillary, k is a constant accounting for the tortuosity that depends on the particle size and 43 packing, yL is the surface tension of the liquid, 9 is the contact angle, 77 is the viscosity of the liquid and t is the time. Electronic Balance Tube with sample Beaker with test liquid Lab-jack Figure 4.10: Capillary rise method to determine the surface energy of a powder or a liquid. The height is related to the mass of liquid, A w , which has penetrated the column by . Aw = sp,7rRfh [4.9] where e is the porosity of the packed powder column, p, the density of the liquid, and R, the inner radius of the tube. Thus, the modified Washburn equation can be written as (Laskowski et. a l , 1996; Laskowski, 2001) Aw = c p,2yL cos0 [4.10] where the term c is a geometric factor, which is a constant as long as the packing and the particle size remain the same. It has to be experimentally determined for each type of particle packing. The last equation can be rewritten as Aw =m-t [4.11] p, y, cosd 2 where m = c—-—- . Thus, from a plot of Aw versus t a straight line should be obtained whose slope m depends on the geometric factor c, and the contact angle 9. These parameters can 44 be found with the help of a liquid that wets the packed solid particles completely {0 & 0°). H F E -7500 was assumed to be such a liquid, since it has a surface tension lower than that of P T F E . Figures 4.11 and 4.12 show capillary rise experimental runs for lubricants Isopar® G and H F E 7500, respectively. Only the straight portion of the individual curves was considered in the calculations of the slopes. A n average slope was determined from the multiple experimental runs. It is noted that HFE-7500, which has a smaller surface tension compared to P T F E (implies excellent wetting properties with PTFE-assumed contact angle of about 0°) has shown the smaller standard deviation together with Isopar® C. Liquids such as Isopar® G , M and V whose surface tensions are higher than that of P T F E have shown larger standard deviations in repeated experiments. From Equation 4.11, the slope of the straight portions of the curves depicted in Figures 4.11 and 4.12 can be written as the physical properties of the liquid involved such as density pi, viscosity rj, and surface tension, YL- A s mentioned before, the geometric factor c depends on the packing and the particle size (these essentially remain constant). The parameter a changes since it depends on the operating conditions (T and P) and the type of liquid used. Table 4.2 lists the physical properties of the Isopar and HFE-7500 lubricants as well as their corresponding values of the parameter a determined from these capillary rise experiments. Equation 4.12 applied to a lubricant "z" for the same packed powder can be written as: m = a-c- cosd [4.12] where c is the geometric factor discussed before and a = pfy'L/TJ is a constant, which groups m, = a-c- cos9 ; [4.13] or c = a, cos 6, [4.14] Now, combining Equation 4.14 for liquids , "f and "k" results: [4.15] 45 If the contact angle of any of the above liquids with a particular P T F E powder is known, then the contact angle of the other liquids with this powder can be calculated. —> T " 1 1 1 1 • /// Run#1 ™ / 's / '/ Run #2 / y Run #3 • • 0 500 1000 1500 2000 2500 3000 3500 4000 Time (s) Figure 4.11: Capillary rise experiment of Isopar® G through a tube filled with P T F E powder at 25°C. 3.0 Time (s) Figure 4.12: Capillary rise experiment of H F E 7500 through a tube filled with P T F E powder at 25°C. 46 To determine the validity of Equation 4.15, sessile drop measurements using the Isopar" liquids on a P T F E substrate were also carried out. For a direct contact angle measurement, a drop i f the test liquid was placed on a substrate made of compacted P T F E . The substrate was prepared by pouring 2 g of powder into a 27.0 mm inner diameter ring and compressing at 5 M P a for 10 minutes. This way, a relatively smooth P T F E substrate can be prepared. The drop was placed on the substrate with a syringe kept in a vertical position and a few centimeters from the surface by a holder. Instead of obtaining a still picture, a movie was shot with a C C D camera from the moment the drop left the syringe until it touched the surface of the substrate. The movie was subsequently analysed frame by frame to find the precise moment at which the droplet equilibrates on the substrate. Figures 4.13a and 4.13b show typical pictures of drops of water and Isopar® V on P T F E substrates. The average contact angle for Isopar® V was found to be 54.5° ±1.8° and that for Isopar® M 49.7°±3.2°. These values are very close to those estimated by using the Young-Dupre equation. This equation can be written as follows (Wu, 1982): t + cos0=2Jyf r **• J { n ) [4.16] (a) (b) Figure 4.13: Drops of liquid placed on P T F E substrate, (a) Water, (b) Isopar® V . where y® is the dispersive (non-polar) contribution to the surface energy of the substrate (PTFE is this case) and y^D is the non-dispersive (polar) contribution to the surface energy of the substrate. Since, P T F E is a non-polar polymer (repelling water), it is reasonable to assume tha t^^ = 0 . Thus, the second term in the right side of Equation 4.16 can be neglected. In 47 addition, i f we assume that none of the liquids have a polar contribution component to their surface tension (hydrocarbon liquids), t h e n / f = yL and Equation 4.16 can be written as follows: cos 0 - 2 - 1 [4.17] Table 4.5 summarizes the surface tension and contact angle values for P T F E and several liquid lubricants calculated from Equations 4.15 and 4.17. The contact angle values measured from the sessile drop method are also listed. The agreement seems satisfactory. The work of spreading, Ws, in Table 4.5 was calculated from: The estimation of W s and W; involved the values of YL reported by the manufacturer and 6 estimated with Equation 4.17. According to Equation 4.18, 0=0 means that the liquid w i l l readily spread over the solid (Ws = 0). The more negative the value of Ws is, the poorer is its wetting characteristic with the solid substrate. On the other hand, according to Equation 4.19, a value of 0< n/2 {Wt > 0) means that a particle w i l l spontaneously be incorporated into the liquid. It can also be seen from Table 4.5 that the value of the contact angle of Isopar® V predicted by Equation 4.15 matches well with that predicted by the Young-Dupre equation. The contact angles for Isopar® V and G predicted by Equation 4.15 fall within +10% of the values predicted by Equation 4.17. In most cases, the various methods used for estimating the wetting characteristics of the various lubricants agree relatively wel l giving confidence about the consistency of the experimental results. It is noted that direct contact angle and capillary rise experiments with the more volatile liquids could not be performed as these evaporate easily and the increase of weight of the liquid penetrating within the column can not be established with certainty. Using the experimental results listed in Table 4.5, it can be concluded that the wettability of Isobar ® lubricants decreases with an increase of density and viscosity. While one might Ws=yL(cos0-l) [4.18] and the work of immersion, Wt, calculated from: Wi - yi cos 6 [4.19] 48 expect that a higher viscosity would be desirable in paste extrusion (minimum liquid migration), the poor wettability would not lubricate properly the flow as wel l as would not help in overcoming the friction developed between the individual particles (McLeod, 1977). This might result into a small degree of fibrillation that would have a detrimental effect on the mechanical properties of the final P T F E extrudates. As can also be seen from Table 4.5, lubricants having about the same viscosity and different surface tension (various wettabilities with P T F E ) are not available. Therefore, the effect of surface tension cannot be assessed, independently, perhaps with the exception of the pair of HFE-7500 and Isopar® G . The effect of viscosity can be assessed by using all Isopar® lubricants to some extent, which in some cases have significantly different viscosities and similar surface tensions, i.e. comparing the performance of Isopar® C, E and G (although C is very volatile and difficult to use). Therefore, some other lubricants should be prepared in order to study these effects. Below a surfactant (AOT) is used as an additive to Isopar® G in order to prepare additional lubricants having various viscosities and surface tension's' that result in various wettabilities with P T F E . Table 4.5: Comparison of contact angles of various lubricants with a P T F E substrate obtained by the Young-Dupre equation, the capillary rise and sessile drop methods. YL f dynes ^ I cm J ** YL 'dynes^ I cm J Contact Angle, 9 (°) Young- Sessile Capillary Dupre Drop rise ws fdynesN I cm J Wt ( dynes "| I cm J P T F E 18.0 - - - - - -Isopar® C 21.2 20.5 32.6 - 37.3 -3.33 17.87 Isopar® E 22.5 22.3 37.9 - 36.1 -4.75 17.75 Isopar® G 23.5 23.7 41.4 25.5±4.8 40.0 -5.87 17.63 Isopar® M 26.6 26.8 49.8 49.7±3.2 50.4 -9.44 17.16 Isopar® V 30.8 28.1 58.1 54.5±1.8 63.1 -14.51 16.29 HFE-7500 16.2 17.0 0 - 0 0 16.20 * Values reported by the manufacturer ** Values measured by using du Noiiy Ring method. 4.4.3 Effect of surfactant on lubricant surface tension & wettability A s already discussed above, the main idea of adding a surfactant to the lubricants is to see i f it is possible to modify their surface tensions so that the effects of surface tension (wettability with P T F E ) and viscosity on paste extrusion could be studied independently. The 49 presence of this chemical in Isopar® G affects not only the viscosity of the lubricant, but also its density. Table 4.3 summarizes the physical properties of Isopar® G solutions as a function of A O T concentration. It can be seen that the viscosity increases exponentially while the density increases linearly with increase of the surfactant concentration. The surface tension values shown in Table 4.3 represent average values of several measurements using the du Noi iy ring tensiometer. This method falls in the detachment method classification of measuring the surface and interfacial tension of liquids. It is based on measuring the maximum equilibrium force required to detach a circular ring from a liquid surface. The surface tension, yL , can be determined from FR Y l " AnRR f ' RR RR ^ [4.20] where FR is the force required to detach a circular ring from a liquid surface; RR and RR are the radius of the ring and the ring's wire, respectively;/is a correction factor; VR is the volume of the liquid raised above the flat level of the liquid surface and is given by FR/(p, - pn)g where, pi and pa are the density of the liquid and the air, respectively and g is the gravity. The correction factor takes into account that the rupture of the interface occurs at the plane where the film is thinnest leaving some liquid on the ring and that neither the inner nor the outer surface is vertical (Huh et al., 1975 and 1977). The values of surface tension in Table 4.3 have been corrected by taking into account the effect of the atmospheric pressure and hence the density of the solutions (Zuidema et a l , 1941). In spite of these corrections, it seems that the surfactant does not have a significant effect on the surface tension since the variability o f these values falls within experimental error. Using these values of surface tension, the contact angles of the various liquids with P T F E can be determined. In addition, the works of spreading and immersion can be calculated by means of Equations 4.16 and 4.17. For this purpose, capillary rise experiments were conducted. The results are plotted in Figure 4.14 and straight lines were fitted to the straight portions of the curves to determine the contact angles via Equation 4.10. Table 4.6 lists the results of the contact angle as well as the works of immersion and spreading calculated using Equations 4.16 and 4.17 and taking HFE-7500 as a reference liquid (assumed contact angle of 0°). It can be seen that the contact angle increases with increase of the concentration, while the total surface tension remains about the same. Based on the results in 50 Table 4.6, the viscosity of the lubricant can be fixed and the effect of surface tension (wettability) can be assessed in a more comprehensive way. Table 4.7 shows the physical properties of Isopar® G - A O T solutions prepared at different concentrations to mimic the viscosity of other lubricants, while keeping the surface tension similar to Isopar® G . Figure 4.14: Capillary rise experiment of Isopar® G - A O T solutions through a tube filled with P T F E resin at 25°C. Returning again to Table 4.6, it can be seen that the total surface tension is the same at all concentrations, although the wettability (contact angle) with P T F E changes. Due to the fact, that A O T possesses a polar group in its molecular structure, it possibly alters the individual contributions to surface tension. It is also possible that A O T may deposit a film on the P T F E surface, and the concentration of A O T has no effect on the surface tension of the Isopar liquid (Wu, 1982; de Gennes, 1985; Chapius, 1984). While Isopar® G is a non-polar liquid, the presence of A O T brings polarity into the total surface energy of these solutions. For solutions of A O T in Isopar®G, Equation 4.16 is more appropriate to use and it takes the following form, l + cos6 = 2Jyf [4.21] 51 It was assumed that y"D = 0 (PTFE is non-polar). The difference between Equations 4.16 and 4.21 is that n o w ^ f & yL. Equation 4.21 was used to estimate the dispersive component of surface tension component of the solutions. This is the column labelled as yl in Table 4.4. As can be seen, the dispersive component of surface tension drops with increase of A O T concentration while the non-dispersive component increases. Table 4.6: Contact Angle of Isopar® G - A O T solutions on a P T F E substrate at 25°C. Concentration yL 0 W s W ( yuL w% (dynes/cm) (dynes/cm) (dynes/cm) (dynes/cm) 0.00 23.5 0.75 41.4 -5.87 17.63 23.5 10.03 23.6 0.76 40.2 -5.56 18.04 19.1 20.22 23.6 0.71 45.0 -6.92 16.68 22.5 30.26 23.3 0.69 46.3 -7.21 16.09 21.6 39.41 23.4 0.67 47.6 -7.63 15.77 21.3 56.50 23.9 0.46 62.5 -12.87 11.03 16.9 Having now available this variety of lubricants, the effects of their physical properties on paste perform (axial and radial lube migration and perform density) as wel l as paste extrusion and rheology can be assessed. This work is carried out in the subsequent chapters. Table 4.7: Physical properties of Isopar® G - A O T solutions. wt% of A O T in Isopar® G Concentration of A O T (wt%) Isopar G 11.23% 29.11% 50.47% Density (g/cc) @ 25°C 0.74 0.77 0.83 0.88 Viscosity (mPa*s) @ 25°C 1.00 1.24 2.54 7.33 wt% of Isopar® G in paste 18.0 16.5 14.3 11.5 4.4.4 Preforming Preforming was carried out using the unit described above with reference to Figure 4.2. A blind die was attached at the bottom of the barrel and the paste was loaded. The tests were run at 25°C. The speed of the motor was initially set at 0.85 mm/s and manually changed until the desired pressure was reached. Once the pressure was attained, it was kept there for a certain period of time. 52 To determine the axial variation in density and lubricant concentration, the preform was removed from the barrel by moving the piston downward once the blind die was removed. The preform was then cut in portions of about 20 mm in length as indicated in Figure 4.15a. For radial liquid migration studies, each portion was then sliced in sections o f about 3 mm in thickness along the axis as shown in Figure 4.15b. Additional cuts were made along the axis as shown in Figure 4.15c. Only the portions in the center were analysed. The pieces were immediately weighed and dried in a vacuum oven at 100°C for 24 hour to ensure that the lubricant had been removed completely. From the difference between the initial and final weights, the lubricant concentration was determined as a percentage: wt%Lub = (w, -wf) — ^-xlOO [4.19] 25.4 mm ECDCE 3 h - H 20 mm (a) 1 \ ii ir~7 (b) (c) Figure 4.15: (a) Preform paste slicing for determination of the axial density variation and liquid migration, (b) Preform paste slicing for determination of radial liquid migration, (c) Top view of the preform sliced for radial liquid migration. For the axial density distribution study, similar experiments were conducted where the preform was sliced as shown in Figure 4.15a. After drying, the density of each slice was determined by means o f the Archimedes' principle. The sample was hung on the bottom o f an analytical balance and immersed in water. The buoyancy was estimated from the difference between the weight of the P T F E portion in air and water. Water was used because it does not wet P T F E due to its high polarity and surface tension. It has been assured that water does not flow into the pores of the P T F E slices. 53 4.4.5 Extrusion Paste extrusion was performed using the same Instron capillary rheometer. A s usual, preforming was performed prior to extrusion by using a blind die. Once this step was completed, the blind die was replaced with a tapered capillary die and the paste was extruded at constant piston speed. To study the effect of shear rate, extrusion runs were conducted at different piston speeds. Also various capillary dies having different geometrical characteristics were used. The extrudates obtained were collected for further analysis. 4.4.6 Extrudate analysis The extrudates obtained from extrusions, were dried as discussed above. Part of the dried extrudates was used for sintering. Dried extrudates, sintered and unsintered, were tested to determine their tensile strength by using the C O M - T E N equipment following A S T M D1710-96 standard. The extensional rheology was studied by using the S E R rheometer (Figure 2.3) attached to the V O R Bohl in rheometer. The thermal properties of the extrudates were determined using D S C according to A S T M D3418-82 standard. 54 CHAPTER 5 PTFE Paste Preforming 5.1 Introduction Paste preparation is the first step in P T F E paste extrusion. In this stage, the fine powder resin is mixed with an appropriate amount of a processing aid (lubricant). A typical lube concentration varies from 16 to 25 wt% (Daikin technical bulletin), however the optimal amount of lubricant depends on its physical properties. In fact, the physical properties of the lubricant such as density, viscosity and surface tension, play an important role in P T F E paste preparation and they also have an enormous effect on preforming quality and extrusion. During the extrusion process, the pressure undergoes fluctuations. These variations can be present even for the steady-state region and they are the consequence of an uneven densification of the paste before extrusion. Correspondingly, these variations in extrusion pressure w i l l affect the quality of the extrudate (Ariawan, 2002). Therefore, it becomes important to study carefully the factors that influence the preforming of paste. A number of studies have been performed on liquid migration during extrusion in the past (Benbow and Bridgwater, 1993; Burbidge et a l , 1995; Bridgwater, 1989; Ariawan et al., 2001). The subject of liquid migration through the soil and soil consolidation has been of special interest in soil mechanics (Craig, 1997). However, none of these reports have addressed the effect of the physical properties of the liquid on the quality of the preform. In this work, P T F E paste preforming is studied, focusing on the liquid migration and the density distribution during the preforming stage. Emphasis is placed on the effect of the physical properties of the lubricant on liquid migration and densification during preforming. These properties are expected to have a significant impact on the process of paste extrusion as viscosity would influence the liquid migration whereas surface tension affects the wettability between P T F E and the lubricant and thus the quality of the final mixture. Furthermore, these characteristics might significantly affect the quality of the final extrudates during the extrusion stage. 5.2 Densification studies Ariawan et al. (2001) have reported that a pressure of 2 M P a applied for a period of 30 s ensures an even density distribution along the preforms. They have reported that while longer 55 preforming may reduce the variation in preform density, it also significantly increases the extent of lubricant migration. Thus, maintaining an applied pressure of 2 M P a for about 30 seconds is sufficient to yield a uniform lube distribution along preforms of high molecular weight resins (Ariawan et al., 2001). To study the effect of applied pressure on the preform density, different types of pastes were prepared (see Chapter 4) with three lubricants: Isopar® V , M and G at concentration of about 18 wt% and subjected to pressures of 1, 2 and 3 M P a . The preform was removed from the barrel, sliced and analyzed for density and lube concentration as discussed before (see section 4.4.4). Figures 5.1, 5.2 and 5.3 depict typical results. It can be seen from Figure 5.1 that a pressure of 1 M P a is not enough to achieve a uniform density in preforms prepared with Isopar® V and Isopar® M , due to their high viscosities. These resist rapid fluid motion due to volume reduction of the paste. However, application of a higher pressure (2 M P a and 3 MPa) produces a preform of more uniform density even for the liquid having the highest viscosity (see Figures 5.2 and 5.3). E (/) c 0) Q 1.5 1.4 1.3 h 1.2 \-1.1 r-1.0 • — Isopar VJ - A — Isopar M - • — Isopar G 20 40 60 80 Distance from bottom (mm) 100 120 Figure 5.1: Variation of preform density in axial direction resulting from an applied pressure of 1 M P a for 30 s on F104 L M W resin + 18 wt% of lubricant. 56 1.5 ' 1-P = 2 MPa T = 25°C 1.4 h E o S 1.3 I-(/) c (D Q 1.2 1.1 Isopar V Isopar M Isopar G 20 40 60 80 100 Distance from bottom (mm) 120 Figure 5.2: Variation of preform density in axial direction resulting from an applied pressure of 2 M P a for 30 s on F104 L M W resin + 18 wt% of lubricant. 1.5 E o "5) v> c a> a 1.4 h 1.3 1.2 1.1 — • — Isopar V — ± — Isopar M —®— Isopar G P = 3 MPa T = 25°C 20 40 60 80 100 Distance from bottom (mm) 120 Figure 5.3: Variation of preform density in axial direction resulting from an applied pressure of 3 M P a for 30 s on F104 L M W resin + 18 wt% of lubricant. 57 5.3 Liquid migration Preforming was performed using a typical capillary rheometer according to section 4.4.4. Two different barrels were used having diameters of 0.952 and 2.54 cm in order to ensure that the results are size independent. To analyze the liquid migration in the axial and radial directions during preforming, several experiments were conducted. The liquid content in all experiments was kept constant and equal to about 18 wt%. This is particularly important in comparing the behavior of the various lubricants within the context of this work and with results reported by others. It is noted that all lubricants have densities (see Table 4.2) that differ significantly in some cases and therefore a constant weight percentage does not imply a constant volume percentage. 5.3.1 Axial liquid migration Extensive work on axial liquid migration under different operating conditions has been carried out in the past for a variety of P T F E resins (Ariawan et al., 2002). In this work, the effect of the physical properties of the lubricants on preforming is studied. For that purpose different lubricants were used to prepare the paste. In most cases, the paste was subjected to a pressure o f 2 M P a for about 30 s according to the previous section (Ariawan et al., 2001). Also , it was preformed in two different ways: namely, one-sided and two-sided. In the former, the paste was preformed by applying pressure only on one o f the ends. In the latter, the sample was flipped over after the first application of pressure and pressure applied again on its other side. Figure 5.4 is a plot showing the axial liquid migration of three lubricants (Isopar® G , M and V ) . In all cases the samples were preformed one-sided (2 M P a for 30 s) using the larger diameter barrel (2.54 cm). It can be seen that the higher viscosity of the lubricant is, the lower is the degree o f lubricant redistribution. Variability o f lubricant concentration is only present at the end of the preform (shown as TOP) at which the pressure is applied. In addition, the difference between the horizontal lines labelled as initial lubricant concentration and the experimentally determined profiles indicate the loss o f lubricant through evaporation during the experimental procedure. These differences were even higher for the low viscosity and high vapour pressure lubricants, i.e. Isopar® C and E . Similar experiments using the barrel having a smaller diameter (0.952 cm) gave similar results. Therefore, it can be concluded that these viscosity effects are not geometrically dependent. 58 20 I 1 1 1 ' 1 ' 1 ' 1 ' r 15 h 14 t" i i i • • i • • • 1 0 20 40 60 80 100 120 140 D i s t a n c e f r o m bot tom (mm) Figure 5.4: L iquid migration in axial direction of Isopar® G , M and V through one-sided preformed F303 paste when a 2 M P a pressure was applied for 30 s at 25°C. Figure 5.5 shows the axial liquid migration of the lubricants Isopar® G , M and V when the samples were preformed by applying pressure at both ends (two-sided preforming). Again, Isopar® V exhibits the highest lubricant concentration followed by Isopar® M . Isopar® G due to its relatively high volatility exhibits a lower amount compared to its initial concentration. A l l the lubricants show an even lube distribution in the middle. A s a result of the two-sided preforming sample, the lubricant has migrated and accumulated in the middle. For lubricants Isopar® V and M , these variations are minor due to their high viscosities, which resist liquid motion. However, for Isopar® G these seem to be more significant. Therefore, it can be concluded that the higher the viscosity of the lubricant is, the better is the quality of perform. However, the high viscosity of the lubricant is expected to increase the extrusion pressure and this might have a deleterious effect on the quality of the final products, i.e. influence the degree o f fibrillation (Ariawan et al., 2002b; Benbow et al., 1987; Mazur, 1995). In addition, the higher the viscosity of the Isopar® is, the higher its surface tension is (see Table 1). This property has an effect on the wetting characteristics with P T F E , and as such it should be considered in selecting an appropriate lubricant. 59 20 19 14 Isopar G - b — Isopar M Isopar V Initial lubricant concentration for Isopar M & Isopar V (18 w%) 20 40 60 80 100 120 D is tance f r o m bot tom (mm) 140 Figure 5.5: A x i a l liquid migration for Isopar® G , M and V for a two-sided sample preformed F303 paste by applying a pressure of 2 M P a for 30 s at 25°C. 5.3.2 Radial liquid migration Figure 5.6 shows the radial and axial liquid migration behavior for Isopar® G for one-sided preforming pastes. The higher concentrations of lubricant are found near the bottom (opposite end from that where pressure is applied) when the paste is one-sided preformed (also seen before). Regarding the radial distribution, it can be seen that it is minimal. This behavior was also verified by the other lubricants examined, namely Isopar® M and V . Figure 5.7 depicts the radial and axial liquid migration for Isopar® G for a two-sided preformed sample. It can be easily seen that the profiles in the axial directions are similar to those discussed with reference to Figure 5.5. The lube concentration is reduced near both ends and is increased in the middle. In addition, the radial distribution is esentially uniform. Similar results were obtained for the other lubricants. Therefore, it can be concluded that the radial distribution is minor for all practical purposes. 60 Figure 5.6: A x i a l and radial liquid distribution of Isopar G for a one-sided preformed sample by applying a pressure of 2 M P a for 30 s at 2 5 ° C . Figure 5.7: A x i a l and radial liquid distribution o f Isopar® G for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 61 Figures 5.8 to 5.11 are 3-D plots depicting the lubricant distribution in both the radial and axial direction for Isopar* M and V . In these figures it is possible to observe how the liquid concentration changes in both directions when the sample is one-sided preformed. Figure 5.8: Ax ia l and radial liquid distribution of Isopar M for a one-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. Figure 5.9: A x i a l and radial liquid distribution of Isopar® M for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 62 On the other hand, when the paste is two-sided preformed the lubricant accumulates in the middle of the preform. In all cases, the concentration variations in the radial direction are minimal Figure 5.11: A x i a l and radial liquid distribution of Isopar V for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 63 Perhaps a better way to see the liquid distribution within the preform is with the contour plots shown in Figures 5.12 to 5.17. Referring to Figures 5.12 and 5.13, it is possible to see how the lubricant with low viscosity (Isopar® G) distributes uniformly in the radial direction even when the pressure is applied just on one of the two ends (one-sided). The radial distribution of the lubricant is quite homogenous but the concentration of the lubricant is lower at the top as a result of the applied pressure on that point. When the paste is two-sided preformed, the distribution of the lubricant is more even in both the radial and axial directions. Figures 5.14 and 5.15 are the corresponding contour plots for the axial and radial distribution of Isopar® M within the paste for one-sided and two-sided preforms, respectively. In the latter, the lubricant is more evenly distributed but still accumulates in the middle. In Figures 5.16 and 5.17, it can be observed that the lubricant with the highest viscosity, Isopar® V , exhibits a higher resistance to flow and obviously the distribution is more homogeneous compared to other lubricants of lower viscosity. The application of pressure on both sides, Figure 5.17, helps to obtain a somewhat more even distribution of the lubricant. 20 2 3 4 5 6 7 8 9 10 Distance from centre (mm) Figure 5.12: Contour plot of axial and radial liquid distribution of Isopar® G for a one-sided preformed sample by applying a pressure o f 2 M P a for 30 s at 25°C. 64 I , , , , 2 3 4 5 6 7 8 9 10 Distance from centre (mm) Figure 5.13: Contour plot of axial and radial liquid distribution of Isopar G for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 2 3 4 5 6 7 8 9 10 Distance from centre (mm) Figure 5.14: Contour plot of axial and radial liquid distribution of Isopar® M for a one-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 65 2 3 4 5 6 7 8 9 10 Distance from centre (mm) Figure 5.15: Contour plot of axial and radial liquid distribution of Isopar M for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 2 3 4 5 6 7 8 9 10 Distance from centre (mm) Figure 5.16: Contour plot of axial and radial liquid distribution of Isopar V for a one-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 66 2 3 4 5 6 7 8 9 10 Distance from centre (mm) Figure 5.17: Contour plot of axial and radial liquid distribution of Isopar* V for a two-sided preformed sample by applying a pressure of 2 M P a for 30 s at 25°C. 5.3.3. Effect of high preforming pressure and its duration on liquid migration Preforming was also studied under extreme conditions (high pressure and long preform times) in an attempt to determine possible effects of the wettability of lubricants on liquid migration at these extreme conditions. Figure 5.18 shows the effect of high preforming pressure (IS (10 MPa) applied for 10 minutes on liquid migration for Isopar M , G , E and H F E 7500. It can be seen that the application of high pressure redistributes the liquid creating non-uniform distribution in all cases except Isopar® M (due to its relatively high viscosity). Surface tension also influences the liquid migration by changing the wetting characteristics with PTFE. For example, compare the behaviour of HFE-7500 with that of Isopar® G , which have similar viscosities. Having good wetting characteristics, the liquid HFE-7500 creates a thin coat around the P T F E particles. This coating cannot be displaced by the application of a high pressure. On the other hand, i f the wettability characteristics are poor, free liquid exists and this can be nonuniformly displaced to create nonuniformities within the sample. 67 1.00 0.98 h ~ 0.96 k _ O > o > 0.94 0.92 0.90 t • r t 1 r — Isopar M - • — Isopar G - A — Isopar E -+—- HFE 7500 1 I L "I 1 P = 10 MPa T = 25°C t = 10 min • _ l_ _L 20 40 60 80 Distance from bottom (mm) 100 120 Figure 5.18: Effect of preforming pressure and duration on the axial lubricant migration at 25°C on a paste prepared with F301 and 38.8 V % of lubricant. c CO o XI 3 17 16 I-15 -14 [• 13 12 f l 10 -5-- •— 50.47 wt% of AOT • 29.11 wt% of AOT -a 11.23 wt%of AOT -L. 20 40 60 80 Distance from bottom (mm) 100 120 Figure 5.19: A x i a l lubricant distribution in a one-sided preformed paste prepared with F301 and various Isopar® G - A O T solutions pastes preformed at 2 M P a for 30 s at 25°C. 68 To study further the effect of wettability on liquid migration, different solutions of Isopar® G with A O T were prepared. A s mentioned before, this surfactant does not change the total surface tension (although it increases its polar component) of the lubricant, but it does change its viscosity, density and 3-phase contact angle. A s a result, the wettability of the lubricant with P T F E changes accordingly (see Chapter 4). The concentration of the solutions as well as their corresponding physical properties can be found in Table 4.3. Pastes with P T F E and these lubricants were prepared and preformed at a pressure of 2 M P a for 30 seconds. A l l pastes were prepared with a lubricant concentration of about 38.8 vol % and the results are plotted in Figure 5.19. It can be clearly seen that the wettability o f these solutions have produced an excellent quality preform. It remains to be seen whether or not the examined viscosity and wettability effects on preform properties, are also reflected during extrusion (see Chapter 6). 5.4 Liquid migration during extrusion Although paste extrusion is investigated in detail in the next chapter, it would be interesting to examine here liquid migration effects during a typical extrusion run and its consequences on the mechanical properties of the extrudate. Figure 5.20 is a typical start up pressure transient plot obtained during P T F E paste extrusion. It has been divided into four zones in which the lubricant migration and extrudate mechanical properties w i l l be examined separately. The paste was prepared with F301 and 18.8 wt % ± 1.8% of Isopar® M in the usual way. The paste was then extruded at a constant shear rate of 2812 s"1 through a tapered die with entrance angle of 2a = 60°, L/D = 20 and RR = 352:1 at 35°C. Four similar experimental runs were carried out in order to check the repeatability. Fresh paste at the same concentration was prepared for each extrusion. The concentration of the pastes was measured prior to preforming. During extrusion, samples from each marked zone were taken, dried and their lubricant concentration and tensile strengths measured. In addition, the paste remaining in the barrel was also retrieved and its lubricant concentration was also measured. Table 5.1 lists the results obtained for the lubricant concentration in each zone. 69 I II III IV Distance in the barrel Figure 5.20: Typical start up of pressure transient during extrusion of paste (F301 + 18 wt% of Isopar® M ) using a die having 2a = 60°, L / D = 20 and R R = 352:1 at yA =2812 5"'and 35 0 C. It can be seen from Table 5.1 that the lubricant concentrations in zones I to IV are about the same for all practical purposes. It is noted that zone V refers to the preform recovered from the barrel and this is usually a bit drier compared to the other zones, although the data does not substantiate this. Table 5.1: Liquid concentration during four extrusion experiments at the conditions listed in Figure 5.20. Zone I Zone II Zone III Zone IV Zone V Test 1 17. 8 18.2 18.6 18.4 17.9 a o Test 2 18.2 18.7 19.2 18.6 18.2 u ltrat Test 3 17.7 18.4 18.4 18.5 17.8 Lubi oncer Test 4 17.7 18.5 18.6 19.2 18.3 u Mean 17.9 18.5 18.7 18.7 18.1 Std Dev 0.3 0.2 0.3 0.4 0.2 70 The tensile strengths of the extrudates were also measured and the results are listed in Table 5.2. The elastic modulus and the elongation at break are also included. The values correspond to the average value estimated from different specimens taken in each zone. The standard deviations are also included in parentheses. Table 5.2: Mechanical properties of the extrudates obtained in different flow zones. zone Tensile Strength (MPa) Elastic Modulus (MPa) Elongation at break (%) I 3.3 (0.8) 64.7 (23.3) 117.8 (67.4) II 2.6 (0.4) 52.2 (10.4) 140.4 (40.4) III 2.7 (0.2) 53.3 (10.1) 136.3 (24.9) IV 2.8 (0.3) 60.1 (9.1) 131.8(20.8) The results of the tensile strength measurements are shown in Figures 5.21 to 5.24 for the four flow zones. Most o f the changes take place in zone I. Initially, as pressure builds, crystallites of neighbouring particles mechanically interlock and thus fibrils are created. These give the good dimensional stability o f the extrudates. A s the pressure increases further, it seems that while fibrils might still be created, their extensibility is low. In the neighbourhood of the peak pressure, the extensibility o f the samples decreases. In all the other zones the tensile strength and extensibility appear to be similar (see discussion below). Similar conclusions have been drawn by Ariawan (2002), who has reported that some fibrils may break at the point of highest pressure. Figure 5.22 shows the stress vs. strain behaviour o f extrudates obtained during flow zone II. It can be seen that significant variations with respect to extensibility occur. A t the beginning o f zone II (after the pressure has reached its maximum) the extrudate is very weak. However, its quality improves when the extrusion pressure decreases toward its steady-state value. 71 5 I—• i i •—i—'—i—i—i—i—i—i—i—i—i—i i ' i i End of Zone I 0 50 100 150 200 250 Strain (%) Figure 5.21: Stress vs. strain plot for extrudates obtained during flow zone I from Test 2 (see Table 5.2). 4 | • • • • i • 1 i i i i i i i i 1 i ' ' 1 0 50 100 150 200 Strain (%) Figure 5.22: Stress vs. Strain plot for extrudates obtained during flow zone II from Test 3 (see Table 5.2). 72 Figure 5.23 presents the results for extrudates obtained during zone III (the steady-state zone). It can be seen that the various extrudates show similar tensile strength and extensibility values. Regardless o f where the sample is taken from, it shows the same trend. Figure 5.24 depicts the stress-strain behaviour of samples obtained during flow zone IV. This is the end of the extrusion process where the pressure starts increasing slowly due to the fact that the paste becomes drier (Ariawan, 2002). It can be seen that the different parts of the sample show consistently the same tensile strength and extensibility as those obtained at steady state. It can also be seen from Table 5.1 that the lubricant content in the paste remaining in the barrel is not very different from the initial concentration and this is the reason that the pressure does not increase much towards the end of the experiment. Figure 5.23: Stress vs. strain plot for extrudates obtained during flow zone III from Test 1 (see Table 5.2). 73 0 50 100 150 200 Strain (%) Figure 5.24: Stress vs. Strain plot for extrudates obtained during flow zone IV from Test 4 (see Table 5.2). 5.5 Summary A number of lubricants were used and examined as possible processing aids in the paste extrusion of P T F E . They were characterized in terms of both flow and surface properties. It was found that it is possible to alter flow and surface properties independently and thus it became possible to study their relative effects in preforming and extrusion. The following conclusions can be drawn so far from the present study: First, the preforming pressure and duration significantly affect the quality of preform. Lack of adequate pressure wi l l result in a preform of non-uniform density which w i l l extrude unsteadily. Increasing the preforming time and pressure improves the uniformity of preform density, indicating that the process of preforming is time dependent. However, lubricant migration becomes important at longer times. Therefore, the applied pressure and its duration need to be optimized depending on the physical properties of lubricant. A pressure of 2 M P a applied for about 30 seconds seems to be optimum for most cases. Moreover, it has been shown that making a preform by compacting the paste on both ends improves the uniformity of preform density without sacrificing its quality in terms of lubricant distribution. 74 The viscosity has a significant effect on producing a uniform preform. The use of a lubricant of high viscosity can produce a more uniform preform as liquid migration is minimized. For the lubricants used in this study a higher viscosity means also a lubricant of lower vapour pressure and thus minimum liquid evaporation. Increasing the wettability of lubricant with P T F E produces better mixture/pastes. Furthermore, this has an effect on the preform preparation. Excellent wetting would produce a uniform preform even under extreme conditions. The quality of the extrudate was found to be very good during all moments of an extrusion run except at the point where the maximum pressure is obtained. 75 CHAPTER 6 PTFE Paste Extrusion 6.1 Introduction Polytetrafluoroethylene (PTFE) cannot be processed by using melting techniques. Instead, it is processed by a technique known as paste extrusion, similar to that used in the processing of ceramics (Ebnesajjad, 2000). The main difference is that when the P T F E particles are squeezed together during flow, fibrils are formed in the contraction zone of the die. The degree of fibrillation is closely related to the geometrical characteristics of the die used for the extrusion. The physical properties of the liquid used as a processing aid also play an important role in this process. At atmospheric pressure conditions, P T F E has two transition temperatures at approximately 19°C and 30°C (see Figure 1.2 and Blanchet, 1997 for more details). Below 19°C, P T F E particles are very hard and shearing w i l l cause its crystals to slide past each other, retaining their identity. Above 19°C, P T F E molecules are packed more loosely and shearing w i l l cause the unwinding o f crystallites causing the creation o f fibrils (Ebnesajjad, 2000; Mazur, 1995). These fibrils connect the particles together, creating a network and giving dimensional stability to the extruded paste. At temperatures greater than 30°C, a higher degree of fibrillation can be achieved. This property has made it possible for P T F E paste extrusion to be performed near ambient temperature, producing a mechanically strong extrudate (Ebnesajjad, 2000). The present chapter studies the process of P T F E paste extrusion under different operating conditions by using different die geometries and lubricants having different physical properties. First, it addresses the effects of the lubricant physical properties on the extrusion pressure and the mechanical properties of dried and sintered extrudates. Then, the effects of the die geometry characteristics are assessed. The effect of the temperature in P T F E extrusion is also studied to a certain extent. 76 6.2 Pressure transient in PTFE extrusion Figure 6.1 depicts a typical pressure transient obtained during P T F E paste extrusion using a capillary rheometer. The horizontal axis labelled as distance in the barrel is equivalent to time once the constant piston speed is used to divide the distance. The curve has now been divided into three zones (Ariawan, 2001; McLeod , 1997). In zone I, the pressure gradually increases and goes through a maximum. This pressure peak has been thought to be due to the initial filling and wetting of conical zone of the die (Mazur, 1995; Ariawan, 2001; McLeod , 1997; Benbow & Bridgwater, 1987). Experiments performed by using dies having a 180° angle, have also shown the existence of this peak. In other cases, the conical zone was filled before extrusion and the pressure peak still appeared (Ariawan, 2001; Ariawan et al., 2002b). Therefore, the presence of the pressure peak is not due to the initial wetting and filling of the die conical zone (Ariawan, 2001; Ariawan, et al., 2002b). The origin of this maximum is discussed below. i_ 3 (A (A <1> Q_ C o '55 3 l_ M w Distance in the barrel Figure 6.1: Typical start up of pressure transient obtained in P T F E paste extrusion. Zone II is taken to be the steady-state part of the extrusion process. The recorded average pressure in this zone is reported as the extrusion pressure. Final ly in zone III, the pressure gradually increases due to the fact that the final part of the preform becomes drier due to liquid 77 migration. The network of P T F E particles plays the role of an apparently immobile screen. The net result of this is that the lubricant is moving slightly faster than the assembly of particles and therefore causes the last part of the preform to become drier (lower lubricant concentration) and therefore to extrude at a higher pressure. The maximum in the extrusion pressure obtained in zone I during a typical pressure transient (defined as the yield pressure in Figure 6.1) deserves further discussion. This maximum is essentially due to the finite compressibility and the yield stress of the paste in the barrel. Pastes in general are visco-elasto-plastic materials exhibiting a small but finite yield stress (Ebnesajjad, 2000; Ariawan et. al, 2000b; Snelling and Lontz, 1960). It is reasonable to argue that the existence of a yield stress causes the appearance of the yield pressure (peak pressure). Unti l this point is reached, the paste flows in the die at very low speed. The paste is been compressed in the barrel and as a result the static pressure increases gradually. During this compression period, the paste is in a state of jamming, which is defined as the conversion of a liquid system into a solid by imposed stress (Haw, 2004). This essentially means that there is a number of immobile clusters of particles upstream of the die entrance that is responsible for the jamming (Breedveld and Pine, 2003; Manoharan et al., 2003). Collapse of these immobile clusters of particles initiates the flow and this happens once the yield pressure is reached (Haw, 2004). Jamming and flow initiation at a yield point similar to that depicted in Figure 1, have been observed in the ram extrusion of cold chocolate (Chen and Mackley, 2004). During this stage when the extrusion pressure is rising, the extrudate undergoes some distortion and in some cases severe fracture and breakage. After this point is reached, the flow experiences an acceleration and the pressure drops to its steady-state value. Further convincing evidence that the initial jamming is due to a few immobile clusters of particles is provided in Figure 6.2. This figure depicts the extrusion of paste prepared with F104 H M W and Isopar® M . During this test, the extrusion was stopped after reaching the steady-state region and the paste was allowed to relax for different periods of time. For the small relaxation period of 90 seconds, the yield pressure needed to be overcome in order to initiate the flow is very small compared to the initial yield pressure. This shows that the yield surfaces have only been recovered partially. A s the relaxation time increases the yield pressure needed to initiate the flow increases. Finally, for the large relaxation time of 40 hours, the immobile clusters of particles have been reinstated completely. In this case the extrusion pressure has to be increased to levels equal to the initial yield pressure in order to initiate the flow. While the yield pressure is a function of relaxation time, the steady-state preassure is about the same. The small increase 78 in the steady-state preassure after the 40-hours relaxation time is mainly due to the partial evaporation of the lubricant. 140 I 1 1 1 | i i i | i 1 i | • | 0 I i I i l i I 1 1 1 1 • 1 • 1 • 1 0 20 40 60 80 100 120 140 160 Distance (mm) Figure 6.2: Extrusion of F104 H M W + 38.8 V % of Isopar® M . The extrusion was stopped and restarted after (a) 1.5 minutes, (b) 10 minutes, (c) 45 minutes, (d) 40 hours. It can also be argued that the yield pressure should depend on the contraction angle, the reduction ratio, and the type o f resin and lubricant and it should be independent of the apparent shear rate. Figures 6.3 to 6.6 show typical pressure transients obtained by extruding various pastes (different lubricants and P T F E resins) using various die geometries and conditions in order to support these hypotheses. The yield pressure is independent of the apparent shear rate, although the steady-state value scales with it (Figure 6.3). A statistical analysis of the large body of data generated during this work supports this point of view, whereas the results plotted in Figure 6.3 are only typical. Figure 6.4 shows that the yield pressure depends on the physical properties of the lubricant. Viscosity and surface tension cause the immobile clusters of particles to yield at different levels depending on the lubrication and wettability properties of the PTFE/l iquid interfaces. The yield pressure also depends on the type of resin (Figure 6.5). Different P T F E molecular structures result in particles of various sizes (primary and secondary) as well as particles having different crystallinity, hardness and roughness. A s pressure increases, the 79 particles are squeezed against each other and various levels of mechanical interlocking between crystallites across the contact interface between particles occurs. This influences the nature and strength of the immobile clusters and therefore the yield pressure at which flow is initiated. Note that resins F104 H M W and F104 L M W are similar, and thus exhibits the same yield and steady-state pressures. Figure 6.6 shows that the yield pressure is a function of the reduction ratio (compare curves 3 and 4) and a function of the contraction angle (compare curves 1 and 2). It is noted that the results plotted in Figures 6.3 to 6.6 are only representative results and the conclusions drawn are based on the large body of experimental data generated during the course of this study. Finally it should be stressed that the experimental observations discussed in this section can be put into the right perspective, i f one simulates a simple compressible viscoplastic fluid in capillary flow (including the conical zone into the simulation) to see whether or not a yield pressure is predicted. In addition it would be important to check through simulation whether or not the predicted yield pressure depends on L / D ratio, reduction ratio and contraction angle o f the die as well as whether or not it is independent of the apparent shear rate. If these are true assumptions, then inverse simulation might be a good way of determining the yield stress of these types of fluids in transient capillary flow. 80 I i 1 i — i i — i i — i • 1 • r Distance (mm) Figure 6.3: Pressure transients during extrusion of P T F E paste prepared with F104 H M W and Isopar G at different apparent shear rate values. 80 90 I 1 1 1 1 1 1 1——i 1 1— • r 80 J-0 20 40 60 80 100 120 140 Distance (mm) Figure 6.4: Pressure transients during extrusion of P T F E paste prepared with F104 H M W and different lubricants at different apparent shear rate values.. 70 I — i — i — i — i — • — i — i — i — ' — i — i — i — • — r 0 20 40 60 80 100 120 140 160 Distance (mm) Figure 6.5: Pressure transients during extrusion of P T F E paste prepared with different resins and Isopar G . 81 0 20 40 60 80 100 120 140 Distance (mm) Figure 6.6: Pressure transients during extrusion of P T F E paste prepared with F104 H M W and Isopar G at different conditions and dies. 6.3 The effect of the physical properties of lubricants on PTFE paste extrusion 6.3.1 The effect of surface tension Figures 6.7 and 6.8 depict the effect of lubricant surface tension and apparent shear rate on the extrusion pressure of two different P T F E pastes. First, Figure 6.7 compares the behavior of Isopar® G + 11.2 wt% A O T with that of HFE-7500 in the paste extrusion of resin F104 H M W . The viscosities of these lubricants at 25°C are equal to 1.24 mPa s. However, the H F E -7500 has a surface tension of 16.2 x 10"3 N / m compared to 23.6 x 10"3 N / m of Isopar® G + 11.2 wt% A O T . Given that the surface tension of P T F E is about 18 x 10~3 N / m , the wettability of HFE-7500 for P T F E should be complete. The contact angle of HFE-7500 with P T F E has been reported to be 0°, whereas that of Isopar® G + 11.2 wt% A O T with P T F E about 40° (Ochoa and Hatzikiriakos, 2004). It can be seen from Figure 6.7 that the enhanced wettability of HFE-7500 with P T F E decreases significantly the extrusion pressure. 82 F104 HMW + 38.8 vol% Lubricant, T = 35 °C, 2a = 30°, L/D = 20, RR = 352:1 20 ^ * * ' ' 1 * ' ' * ' ' * * * 1 ' ' * * ' * * * * ' * * * * 1 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s'1) Figure 6.7: The effect of lubricant wettability on the extrusion pressure of paste prepared with resin F-104 H M W and two different lubricants having about the same viscosity and different wettability properties at 35°C. Figure 6.8 presents a similar case. It compares the behaviour o f Isopar® G + 50.5 wt% A O T with Isopar® V in the paste extrusion of resin F301. The viscosities of the two lubricants at 25°C are equal to 7.5 mPa s. However, the solution Isopar® G + 50.5 wt% A O T has a surface tension of 23.6 x 10"3 N / m compared to 30.8 x 10~3 N / m of Isopar® V . The corresponding contact angles of these two lubricants with P T F E are about 56° and 60° respectively (Ochoa and Hatzikiriakos, 2004). The effect of wettability (surface tension) on the steady-state extrusion is clear again. Better wettability decreases the extrusion pressure. It is also noted that the actual amount o f liquid Isopar® G in the Isopar® G - A O T mixture is only 11.5 wt% (the rest is A O T ) compared to about 19.2wt% of Isopar® V . Using such a small amount of lubricant, the pressure was expected to be extremely high (Horrobin, 1998). However, the effect of wettability is dominant, keeping the pressure at low levels. 83 80 Q. l _ 3 (A (A 0) L -0. c o "35 3 l_ "R UJ 70 60 50 T ! v— •5 : --JE- Isopar V Isopar G + 50,5 wt% AOT F-301 + 38.8 vol% Lubricant, T = 35 °C, L/D = 0, 2a= 90°, R=352:1 40 i—'—>-1000 I i i i i i l i 2000 3000 4000 5000 6000 . 7000 Apparent Shear Rate (s~) Figure 6.8: The effect of lubricant wettability on the extrusion pressure of paste prepared with resin F-104 H M W and two different lubricants having about the same viscosity and different wettability properties at 35°C. Figures 6.9 and 6.10 plot the tensile strength o f the extrudates obtained from the extrusion experiments plotted in Figures 6.7 and 6.8. It can be seen that the tensile strength increases with a decrease in the extrusion pressure, an observation that is counterintuitive. The tensile strength of the extrudates in the extrusion direction is due to the presence of fibrils (Ebnesajjad, 2000; Mazur, 1995). Fibrillation occurs in the conical zone of the die, where the particles are mechanically interlocked under the action of high pressure. A s particles are accelerated into the conical zone, due to the nature of the flow (extensionally dominated flow), mechanically locked crystallites across the area of contact between particles are unwound and create fibrils. These fibrils give dimensional stability to the extrudates (Ariawan et al., 2002b). A higher pressure usually increases the degree of fibrillation and therefore the tensile strength of the extrudates (Ariawan et al., 2002). In the present case, the opposite is happening and this is certainly due to wettability. It seems that the enhanced wettability distributes the lubricant uniformly within the paste. This minimizes frictional effects. It is also apparent that the formation of fibrils under minimized frictional effects makes them more stable. Although an excessive pressure due to a lack of lubrication causes a significant degree of fibrillation, many of these fibrils break (Ariawan et al., 2002b). 84 It can also be seen from Figures 6.9 and 6.10 that the tensile strength decreases with increase of apparent shear rate. While excessive pressure might be the origin of this decrease (note that pressure increases with apparent shear rate), the Hencky strain and strain rate undergone by the fibrils at the conical zone is the dominant mechanism for this. The total Hencky strain remains the same as this depends on the reduction ratio o f the die. For example, the total Hencky strain, sH, experienced by a fluid element moving along the centreline of the contraction region from far upstream in the barrel to the die exit is given by (Rothstein, 1999) Vl(z=L) V j ( - o o ) :H = dt= | ^ = In D b D = \n[RR] (6.1) where t0 is the time spent in the centreline, Dt/D is the barrel diameter to the die diameter ratio and RR is the reduction ratio defined as (Dt/D) 2 . However, a higher apparent shear rate corresponds to a faster extensional rate (Hencky strain rate) at the entrance. Reaching the same extensional (Hencky) strain at a higher extensional (Hencky) strain rate causes breakage of some of the fibrils. A s a result, this causes a decrease in the tensile strength. re Q_ O) c +-> (/) '</> c X _ HFE-7500 • • -Isopar G + 11.2 wt% AOT F104 HMW + 38.8 vol% Lubricant, T = 35 °C, 2a = 30°, L/D = 20, RR = 352:1 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s ) Figure 6.9: Tensile strength of extrudates obtained from paste prepared with resin F104 H M W and two different lubricants having about the same viscosity and different wettability properties with F104 H M W at 35°C. 85 1.2 t% A O T Isopar V —-w 2:1 u.u I I I I I I I 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s 1) Figure 6.10: Tensile strength of extrudates obtained from paste prepared with resin F-301 and two different lubricants having about the same viscosity and different wettability properties with F301 at 35°C. 6.3.2 The effect of viscosity Figure 6.11 shows the effect of the lubricant viscosity on the steady-state extrusion pressure of P T F E pastes prepared with the homopolymer F104 H M W and lubricants having similar surface tensions but significantly different viscosities. It can be seen that the extrusion pressure generally increases with increase of the lubricant viscosity and apparent shear rate. The higher pressure is due to the high viscosity of the lubricants increasing the resistance to flow. The lubrication resistance between particles in contact and at the paste/wall interface also increases with lubricant viscosity. In a similar way, one may argue that the effective viscosity of the mixture increases with lubricant viscosity and hence a higher extrusion pressure is needed to cause the paste to flow. Although results are presented for only one P T F E resin, a similar behaviour was found for the pastes prepared with all the other P T F E resins. re Q. U) c <l> w '35 c 1.0 h 0.8 0.6 0.4 0.2 Isopar G + 50.5 w - T -V7 F-301 + 38.8 vol% Lubricant T = 35 °C, L/D = 0, 2a= 90°, R=35i 86 70 65 Q. L 60 d> i_ 3 V> S 55 O 50 '55 3 <^ 45 i i i i I i i i i I i i i i I i i i i I i i • • I i i • • F104 HMW + 38.8 vol% Lubricant, T = 35 °C, 2a = 30°, L/D = 20, RR = 352:1 Isopar G + 50.5 wt% AOT 40 1 1000 i Isopar G + 11.2 wt% AOT . I i i i i i i i i 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s") Figure 6.11: Effect of lubricant viscosity on extrusion pressure of F104 H M W . Figure 6.12 depicts the tensile strengths of the dried extudates obtained from the extrusion experiments plotted in Figure 6.11. The tensile strengths not only exhibit a decrease with an increase o f the shear rate, but also with an increase in viscosity due to the higher pressures encountered as the vicosity is raised which possibly cause breakage of fibrils (discussed above). re U) c 0 w 0) '55 c 10 9 8 7 6 5 4 3 2 1 • 1 • • • • i • • • • i • • • • i • • • • i • • • ' F104 HMW + 38.8 vo l% Lubricant, J _ T = 35 °C, 2a = 30°, L/D = 20, RR = 352:1 J - 5--• Isopar G A • —-a*. m - Isopar G + 11.2 wt% A O T J - Isopar G + 50.5 wt% A O T " Ki» _ _ _ ~ -™- 1 • mr m-1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s") Figure 6.12: Tensile strength of dried extrudates of pastes prepared with F-104 H M W and different lubricants having different viscosities and about the same wettability properties. 87 6.4 The effect of geometrical characteristics of die on extrusion pressure 6.4.1 Reduction ratio Figure 6.13 depicts the effect of the reduction ratio of the die on the extrusion pressure of pastes prepared with resin F 1 0 4 H M W and various lubricants. The extrusions were performed at two different shear rates (375 s"1 and 1736 s"1) for each reduction ratio o f 56, 156 and 352. The closed symbols correspond to the apparent shear rate of 375 s"1 and the open symbols to that of 1736 s"1. It can be seen that the extrusion pressure increases with an increase in the reduction ratio in a nonlinear fashion. The corresponding tensile strengths of both dried and sintered extrudates are depicted in Figure 6.14. The volumetric flow rate has kept constant and the corresponding shear rates are indicated in the plot. First, it is noted that the tensile strength of the sintered samples are about 8 to 10 times higher than those o f the dried ones. However, they both follow the same trend. It appears that there is an optimum reduction ratio that maximizes the tensile strength of the extrudates i.e. at a RR around 150 the tensile strength o f the extrudates appears to obtain the highest value. Although the results correspond to different apparent shear rate values, it is noted that the effect of apparent shear rate on the extrusion pressure is much weaker than that of the reduction ratio. CO Q. 0i 1_ 3 (A (A CD l_ Q_ C o '(75 3 "R LU 70 60 50 40 30 20 10 0 • i • • • • i ' F104 HMW + 38.8 vol% Lubricant T T = 35 °C, 2a = 60°, L/D = 20 -% • -: A j A =1736 s"' — - • — -o A Isopar G : Isopar M-HFE-7500' 50 100 150 200 250 300 Die Reduction Ratio 350 400 Figure 6.13: Effect of die reduction ratio on the extrusion pressure of F104 H M W resin. 88 50 I I I i i i i i i i i i i i i i i i i i i i i i i i i i i i q *• • "• 0 50 100 150 200 250 300 350 400 Die Reduction Ratio Figure 6.14: Effect of die reduction ratio on the tensile strength of dried (lower plot) and sintered (upper plot) extrudates obtained from paste prepared with homopolymer F104 H M W and various lubricants at 35°C. In general, it can be concluded that use of extrusion dies having high reduction ratios, causes a significant increase in the extrusion pressure. This causes significant fibril breakages that result in weaker extrudates. Similar observations have been reported by Ariawan (2001) and Ariawan et al. (2002b). 6.4.2 Length-to-diameter ratio (L/D) Figure 6.15 illustrates the effect of the length-to-diameter ratio of the die, L/D, on the extrusion pressure o f pastes prepared with F301 and several lubricants. A s expected, the extrusion pressure increases linearly with increase of the L/D ratio. Note that most of the resistance to flow is due to the conical zone. The pressure needed to extrude the polymer through the conical zone is significantly higher (intercepts on the vertical axis) compared to that needed to extrude it through straight sections of the capillary die (Bridgwater, 1998; Ariawan, 2001). In addition, it is noted that the smallest extrusion pressures were obtained with lubricant HFE-7500. This lubricant has the smallest surface tension and hence is expected to completely wet the P T F E particles (0° contact angle). 89 re Q_ L-3 U) (/> 0) o "35 3 I— "R UJ 130 120 110 100 90 '80 70 60 50 40 30 i r F301 + 38.8 vol% Lubricant T = 35 °C, fA =5860 s"\ 2a = 90°, RR = 352:1 - • — Isopar G - • Isopar M A Isopar V -A—HFE-7500 10 15 20 25 L/D 30 <• 35 40 45 Figure 6.15: Effect of length-to-diameter ratio (L/D) on extrusion pressure of pastes prepared with F301 and various lubricants at 35°C. Figure 6.16 shows the effect of L/D ratio on the tensile strengths of dried and sintered extrudates. It can be seen that the tensile strength of the extrudate increases with the increase o f the L/D ratio up to certain value (L/D = 20) after which there is a slight fall. Short capillaries cause excessive die swell due to unrelaxed high first normal stress effects. These weaken the mechanical properties of the extrudates significantly. A certain length of capillary helps fibrils to relax and orient themselves in the extrusion direction. This also causes the first normal stress to relax and therefore the die swell remains at relatively low levels. Further increase of the capillary length wi l l cause an increase in the extrusion pressure. This has an adverse effect on the tensile strength as high enough pressure cause fibril breakage. Therefore, it appears that an L/D ratio of about 20 optimizes the mechanical properties of extrudates. Similar observations have been reported by Ariawan (2001) and Ariawan et al. (2002b). 90 0 5 10 15 20 25 30 35 40 45 L/D Figure 6.16: Effect of L/D ratio on the tensile strength o f dried (lower plot) and sintered (upper plot) extrudates of paste prepared with copolymerF301 and different lubricants. 6.4.3. Entrance angle The effect o f die entrance angle on the extrusion pressure o f pastes prepared with P T F E F301 and various lubricants is plotted in Figure 6.17. The same trend was found using all other three P T F E resins. It can be seen that the extrusion pressure initially decreases and subsequently increases with increase of the die entrance angle. The decrease in the extrusion pressure at small entrance angle values is similar to the trend predicted for polymer melts and other viscous liquids using the lubrication approximation (Dealy and Wissbrun, 1990). A theoretical derivation similar to that employed in the lubrication approximation, has been used by Benbow and Bridgwater (1993) in their modeling work on paste flow. When the die entrance angle is sufficiently small, paste flow in the die conical zone follows essentially a plug flow pattern for the most part similar to flow in the barrel (Benbow and Bridgwater, 1993). The lubrication approximation approach is valid here. However, the lubrication approximation predicts a monotonic decrease in the extrusion pressure with increasing die entrance angle, which is not consistent with the experimental results plotted in Figure 6.17. Beyond a certain entrance angle, the extrusion pressure increases with increasing angle, as is commonly observed with the extrusion of elastic solids (for example, see Horrobin and Nedderman (1998) and the references 91 therein). A s fibrils are created, the paste attains significant elastic extensional properties that cause a significant increase in the extrusion pressure at high contraction angles. Figure 6.18 illustrates the effect of entrance angle on the tensile strengths of the dried and sintered extrudates. It can be seen that the tensile strength initially decreases with increase of the entrance angle up to about 60° and then increases slightly. In the case of sintered extrudates it can be argued that a similar trend exists although of a milder degree. A small decrease in the tensile strength with increase o f the contraction ratio is expected. A s discussed before, in all extrusion cases plotted in Figures 6.17 and 6.18, dies having the same reduction ratio were used (RR = 352:1). Therefore, the total extensional (Hencky) strain undergone by the pastes was the same. Increase of the contraction angle corresponds to an increase of the extensional (Hencky) strain rate without increasing the apparent shear rate. Note that the latter depends on the final die diameter. A s argued above, the high extensional ratio causes breakage o f fibrils resulting in slightly weaker extrudates. Q. i_ 3 (/> (S) C o '35 3 k. •s UJ 110 100 -90 -80 -70 -60 -50 -40 30 20 10 0 I—1—i-- •— Isopar G • Isopar M a Isopar V • HFE 7500 F301 + 38.8 voI% Lubricant T = 35 °C, J A = 5 8 6 0 s_1> L / D = 20, RR = 352:1 I i 1 10 20 30 40 50 60 70 80 90 100 Die Entrance Angle (2a) Figure 6.17: Effect of die entrance angle on extrusion pressure of F301 resin. 92 60 50 re Q. 40 ±= 30 o> c co o '55 c / 4 3 2 i i i F301 + 38.8 vol% Lubricant T = 35 °C, yA =5860 s"1, L/D = 20, RR = 352:1 [ • Isopar • • Isopar M ^ = a *»«^0 r ^—A— Isopar V • Hr- .HF .E-75ap • • 10 20 30 40 50 60 70 Die Entrance A n g l e (2a) 80 90 100 Figure 6.18: Effect of die entrance angle on tensile strength of dried (lower plot) and sintered (upper plot) extrudates obtained from pastes prepared with copolymer F301 and different lubricants at 35°C. 6.4.4 Molecular structure of the resin Figure 6.19 shows the extrusion pressure as a function of the apparent shear rate for pastes prepared with all four P T F E resins and Isopar® G. These have all been extruded under the same conditions by using the same die and lubricant. It can be seen that both homopolymers extrude at higher pressure compared to their copolymers counterparts. The increase in the extrusion pressure with the resin molecular weight is caused by the hardness of the particles of the higher molecular weight resins. In general, the higher the molecular weight, the higher the extrusion pressure is. Copolymers consist of smaller and softer particles (primary particles) that might be the origin of the lower extrusion pressure. Contact angle measurements could not distinguish any wettability differences of lubricants with homopolymers and copolymers. Therefore, these effects probably depend on the hardness and size of particles. The corresponding tensile strength results of sintered and dried samples are depicted in Figure 6.20. It can be seen that the homopolymers exhibit higher tensile strength values. Local roughness on the particle surface might also influence the mechanical interlocking o f particles which might lead to an increased amount of fibrillation. 93 re CL 03 U 3 M W 03 •_ CL C o •(/) 3 X LU 70 60 50 40 30 i i i i I i i i i I i i i i I i i i i I i i PTFE + 38.8 vol% of Isopar G T = 35 °C, 2a = 30°, L/D = 20, RR = 352:1 F104-LMW " I F104-HMW -yfc F301 F303 20 I i i i i I i i 1 • * * 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s ) Figure 6.19: Effect of the molecular structure of the resin on the extrusion pressure. re CL B c 03 .*-» w 03 '55 c 60 50 40 30 8 6 4 2 i i i i I i i i i l i i i i I i i i i I i i i i I • i i i — • — PI 04 LMW PTFE + 38.8 vol% of Isopar G, Unsintered _ .„ . . — • F104 HMW T = 35 °C, 2a = 30, L/D = 20, RR = 352:1 * F 3 0 1 * * - * : • * • 1 • • 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s ) Figure 6.20: Effect of the molecular structure of the resin on the tensile strength of dried (lower plot) and sintered (upper plot) extrudates. 94 6.5 Effect of temperature on PTFE paste extrusion To study the effect of temperature on the P T F E extrusion process, paste with F104 H M W and Isopar M at 38.8 vol % was prepared. Isopar M was selected because it has a boiling point o f 224° C (vapour pressure o f 3.1 mm H g at 38°C) which makes it suitable for processing at high temperatures (minimal evaporation). The extrusions were carried out in the regular way by using the Instron capillary rheometer. In order to extrude at temperatures below room temperature, copper tubing was wound around the barrel and cold water was circulated by using a refrigerator-bath circulator. Different shear rates varying from 1875 s"1 to 5859 s"1 were attained by changing the plunger speed (from 0.34 to 1.06 mm/s) and using a cylindrical die with an entrance angle 2a of 30°, L/D ratio of 20 and a RR of 352. The extrudates were then dried and the tensile strengths were measured. Figure 6.21 depicts the extrusion pressure of the paste at different temperatures. A t low temperature, the extrusion pressure was very low mainly due to limited fibril formation. P T F E experiences its first transition temperature at 19°C. Below this temperature, the P T F E particles are strong enough to resist any deformation and therefore few fibrils are formed. Since the viscosity and surface tension are functions of temperature, the lubricant at low temperature can neither wet the P T F E particles properly nor move freely within the paste and its distribution is expected to be very poor. Thus, even though the extrusion pressure is very low, the extrudates appear very weak as is confirmed by their low tensile strengths. A s the temperature increases, the extrusion pressure also increases and the appearance of the extrudate improves. However, at temperatures beyond 45°C, the extrusion pressure experiences a sudden decrement and there is no significant difference in the extrusion pressure at 55°C and 65°C. Figure 6.22 shows the tensile strengths of the extrudates obtained at different temperatures. The plots follow the usual behaviour found previously: "The higher the shear rate, the lower the tensile strength." However, it can also be seen that the tensile strength increases with an increase in the temperature. There is no significant difference in the tensile strength of the extrudates obtained at 45°C and 55°C, in fact the tensile strength at 55°C seems to be lower than at 45°C. At 65°C the tensile strength experiences an increase. 95 65 60 CL 55 r-i_ 3 <f> 1/5 0> i_ CL C o '(/) 50 h 2 45 h x UJ 40 r-35 ' ' • • • * • ' • ' F104 HMW + 38.8 vo l% Isopar M 2a = 30°, RR = 352, L/D = 20 1000 2000 3000 4000 5000 6000 Apparent Shear Rate (s ) 7000 Figure 6.21: Effect of temperature on extrusion pressure. n • L +-* u> c m CO 16 14 12 10 8 6 4 2 F104 HMW + 38.8 vol% Isopar M 2a = 30°, RR = 352, L/D = 20 I i i i i - • - T = 15°C • T = 18"C A T = 22°C - T - T • 35°C T = 4S°C + T = SS'C _ L 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s") Figure 6.22: Effect of temperature on tensile strength. Figure 6.23 and 6.24 are contour plots which allows a more comprehensive visualization of the effects of temperature on extrusion pressure and tensile strength, respectively. 96 1875 2375 2875 3375 3875 4375 4875 5375 5875 Apparent Shear Rate (1/s) Figure 6.23: Effect of temperature on extrusion pressure. Contour plot of the results plotted in Figure 6.21. 1875 2375 2875 3375 3875 4375 4875 5375 5875 Apparent Shear Rate (1/s) Figure 6.24: Effect of temperature on tensile strength. Contour plot of the results plotted in Figure 6.22. 97 6.6 Appearance of PTFE extrudates S E M micrograph pictures of P T F E extrudates obtained at different conditions are examined below. These pictures are not intended to quantify the degree of fibrillation during P T F E paste extrusion. However, it is possible to draw conclusions by making observations about the quality of the fibrils. The latter may be correlated with the mechanical properties discussed above. Figures 6.25 to 6.28 are S E M micrograph of extrudates obtained at yA = 5859 s"1 using dies having different entrance angles (2a = 15, 30, 60 and 90°) and the same L/D = 20 and RR = 352:1. The paste used was F104 H M W mixed with 38.8 V % of Isopar® M . It is possible to observe differences in the degree of fibrillation as a function of the entrance angle. The highest tensile strength of 4.39 M P a is obtained at 2a = 15° and this is reflected in the thickness and density of the fibrils. The excessive pressures at 2a = 60° and 90° make the fibrils weak and perhaps many of these break due to the high Hencky strain rate that occurs for the dies having higher contraction angles. Figure 6.25 F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 15°, L / D - 20, R R = 352, yA = 5859 s"1. Extrusion Pressure: 59.3 M P a . Tensile Strength: 4.4 M P a . 98 Figure 6.26: F104 H M W + Isopar® M at 38.8 vo l%. 2a = 30°, L / D = 20, R R = 352, yA = 5859 s"1. Extrusion Pressure: 53.8 M P a . Tensile Strength: 3.9 MPa . . 99 Figure 6.28: F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 90°, L / D = 20, R R = 352, yA = 5859 s"1. Extrusion Pressure: 81.0 M P a . Tensile Strength: 3.2 MPa . Figures 6.29 to 6.31 show S E M pictures of extrudates obtained with dies having different L/D ratios from 0 to 40 at yA = 5859 s"1 and 35°C. The case of L/D = 20 is shown in Figure 6.28. The thickest fibrils in Figure 6.30 are deformed fibrils which were formed during sample preparation and should not be considered as an effect of die geometry. In all cases, it is possible to see the fibrils connecting the P T F E particles. More specifically, at L/D of 0 and 10, empty spaces can be seen among the particles which make the extrudates weaker. A t L/D - 20 (Figure 6.28) the size of these spaces have been reduced and it is possible to observe that the fibrils connect the particles in both the axial and transverse directions. At L/D = 40, the amount of empty space is minimal, but less fibrils are formed due to the high extrusion pressure. 100 Figure 6.29: F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 90°, L /D = 0, R R = 352, yA = 5859 s"1. Extrusion Pressure: 73.0 M P a . Tensile Strength: 0.7 M P a . Figure 6.30: F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 90°, L /D = 10, R R = 352, yA = 5859 s"1. Extrusion Pressure: 77.6 M P a . Tensile Strength: 3.2 MPa . 101 Figure 6.31: F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 90°, L / D = 40, R R = 352, yA = 5859 s"1. Extrusion Pressure: 93.0 M P a . Tensile Strength: 2.8 M P a . Figures 6.32, 6.33 and 6.34 are S E M pictures of extrudates processed with dies having different reduction ratios at yA = 5859 s"1. It can be easily seen that the degree of fibrillation increases with reduction ratio causing an increase in the tensile strength. Figure 6.32: F104 H M W + Isopar® M at 38.8 vo l%. 2a - 60°, L / D = 20, RR = 352, yA = 5859 s"1. Extrusion Pressure: 73.8 M P a . Tensile Strength: 2.3 M P a . 102 Figure 6.33: F104 H M W + Isopar® M at 38.8 vo l%. 2a = 60°, L / D = 20, RR = 156, yA = 5859 s"1. Extrusion Pressure: 24.9 M P a . Tensile Strength: 2.4 MPa . Figure 6.34: F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 60°, L / D = 20, RR = 56, f = 5859 s"1. Extrusion Pressure: 9.8 M P a . Tensile Strength: 1.2 M P a . 103 Figures 6.35 to 6.38 are S E M pictures of selected extrudates obtained from pastes prepared with F104 H M W and 38.8 v o l % Isopar® M and extruded at yA = 5859 s"1 with a die having 2a = 30°, L/D = 20, and RR = 352. The extrusions were performed at temperatures varying from 15°C to 65°C. The S E M micrographs show the effect of temperature on P T F E extrudate appearance. Referring to Figure 6.22, when the extrusion temperature is increased from 15°C to 65°C, the extrusion pressure initially increases, before it starts decreasing at about 45°C. The tensile strength, however, shows a monotonic increase with increase of temperature. It is possible to observe from Figures 6.35 to 6.38 that the quality and quantity of fibrils also increase with temperature. The fibrils connecting the particles are becoming thicker and longer and the density of the sample seems to increase since the empty spaces exhibited by the former samples are reduced and filled with interconnected particles. 104 Figure 6.36: F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 30°, L / D = 20, R R = 352, yA = 5859 s"1, T = 22°C. Extrusion Pressure: 55.9 M P a . Tensile Strength: 3.6 M P a . Figure 6.37: F104 H M W + Isopar® M at 38.8 vo l%. 2 a = 30°, L / D = 20, R R = 352, yA = 5859 s"1, T = 35°C. Extrusion Pressure: 53.8 M P a . Tensile Strength: 3.9 MPa . . 105 Figure 6.38: F104 H M W + Isopar® M at 38.8 vo l%. 2a = 30°, L / D = 20, R R = 352, = 5859s" 1, T = 65°C. Extrusion Pressure: 53.2 M P a . Tensile Strength: 7.0 M P a . 6.7 Mechanical properties of PTFE extrudates Tensile strength is not the only mechanical property that should be taken into account when selecting a material for a certain application. Depending on the final application of the product, there are other mechanical properties such as the elastic modulus, extensibility, modulus of resilience and modulus of toughness, which define a material as hard, tough, brittle, ductile, etc. A l l these properties are functions of the conditions at which the extrudates are produced as well as functions of the die geometry and physical properties of the lubricants used for their extrusion. Table 6.1 lists some of the mechanical properties of the extrudates obtained for the various pastes extruded under different conditions using different die geometries and lubricants. The first column lists the tensile strength values already discussed above. The other two columns are the elastic modulus and the % elongation at break which are related to the elastic and plastic properties, repsectively, of the material. A l l these properties have been defined in section 2.6 and are useful in classifying the materials as hard, soft, tough, brittle, and so on (Carswell, 1944). It can be seen that the homopolymers exhibit the highest elastic modulus. 106 These also possess a higher extensibility. Regarding the copolymers, F301 has a higher elastic modulus and extensibility compared to F303. A similar classification was concluded previously in terms of tensile strength of extrudates obtained under various conditions. The homopolymers always exhibited a higher tensile strength compared to the copolymers. The physical properties o f lubricants also affect the mechanical properties of the extrudate. Lubricants having a lower surface tension (good wettability with PTFE) , and lower viscosity increase the tensile strength and the elastic modulus o f the extrudates. The effect o f apparent shear rate on the mechanical properties seems to be negligible in general. Finally, temperature seems to have a strong effect on the mechanical properties. A s temperature increases, tensile strength, elastic modulus, and elongations at break increase significantly (see Table 6.1). 107 Table 6.1: Mechanical properties of P T F E resins extruded under different conditions. Resin/Condition Tensile Strength (MPa) Elastic Modulus (MPa) % Elongation at Break Resin+ Isopar M , L/D =20, la = 30, ^ = 5859 s\RR = 352:1 F104 H M W F104 L M W F301 F303 5.4 (0.1) 5.7(0.1) 4.4 (0.2) 3.6 (0.2) 89.6 (3.7) 82.6 (3.9) 77.6(11.2) 48.6 (4.0) 100.3 (13.9) 100.1 (8.8) 62.7(15.2) 38.8 (5.2) F104 H M W r Lubricant, L/D =20, 2a = 30, RR = 352:1, ^ = 5859 s 1 Isopar® G Isopar® M Isopar® V HFE-7500 5.6 (0.2) 5.4 (0.1) 4.5 (0.2) 5.6(1.3) 97.0(5.5) 89.6 (3.7) 78.3 (3.3) 160.4 (58.5) 90.5 (5.4) 100.3 (13.9) 162.6 (13.2) 81.9(8.6) F104 H M W + Isopar® M , L/D =20, 2a = 60, yA = 5859 s"1 RR = 352:1 RR = 156:1 RR = 56:1 3.9 (0.2) 2.3 (0.1) 1.2 (0.1) 82.5 (6.5) 51.2 (3.8) 42.2 (2.4) 131.9(18.2) 347.3 (36.2) 373.5 (57.6) F104 H M W + Isopar® M , L/D = =20, RR = 352:1, yA = 5859 s-1 2« = 15 2a = 30 2« = 60 la = 90 5.0 (0.1) 3.8 (0.1) 2.3 (0.1) 3.2(0.1) 79.1 (4.4) 66.0 (2.2) 62.1 (3.8) 72.5 (4.7) 136.1 (4.3) 149.4 (23.6) 171.8 (7.3) 157.6 (19.8) F104 H M W + Isopar® M , 2a = 9 0 , ^ = 352:1, yA = 5859 s1 L/D= 0 L/D= 5 L/D = 10 L/D = 20 L/D = 40 0.7(0.1) 2.0 (0.1) 3.2(0.1) 3.2 (0.1) 3.0 (0.2) 38.0(1.3) 64.8 (6.5) 73.9 (2.7) 72.5 (4.7) 79.6 (4.0) 171.2 (24.8) 133.0 (20.0) 178.6(16.5) 157.6(19.8) 129.7 (20.2) F104 H M W + Isopar® M , L/D = 20, 2a = 30, RR = 352:1 yA = 1875 s"1 6.1 (0.2) 94.7 (4.8) 99.70 (4.1) yA = l%\l s"1 5.9(0.1) 88.7 (2.7) 102.22 (7.6) yA = 3750 s_1 5.7(0.1) 84.9 (4.9) 114.17 (11.5) yA = 4688 s"1 5.5 (0.1) 83.4 (5.6) 103.45 (7.6) ^ = 5859 s"1 5.4 (0.1) 89.6 (3.7) 100.26(13.9) F104 H M W + Isopar® M , L/D = 20, 2a = 30, RR = 352:1, yA = 5859 s"1 T= 15°C r = i 9 ° c r = 2 2 ° C 7-=35°C J = 4 5 ° C r = 5 5 ° C r = 6 5 ° C 2.7 (0.4) 4.1 (0.2) 3.7(0.1) 5.4 (0.1) 7.5 (0.2) 7.0 (0.4) 8.2 (0.2) 63.0 (3.9) 69.2 (2.9) 61.2 (3.4) 89.6(3.7) 92.0(11.2) 93.1 (2.8) 106.5 (3.4) 30.7 (9.9) 45.3 (7.3) 105.8(15.4) 100.3 (13.9) 86.0 (5.8) 110.4 (5.3) 92.0 (4.6) 108 6.8 Interpretation of PTFE paste extrusion It has been pointed out that fibril formation during P T F E paste extrusion is a critical factor. The quality of these fibrils has been described in terms of their degree of orientation by using Raman spectroscopy (Lehnert et al., 1997; Ariawan, 2001). Ariawan (2001) has reported typical Raman spectra of unprocessed and processed powder. In the case of unprocessed powder, no difference in the scattering intensity at all Raman shifts was observed between the two polarization geometries (i.e. parallel or perpendicular to the extrusion direction), indicating no preferred orientation (isotropicity). In the case of processed powder, however, a difference in the scattering intensity at major Raman shifts between the two polarization geometries was observed. This anisotropicity was interpreted as fibril orientation due to flow. Paradoxically, the high fibril orientation seen in the Raman spectra during extrusion is lost when the pressure reaches its highest point (yield pressure or maximum pressure). This was attributed to the increased level of fibril breakages which now are no longer oriented by the flow. It is well known that the extrusion pressure can be used as a quantitative measure of the extent of fibrillation occurring during extrusion. High extrusion pressure usually means the formation of a higher number of fibrils. However, it is also true that an excessive pressure can cause the fibrils to break. The degree of fibrillation in an extrudate has been quantified in the past by using D S C analysis of processed and unprocessed samples (Ariawan, 2002). Since the first heat of melting of a polymer is directly proportional to the degree of resin crystallinity, the extent o f fibrillation and the quantity o f the fibrils can be assessed for different P T F E extrudates by measuring the difference in the first heat of melting of the paste before and after extrusion. Such a difference w i l l suggest that the resin crystallinity after extrusion has changed compared to the virgin resin and this is an indication of the amount of fibrils formed during extrusion. The larger the difference, the higher the degree of fibrillation and hence the better the mechanical properties of the product. It is noted that fibrils are crystallites which have been unwound due to the flow and have assumed an amorphous state. The D S C results are shown in Table 6.2. The values obtained by D S C analysis in many cases can be correlated with the results observed during extrusion and tensile strength measurement. 109 Table 6.2: Heat of melting and melting point of P T F E resins extruded at different conditions. Resin/Condition Melting Point (°C) Heat of melting (J/g) ^m,R ~AHm,S m,R F104 H M W 333.2 (0.4) -78.3 (0.9) Reference F104 L M W 332.5 (0.4) -75.8 (0.4) -F301 331.2 (0.3) -74.1 (1.2) -F303 334.0 (0.8) -68.6(1.7) -F l 04 H M W + Lubricant, L /D =20, 2a = 30, RR = 352:1, yA = 5859 s"1 Isopar® G 333.0 -62.9 0.20 Isopar® M 332.8 -65.3 0.17 Isopar® V 332.7 -61.6 0.21 F104 H M W , Isopar® M , L / D =20, 2a = 60, yA = 5859 s'1 RR = 352:1 332.8 • -76.6 0.02 R R = 156:1 333.2 -66.2 0.15 RR = 56:1 333.1 -61.4 0.78 F104 H M W , Isopar® M , L/D =20, RR = 352:1, yA = 5859 s"1 2a = 15 333.7 -69.3 0.88 2a = 30 332.8 -65.3 0.17 2a = 60 332.8 -76.6 0.98 2a = 90 332.8 -71.5 0.09 F104 H M W , Isopar® M , 2a = 90, RR = 352:1, yA = 5859 s"1 L / D = 0 331.8 -77.6 0.02 L/D = 10 333.2 -54.2 0.31 L/D = 20 332.8 -71.5 0.09 L/D = 40 332.9 -72.8 0.07 F104 H M W + Isopar® M , L/D = 20, 2a = 30,RR = = 352:1 ^ = 1875 s'1 332.4 -72.5 0.07 yA = 2812 s'1 333.0 -71.5 0.09 yA = 3750 s"1 332.7 -64.7 0.17 ^ = 4688 s"1 333.5 -70.0 0.11 ^ = 5859 s"1 332.8 -65.3 0.17 F104 H M W + Isopar® M , L/D = 20, 2a = 30, RR = 352:1 , ^ = 5859 s'1 T = 15°C 331.6 -75.2 0.04 T = 22°G 332.4 -70.8 0.10 T = 35°C 332.8 -65.3 0.17 T = 55°C 332.3 -66.0 0.16 110 6.9 Summary In this chapter, the effects of die design, resin molecular structure and physical properties o f lubricants on the paste extrusion pressure and the mechanical properties of extrudates obtained during extrusion of pastes prepared with a variety o f P T F E powders and lubricants have been studied. It was found that a balance between fibril quantity and quality is necessary to ensure commercially acceptable products. Specifically, it was found that the physical properties of the lubricant play a significant role in the extrusion o f P T F E pastes. Increasing the wettability o f the lubricant with P T F E and decreasing the lubricant viscosity causes a reduction in the extrusion pressure and an increase in the tensile strength of the extrudates. It was also found that the geometrical characteristics of dies also play a significant role in the process. The extrusion pressure increases with L/D ratio and reduction ratio, while it exhibits a minimum with the contraction angle at about 60°. These effects are also reflected in the mechanical properties o f extrudates. The tensile strengths o f dried and sintered extrudates exhibit optimum values at an L/D equal to about 20, and reduction ratio equal to about 150, whereas they exhibit a minimum value at a contraction angle of about 60°. Finally, it was found that a higher molecular weight resin produces stronger fibrils that account for the mechanical superiority of the final extrudates. Therefore, i f the objective is to prepare a product having a high tensile strength, a homopolymer o f high molecular weight should be used in combination with a lubricant having a low surface tension such as HFE-7500 and minimum viscosity greater than a certain value. Too low a viscosity would produce a nonuniform preform. A s far as die selection is concerned, this should have an L/D ratio of about 20, reduction ratio of around 150 and a contraction angle of no more than 60°. I l l CHAPTER 7 Rheology of Preformed and Extruded PTFE Pastes 7.1 Introduction A s previously discussed, when P T F E paste flows from a large reservoir into a die of significantly smaller diameter and consequently into the die land, fibrils between particles form that continuously change the rheology of the paste. It is desirable to formulate a constitutive equation that would be suitable for describing the rheological behaviour of the paste taking into account the continuous change of its structure. Initially the preformed paste is a two phase material where the individual P T F E particles retain their identity. In other words, they are independent of each other having a thin coat of a lubricant around them. A s these particles flow through the contraction area of the extrusion die, mechanical binding occurs that locks the particles together and the extensional nature o f the flow (contraction) causes unwinding of crystallites. Thus, fibrils are formed that interconnect the particles giving a dimensional rigidity to the extrudate (see Figures 6.25 to 6.38). To describe the rheology of such a complicated system, the following constitutive equation is proposed: T = (1 - £ ) X p + [7-1] where X p is the contribution to the stress tensor from the presence o f the unfibrillated particles, and X f is the contribution due to the fibrillated particles and £ represents the fraction of the fibrillated particles, where £ = 0 corresponds to an unfibrillated paste, i.e. just preformed paste before it is subjected to flow, and £ = 1 to a fully fibrillated paste. This constitutive equation can be used for flow simulations in conjunction with an equation that can describe the dynamics of In the present chapter, two individual equations are formulated for the two extreme cases: (i) X p for the rheology of preformed paste (absence of fibrils) and (ii) T f for the rheology of a "fully" fibrillated paste, although it is difficult to determine experimentally, when a P T F E paste has become fully fibrillated. 112 7.2 Rheology of dry PTFE powders and preformed pastes The study of the rheology of preformed pastes using various P T F E resins was carried out using a rate-controlled rheometer equipped with the parallel-plates geometry ( V O R Bohlin). A two-sided tape (the same size as the plate) was glued on the lower plate in order to prevent slippage of the powder or paste. Similarly, the upper plate was serrated in order to avoid slippage during the test. Initially 1 g of resin was placed on the lower plate and the plates were brought together to adjust the sample thickness. While pressing the powder between the plates, some resin was squeezed out and this excess material was removed. Figure 7.1 shows a strain sweep test in order to find the limits of linear viscoelasticity. The resin used was F104 L M W and the test was carried out at 1.5 H z and 35°C. It seems that strains up to 1% can be used safely for linear viscoelasticity measurements. Strain,y Figure 7.1: Strain sweep test of F l 04 L M W powder at 1.5 H z and 35°C. Frequency sweep tests were performed for the four different P T F E resins. The same amount o f resin was always used (1 g) and the small amplitude oscillatory shear tests were performed using 1% strain at 35°C. The results are shown in Figure 7.2 for pastes prepared with the four resins and 38.8 v o l % of Isopar M . Only one run for each paste is shown in this figure although several runs were carried out. A l l the runs for each paste were within 10% of experimental error. A s it can be seen, there are no significant differences between the linear 113 viscoelastic properties of these resins under these conditions. Note that the strain used is very small (1%) and the structural strength of the various powders in the presence or absence of a lubricant is preserved. It is also possible to observe from Figure 7.2 that G ' » G " indicating the solid-like behaviour of the samples (Larson, 1999). Q_ (0 b Frequency, ra (Hz) Figure 7.2: Frequency sweep test of different resins (1% o f strain and 35°C). The schematic depicted in Figure 7.3 shows another way by which the samples were prepared and loaded onto the parallel plate rheometer. One gram o f the resin was placed in a metallic ring and consequently compacted at the desired pressure for 60 s. This procedure assured a sample having a constant diameter of 25.4 mm and a thickness o f about 1.6 mm. There was some concern about the development of strains inside the sample due to compression. For this reason, some samples were tested in a strain sweep test under the same conditions at various times after their compression in order to examine the effect of these stresses. Figure 7.4 shows the results. The samples exhibit almost the same viscosity within the experimental error. This result is important especially for the test involving the presence of lubricant (paste). Due to its volatility, a significant amount of lubricant may evaporate during the time taken to release the stress. These results show that the samples can be tested immediately after compression as the effects of stresses developed during this step (compressions) are insignificant. 114 Figure 7.5 shows the effect of preforming pressure. It can be seen that samples preformed at lower pressure exhibit higher viscosities. For pressures higher than 2 M P a the effect becomes insignificant. It should be mentioned that using a higher pressure to preform the paste with the method depicted in Figure 7.3 causes a significant loss of lubricant. Figure 7.3: Preparation of sample for parallel plate rheological test. Once the region of linear viscoelasticity was determined, frequency sweep tests were carried out at 1 % o f strain. Figures 7.6-7.8 show the effect o f temperature for a pure resin preformed at different pressures. It can be seen that the temperature has a small effect on the viscoelastic properties of pastes. 105 > — • — — « — & — Just r. After After After irefc 15 rr 50 rr 24 h >rmec lin lin i i 10"3 10"2 10"1 Strain,y Figure 7.4: Strain sweep of F104 H M W resin (frequency of 1.5 H z and 35°C). 115 Figure 7.5: Strain sweep test of F104 H M W preformed at different pressures (frequency of 1.5 H z a n d 3 5 ° C ) . 10° 101 Frequency, co (Hz) Figure 7.6: Frequency sweep of F104 H M W resin preformed at 0.5 M P a and tested at different temperatures. 116 Figure 7.7: Frequency sweep of F104 H M W resin preformed at 2 M P a and tested at different temperatures. 10 3 -! 1 1 1 » 10-2 10"1 10° 10 1 10 2 Frequency, co (Hz) Figure 7.8: Frequency sweep of F104 H M W resin preformed at 10 M P a and tested at different temperatures. 117 Figure 7.9 plots frequency sweep tests performed on different resins (dry powder). The resins were preformed at 0.5 M P a and tested at 35°C. No differences among the resins are observed at such small strain (1%). Figure 7.10 compares the behaviour of the pastes prepared with different P T F E resins and 38.8 v o l % Isopar® M . A l l the samples were preformed at 0.5 M P a for 30 seconds and the tests were performed using 1% strain at 35°C. There are practically no significant differences between the pastes. In fact, there is no effect of the presence of lubricant when the pastes are compared with the pure resins. The linear viscoelastic measurement presented in this section show that the preformed powders and pastes show a solid-like behaviour that preserves their strength at small values of strain, i.e. up to strains of 1%. This is also an indication of the existence of yield stress and, once this is exceeded, the powder and pastes wi l l exhibit signs of fluid-like behaviour. Finally, the temperature and the presence of lubricant do not have any significant effect on these viscoelastic measurements. These might be more important at larger deformations where the powder and pastes start flowing. However, these need other techniques or other types of rheometers such as a sliding plate rehometer. 10-2 10-1 10° 101 102 Frequency, GO (HZ) Figure 7.9: Frequency sweep tests of different P T F E resins preformed at 0.5 M P a (1% strain and 35°C). 118 If) •* CO CL CO CL "co~ CL b 10"1 10° Frequency, co (Hz) Figure 7.10: Frequency sweep tests of paste prepared with different resins and Isopar M at 38.8vol% and preformed at 0.5 M P a (1% strain and 35°C). 7.3 Yield stress of PTFE pastes Concentrated solid-liquid suspension systems having strong interparticle interactions often exhibit unique plastic flow behaviour and the presence of a yield stress (Dzuy and Boger, 1983). Under the application of a small stress these systems deform elastically with finite rigidity, but when the applied stress exceeds the yield value continuous deformation occurs with the material flowing like a viscous fluid. The yield stress can thus be considered as a material property denoting a transition between solid-like and liquid-like behaviour. The yield stress is then the minimum shear stress corresponding to the first evidence of flow, i.e., the value of the shear stress at zero velocity gradient (Dzuy and Boger, 1983). Bingham and Green in 1920 first recognized and introduced the concept of a yield stress in fluid-like materials (Dzuy and Boger, 1983). Many workers have studied the measurement of yield stress, but there is a general disagreement in results between the different methods used. In fact, there is doubt whether yield stress exist at all. Some people state that yield stress exists as a well-defined quantity and its value is unique for a given material. Others maintain that yield stress does not really exist (Cheng, 1986). 119 In this work, the yield stress of four different P T F E resins was measured by direct and indirect methods. A l l the different methods were carried out in a stress-controlled rheometer equipped with parallel serrated plates (Bholin C - V O R ) . The first method employed was a ramp stress test. This test is a quick way to find the yield stress of a material but it is not accurate i f insufficient time to reach steady state is allowed. The test involves applying a gradually increasing stress and monitoring the instantaneous viscosity estimated as: % - - [7-2] 7 where a is the applied shear stress, andy is the measured shear rate upon the application of the stress. A plot o f the instantaneous viscosity versus shear stress is obtained and the yield stress is read directly from the plot as the maximum instantaneous viscosity. Figures 7.11 to 7.14 show such plots for homopolymers F104 H M W and F104 L M W and copolymers F301 and F303, respectively. The samples were dry powders prepared by compression at 0.5 M P a for 30 seconds as depicted in Figure 7.3. 30x106 i 1 0 I 1 1 1 1 1 1 0 500 1000 1500 2000 2500 3000 Shear Stress, a (Pa) Figure 7.11: Y i e l d stress measurements for F104 H M W resin at 35°C. 120 (0 CL-IO O O CO CO 3 o <D C TO C CO c 30x106 25x106 > 20x106 15x106 10x106 ™ 5x10€ 7/ v \ \ f Run#1 CTo = 1028.3 Pa| Run#2o o= 840.7 Pa Run #3 CTo = 934.5 Pa Run #4 a o = 887.6 Pa Run#5o-0 = 840.7 Pa Run#7a c= 699.1 Pa Run #8 o\. = 652.2 Pa 500 1000 1500 2000 Shear Stress, a (Pa) 2500 3000 Figure 7.12: Y i e l d stress measurements for F104 L M W at 35°C. 40x106 Shear Stress, a (Pa) Figure 7.13: Y ie ld stress measurements for F301 at 35°C. 121 40x10 to * CO 30x106 '</) o o g 20x106 to 3 O o c jS 10x106 c rc +j to c Run #1 a 0 = 1028.3 Pa Run#2ci 0 = 981.4 Pa Run#3a D = 746.9 Pa Run #4 CT„ = 887.6 Pa 500 1000 1500 2000 Shear stress, a (Pa) 2500 3000 Figure 7.14: Y ie ld stress measurements for F303 at 35°C. Table 7.1 summarizes the results for the mean yield stress values determined from the above plots with the standard deviation from various tests in parenthesis. Table 7.1: Yield stress of PTFE resins. Resin Y i e l d Stress (Pa) F104 H M W 869(103) F104 L M W 840(130) F301 1044 (97) F303 911(124) The determination of yield stress usually implies steady shear under prolonged application of the shear stress. When the stress is first applied, however, the material shows a creep response. For low values of stress, the elastic component of the material w i l l play a more important role than the viscous part. The strain eventually w i l l attain a constant value depending on the level o f stress. However for high values of stress, the strain w i l l increase indefinitely since the viscous component of the material is more dominant and it is the shear rate which wi l l reach a constant value. 122 Figures 7.15 to 7.18 show creep tests for P T F E fine powder resins. The samples were prepared using the same method described before (see Figure 7.3). For these tests, a stress of 600 Pa for 100 seconds was applied. The level o f the applied stress was selected to be smaller than the yield stress determined from the first method (see values in Table 7.1). If this is true then according to the values listed in Table 7.1, a constant value for the strain (or alternatively for the compliance) should be reached. However, it can be seen from Figures 7.15 to 7.18 that the compliance keeps increasing, indicating that either the stress applied is above the yield stress or the elapsed time is not large enough. In addition, the repeatability of each test suffers significantly. In order to determine the yield stress, a lower stress should be applied. However, there is a practical complication in fixing the duration of the test and trying to decide whether a sample has attained constant strain or is still deforming. In general, the longer the observation period the lower the yield stress. This means that the yield stress is a time dependent property (Cheng, 1986). 12x10-6 £ 2x10"6 -0 I 1 1 1 1 1 0 20 40 60 80 100 T i m e (s) Figure 7.15: Creep test for F104 H M W fine powder resin at 35°C (cr= 600 Pa, r = 100 s). 123 50x10"( 0 I 1 1 1 1 ' ' 0 20 40 60 80 100 120 T ime (s) ure 7.16: Creep test for F104 L M W fine powder resin at 35°C (cr= 600 Pa, r = 100 12X10"6 2 2x10"6 -0 20 40 60 80 100 120 T i m e (s) Figure 7.17: Creep test for F301 fine powder resin at 35°C (cx= 600 Pa, t = 100 s 124 10X10- 6 o O a. to 2X1G"6 -u O 0 I 1 1 1 1 1 0 20 40 60 80 100 120 T i m e (s) Figure 7.18: Creep test for F303 fine powder resin at 35°C (<j= 600 Pa, t = 100 s). Figures 7.19 to 7.22 show the results for creep tests with a duration of about 1600 s. For each resin, different values of stress were selected. In each run, the sample was subjected to the given stress and the sample was discarded after each run. A high value of stress was taken as the initial guess according to Table 7.1. It can be seen how the slope of the creep compliance keeps increasing with the application of a high stress to the sample indicating that this high value o f stress does not correspond to the yield stress of the resin. The stress was then decreased until the compliance remained almost constant for a certain period o f time until the end of the test. Due to the nature of the test, it can be said that F104 H M W exhibits a yield stress between 90 and 100 Pa; F104 L M W shows a yield stress between 120 andl25 Pa; for F301, the yield stress is around 160 Pa; while for F303, the yield stress falls between 160 and 170 Pa. 125 ro Q l O c ro E o o a a> 0) 35x10"6 30x10-6 25x10"6 20x10"6 15X10"6 10x10"6 i i O 5x10J I V • © a • v i 90 Pa 100 Pa 120 Pa 125 Pa 127.5 Pa 130 Pa 150 Pa 200 400 600 800 1000 1200 1400 1600 1800 T i m e (s) Figure 7.19: Creep test for F104 H M W resin at different levels of stress. ro Q_ o c ro Q. E o o a a) 30x10"6 25X10- 6 20X10"6 15X10"6 10x10"6 • A 0 0 ,«r 5x10-' n • • • A 0 • A 0 s V A <$> O A * © © V • c • A V • c © 120 Pa 125 Pa 130 Pa 140 Pa 160 Pa 170 Pa 180 Pa 200 400 600 800 1000 1200 1400 1600 1800 T i m e (s) Figure 7.20: Creep test for F104 L M W resin at different levels of stress. 126 50x10-6 Q. S: 40x10"6 • V • <D O C ro "EL E o O a o 30x10"6 20x10"6 10X10"6 i 160 Pa 165 Pa 170 Pa 190 Pa 200 Pa 400 Pa 2 8 • 0 200 400 600 800 1000 1200 1400 1600 1800 T i m e (s) Figure 7.21: Creep test for F301 resin at different levels of stress. 16x10"6 . a • A A A * S i £- 4x10"6 <x> l_ ° 2x10"6 o o • • 160 Pa a 170 Pa A 180 Pa 200 400 600 800 1000 1200 1400 1600 1800 T i m e (s) Figure 7.22: Creep test for F303 resin at different levels of stress. 127 Another way to determine the yield stress is by performing a step stress test. This test is basically a multiple creep test that allows measurement of the yield stress in a more accurate way although the test lasts longer. For this method, a set of stress values are selected. Each stress level is applied and held for a pre-defined time, while the strain response is measured. The stress is gradually stepped up until a measurable flow is obtained. Subsequently, the shear rate is plotted as a function o f shear stress and the yield stress is determined when a change in the shear rate is attained. Figures 7.23 to 7.26 depict the results of the step stress tests applied to the P T F E samples preformed at 0.5 M P a for 60 seconds. The plotted data suggest the existence of a yield stress. The initial portion of the curves where the shear rate remains constant is clear and so is that portion when the shear rate starts increasing, i.e., when the sample starts to flow. 30x10"6 ra o CO -6 L 25x10 « . 20x10"6 of 15x106 £ 10X10"6 5x10-' • ••• 0 200 400 600 800 1000 1200 1400 1600 S h e a r S t r e s s , a (Pa) Figure 7.23: Step stress test for F104 H M W fine powder resin preformed at 0.5 MPa . 128 3 0 x 1 0 - 6 2 5 x 1 0 - 6 S 20x10" 6 CD "JS 15X10" 6 co CO (/) £ 10X10" 6 5x10"' V 0 2 0 0 4 0 0 600 800 1 0 0 0 1 2 0 0 1 4 0 0 1600 S h e a r S t r e s s , a (Pa) Figure 7.24: Step stress test for F104 L M W fine powder resin preformed at 0.5 M P a 3 0 x 1 0 CO 10X10" 6 CO 2 0 0 4 0 0 6 0 0 8 0 0 S h e a r S t r e s s , a (Pa) 1000 Figure 7.25: Step stress test for F301 fine powder resin preformed at 0.5 MPa . 129 30x10"6 25x10"6 to, 20x10"6 0 or 15x106 L ra o -C CO £ 10x10"* I 5x10-6 4 * J " 5 - - - * * ° 0 200 400 600 800 1000 1200 1400 1600 S h e a r S t r e s s , a (Pa) Figure 7.26: Step stress test for F303 fine powder resin preformed at 0.5 MPa . A n indirect method can be used to determine the yield stress from Figures 7.23 to 7.26, i.e., by fitting to the data with well known models where the yield stress is a parameter of the model. Here, the following models were used: Bingham (j = cr0+T]r [7.3] Herschel-Bulkley <T = CTo+riy [7.4] Casson V. . v. a" = <j'0' +tj"y" [7.5] Figures 7.27 to 7.30 show the shear stress-shear rate plots with fits o f the three viscoplastic constitutive equations presented above. Only the straight portions of the plots have been fitted and the parameters of the models are listed in Table 7.2. Even though the Herschel-Bulkley model fits the data better in some cases than the other two models (see R2 in Table 7.2), the yield stress values determined with this model are always negative. Therefore, it seems that this model is not suitable to represent the whole range o f data. From the other two models, the Casson model seems to perform better and therefore might be a good choice to represent the 130 rheology of the paste as a first approximation. The values of the yield stress determined from this model are in general smaller than those reported in Table 7.1 but higher than those obtained from the creep test. Therefore, one may conclude that the yield stresses o f the powders are very small and this is the reason why fitting procedures some times yield negative values for the yield stress. Similar conclusion has been drawn by Ariawan (2001) who has neglected the yield stress. Figure 7.2: Y ie ld stress of various pastes determined by means of fitting viscoplastic models to the experimental data depicted in Figures 7.23 to 7.26. Parameter Herschel-Bulkley Casson Bingham F104 H M W Oo (Pa) -1 .35xl0 7 330.5 570.3 r] (Pa s") 1.35xl0 7 1.62xl0 7 3.723xl0 7 k (dimensionless) 2.983xl0" 5 - -R2 0.959 0.971 0.965 F104 L M W o0 (Pa) -2 .126xl06 744.0 945.5 77 (Pa sm) 2013x l0 6 , 1.041xl0 6 4.648xl0 7 k (dimensionless) 1.172xl0" 4 - -R2 0.995 0.967 0.930 F301 (Jo (Pa) -4 .786xl0 6 595.2 825.5 rj (Pa sm) 4 .791xl0 6 3.247xl0 6 L l O l x l O 7 k (dimensionless) 6.25xl0" 5 - -R2 0.976 0.935 0.891 F303 (Jo (Pa) -1 .053xl0 7 518.6 759.4 TJ (Pa sm) 1.054x107 9.021xl0 6 2.739xl07 k (dimensionless) R2 3.251xl0" 5 - -0.986 0.977 0.957 131 ro 0-to to o 1_ •«-> CO l_ re o CO 1600 1400 1200 1000 800 600 400 200 Experimental Data — Herschel-Bulkley Casson Bingham 5x10" 10x10"6 15x10"6 S h e a r Rate, x(s' 1 ) 20x106 25x106 Figure 7.27: Fitting viscoplastic models to the rheological data of F104 H M W fine powder resin. 1600 1400 V ro to CD CO ro cu .c CO • Experimental Data Casson Herschel-Burkley Bingham 0 20x10"6 40x10"6 60x10"6 80x106 100x10"6 120X10-1 S h e a r R a t e , / ( s 1 ) Figure 7.28: Fitting viscoplastic models to the rheological data of F104 L M W fine powder resin. 132 1600 1400 h 2 1200 r b to 1000 r 10 0 CO 800 h CO a> £ 600 I- . f 400 r _.° 200 • Experimental Data Casson Herschel-Burkley "] Bingham 20x10-6 40x10-6 60x10"6 80x10"6 Shear Rate,^ (s'1) Figure 7.29: Fitting viscoplastic models to the rheological data of F301 fine powder resin. to CL 1600 1400 1200 b 1000 10 CO 0) 800 CO co 600 (J) .c W 400 200 Experimental Data Bingham Herschel-Burkley Casson 10x10"6 20x10"6 Shear Rate,^ (s'1) 30x10"6 Figure 7.30: Fitting viscoplastic models to the rheological data of F303 fine powder resin. 133 7.4 Extensional reology of extrudates obtained from slit die extrusion Two different pastes with F104 HMW-Isopar M and F301-Isopar M at 38.8 v o l % of lubricant were prepared in the usual way. A slit die was used to extrude the pastes in order to produce rectangular shaped samples to load them onto the S E R extensional rheometer. The slit die has an entrance angle of 2a = 60° and L/H = 20 whereas the slit is 2.62 mm wide and 0.508 mm high. The pastes were extruded at shear rates varying from 854 to 5859 s"1 at 35°C. Figures 7.31 and 7.32 show the steady-state extrusion pressure and the tensile strength, respectively, at different shear rates. The tensile strength was measured with a Corn-Ten apparatus by stretching the sample at a constant speed of 13 mm/s until the sample fails. The dimensions of the sample were: 80 mm in length, 2.54 mm in width and 0.34 mm in thickness. As with the cylindrical dies, the extrusion pressure increases with increase of the apparent shear rate (Figure 7.31) while the tensile strength decreases with increase of the shear rate (Figure 7.32). It means that better quality products are obtained at lower extrusion rates. ig I . . . . i . . . . i . . . . i . . . . i . . . . i . . . . i . . . . i 0 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s~1) Figure 7.31: The extrusion pressure of various paste extruded with a slit die as function of the apparent shear rate at 35°C. 134 3.0 CO a 2.5 h 2.0 h W 1.5 h m .*-* CO .2 1.0 (/> C 0) r- 0.5 f-i I i i i i I i i i i I i i i i I i i i i I i i i i I i • • i —•—F104 HMW • F104LMW — A — F301 • F303 0.0 I i i i i I i i i I i i i i I 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s 1) Figure 7.32: Tensile strength of extrudates obtained from slit die at 35°C as a function of the apparent shear rate. The samples were subjected to steady Hencky strain rate extensional rheology tests. As discussed before, a Senmanat Extensional Rheometer (SER) was attached to the strain controlled rheometer for these measurments. A l l tests were performed at 35°C. The following equations were applied in the data analysis and interpretation. The linear strain, e, is defined as follows: £ I I AL L0 L0 [7.6] where L0 is the initial length of the sample, L is the length of the sample at any time and AL is the increment of length. The Hencky strain, £H, is defined as: sH = ln fL^ v A) j [7.7] which can also be written as: eH = ln L LQ + L0 L 0 J = ln f AT \ AL , — + 1 J [7.8] Combining Equation 7.6 with 7.8, sH = \n(s +1) [7.9] 135 The linear strain, e, can be expressed in term of the Hencky strain, en, as follows: e = exp(sH)-l [7.10] The engineering tensile stress, <JS, was calculated with the following formula: crs=^— [7.11] s 2RA0 where T is the torque, R is the drum radius and Ao is the initial sample cross sectional area. The true tensile stress, <7g, was calculated as follows: aE= = ^ [7.12] 2RA0Qxp(-tsH) exp(-t£H) The tensile stress growth coefficient was estimated with the following generalized formula for SER: T ? E = ^ - [ 7 . 13] First, the collected extrudate samples obtained at different apparent shear rates were stretched at the same Hencky strain rate of 0.0113 s"1. The engineering tensile stress was calculated and plotted as a function of the linear strain. The results for F104 H M W and F301 resins are shown in Figure 7.33 and 7.34, respectively. The lines in these figures correspond to averages from several tests carried out with different specimens from the same extrudate. The response for both materials are similar and resemble the responses obtained with the Corn-Ten tester; that is the tensile strength (maximum tensile stress value in the corresponding curve) increases with a decrease in the shear rate at which the corresponding specimen was extruded. This means that more fibrils are present in the specimens extruded at smaller shear rates. 136 Figure 7.33: Engineering tensile stress response of F104 H M W extrudates atsH = 0.011 Linear Strain, e Figure 7.34: Engineering tensile stress of F301 extrudates at eH = 0.0113s 137 The stress growth coefficients of these samples were calculated by using Equation 7.13. The results are plotted in Figures 7.35 and 7.36 for the F104 H M W and F301 extrudates, respectively. There are no significant differences among the extensional viscosities for samples extruded at different shear rates. It seems that the extensional behaviour of all samples of the same resin are essentially the same, i.e. the degree and orientation of fibrillation are similar. However, the difference is perceptible for different resins as shown in Figure 7.37. The homopolymer F104 exhibits higher values than the copolymer F301. It seems that F303 exhibits the lowest extensional transient viscosity. Time (s) Figure 7.35: Stress growth coefficient of F104 H M W extrudates obtained from a slit die with L/H= 20 and different apparent shear rates at 35°C. 138 Figure 7.36: Stress growth coefficient of F301 extrudates obtained from a slit die with L / H = 20 and different apparent shear rates at 35°C. 10-1 10° 101 102 103 Time (s) Figure 7.37: Comparison of extensional behaviour of slit die extrudates obtained at yA =3750 s"1 and subjected to an extension at zH = 0.0113 s"1. 139 Another series of tests was carried out on extrudates obtained when the pastes were extruded at an apparent shear rate of 3750 s"1. The samples were stretched at Hencky strain rates varying from 0.00113 s"1 to 11.3 s~\ The stress growth coefficients were calculated from Equation 7.13 and the results are shown in Figures 7.38 to 7.41. Again, each line in these figures is the average calculated from several tests performed at the same Hencky strain rate. The response is typically that obtained from a linear molten polymer and the lack of plateau in the plots is an indication of a viscoelastic material. i o - 2 i d - 1 io° i o 1 10 2 10 3 10 4 i o 5 Time (s) Figure 7.38: Stress growth coefficient for F104 H M W at different Hencky strain rates. Samples used were produced by extruding the resin at yA = 3750 s~ . 140 10-2 1CV1 10° 101 102 103 104 105 Time (s) Figure 7.39: Stress growth coefficient for F301 at different Hencky strain rates. Samples used were produced by extruding the resin at yA = 3750 s" . 10"2 -I — i : — — i 1 i —i 1 -i 10 2 10"1 10° 101 102 103 104 105 Time (s) Figure 7.40: Stress growth coefficient for F104 L M W at different Hencky strain rates. Samples used were produced by extruding the resin at y A = 3750 s~. 141 10-2 10-1 10° 101 102 1 03 1 04 1 05 Time (s) Figure 7.41: Stress growth coefficient for F303 at different Hencky strain rates. Samples used were produced by extruding the resin at yA = 3750 s'1. 7.5. Yielding and deformation behaviour in extension Figures 7.42 to 7.45 are plots of the engineering tensile stress, <Js, versus strain, s, for extrudates subjected to uniaxial extension at different strain rates and at room temperature. The same scale has been used in all the plots for comparison. The strain was estimated from the Hencky strain by means of Equation 7.10. From each curve two fundamental quantities may be obtained. First the yield stress, <ry, as defined in section 2.5 as the value of the stress at the first knee in the stress-strain curve. It is obtained at a certain strain value which is defined as the yield strain,e y. It can be seen from Figures 7.42 to 7.45 how the yield stress (<7y) changes as a function of the Hencky strain rate {sH). The strain rate effects follow the same trend as for molten polymers (Crist, 1993), i.e. increasing eH by one order of magnitude increases ay by about 50 %. In addition, the yield strain (e ) and the tensile modulus (E) are essentially independent of the strain rate except for a very high value of eH. In summary, the changes in qj,, 142 sy and E at the highest sH resemble the behaviour of a glassy polymers near Tg (Crist, 1993). The values of <jy, and sv are listed in Table 7.3. Table 7.3: The yield stress and strain of P T F E extrudates at room temperature. F104 H M W F104 L M W F301 F303 (•"•) CTy (MPa) CTy (MPa) £y a y (MPa) h CTy (MPa) h 0.00113 1.4 1.0 1.0 1.0 1.0 1.3 1.6 0.4 0.0113 1.8 0.8 1.8 1.0 1.6 0.9 1.7 0.4 0.113 2.6 0.8 2.2 1.0 2.0 1.2 2.0 0.4 1.13 4.2 1.2 3.6 1.3 2.8 1.0 2.8 0.6 The data listed in Table 7.3 indicate that F301 shows the higher extensibility followed by the two homopolymers and finally by F303, which has the smallest extensibility. Figure 7.42: Engineering tensile stress-strain curves for F104 H M W as a function of eH. 143 ro CL in b CO CO o k. CO Q) 'co c 0 h-O) c 0 0 C '5) c LU 3 4 5 Linear Stra in, £ Figure 7.43: Engineering tensile stress-strain curves for F104 L M W as a function of eH ro CL 4 r id b US to 0 ft 3 0 'co § 2 c 03 0 c "5> c LU Hencky strain rate, £ H (s") • X X 3 4 5 Linear stra in , e 0.00113 0.0113 0.113 1.113 Figure 7.44: Engineering tensile stress-strain curves for F301 as a function of s 144 ^ 5 ro CL v> 4 CO "5 3 to '</> § 2 I-Ui c "C co CO c c LU ' ' ' ' I i i i i I i i i i I i i r / i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Hencky strain rate, £ w (s1) 0.00113 0.0113 0.113 1.13 0 I i i i • i • • • • 1 8 2 3 4 5 6 7 Linear Stra in, s Figure 7.45: Engineering tensile stress-strain curves for F303 as a function off , 7.6. Modelling the extensional behaviour through the strain-energy function Stress, defined as a force per unit area may be tensile, compressive, or shear. Nine separate quantities are required to completely describe the state of stress in a material. Stress is indicated as ay where the first subscript refers to the orientation of the face upon which the force acts and the second subscript refers to the direction of the force. Usually, in rheology numbered coordinate directions are used and the components of the stress tensor are written as: r,, ex,, cr, ° 2 1 a 2 2 '23 '33 J [7.13] The diagonal components in Equation 7.13 correspond to extensional stresses whereas the other components correspond to shear stresses. In addition, the stress matrix is symmetrical, i.e., atj = ay when i j; meaning there are only six independent components in the stress tensor represented by Equation 7.13. In a similar way, the deformation experienced by the material under stress can be expressed with as strain tensor. Considering the change in the deformation of a material element in present state, t, with respect to the past state,/', defines the displacement gradient tensor, Ftf. 145 where x x' represent the present and past position, respectively and the subscripts represent coordinate directions. A more common strain tensor used in rheology is the Finger tensor, By, defined as the dot product of the Fy and its trasposse: dx. dx; B«=Fik-Fik=^r J- [7.15] 3x 4 3xk When dealing with viscous material, it is common to consider the material at rest when it can support only uniform normal stresses (hydrostatic pressure p) and when in motion. Thus the total stress, t , is the sum of these two terms. In vector and tensor notation this is written as: T = -pI + a [7.16] where / is the identity tensor and j j is the viscous strees tensor or just stress tensor (Equation 7.13). Only stress differences have meaning. Two such normal stress differences are used: Nl = r i l ~T22 = C J 1 1 - ° " 2 2 ^ — 2*22 ~^33 — ^"22 ^ 3 3 where N/ and define the first and second normal stress differences. The stress-strain data obtained from the uniaxial extension tests and presented in sections 7.4 and 7.5 indicate that these materials behave like a viscoelastic solid since they essentially fail after yielding. The materials have been subjected to uniaxial extension. The stress applied during the process is: A where F is the force applied on a plane of area A perpendicular to the direction of deformation. The area, A, changes during the process and then an is refered as the true tensile stress, cr£. If A0 is the initial area, then the stress is refered as the engineering tensile stress, as. In extension, it is common to use the extensional ratio, ot\, defined as: JLv; 1,0 to denote deformation where Li0 and Z, are the length in the / direction at t = 0 and t - t, respectively. 146 The mechanical properties of a perfectly elastic material may conveniently be represented in terms of the strain energy W. For a perfect elastic solid at equilibrium, the stress can only be a function of the change in the internal energy U o f the sample away from its reference state due to a deformation ^r j T = p [7.20] SB where B is the Finger strain tensor deifned before (Equation 7.15) For an incompressible material, Equation 7.20 is expressed as (Macosko, 1994): T = - p I + 2 ^ B - 2 ^ B - < [7.21] diB diiB where Wis the strain energy function. Here the material functions are derivatives of the strain-energy function with respect to the invariants o f B . If the material is considered incompressible with respect to volume, the principal extension ratios (Dzuy and Boger, 1983) are related by: a , a 2 a 3 =1 [7.22] Then the two strain invariants can be expressed by: IB =a] +OC2+CC3 and IIB = a\2 + a j 2 + a~2 [7.23] where IIIB — 1 since the material is considered incompressible. In each case, W is not known but must be determined experimentally. Since W is a function of h and IIB, Valanis and Landel (1967) proposed that Wis separable into the sum of the same function of each of the principal extensions ccj W = vv(a,) + vv(a 2) +vv(oc3) [7.24] They found that an exponential function fit data w(ai) = mianii [7.25] In a uniaxial extension test the main extension ratio is just a/ and the following simplifications are found 2 1 a 2 = a 3 = a 1 ~ 1 / 2 I B = a 2 - f — IIB=2aj+ — [7.26] a! a , The extensional ration, cti, can be related with the linear strain (Equation 7.6), e, and the Hencky strain (Equation 7.7), 8 h , as follows: a, = s +1 and eH = ln(al) [7.27] 147 Thus, the principal stress cr,, is given by. an = a]w'(al)-a1'U2w'(a~U2) [7.28] where \v'(ct\) is the derivative of PTwith respect to « / . Once an analytical expression for w' is found, W can be determined. Extensional and compression experiments or biaxial extension tests should be conducted in order to apply the separation method to find this analytical form of ^ ( V a l a n i s and Landel, 1967). However, once the function is found, it can be used to fit simple extension data (Kearsley and Zapas, 1980). Ogden (1972) proposed a strain-energy function which is a linear combination of strain invariants discarding the requirement that W shall be an even-powered function of the extension ratios (Jones and Treloar, 1975) and finding an expression for W as VH- I H; U- 71-[7.29] W = T—W + a 2 l + a 3 l - 3 i nt The Ogden model fits experimental data much better than the Mooney-Rivl in model (Jones and Treloar, 1975; H u and Desai 2004) without the constraint imposed by the latter about the material constants. The number of terms included in the summation is to be determined by comparison with the experimental data. From the incompressibility of the material (Equation 7.26), Equation 7.29 can be written as: W=>Z m: a"1 + 2 « , 2 - 3 and the derivative with respect to a\ is dW da, = 5 > . a ^ - a ^ 2 [7.30] When Equation 7.30 is substituted into Equation 7.28 the following expression for a, , results: ax 1 - a . 2 [7.31] Equation 7.31 was used to fit the data shown in Figures 7.42 to 7.45 obtained from extensional rheology. Just two parameters were used to fit the data since no improvement was noticed when four parameters or more were used. Thus, the extensional data can be modeled by an equation having the following form: 148 <rn =m(a']' -a;"12) The tensile or Young's modulus, E, for uniaxial extension can be defined as: [7.32] E = 1 im £->0 Recalling that the extensional ratio, at, can be expressed in term of the linear strain, e, Equation 7.32 can be used to estimate E as follows: — —m-n 2 [7.33] Table 7.4 lists the values of the constants for the extrudates obtained from pastes prepared with the four different P T F E resins and Isopar M . The engineering tensile stress and Young's modulus obtained from Figures 7.42 to 7.45 as well as those obtained by Equations 7.32 and 7.33 are also included. The fittings were performed with a program that is listed in the Appendix. Table 7.4: Ogden's parameters for P T F E samples subjected to different Hencky strain rates. Hencky Tensile Stress (MPa) Elastic Modulus strain m (MPa) n (MPa) rate Measured Equation Measured Equation (V 1 ) 7.35 7.37 0.00113 12.76 0.22 1.5, 1.63 10.10 . 4.17 0.0113 16.63 0.22 1.9 2.15 5.49 r £ 0.113 74 .24x l0 2 7.0xl0" 4 2.6 2.87 7.80 1.13 87 .20xl0 3 8.5xl0" 5 4.2 4.09 11.12 0.00113 22.17 8.9xl0" 2 1.0 1.11 11.56 2.95 0.0113 24.90 0.14 1.9 1.98 5.18 T O 0.113 8.271xl0 2 5.2xl0" 3 2.2 2.38 6.45 E 1.13 80 .00xl0 3 8.0xl0" 4 3.7 3.53 9.60 0.00113 39.11 4.9xl0" 2 1.0 1.07 6.96 2.87 © 0.0113 19.42 0.15 1.5 1.62 4.24 0.113 146.9xl0 2 2.6x10"4 2.0 2.07 5.62 1.13 41 .25x l0 3 1.3xl0' 4 2.9 2.82 7.67 0.00113 19.71 0.24 1.4 2.78 9.54 7.06 fO © 0.0113 4739 9.2xl0"4 1.7 2.41 6.54 0.113 115.7xl0 2 3.8xl0" 4 2.1 2.41 6.56 1.13 17.50xl0 3 2.9xl0" 4 2.8 2.89 7.84 Figures 7.46 to 7.49 show the fits obtained by using Equation 7.32 for the samples stretched at different Hencky strains. The scale in each plot has been kept the same for the sake 149 of comparison. It can be seen that Equation 7.32 fits the data reasonably well at low Hencky strain rates, but exhibits some problems for high Hencky strains due mainly to the abrupt fall o f the curve. Resin F303 displays the lower extensibility and the model is incapable of fitting these values since it was developed with a rubber-like material in mind. One possible solution to this discrepancy could be to use Equation 7.32 with more parameters, but as was mentioned earlier, there is no significant improvement. Ogden (1972) recommends splitting the plot into as many regions as needed and finding the parameter for each region. Then by a linear combination of those equations and adjustment of the parameters, the final expression for the model can be found. This can be carried out by trial and error. The values of the parameters for a high Hencky strain rate look out of proportion, but those values are necessary for the model to follow the trends shown by the data. In addition, the tensile stresses calculated with these parameters by means of Equation 7.32 are very close to those read directly from the corresponding plots. On the other hand, the elastic modulus calculated from Equation 7.33, continues to vary as a function of the Hencky strain rate which is not true as can be seen from Figures 7.42 to 7.45. It can also be seen from Figures 7.46 to 7.49, how the maximum of the fitting data is attained at the same extensional ratio, a\ = e. This is not surprising since, according to Equation 7.32, the extensional ratio, a.\, at which the maximum stress is reached, is a function of the parameter n only with the form: which tends to the value e when n tends to zero. In order for the engineering tensile stress, a, to be a maximum, n has to be between 0 and 1 in Equation 7.34. In general, and in spite o f few discrepancies, it can be said that the model works fairly well and is especially useful as it can classify the various P T F E pastes according to their mechanical properties. [7.34] 150 Linear Stra in, e Figure 7.46: Uniaxial extension of F104 H M W samples stretched at different Hencky strain rates. Continuous line represents the model fitting. 0 1 2 3 4 5 6 7 8 9 10 Linear Stra in , e Figure 7.47: Uniaxial extension of F104 L M W samples stretched at different Hencky strain rates. Continuous lines represent the model fittings. 151 Figure 7.48: Uniaxial extension of F301 samples stretched at different Hencky strain rates. Continuos lines represent the model fittings. 20 i i i i i i i i i i i i i i i i i i i i i i i i i • • • • i i i i i i i i i i i i i i i i CO 0L * 15 Hi b w (0 £ 1 0 a> '</> c a> a; 3 Hencky strain rate, £ H (s1) 0.00113 0.0113 0.113 1.13 0 w i * * ' 0 1 2 3 4 5 6 7 Linear Stra in, s 8 9 10 Figure 7.49: Uniaxial extension of F303 samples stretched at different Hencky strain rates. Continuous lines represent the model fittings. 152 7.7 Summary In this chapter the rheology of processed and unprocessed P T F E paste has been studied. The formation of fibrils during P T F E paste extrusion introduces a complication in the study of this material since their continuous formation and breakage change the rheology of the material. In an attempt of modelling the rheological behavour of P T F E paste during extrusion, an appropiate constitutive equation was proposed as follows: T = ( 1 - £)T p + tJT f Regarding rp, it seems that the unprocessed paste follows the Casson model. The yield stress values predicted by this model fall between those values obtained from two different tests and perhaps they must be considered reasonable as a first approximation. It is worthwhile to mention that the presence of the lubricant does not seem to influence the value of the yield stress. Experiments at large strains and strain rates should be performed to evaluate the other parameters with certainty. Regarding ry, the extensional rheology of the processed resin has shown that extrudates behave as linear elastic polymers. It has been observed that the yield stress and strain are independent of the rate at which the samples are stretched, but they depend on the rate at which the paste is extruded. It is noted that the latter influences the degree of fibrillation. It has been discussed in this chapter that the processed paste can be modelled by means of the Ogden model rather than Mooney-Rivl in model. Therefore the constitutive equation can be written as above with TP to be obtained from: r X = C T X + ^ X [7-5] and Tf from • f < -a, 2 [7.32] Finally, an additional equation for df should be formulated. The parameter £ depends on the kinetics of the flow. This equation coupled with the Cauchy equation for flow and the constitutive equation developed in this chapter can be solved to predict important flow parameters such as pressure, velocity profiles and fibrillation profiles. 153 CHAPTER 8 Extrusion of PTFE Blends and Effects of Various Additives 8.1 Introduction P T F E paste can be extruded at room temperature and the extrudates display good mechanical properties even without sintering, e.g. unsintered tape. During P T F E extrusion, the distribution of the processing aid in the paste matrix confined in the barrel changes with the position and time due to the high pressure extrusion, especially when a long extrusion time is involved. In certain instances, the product can exhibit fractures from mild to severe depending on the processing conditions. To help minimize or eliminate these defects in the extrudate, several alternative processing aids are studied and proposed in this chapter. Moreover, blending of P T F E resins is examined in order to exploit the possibility of producing a resin that can be processed better than any of its individual components. Another option to enhance processability is to utilize mixture of lubricants in order to fix physical properties to certain values. Some processing aids such as fluoropolymers, boron nitride and nanoclays commonly used in the extrusion of polyethylenes are tested here to determine their effect on P T F E paste extrusion. 8.2 PTFE blend extrusion Blends of various types of P T F E (homopolymer and copolymer) were prepared and extruded in order to study whether or not synergistic effects exist in fibril formation. In other words, it is desirable to study the effect of blending on the mechanical properties of extrudates and more specifically to determine i f these (mechanical properties) are better than those o f the individual components of the blend when they are extruded under identical conditions. The various extrusion experiments were performed using a die having an entrance angle, 2a, o f 30°, a length-to-diameter ratio, L/D, o f 20, a reduction ratio, RR, o f 352 and different shear rates at 35°C. As usual, all the extrudates were dried for 24 h at 120°C and the tensile strengths were measured in a Corn-Ten apparatus equipped with an 18 N load cell. During testing, the samples were stretched at a rate of 13 mm/s. 154 The various blends were prepared in two different ways. In the first method, pastes were prepared with each resin separately. These were subsequently mixed at a 1:1 ratio. In the second method, the powders were first mixed at a 1:1 ratio and subsequently the lubricant was added at the desired concentration. The results for a blend of a homopolymer (F104 H M W ) with a copolymer (F301) are summarized in Figures 8.1 and 8.2. The results for pastes prepared with the individual components of the blend are also included for the sake of comparison. First, the effect of the method used to prepare the blend is insignificant and the differences are within the experimental error. Secondly, the extrusion pressures and the tensile strengths of the blend are generally falling between those of the pure components and closer to the component that exhibits the lower values. A similar blend was prepared with the two copolymers, F301 and F303, at a 1:1 ratio. Figures 8.3 and 8.4 depict the extrusion pressure and the tensile strength as a function o f the apparent shear rate, respectively. The results for pastes prepared with the individual components of the blend are also included. Once again the results are not surprising as both the extrusion pressure and tensile strength are falling between those of the pure components and/or closer to that component that exhibits the lower values. 3 CO to c o 'to 3 i_ * J X LU 60 55 CO 0 . * 50 0) 45 40 35 30 i i i i I i—i i i | i • • • | '—1—1—1—I—•"" 2a=30°; L/D = 20; RR = 352:1; T = 35°C i i I i i i 1000 — • — F104 HMW-lsopar M + F301-Isopar M • F104 HMW & F301 + Isopar M — • — F104 HMW + Isopar M —A— F301 + Isopar M _i l—i—i i i 2000 3000 4000 5000 6000 Apparent S h e a r Rate (s'1) 7000 Figure 8.1: The extrusion pressure of a blend of a homopolymer (F104 H M W ) and a copolymer (F301) extruded at various apparent shear rates at 3 5 ° C . 155 co Q. c CD CO "35 c CD 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 i i i i I i i i i I i i i i | i 2a=30°; L/D = 20; RR = 352:1; T = 35°C i i I i i i i I - • — F104 HMW-lsopar M + F301-lsopar M - • — F104 HMW & F301 + Isopar M - • — F104 HMW + Isopar M A F301 + Isopar M i . . . . i—i i i i— 1000 2000 3000 4000 5000 Apparent S h e a r Rate (s'1) 6000 7000 Figure 8.2: The tensile strength of a blend of a homopolymer (F104 H M W ) and a copolymer (F301) extruded at various apparent shear rates at 35°C. o. CD L . 3 (/) (/> CD CL C o 3 X LU 50 45 h 40 \-35 30 i i i i I i i i i I i i i i I i i i i I i i ' 2a=30°; L/D = 20; RR = 352:1; T = 35°C — • — F301 -Isopar M + F303-lsopar M • F301 + Isopar M A- F303 + Isopar M i i i i i 1000 2000 i i i I i i i 3000 4000 5000 6000 7000 Apparent Shear Rate (s'1) Figure 8.3: The extrusion pressure of a blend of two copolymers (F301 and F303) extruded at various apparent shear rates at 35°C. 156 CL c d) co to c a) 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 I i i i i I i i i i I i i i i I i i i i — • — F301-Isopar M + F303-lsopar M — • — F301 + Isopar M •A F303 + Isopar M 2a=30 ; L/D = 20; RR = 352:1; T = 35 C 3.0 r i i i 1000 * • • • 1 • • 1 * • 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s'1) Figure 8.4: The tensile strength of a blend of two copolymers (F301 and F303) extruded at various apparent shear rates at 35°C. 8.3 The effect of lubricant mixture on PTFE paste extrusion In a different type of experiment, Isopar® G and Isopar® V were mixed at different weight percentages to see whether or not it is possible to fix the physical properties of the lubricant at desired values, i.e. viscosity and surface tension. A l l physical properties o f these mixtures were measured at 25°C. Figures 8.5, 8.6 and 8.7 summarize the results for the density, viscosity and surface tension of the mixtures, respectivelly. While the density changes in a linear fashion, the other two physical properties change nonlinearly. A paste of F104 H M W was prepared using a mixture of 60 wt% of Isopar® G with 40 wt% of Isopar® V . Figures 8.8 and 8.9 show the results on the extrusion pressure. A s previously, the results for the blend are falling between those of the individual pure components or the effect is very small and is within experimental error. 157 0.85 \-0.70 ' 1 1 1 1 _ I 0 20 40 60 80 100 wt% of Isopar V Figure 8.5: The density of mixtures of Isopar® G and Isopar® V as a function of composition at 25°C. o 1 1 — 1 1 ' 0 20 40 60 80 100 wt% of Isopar V Figure 8.6: The viscosity of mixtures of Isopar® G and Isopar® V as a function of composition at 25°C. 158 20 40 60 wt.% of Isopar V 100 Figure 8.7 The surface tension of mixtures of Isopar® G and Isopar®. V as a function of composition at 25°C. , co 0 1_ 3 10 (A CO c o to 3 s_ X LU 80 70 60 50 40 —•—F104 HMW + Isopar G •—• F104 HMW + Isopar V A F104 HMW + Isopar G-V • • -..A • * A - • ' • ^ ^ ^ ^ ^ • 2a=30°; L/D = 20; RR = 352:1; T = 35°C ' . . i . . . . i . . 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s*) Figure 8.8: Steady state extrusion pressure of a paste prepared with homopolymer F104 H M W and a mixture of Isopar G & V at 35°C. 159 CL c 2 53 "55 c 8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 i-4.0 3.5 '-3.0 i i I i i i i I i i i i •—F104 HMW + Isopar G • — F104 HMW + Isopar V F104 HMW + Isopar G - V * * * 1 * • 2a=30 ; L/D = 20; RR = 352:1; T = 35 C * • • 1 • • * • 1 * • • • 1 * * * 1 1000 2000 3000 4000 5000 6000 7000 Apparent S h e a r Rate (s ' ) Figure 8.9: Tensile strength of a paste prepared with homopolymer F104 H M W and amixture o f I s o p a r G & V a t 3 5 ° C . 8.4 Effects of additives on paste extrusion Pastes of F104 H M W were prepared with the addition of boron nitride (BN2, CTF5) or nanoclays (Nanomer® I.44P, Nanomer® P G V ) and Isopar® M as a lubricant. The blends were prepared by mixing first the two solid phases (PTFE and either boron nitride or nanoclay) in the desired proportions prior to the addition of the lubricant. In all cases the lubricant concentration was kept at 18.7 wt%. The results are depicted in Figures 8.10 to 8.15. The results of the corresponding virgin paste (no additives) are also included for the sake o f comparison. First, the addition of 5wt% B N 2 increases the extrusion pressure significantly (Figure 8.10). Surprisingly, this increase in pressure has a positive and significant effect on the tensile strength o f the final dried extrudate. The addition of 2 wt% o f B N 2 also increases the extrusion pressure at higher shear rates, but the tensile strength does not increase significantly. On the other hand, the addition of 2wt% of CTF5 increases the extrusion pressure, although the tensile strength does not increase accordingly. Finally, addition of 5wt% of C T F 5 decreases the extrusion pressure possibly by enhancing slip effects. 160 CO Q. •— 3 CO CO C o '(/> 3 X LU 75 70 65 60 55 50 h 45 t-40 i i i i I i i i i I i i i i I i i i i I i i i i I i i 2ct=30°; L/D = 20; RR = 352:1; T = 35°C • 1000 I i i — • — F104 HMW + Isopar M A F 1 0 4 HMW & 2% BN2 +Isopar M j — • — F104 HMW & 5% BN2 + Isopar M J — • — F104 HMW & 2% CTF5 + Isopar M —T— F104 HMW & 5% CTF5 + Isopar M * 1 • • • • 1 * * * • 1 * • • • 2000 3000 4000 5000 6000 7000 Apparent shear rate (s~) Figure 8.10: Extrusion pressure of F104 H M W + B N blends extruded at 35°C co CL c co 'to C 8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 1000 • A I | I I I I | I I I I | • I • I 2a=30°; L/D = 20; RR = 352:1; T = 35°C F104HMW+ Isopar M F104 HMW & 2% BN2 + Isopar M F104 HMW & 5% BN2 + Isopar M F104 HMW & 2% CTF5 + Isopar M F104 HMW & 5% CTF5 + Isopar M • * 1 * * • • 1 * • • • 1 • 2000 3000 4000 5000 6000 7000 Apparent S h e a r Rate (s") Figure 8.11: Tensile strength of F104 H M W + B N blends extruded at 35°C. 161 The addition of nanoclays, Figures 8.12 to 8.15, has a similar effect as that of B N 2 . In fact, the blend at 5% o f nanoclay extrudes at significantly higher pressure and the extrudates exhibit higher tensile strengths compared to those of the pure resin. It is worthwhile to notice thafeeven though the extrusion pressure increases with the inclusion of the additives, there is no effect on the appearance of the extrudates. In other words, that the extrudates do not exhibit any visible fracture or surface defects. 70 CO 0_ <D v. 3 (A in co i_ Q_ C o "55 ' 3 HI 65 \-60 55 i i I i i i i I i i -F104 HMW + Isopar M T F104 HMW & 2% I.44P + Isopar M A F104 HMW & 5% I.44P + Isopar M 50 1000 2a=30°; L/D = 20; RR = 352:1; T = 35°C • • • • • 2000 3000 4000 5000 6000 7000 Apparent Shear Rates (s*1) Figure 8.12: Extrusion pressure of F104 H M W + Nanomer® I.44P blends extruded at 35°C. 162 8.0 (0 CL C 2> <-» w _o '35 c CD H 7.5 h 7.0 p 6.5 h 6.0 h 5.5 \-5.0 i i i I i i | I I I I | I I I I | I I I I F104 HMW + Isopar M F104 HMW 8. 2% I.44P + Isopar M F104 HMW & 5% I.44P + Isopar M 2oc=30 ; L/D = 20; RR = 352:1; T = 35 C • * • • 1 • • • • 1 • * • * 1 • • * * 1 * * 1000 2000 3000 4000 5000 Apparent Shear Rate (s 1 ) 6000 7000 Figure 8.13: Tensile strength of F104 H M W + Nanomer® I.44P blends extruded at 35°C. 60 (0 CL 1< 55 h Oi v_ 3 CO CO <D CL C o "35 3 X LU 50 h 2a=30°; L/D = 20; RR = 352:1; T = 35°C / / A'' / • — • — F104 HMW + Isopar M . — • — F104 HMW + 5% PGV . A F104 HMW +2% PGV . 1000 2000 3000 4000 5000 6000 Apparent S h e a r Rate (s'1) 7000 Figure 8.14: Extrusion pressure of F104 H M W + Nanomer® P G V blends extruded at 35°C. 163 CO Q L O) c CO c -*-» CO _co '55 c CD 7.5 7.0 6.5 6.0 5.5 5.0 4.5 h 4.0 i i i • I i • i i I i i i i I i i i • I i i • i I i i i i 2ct=30°; L/D = 20; RR = 352:1; T = 35°C F104 HMW + Isopar M F104HMW + 5 % P G V F104HMW + 2 % P G V 1000 2000 3000 4000 5000 Apparent S h e a r Rate (s 1 ) 6000 7000 Figure 8.15: Extrusion pressure of F104 H M W + Nanomer® P G V blends extruded at 35°C. Figures 8.16 and 8.17 compare the effect of all the additives at different concentrations. Boron nitride seems to have a stronger effect on paste extrusion than that of the clays. LO-CO 1_ 3 CO V) CO c o 'co 3 i— -*-» X LU 75 70 65 60 55 k 50 h [ 2a=30°; L/D = 20; RR = 352:1; T = 35°C 45 • i I i I ' 1 ' 1000 2000 3000 4000 5000 Apparent S h e a r Rate (s~) • — Isopar M 2% BN2 O—5%BN2 " A 2% CTF5 & 5% CTF5 • - 2% I.44P , V — 5% I.44P • 2% PGV O 5% PGV 6000 7000 Figure 8.16: The effect of B N and clay addition on the extrusion pressure of F104 HMWpastes. 164 Figure 8.17: The effect of B N and clay addition on the tensile strength of F104 H M W pastes. Figures 8.18 and 8.19 depict the extrusion pressure and tensile strength of extrudates obtained from blending of F104 H M W with boron nitride or nanoclay and Isopar® G . The effect is essentially the same as was previously observed in Figures 8.10 to 8.13. The blend with Nanomer® I.44P extrudes at higher pressures and its tensile strengths increase accordingly. In all other cases the tensile strength decreases. Table 8.1 lists the mechanical properties of these extrudates at the shear rate of 5859 s ' . The tensile strength is generally lower than that of the paste with no additive. The elastic modulus of the blends with I.44P exhibit higher values, but their extensibility decreases. The addition of CTF5 at any concentration also decreases the elastic modulus of the extrudate. However, addition of 5 wt% C T F 5 slightly decreases the elastic modulus while its extensibility increases significantly. In general, it can be concluded that the incorporation of additives such as clays and boron nitride into the P T F E matrix, causes the extrudate to behave as a more brittle material. On the other hand, the addition of a specific type of boron nitride (BN2) was found to increase significantly both the extrusion pressure and the tensile strength of the P T F E extrudates. 165 Table 8.1: Mechanical properties of PTFE-additive blends + Isopar G extruded at different conditions. Additive Tensile Strength (MPa) Elastic Modulus (MPa) % Elongation at Break F104 HMW + Isopar® G, 2a = 30°, L/D = 20, RR = 352:1, yA = 5859 s No Additive 5.6 (0.2) 97.0(5.5) 90.5 (5.4) CTF5 @ 2 wt% 5.4 (0.2) 90.8 (7.9) 71.9(5.7) CTF5 @ 5 wt% 5.1 (0.1) 81.8(6.5) 122.5 (10.8) I.44P @ 2 wt% 5.5 (0.1) 103.1 (4.1) 74.6 (2.3) I.44P @ 5 wt% 5.8 (0.2) 104.9(2.1) 59.3 (5.8) 65 CO Q . 55 50 £ 3 CO to o 0 . c o "(0 3 P. 45 40 i i i i I i i i i I i i i i I i i i i I 2a=30°; L/D = 20; RR = 352:1; T = 35°C i i i I i i i I • F104 HMW + Isopar G F104 HMW & 2% I44P + Isopar G F104 HMW & 5% I44P + Isopar G F104 HMW & 2% CTF5 + Isopar G • F104 HMW & 5% CTF5 + Isopar G • • * * * * * * * * * * * * 1000 2000 3000 4000 5000 6000 7000 Apparent S h e a r Rate (s 1 ) Figure 8.18: Extrusion pressure of blends of F104 H M W + Isopar® G and Boron Nitride. 166 CO Q . C co "55 c CO 8.0 7.5 7.0 6.5 6.0 : 5.5 -5.0 4.5 4.0 • I ' • • ' I 1 I i i i i I i i i i I i i i i — • — F104 HMW + Isopar G • F104 HMW & 2% I44P + Isopar G - A F104 HMW & 5% I44P + Isopar G — T — F104 HMW & 2% CTF5 + Isopar G — • - F104 HMW & 5% CTF5 + Isopar G 2a=30 ; L/D = 20; RR = 352:1; T = 35 C • • • • 1 • • • • 1 • * • • 1 • • • 1 * * * 1000 2000 3000 4000 5000 6000 7000 Apparent Shear Rate (s~) Figure 8.19: Tensile strength of blends of F104 H M W + Isopar® G and Boron Nitride. 8.5 Summary A series o f processing aids different from the isoparaflnnic lubricants commonly used have been tested in order to identify alternative enhanced processing aids. In addition, blends of different P T F E fine powder resins have been prepared and extruded in an attempt to improve the P T F E paste extrusion process. The pastes and blends prepared in the regular way were extruded under conditions that have been found to be optimum for the P T F E paste with isoparaflnnic lubricants and their mechanical properties were measured. First, 1:1 mixtures of P T F E resins (homopolymer + copolymer and copolymer + copolymer) were made and this was mixed with the lubricant to prepare the paste. In a second method, the respective pastes were first prepared prior to blending. Regardless of the way the blend was prepared, it was found that there is no significant effect on the extrusion conditions and the mechanical properties of the extrudates. In fact, these properties fall between those exhibited by the pure components. One possible reason for this behaviour is that all the resins used in this work have very similar particle size distributions. In a different experiment, a mixture of two isoparaflnnic lubricants (having different physical properties) were prepared and then incorporated with the resin to make up the paste. 167 Once again, the extrusion conditions and mechanical properties of the resulting extrudates fell between those of the pure components. The incorporation of additives into the resin-lubricant matrix yielded promising results. These additives are commonly used as polymer processing aids to reduce or eliminate surface fracture. The additives were added in different proportions, but the lubricant concentration was kept always constant, namely at about 18.7 wt% of lubricant. It was found that in the case of boron nitride, the presence of the additive increased the extrusion pressure and significantly improved the mechanical properties of the extrudates. However, not all the additives exhibited a beneficial effect. The addition of clay was found to decrease the elastic modulus of the extrudates and to increase the extensibility significantly. 168 CHAPTER 9 Conclusions, Recommendations and Contribution to knowledge 9.1 Conclusions The rheological properties of a number of polytetrafluoroethylene (PTFE) pastes were studied relevant to paste extrusion process. The effects of the physical properties of lubricants and the geometrical characteristics o f the extrusion die on the extrusion pressure and mechanical properties of the final extrudates were also examined. Liquid migration and preform inhomogeneities were studied as functions of the physical properties of the lubricants, and the level and duration of pressure applied. First, a number of lubricants were identified as suitable processing aids for the paste extrusion of polytetrafluoroethylene (PTFE). They were characterized in terms of both flow and surface properties. It was found that it is possible to alter the flow and surface properties of these lubricants independently. Thus, it became possible to study their relative effects on preforming and P T F E paste extrusion. Based on this study, it was concluded that preforming quality increases with increase of lubricant viscosity and with improvement in the wettability characteristics of the lubricant with P T F E . However, lubricant migration becomes important at longer times. Therefore, the applied pressure and its duration need to be optimized depending on the physical properties of lubricant. It was also found that the physical properties of the lubricants (viscosity and surface tension) play a significant role. First, the use of a lubricant having a higher viscosity can produce a more uniform preform as liquid migration is minimal. In addition, increasing the wettability of lubricant with P T F E produces better mixture/pastes. Furthermore, this has an effect on the preform preparation. Excellent wetting would produce a uniform preform even under extreme conditions. The physical properties of lubricants were found to play a significant role in the extrusion of P T F E pastes. Increasing the wettability of lubricant with P T F E and decreasing the lubricant viscosity causes a reduction in the extrusion pressure and an increase in the tensile strength o f the extrudates. It was also found that the geometrical characteristics o f dies also play a significant role in the process of paste extrusion. More specifically, the extrusion pressure increases with L/D ratio and reduction ratio, while it exhibits a minimum with the contraction angle at about 60°. These effects are also reflected in the mechanical properties of the 169 extrudates. The tensile strengths of dried and sintered extrudates exhibit optimum values at an L/D equal to about 20, and a reduction ratio equal to about 150, whereas they exhibit a minimum value at about 60°. Finally, it was found that a higher molecular weight resin produces stronger fibrils that account for the mechanical superiority of the final extrudate. Therefore, i f the objective is to prepare a product having a high tensile strength, a homopolymer of high molecular weight should be used in combination with a lubricant having a low surface tension such as HFE-7500 and minimum viscosity up to a certain value. To low a viscosity would produce a nonuniform preform. A s far as die selection concerns, this should have an L / D ratio of about 20, a reduction ratio of around 150 and a contraction angle of no more than 60°. The rheology of P T F E paste was found to be complex in relation to the paste extrusion process. The paste starts as a two phase fluid and behaves as a semisolid at the exit of the die due to the formation of fibrils. The rheology of the initial state and final states were studied in detail. The initial oversaturated suspension was found to exhibit yield stress which although small was measureable. Once this yield stress is exceeded, the structure breaks and flow is initiated. The viscosity then exhibits a shear thinning behaviour. The rheology of the final state can be approximated by an Ogden elastic body at least based on the available data. Plasticity effects are present, although it is believed that during extrusion due to the presence of lubricant large deformations of fibrilated zones are prevented i.e. perhaps due to significant slippage. Overall it was concluded that the rheology can be represented by a constitutive equation having the following form: * = . 0 " £ ) * p + [7.1] where T is the overall stress, ^ p is the contribution to the stress tensor from the presence of unfibrillated particles (initial state of the oversaturated suspension), T f the contribution to the stress tensor from the presence o f the fibrillated particles and £, represents the fraction of the fibrillated particles with £ = 0 representing an unfibrillated paste i.e. just preformed before subjected to flow and £ = 1 representing a fully fibrillated paste. This constitutive equation can be used for flow simulations provided that an equation for the dynamics of £ is also developed. Regarding the use of additives, different processing aids used with molten polymers were tested. Promising results are reported in this work. Due to the presence of these additives the steady-state extrusion pressures experience an incremease. However, the mechanical 170 properties of the extrudates are also affected in various manners. The presence of boron nitride increases the tensile strength of the extrudate wheeras the presence of clay decrease their elastic modulus while increasing their extensibility. 9.2 Contributions to Knowledge Several novel contributions to knowledge have resulted from this research work. These are identified as follows. 1. The current commercial procedure for P T F E paste extrusion has been analyzed in detail, and the physical significance of each experimental aspect of the process has been investigated. Specific variables have been explored in an attempt to improve process efficiency. These are more related to the type o f lubricant recommended for use. 2. The preforming behavior of P T F E pastes has been studied as a function of the physical properties of the lubricants. The results provide an understanding on how various operating variables affect the quality o f P T F E preforms. 3. The rheological behavior of P T F E pastes has been studied experimentally at both states before and after the extrusion. Effects of various operating variables have been determined and discussed. 4. The effects of various operating variables on the quality of P T F E paste extrudates have been analyzed. The results provide an understanding of the role of fibrillation in defining the final product properties. With such understanding, it is possible to optimize the' extrusion operating variables in order to produce extrudates that are commercially acceptable, with the ultimate objective of reducing the amount of process rejects. The results can also be used as a basis for resin selection, for a desired particular end use. Overall this work has contributed to the fundamental knowledge of P T F E paste extrusion, which is still in its infancy as far as research is concerned. Undoubtedly, more in-depth studies need to be performed in the future to completely unravel the science behind the process. However, many of the findings in this work have provided significant initial steps towards a better macroscopic and microscopic understanding of the process and, therefore, allowed the commercial implementation of P T F E paste extrusion to be carried out with greater confidence. The introduction of the slit die to produce rectangular-shape extrudates has facilitated the extensional rheology of the samples allowing a different approach in this area. 171 9.3 Recommendations for Future Work Several important aspects of P T F E paste extrusion are yet to be studied. These are recommended below, as possible objectives for future research work. 1. The one-dimensional mathematical model developed by Ariawan (2000) to predict the flow of P T F E pastes is dependent on several material constants which can be studied by using rheological experiments. This way the model can be validated and become more useful. Inconsistencies resulting from this exercise can be corrected by modifying the proposed model. 2. In order to make the rheological study of P T F E pastes more complete, the effects of other variables, such as resin particle size and its distribution ( if it is indeed possible to vary in practice) should be investigated in the future. The flow of P T F E pastes through a hyperbolic die and a crosshead die for a wire coating process are also interesting and commercially useful. 3. Flow simulations should be performed by utilizing the proposed constitutive equation. This way the usefulness of this model can be validated and perhaps this w i l l lead to development of other advanced models. 4. The maximum pressure that occurs during start up of pressure transient in paste extrusion needs further investigation. 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The parameters are found by using simplex % method c a l l e d by N_M function format short g D = csvread('hel_13.txt'); % I n i t i a l values x = D ( : , l ) ; % Shear stress (MPa) y = D(:,2); % Extensional r a t i o , alpha np = 2; % Number of parameters q = (sqrt(np+1)-1)/(np*sqrt(2) ) ; p = q + 1/sqrt(2) ; K = [0 0;p q;q p]; [kopt,stage,k_plot,y_plot] = N_M(K,x,y); % Calculating the f i t t e d function value y_cal = f e v a l ( 1 go' ,kopt,x) ; % P r i n t i n g out f p r i n t f ( ' \ n f p r i n t f ( ' \ n f p r i n t f ( ' \ n f p r i n t f ( ' \ n f p r i n t f ( 1 f p r i n t f ( 1 \ n f p r i n t f ( ' \ n f p r i n t f ( 1 \ n f p r i n t f ( ' \ n f p r i n t f ( ' \ n f p r i n t f ( ' \ n f p r i n t f ( ' \ n f p r i n t f ( ' \ n the r e s u l t s Nelder-Mead Simplex Method \ 1) Parameter Values the Objective to Minimize \n' Function \ 1) _ \n' I \n' ) m n %7 %7 .4f .4f \n \n ,kopt (1)) ,kopt (2)) Number of Iterations %3 . Of \n' \n' \n' Minimum value of the Objective Function V) %6 . 3f \ 1 , y _ p l o t ( l e n g t h ( y _ p l o t ) ) ) f p r i n t f ( ' \ n f p r i n t f ( ' \ n Optimum Value of the \') f p r i n t f ( 1 \ n Function \',y_cal(length(y))) f p r i n t f ( ' \ n %6 . 3f ) , stage) \n' \n' ) % Ploting the r e s u l t s n = 1:stage; subplot(2,2,1); plot(n,k_plot(n,1),'b 1,n,k_plot(n,2),•r 1) t i t l e ( ' V a l u e of parameters at each i t e r a t i o n ' ) legend('m','n') xlabel('Number of i t e r a t i o n s ' ) ylabel('parameters ' ) subplot(2,2,2) ; plot(n,yjplot) t i t l e ( ' V a l u e of the Objective Function at Each Iteration') xlabel('Number of Iterations') ylabel('Value of the Objective Function') subplot(2,2,3) ; plot(x,y, 'r',x,y_cal, 'b ' ) 179 legend('Observed Data','Fitted Data') title('Comparison Between Observed and F i t t e d Data 1) xlabel('alpha = L/LO') y l a b e l ( 1 Sigma (MPa) 1 ) % N_M.m i s program to use Nelder-Mead (simplex) method % to f i n d the parameters that best f i t experimental data function [kopt, stage, k j p l o t , y_jplot] = N_M(K,x,y) % Defining the Nelder-Mead c o e f f i c i e n t s f o r the basic operations alpha =1; % R e f l e c t i o n c o e f f i c i e n t betha =0.5; % Contraction c o e f f i c i e n t gamma =2; % Expansion c o e f f i c i e n t n = size(K,2); % Number of independent variables i n the objective function m = n + 1; % Number of v e r t i c e s of the polyhedron % Nelder-Mead method s t a r t s stage = 0; c r i t e r i a = 1; epsilon = le-6; nstages = 3000; while (stage < nstages) & ( c r i t e r i a > epsilon) % Evaluating the function i n each v e r t i x of the simplex for i = l:m S(i) = f e v a K ' f o ' ,K(i, :) ,x,y) ; end % Setting the i n i t i a l optimum values to f i n d those that optimize the function sh = S(1);h = 1; kh = K(h, ss = S(1);s = 1; ks = K(s, s i = S(1);1 = 1; k l = K ( l , % Temporary maximum % Temporary second maximum kopt = k l ; % Temporary minimum % Finding the maximum and minimum value of the function for i = 2:m i f S(i) > ss i f S(i) > sh S S = sh; S = h; ks = K(s,:); sh = S ( i ) ; h = i ; kh = K(h,:); else ss = S (i) ; S = i ; ks = K(s, :) ; end e l s e i f S(i) < s i s i = S (i) ; 1 = i ; k l = K ( l , :),; kopt = k l ; end end k_plot(stage+1,:) = kopt; y_plot(stage+1) = s i ; 180 % C a l c u l a t i n g the coordinates of the centroid of the simplex for i = l : n sumk = 0; for j = l:m sumk = sumk + K ( j , i ) ; end ko(i) = (sumk - kh ( i ) ) / n ; end kr = ko + alpha * (ko - kh); through the centroid sr = f e v a l ( ' f o ' , k r , x , y ) ; at the r e f l e c t i n g points % R e f l e c t i n g the xh point % and evaluating the function i f sr < s i ke = gamma * kr + (1-gamma)*ko; se = feval('fo',ke,x,y); the expanding points i f se < s i kh = ke; K(h,:) = kh; sh = se; else kh = kr; K(h,:) = kh; sh = sr; end e l s e i f sr < ss kh = kr; K(h,:) = kh; sh = sr; else i f sr < sh kh = kr; K(h,:) = kh; sh = sr; kc = betha * kh + (l-betha)*ko; sc = feval('fo',kc,x,y); the contracting points i f sh > sc kh = kc; K(h,:) = kh; sh = S C ; else for i = l:m K(i,:) = (K(i,:)+kl)/2; end end else for i = l:m K(i,:) = (K(i,:)+kl)/2; end end end % Expanding the polytope % Evaluating the function at % Contracting the polytope % Evaluating the function at % Shrinking the polytope % C a l c u l a t i n g the c r i t e r i a of converge sumconv = 0; for i = l:m sumconv = sumconv + ( f e v a l ( ' f o ' , K ( i , : ) , x , y ) - f e v a l ( 1 f o 1 , k o , x , y ) ) " 2 ; end c r i t e r i a = (sumconv/ra)A0.5; stage = stage + 1; kopt = k l ; 181 end function z = f(k,x,y) n = length(x); sum = 0 ; for i = l : n T i l = k ( l ) * ( x ( i ) A ( k ( 2 ) -1) - x ( i ) * - ( l + k ( 2 ) / 2 ) ) ; sum = sum + ( y ( i ) - T i l ) * 2 ; end z = sum; function z = g(k,x) n = length(x); for i = l : n z(i) = k ( l ) * ( x ( i ) A ( k ( 2 ) - 1 ) - x ( i ) A - ( l + k ( 2 ) / 2 ) ) ; end 182 

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