RHEOLOGY AND PROCESSABILITY OF TEFLON FEP RESINS FOR WIRE COATING by E V G U E N I E . ROZENB A O U M Candidate of Technical Science, Moscow University of Chemical Technology, 1993 Dip. Chem. Eng., Moscow University of Chemical Technology, 1988 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Faculty of Graduate Studies Department of Chemical and Bio-Resource Engineering We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH COLUMBIA July 1998 © 1998 Evgueni E. Rozenbaoum In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date Pc^r. / V . / ? 9 / DE-6 (2/88) RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING ii Abstract Experiments were carried out in both parallel plate and capillary rheometers for a variety of tetrafluoroethylene/hexafluoropropylene (TFE/HFP) copolymers and TFE/F£FP/per-fluoro(alkyl vinyl ether) (TFE/HFP/PAVE) terpolymers, also known as Teflon® FEP polymers, having different molecular weights and compositions (FfFP and PAVE content). The critical conditions for the onset of melt fracture and the influence of temperature, molecular weight, and composition of the resins are determined. The critical molecular weight for the onset of entanglements was found to be about 100,000, a value much higher than those previously reported. The relationships between the processability of the wire coating Teflon® FEP resins and their composition, viscosity, ability to crystallize, and melt elasticity were established. The experimental data were used for a thorough rheological modeling of the behavior of these resins. The latter includes calculation of their linear relaxation time spectra and nonlinear parameters using a multi-mode Phan-Thien and Tanner (PTT) constitutive equation. A new data analysis procedure based on a mathematical model for the nonisothermal capillary flow of polymer melts coupled with heat transfer is developed. The computer simulations proposed can be used to provide detailed velocity, temperature, and pressure distributions and to recover the parameters of the employed slip velocity model corrected for the effect of viscous heating. Finally, the effect of various processing aids on the processability of fluoropolymers and polyolefins during extrusion and wire coating was studied. It was found that polyethylene works as a processing aid in the extrusion of Teflon® FEP resins in the same way as fluoropolymers do in the extrusion of polyolefins. Finally, the processing additive based on a boron nitride (BN) composition was found to eliminate sharkskin melt fracture and postpone gross melt fracture to significantly higher shear rates for a variety of polymers. RHEOLOGY AND PROCESSABILITY OF TEFLON 1 1 ' FEP RESINS FOR WIRE COATING . i i i Table of Contents A B S T R A C T i i T A B L E O F C O N T E N T S i i i L I S T O F F I G U R E S v i L I S T O F T A B L E S x i i i A C K N O W L E D G E M E N T S x i v 1 I N T R O D U C T I O N 1 2 L I T E R A T U R E R E V I E W 5 2.1 C H E M I C A L S T R U C T U R E A N D P H Y S I C A L PROPERTIES O F F L U O R O P L A S T I C S 5 2 .2 R H E O L O G I C A L M E A S U R E M E N T S 6 2.2.1 Sliding Plate Rheometer 10 2.2.2 Parallel Plate Rheometer 10 2.2.3 Capillary Rheometer 12 2.3 F L O W C U R V E 17 2.4 M E L T F R A C T U R E 18 2.5 M E C H A N I S M S TO E X P L A I N M E L T F R A C T U R E 2 1 2.5.1 Mechanisms to explain sharkskin phenomenon 21 2.5.2 Die entry effects 23 2.5.3 Wall slip 24 2.6 P R E S S U R E D R I V E N F L O W OF M O L T E N P O L Y M E R S 2 9 2.6.1 Viscous Heating 29 2.6.2 System of Equations 31 2.6.3 Constitutive Equation and Relaxation Time Spectrum 31 3 O B J E C T I V E S 3 5 4 O S C I L L A T O R Y F L O W M E A S U R E M E N T S O N T E F L O N ® F E P R E S I N S 3 9 4.1 INTRODUCTION 4 0 4 .2 E X P E R I M E N T A L 4 2 4.2.1 Materials and Characterization 42 4.2.2 Rheological Measurements 44 4.3 R E S U L T S 4 5 4.3.1 Low Melting Point TFE/HFP Resins (Group A) 45 4.3.2 High Melting Point FEP Resins (Group B) 50 RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING iv 4.3.3 Terpolymers TFE/HFP/PAVE (Group C) 57 5 C A P I L L A R Y F L O W M E A S U R E M E N T S O N T E F L O N ® F E P R E S I N S 6 1 5.1 INTRODUCTION 6 1 5.2 E X P E R I M E N T A L 6 3 5.3 T H E B A G L E Y E N D C O R R E C T I O N 6 4 5.4 VISCOSITY 6 6 5.5 T H E F L O W C U R V E 6 7 5.6 T H E E F F E C T OF P R E S S U R E O N T H E F L O W C U R V E 7 0 5.7 W A L L SLIP 7 3 5.8 E X T R U D A T E DISTORTIONS 7 6 5.9 T H E O S C I L L A T I N G M E L T F R A C T U R E 7 9 5 . 1 0 A C O M P A R I S O N OF T H E P R O C E S S A B I L I T Y OF T H E T W O F E P R E S I N S 8 2 5 . 1 1 E F F E C T OF T H E M O L E C U L A R W E I G H T 8 4 5 . 1 2 E F F E C T OF T H E P A V E C O N T E N T 8 6 6 R H E O L O G I C A L C H A R A C T E R I Z A T I O N O F T E F L O N ® F E P R E S I N S 8 8 6.1 INTRODUCTION 8 8 6.2 M E T H O D OF E V A L U A T I N G R E L A X A T I O N T I M E S P E C T R U M 92 6.3 R H E O L O G I C A L C H A R A C T E R I Z A T I O N U S I N G R E L A X A T I O N S P E C T R A 9 7 6.3.1 A Method to Estimate the Critical Molecular Weight 97 6.3.2 The Relaxation Spectrum ofTFE/HFP Copolymers 101 6.4 CONSTITUTIVE M O D E L I N G 106 7 M O D E L I N G O F C A P I L L A R Y F L O W O F M O L T E N P O L Y M E R S I l l 7.1 INTRODUCTION I l l 7.2 M A T H E M A T I C A L M O D E L 114 7.3 P H Y S I C A L PROPERTIES OF T H E P O L Y M E R S STUDIED 118 7.4 N U M E R I C A L A N A L Y S I S A N D R E S U L T S 119 7.5 D A T A A N A L Y S I S T E C H N I Q U E . . . . .127 7 .6 INTERPRETATION O F E X P E R I M E N T A L D A T A 129 7.6.1 Polypropylene 129 7.6.2 Linear Low Density Polyethylene 142 7.6.3 High Density Polyethylene 146 7.6.4 Teflon®FEP 149 8 E X T R U S I O N O F M O L T E N P O L Y M E R S W I T H P R O C E S S I N G A I D S 1 5 3 8.1 INTRODUCTION 154 RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING V 8.2 POLYETHYLENE AS A PROCESSING AID IN THE EXTRUSION OF TEFLON® F E P 156 8.2.1 Experimental Evidence 156 8.2.2 Mechanism 158 8.2.3 Transient Coating Experiments 159 8.3 EXTRUSION OF FLUOROPOLYMERS AND POLYOLEFINS WITH BORON NITRIDE AS APROCESSING AID 163 5.3.1 Experimental Evidence 163 8.3.2 Extrusion Experiments 164 8.3.3 Polyolefins 166 8.3.4 Fluoropolymers 172 8.3.5 Mechanism 177 8.3.5.1 Change in Rheology 178 8.3.5.2 Effect of the Die Geometry 181 8.3.5.3 Wall Slip 183 8.4 THE COMBINED EFFECT OF B N AND TEFLON® ON THE PROCESSABILITY OF POLYOLEFINS ... 185 9 C O N C L U S I O N S A N D C O N T R I B U T I O N S T O K N O W L E D G E 189 9.1 CONCLUSIONS 189 9.2 CONTRIBUTIONS TO KNOWLEDGE 191 9.3 RECOMMENDATIONS 193 R E F E R E N C E S 195 N O T A T I O N 205 RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING v i List of Figures Figure 2 -1 Simple shear flow 7 Figure 2-2. Velocity profiles in simple shear under no-slip (left) and slip conditions (right) 8 Figure 2-3. Simple extension 8 Figure 2-4. Schematic diagram of the shear stress transducer 10 Figure 2-5 Parallel plate rheometer 11 Figure 2-6 Capillary rheometer 13 Figure 2-7. Wall pressure distribution for capillary flow (from Dealy, 1982) 15 Figure 2-8. Bagley plot for determining the end correction 16 Figure 2-9 A typical apparent flow curve of a linear polymer 17 Figure 2 -10 . How curves under slip condition 26 Figure 2 -11 Mechanical analog of the generalized Maxwell model 33 Figure 4 - 1 . The storage and loss moduli, G \co) and G"(a>), of the TFE/HFP copolymers of Group A (Table 4-1) at 200°C 46 Figure 4 -2 . The complex viscosity \r}*i.a>)\ of the TFE/HFP copolymers of Group A at 200°C. The zero-shear viscosity is clearly obtained for all resins of this group 47 Figure 4 - 3 . The normalized complex viscosity \n*(co)\/t]o of the TFE/HFP copolymers of Group A at 200°C 48 Figure 4 -4 . The molecular weight dependence of the zero-shear viscosity n0 of TFE/HFP copolymers (Group A)at200°C 49 Figure 4 -5 . Master curves of the storage modulus G '(co), loss modulus G '(a), and complex viscosity | ?7*(), and loss modulus, G\a), of Teflon® FEP-2 copolymer at the reference temperature of 300°C with preheating at 330°C 54 RHEOLOGY AND PROCESSABILITY OF TEFLON18 FEP RESINS FOR WIRE COATING v i i F i g u r e 4-8 . The horizontal shift factor, aT, resulted from the application of the time-temperature superposition of dynamic linear viscoelastic experimental data for Teflon® FEP-2 copolymer 55 F i g u r e 4 -9 . The dependence of the zero-shear viscosity of the TFE/HFP copolymers of Group B onMw at 300°C (present work; TumineUo, 1989) and 340°C (Wu, 1985) 56 F i g u r e 4 -10 . The storage modulus, G '(ca), loss modulus, G '(co), and complex viscosity, | TJ*\, of Teflon® FEP terpolymers (Group C) at 300°C with preheating at 330°C 58 F i g u r e 4 - 1 1 . Viscosity of Teflon FEP resins (Group C) measured during programmed cooling at 0.1 rad/s 59 F i g u r e 5 -1 . The Bagley end correction of resin FEP 4100 at 325 °C as a function of the apparent shear rate 64 F i g u r e 5-2. The Bagley end correction of resin FEP 4100 at 325 °C as a function of the wall shear stress 65 F i g u r e 5-3 . The reduced viscosity of resins FEP 3100 and 4100 at 325 °C and ambient pressure 66 F i g u r e 5-4. A typical flow curve of resin FEP 4100 at 350 °C using a capillary die having a diameter of 0.762 mm and a length-to-diameter ration of 40. The various flow regions are also illustrated 68 F i g u r e 5-5 . The effect of pressure on the flow curves of resin FEP 4100 at 350 °C using capillary dies having a diameter of 0.762 mm and various length-to-diameter ratios 70 F i g u r e 5-6. Pressure-corrected flow curves of resin FEP 4100 at 350 °C 72 F i g u r e 5-7. The effect of the capillary diameter on the flow curve of resin FEP 4100 at 350 °C. Wall slip is present in the regions where the flow curve becomes diameter dependent 74 F i g u r e 5-8. The effect of the capillary diameter on the flow curve of resin FEP 3100 at 325 °C. Wall slip is present in the regions where the flow curve becomes diameter dependent 75 F i g u r e 5-9. Representative photographs to illustrate the extrudate appearance of FEP 4100 extrudates in the five flow regions 77 F i g u r e 5 -10 . The effect of temperature on the flow curve of resin FEP 4100. Note the strong effect of T on the superextrusion flow region 78 F i g u r e 5 -11 . Pressure drop oscillations during capillary extrusion of resin Teflon FEP 4100 at 350 °C. Note that the frequency of pressure drop oscillations increases with decrease of the material in the barrel 79 RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING .viii F i g u r e 5 -12 . The period of oscillations as a function of the volume of polymer (FEP 4100) in the rheometer reservoir for three capillary dies having different L/D ratios and a constant diameter at 350 °C 80 F i g u r e 5 -13 . A repeat of the experiment plotted in Figure 5-11. Instead of persisting oscillations, a stable response is obtained 81 F i g u r e 5-14. A comparison of the flow curves for two FEP resins (FEP 3100 and FEP 4100) at 325 °C... 83 F i g u r e 5 -15 . The effect of molecular weight on the flow curve of TFE/HFP copolymer resins (FEP-1, 2, and 3 of Group B in Table 4-2) 85 F i g u r e 5-16 . The effect of PAVE content on the flow curve of TFE/HFP/PAVE terpolymer resins (TFE/HFP/PAVE-1, 2, and 3 of Group C in Table 4-3) 86 F i g u r e 6 -1 . The standard deviation between the best possible fit and data. The fit improves when the number of Maxwell modes increases. Above a certain number of modes, the fit does not improve much further and the problem becomes ill posed (from Winter et al, 1993) 90 Figure 6 -2 . Storage and loss moduli for Dowlex 2049 at 200°C. Solid lines correspond to fitting obtained by means of UBCFIT software 94 F i g u r e 6-3 . Dependence of the standard deviation on the number of relaxation mode 95 F i g u r e 6-4. Relaxation time spectrum for Dowlex 2049 at 200°C (8 modes) 95 F i g u r e 6 -5 . Storage and loss moduli for star polymer polybutadiene 12807 (Vlassopoulos et al., 1997). Solid lines represent the fit obtained by means of UBCFIT software 96 F i g u r e 6-6. Dependence of the standard deviation on the number of relaxation mode for star polymer PB 12807 96 F i g u r e 6-7. Relaxation time spectrum for PB 12807 at -83°C. Comparison of the UBCFIT and IRIS spectra 96 F i g u r e 6-8 . The storage modulus G\a>) of the TFE/HFP copolymers of Group A at 200°C. The solid lines represent the fit with the parsimonious (PM) spectrum. The dash-dotted lines are the fit with the BSW spectrum with stretched exponential cut-off calculated from the full set of experimental data. Finally, the dotted lines are the fit with the BSW spectrum to the terminal zone data points (closed symbols). The plateau modulus determined from the data analysis is also drawn as reference 99 RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING ix Figure 6-9. The loss modulus G"(o) of the TFE/HFP copolymers of Group A at 200°C. The solid lines represent the fit with the parsimonious (PM) spectrum. The dash-dotted lines are the fit with the BSW spectrum with stretched exponential cut-off calculated from the full set of experimental data. Finally, the dotted lines are the fit with the BSW spectrum to the terminal zone data points (closed symbols) 100 Figure 6 -10 . Comparison of the continuous BSW (continuous lines) and the discrete parsimonious (PM) spectra of the TFE/HFP copolymers of Group A 102 Figure 6 -11 . The molecular weight dependence of the longest relaxation time of the TFE/HFP copolymers of Group A calculated from the parsimonious (PM) model 102 Figure 6 -12 . The discrete parsimonious (PM) spectra of the TFE/HFP copolymers of Group B (FEP resins) 103 Figure 6 -13 . The storage modulus, G \a>), of the TFE/HFP copolymers of Group B at 300°C. The dashed lines represent the fit with the parsimonious (PM) spectrum, while the solid lines are the fit with the BSW spectrum using stretched exponential cut-off. 104 Figure 6 -14 . The loss modulus, G"(a), of the TFE/HFP copolymers of Group B (FEP resins) at 300°C. The dashed lines represent the fit with the parsimonious (PM) spectrum, while the solid lines are the fit with the BSW spectrum using a stretched exponential cut-off .105 Figure 6 -15 . The dynamic moduli mastercurves for Teflon® FEP 4100 at rrey=300°C. Solid lines represent the relaxation spectrum fit 108 Figure 6 -16 . The complex, shear, and extensional viscosity of Teflon® FEP 4100. Solid lines represent the fit obtained by means of a 7-mode PTT constitutive equation ....110 Figure 7-1. Calculated flow curves for a hypothetical material having physical properties listed in Table 7-2 under the influence of a slip boundary condition (slip with no viscous heating case) 121 Figure 7-2. Calculated flow curves for a hypothetical material having physical properties listed in Table 7-2 under the influence of viscous heating effects (no slip with viscous heating case) 122 Figure 7-3. Calculated flow curves for a hypothetical material having physical propertieslisted in Table 7-2 under the influence of slip and viscous heating effects (slip with viscous heating case) 124 Figure 7-4. The effect of viscous heating on slip velocity measurements by means of Mooney plot 125 RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING X Figure 7-5. Experimental and calculated flow curves for a polypropylene resin for three capillary dies having the same L/D ratio of 40 and various diameters 130 Figure 7-6. Experimental and calculated flow curves for a polypropylene resin for three capillary dies having the same diameter and various L/D ratios 132 Figure 7-7. Calculated axial slip velocity, wall shear stress, pressure and average temperature rise in the capillary flow of a polypropylene resin for three dies having the same diameter and various L/D ratios 135 Figure 7-8. Calculated axial slip velocity, wall shear stress, pressure and average temperature rise in the capillary flow of a polypropylene resin for three dies having the same L/D ratio and various diameters 137 Figure 7-9. Calculated radial temperature profiles at the die outlet in the capillary flow of a polypropylene resin for dies having various LID ratios and diameters 138 Figure 7-10. Calculated slip velocity of a polypropylene resin as a function of wall shear stress for capillary dies having various L/D ratios 140 Figure 7-11. Experimental flow curves and those calculated in the absence of wall slip for a polypropylene resin for three capillary dies having the same L/D ratio of 40 and various diameters 141 Figure 7-12. Experimental and calculated flow curves for a linear low density resin (Dowlex 2049) for three capillary dies having the same L/D ratio of 40 and various diameters 144 Figure 7-13. Experimental and calculated slip velocities of a linear low density resin (Dowlex 2049) as a function of wall shear stress for capillary dies having various L/D ratios 145 Figure 7-14. Slip velocity, wall shear stress, and pressure profiles along a capillary die 147 Figure 7-15. Apparent flow curves for Sclair 56B at 180 ° C with capillaries of various diameters and LID=AQ; experimental and calculated 148 Figure 7-16. Sliding friction curve 150 Figure 7-17. Experimental and calculated flow curves for Teflon® FEP 4100 for three capillary dies having the same L/D ratio of 40 and various diameters 151 Figure 8 - 1 . Flow curve of linear polyethylene (PE) and that of polyethylene containing 250 ppm fluoropolymer (from Stewart etal., 1993) 156 RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING xi F i g u r e 8 -2 . The effect of the addition of 0.1 % of polyethylene on the flow curve of resin FEP 4100 at 350 °C 157 F i g u r e 8 -3 . The effect of the addition of 0.1 % of polyethylene on the transient response in the capillary extrusion of FEP 4100 at 325 °C, fA =104.2 s\ L/D=40 andD=0.762 mm 160 F i g u r e 8-4. The effect of the apparent shear rate on the time required to obtain steady state operation in the capillary extrusion of FEP 4100 with the addition of 0.1 % of polyethylene ( 7=325 °C, f A =347.2 s'\ Z/D=40 and £>=0.762 mm). To see the effect compare with Figure 8-3 161 F i g u r e 8 -5 . The effect of the L/D ratio of the capillary die on the time required to obtain steady state operation in the capillary extrusion of FEP 4100 with the addition of 0.1 % of polyethylene ( 7=325 °C, ^=104.2 s-\Z/£>=10andD=0.762mm) 162 F i g u r e 8-6. The effect of the diameter, D, of the capillary die on the time required to obtain steady-state operation in the capillary extrusion of FEP 4100 with the addition of 0.1 % of polyethylene ( 7>325 °C, yA =104.2 s"1, L/D=40 and£>=0.508 mm) 162 F i g u r e 8-7. Structure of BN 163 F i g u r e 8-8. Crosshead die for wire coating (from Buckmaster et al., 1997) 165 F i g u r e 8 -9 . The flow curves for PE Exact 3128 without and with boron nitride obtained in a rheometer with a capillary die having I/£>=40 and D=0.762 mm at 163 °C 167 F i g u r e 8 -10 . The apparent flow curves for PE Exact 3128 without and with boron nitride obtained i n a rheometer with Nokia Maillefer crosshead having 3.00 mm die and 1.52 mm tip at 163 °C 168 F i g u r e 8 - 11 . The effect of the boron nitride concentration on the processability of PE Exact 3128 in an Entwistle extruder with Nokia Maillefer crosshead having 3.00 mm die and 1.52 mm tip at 163 °C 170 F i g u r e 8 -12 . The effect of the boron nitride concentration on the processability of PE Exact 3128 in an extruder with the crosshead having 3.00 mm die and 1.52 mm tip at 204 °C 171 F i g u r e 8 -13 . Extrudate samples of metallocene PE Exact 3128 at 163°C: a) sharkskin for pure PE at yA =80 s"1; b) gross melt fracture for pure PE at f A =800 s"1; c) smooth extrudate for PE with 0.01% BNat ^=800s-' 172 RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING x i i F i g u r e 8-14 . The effect of boron nitride on the processability of Teflon FEP 100 in an Entwistle extruder with the crosshead Nokia Maillefer having 3.00 mm die and 1.52 mm tip at 371 °C 173 F i g u r e 8 -15 . Extrudate samples of Teflon® FEP 100 at 371°C: a) sharkskin for pure PE at fA =320 s'1; b) gross melt fracture for pure PE at yA =4000 s"1; c) smooth extrudate for PE with 0.01% BN at ^=4000s_1 174 F i g u r e 8 -16 . The effect of boron nitride on the processability of Teflon® FEP 4100 in an Entwistle extruder with the crosshead Nokia Maillefer having 3.00 mm die and 1.52 mm tip at 371 °C 175 F i g u r e 8 -17 . Teflon® FEP 4100 insulation samples obtained in 45 mm extruder with the crosshead having a 3.81 mm die and 1.905 mm tip: a) virgin resin; b) with the addition of 0.1% BN 177 F i g u r e 8 -18 . Dynamic moduli and complex viscosity of metallocene PE Exact 3128 (with and without BN) a t l 6 3 ° C 178 F i g u r e 8 -19 . Shear stress decay coefficient, r/~ (t, y)/r/(f), for metallocene PE Exact 3128 as a function of time (s) at 180°C and different shear rates. Solid lines correspond to the virgin resin, dashed lines to the resin with 0.05 wt. % BN, and dotted lines to 0.5 wt. % BN 180 F i g u r e 8 -20 . The effect of the die entrance angle on the extrudability of PE Exact 3128 in the presence of 0.5% BN 182 F i g u r e 8 - 21 . Comparison of the effect of BN and Viton® on the flow curves of the metallocene PE Exceed 116 obtained with a crosshead die at 204°C 184 F i g u r e 8 -22 . The effect of BN and Teflon APA additives on the processability of PE Exact 3128 obtained in a rheometer with Nokia Maillefer crosshead at 204°C 186 F i g u r e 8 -23 . The effect of BN and Teflon APA additives on the processability of PE Exceed 116 obtained in a rheometer with a Nokia Maillefer crosshead at 204°C 187 RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING List of Tables xiii T a b l e 4 - 1 . Molecular parameters of TFE/HFP resins with lower melting temperature (Group A) 43 T a b l e 4-2. Molecular parameters of TFE/HFP (FEP) resins with higher melting temperature (Group B).. 44 T a b l e 4-3. Molecular parameters of TFE/HFP/PAVE resins (Group C) 44 T a b l e 5-1. Circular dies used 63 T a b l e 6 -1 . Discrete relaxation spectrum for Dowlex 2049 at 200°C (6 modes only). Comparison with results obtained by IRIS software 94 T a b l e 6-2. Parameters in the PIT constitutive equation for Teflon® FEP 4100 109 T a b l e 7-1. Physical properties of the studied polymers 119 T a b l e 7-2. Constants in Equations (7-1)- (7-7) for a hypothetical polystyrene fluid 120 T a b l e 7-3. Constants for polypropylene 133 T a b l e 7-4. Calculated parameters of the slip velocity model, Equations (7-15) and (7-17) for PP ...133 T a b l e 7-5. Constants for LLDPE 143 T a b l e 7-6. Calculated parameters of the slip velocity model, Equations (7-15) and (7-17) for LLDPE ....143 T a b l e 7-7. Physical properties and constants in equations for Sclair 56B 146 T a b l e 7-8. Constants for Teflon® FEP 4100 150 T a b l e 7-9. Calculated parameters of the slip velocity model, Equation (7-18) for Teflon® FEP 4100 150 T a b l e 8-1. Influence of boron nitride concentration upon tubular extrudate surface smoothness (extrusion tests in the Entwistle extruder with Nokia Maillefer crosshead 3.0 mm die and 1.52 mm tip) 176 RHEOLOGY AND PROCESSABILITY OF TEFLON* 1 FEP RESINS FOR WIRE COATING xiv Acknowledgements I wish to express my sincere gratitude and appreciation to my supervisor, Prof. Sawas G. Hatzikiriakos, for his skillful guidance, support, and encouragement during the course of this study. His insights and ideas have greatly contributed to the quality of this work. I thank Dr. Charles W. Stewart for his suggestions and discussions during the course of this work. I also thank Stuart K. Randa for his cooperation on the boron nitride study and Dr. Kostas N. Christodoulou for his cooperation on the PTT modeling. This work was supported by the Natural Sciences and Engineering Research Council of Canada and by E. I. DuPont de Nemours & Co., Wilmington, DE, USA. I am also thankful to DuPont for providing me with the polymer samples and their hospitality while I was doing experiments in Wilmington. My colleagues from RheoLab at UBC helped me in various ways. I wish to thank Igor Kazatchkov, Alfonsius Budi Ariawan, and Divya Chopra for their helpful discussions and exchange of ideas. I thank my friends Igor Kazatchkov and Marek Labecki for their friendship during my stay in Vancouver. I thank my parents for their love and continuing support. Most of all, I thank my wife Victoria who has been a source of strength and motivation for success. RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 1 Introduction 1 Tuoropolymers are among the oldest high-performance polymers, dating from the discovery of polytetrafluoroethylene (PTFE) in 1938. Since their commercial introduction, annual worldwide production has grown to about 125 min lbs. (Feiring etal, 1994). Although their production is small compared to other commodity thermoplastics such as polyethylene and polypropylene, fluoropolymers are of great commercial and scientific interest due to their unique combination of properties. These include excellent chemical stability and dielectric properties, anti-stick characteristics, mechanical strength, and low flammability. Their most important uses are in electronics and electrical applications, especially for wiring insulation, chemical processing equipment, laboratory ware and tubing, material for roofing and houseware. PTFE, the homopolymer of tetrafluoroethylene (TFE), was introduced commercially by DuPont as Teflon® in 1950. It is insoluble in any known solvent, has a high melting point (about 327°C) and a very high melt viscosity. Therefore, its processing requires unusual methods such as cold pressing or sintering and paste extrusion. To provide similar product features with conventional processing, the Teflon® FEP (copolymers of TFE and hexafluoropropylene (HFP)) and Teflon® PFA (copolymers of TFE and perfluoropropylvinylether (PPVE)) fluoropolymers were developed by DuPont. These resins combine many of the best properties of Teflon® PTFE with the possibility of conventional melt processing due to their lower melting point. They are widely used as linings for pipe and chemical processing equipment, roll covers, and wire and cable CHAPTER 1 - INTRODUCTION RHEOLOGY AND PROCESSABILITY OF T E F L O N 8 FEP RESINS FOR WIRE COATING 2 coating, including aircraft hookup wire, plenum cable, fire alarm cable, flat cable and others. The wire-coating process is one of the most important applications of Teflon® FEP resins. This process involves a continuous extrusion for primary insulation of conducting wires with molten polymers for mechanical strength and environmental protection purposes. There are two basic types of coating dies used at present: pressure-coating and tube-coating dies. In the pressure-coating die, the wire is coated under pressure in the die. This technique is used usually for the application of the primary coating where good adhesion is important. In the case of the tube-coating die, the polymer coating is applied outside the die in the melt cone controlled by vacuum. Only the latter case is studied in this work. The design problems encountered in wire coating are related to melt flow under stable flow conditions at the highest possible extrusion rate and to production of a coating of specified thickness and uniformity. At some critical condition, polymers undergo flow instabilities which lead to a nonuniform coating. Similar problems are encountered in other types of extrusion processes even though the die geometry is different. It is well known that in many commercially important polymer processing operations, including wire coating, flow instabilities occur (Petrie and Denn, 1976). In these processes, a polymeric melt emerging from a slit or die often shows surface distortions at throughput rates above a critical value. As a result of these instabilities, the final product becomes unattractive and commercially unacceptable. Most of the previous studies on extrusion instabilities known collectively as melt fracture have examined the behavior of various types of polyethylenes (Ramamurthy, CHAPTER 1 - INTRODUCTION RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING .3 1986; Kalika and Denn, 1987; Hatzikiriakos and Dealy, 1992a,b), polyisoprenes and polybutadienes (Vinogradov et al, 1972a; Lim and Schowalter, 1989), polydimethylsiloxanes (El Kissi and Piau, 1990), but very few studies have reported on the processing of Teflon® fluoropolymer resins (Tordella, 1969). Flow instabilities in viscoelastic liquids have been the subject of several major reviews over the past decades (Petrie and Denn, 1976; Boudreaux and Cuculo, 1977; Tanner, 1985; Denn, 1990; Larson, 1992). Although melt fracture was first observed decades ago (Nason, 1945), there is still disagreement about the mechanisms causing these instabilities. The considerable complexity of the physical mechanisms, including the volume rheological properties and interaction with the solid boundaries governing polymer melt flow is the reason for the difficulties and controversies that still exist today. In many cases, the understanding of instabilities in polymer flow is speculative. However, it is evident that melt fracture is a complex phenomenon which may involve several independent mechanisms and much remains to be done in understanding its origins. It is obvious that the rate of production is limited by the onset of the above discussed flow instabilities. To increase the process output, one must eliminate melt fracture or postpone it to higher rates. The most common approach to achieve this objective is the use of processing aids. These are usually fluoroelastomers that can be added to the resin at concentrations of a few hundred ppm, e.g. at the time of processing or introduced as a masterbatch. These processing aids reduce the pressure required to extrude the resin at a particular flow rate and eliminate or postpone melt fracture to higher extrusion rates. CHAPTER 1 - INTRODUCTION RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING .4 The objective of this thesis is to perform a thorough rheological characterization of a number of Teflon® resins, study melt fracture in extrusion of these resins, and provide possible ways to eliminate or delay melt fracture in extrusion and wire coating by use of processing aids. Several aspects of numerical simulation and modeling of the flow of molten polymers in extrusion dies are also studied in this thesis. CHAPTER 1 - INTRODUCTION RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 5 2 Literature Review 2.1 Chemica l Structure and Phys ica l Properties of F luoroplast ics Fluoroplastics are a class of paraffinic polymers that have some or all of the hydrogen replaced by fluorine. They include polytetrafluoroethylene (PTFE), copolymer of tetrafluoroethylene and hexafluoropropylene (FEP), perfluoroalkoxy resin (PFA), amorphous perfluoroplastics (AF), and some others not examined in this thesis. PTFE is a completely fluorinated polymer manufactured by free radical polymerization of tetrafluoroethylene. PTFE is a linear crystalline polymer with a melting point CF 2 CF 2 — of about 327°C. Its density falls in the range between 2,130 and 2,190 kg/m3. PTFE has exceptional resistance to chemicals. Its dielectric constant (2.1) and loss factor are low and stable across a wide temperature and frequency range. FEP is produced by copolymerization of tetrafluoroethylene (TFE) and hexafluoropropylene (HFP). It has — C F 9 CFo CF-, C F — 2 2 2 predominantly linear chains. FEP has a CF 3 crystalline melting point of about 265°C determined by differential scanning calorimetry (DSC) and density of 2,150 kg/m3. It is a soft plastic with tensile strength, wear resistance, and creep resistance lower than those of many other engineering plastics. It is chemically inert with a low dielectric constant (2.1) over a wide range of frequencies and temperature. CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 6 PFA resins are a relatively new commercially available class of melt-processable fluoroplastics. They have a melting point of about 290°C and density in the range of 2,130 to 2,160 kg/m3. PFA is similar — C F 2 CF 2 C F — C F 2 CF 2 — to PTFE and FEP, although it has | O somewhat better mechanical I CnF 2 n + i properties than FEP at elevated temperatures. It is about equivalent to PTFE as far as chemical resistance is concerned. Recently, terpolymers of TFE, HFP, and PAVE) became commercially available. They combine the mechanical properties of FEP and PFA resins. AF is produced by random copolymerization of the cyclic monomer, perfluoro-2,2-dimethyldioxole, with TFE. It combines the outstanding chemical, thermal, and electrical \ properties of the crystalline perfluoropolymers 7~(CF2CF2)n—-m with high optical clarity, better mechanical properties, and solubility in selected fluorocarbon solvents. 2.2 Rheological Measurements Rheology is the science that deals with the way materials deform when forces are applied to them. The key words in this definition of rheology are deformation and force. To learn anything about the rheological properties of a material, one must either measure the deformation resulting from a given force or measure the force required to produce a given deformation. As a measure of force, one can use the stress, which is defined as the CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 7 ratio of the applied force to the area it acts on. Deformation can be described in terms of strain or rate of strain. There are two basic flows used to characterize polymers: shear and shear-free flows. For these two types of flow, the components of the stress and rate of deformation tensors take on a distinct form. The laboratory procedure that most closely approximates simple shear is to place a thin layer of fluid between two flat plates, clamp one of the plates in place, and move the second plate Figure 2-1 Simple shear flow at a constant velocity, u, as shown in Figure 2-1. Under no-slip conditions, the shear strain and shear rate can be written as follows: r<0 = £ h (2-1) r(f) = -h (2-2) The velocity field is given as: v x = f(f)y v y = v* = 0 The components of the rate of deformation tensor are: fa = f(f) fO 1 0} 1 0 0 0 0 0 (2-3) (2-4) and the stress tensor components are of the form: CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING .8 °) XX 0 yy 1° 0 (2-5) When slip is present, the true shear rate is less than the nominal shear rate, as illustrated in Figure 2-2. Figure 2-2. Velocity profiles in simple shear under no-slip (left) and slip conditions (right). For simple (uniaxial) extension (see Figure 2-3), the measure of deformation is the Hencky strain defined as: • F I SXyit) Figure 2-3. Simple extension e = ln (2-6) where SXi(t0) and SXi(i) are the initial length at time t0 of a material element measured in the direction of stretching and at a later time, t, after deformation has occurred, respectively. For a sample with initial length L0, this becomes: e = ln (2-7) The Hencky strain rate is defined as: CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING e = d\nL dt (2-8) The velocity field in uniaxial extension becomes: 1 . The components of the rate of deformation tensor are: 1 . —sz 2 (2-9) (is 0 0 > 0 -s 0 0 0 -e (2-10) and the stress tensor has only diagonal components: 0 °1 0 r,„, 0 yy 0 0 (2-11) Polymer melts are non-Newtonian fluids. This means that they do not obey Newton's law of viscosity, that is r = r/f (2-12) where rj is the constant viscosity. The complexity of the structure of these liquids makes it possible for the structure to vary with the shear rate, and this change in structure results in a change in the viscosity. The complex rheological behavior of polymers has two important practical consequences. First, no single rheological property gives a complete rheological characterization of the material, and, second, the measurement of a rheological property requires careful control. Below, a very short review of the rheological instruments and techniques used for rheological measurements in this thesis is presented. Detailed description of the rheological measurements and equipment can be found in Dealy (1982) and Dealy and Wissbrun (1990). CHAPTER 2- LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF T E F L O N 8 FEP RESINS FOR WIRE COATING 2.2.1 Sliding Plate Rheometer 10 For this work, an Interlaken sliding plate rheometer with a flush-mounted shear stress transducer was used. The basic features of a sliding plate rheometer are shown in Figure 2-4 (Giacomin et al., 1989). ^ ~ To amplifier Moving p i Figure 2-4. Schematic diagram of the shear stress transducer. An end plate is acted on by the shear stress generated by the fluid and transmits the resulting moment to the cantilever beam. To avoid melt penetration into the gap around the end plate, the deflection of the latter must be limited to very small levels. That is why a capacitance system was used, where a capacitor is formed by the probe acting as one of the plates, and the beam as the second plate. The advantages of the sliding plate are that there are no effects of pressure on measurements, and that the edge effects can be eliminated by measuring the shear stress locally (using flush-mounted shear stress transducer). The equations for simple shear presented in previous section are fully applicable to the analysis of the data obtained by means of this instrument. 2.2.2 Parallel Plate Rheometer Measurements of rheological properties at low shear rates and deformations are usually carried out in rotational rheometers such as the cone-and-plate or parallel-plate rheometers (Figure 2-5). In this work, a Rheometrics System IV parallel-plate rheometer CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 11 Fluid sample Pressure transducer was used. The two plates are mounted on a common axis of symmetry, and the sample is inserted in the space between them, The upper plate is rotated at a specified angular velocity co(t) and as a result the sample is subjected to shear. The motion of the upper plate is programmed, and the resulting torque, M , is measured (so called constant strain rheometers). Reproducibility of such a device lies within ±2%. Another mode of operation is fixing the torque and measuring the displacement (constant-stress rheometers). The most widely used experiments to determine the linear viscoelastic properties of polymers are small amplitude oscillatory shear tests. In this experiment, a sample of material is subjected to a simple shear ring deformation such that the shear strain is a Figure 2-5 Parallel plate rheometer function of time given by: y(t) = y0 sin() is the storage modulus and G"(co) is the loss modulus. These two quantities can be calculated from the amplitude ratio, Gd = cr0 /y0, and the phase shift, 8, as follows: G' = Gd cos(£) (2-16) G" = Gd sin(J) (2-17) This allows defining a complex modulus, G*(co), as follows: G\a) = G\) cos(otf) + rj"(a) sin(firf)] (2-19) thus defining the complex viscosity: 77* (a) = ri\co) - i7]"(co) (2-20) 2.2.3 Capillary Rheometer The most widely used type of melt rheometer is the capillary rheometer. This device (Figure 2-6) consists of a melt reservoir, or barrel, for melting the polymer and a plunger or piston that causes the melt to flow through the capillary die of known diameter, D, and length, L. The quantities normally measured are the flow rate, Q, (related to the piston speed) and the driving pressure, AP, (related to force on the piston that is measured by means of a load cell). Reproducibility of capillary rheometers is ±5%. CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 13 Constant force or constant rate Electric heaters' Teflon O-ring 1 Thermocouple Capillary die Figure 2-6 Capillary rheometer Capillary rheometers are used primarily to determine the viscosity in the shear rate range of 5 to 1,000 s'1. To calculate the viscosity, one must know the wall shear stress and the wall shear rate. For steady-state, fully-developed flow of an incompressible Newtonian fluid, the wall shear stress, l8, where X is the characteristic relaxation time, 8 is the spacing, and v is the relative velocity) was reached. In his opinion, this instability is the initial mechanism of polymer melt extrudate distortions. CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON 8 FEP RESINS FOR WIRE COATING .24 Most authors agree in claiming that, above a certain extrusion rate, the flow upstream of the contraction becomes unstable. These instabilities occur in the form of sudden pulsations, which were confirmed by visualization (Piau et al, 1990) and birefringence measurements (Tordella, 1969). They showed that such instabilities started along the upstream flow axis owing to the high elongation stresses that develop in this area. These instabilities trigger the phenomenon of gross melt fracture, which is often seen in the form of a regular helix oscillating at the same frequency as that of the pulsations of the upstream elongational flow (Piau et al, 1990). 2.5.3 Wall slip At this point, it is appropriate to refer to wall slip as a possible explanation of flow instabilities. It is convenient to use the word slip to describe events which are incompatible with the usual no-slip boundary condition of continuum mechanics. This phenomenon has been fully reviewed by several authors in the past (Petrie and Denn, 1977; Schowalter, 1988; Denn, 1992). It has long been recognized that polymer melts may violate the classical no-slip boundary condition of Newtonian fluid mechanics at solid surfaces. The classical experimental example of the effect of slip on the stability of the polymer shear flow is the spurt phenomenon (Vinogradov et al, 1972b). Deviations from the no-slip boundary condition were observed by many other investigators (Laun, 1982; Lin, 1985). Lim and Schowalter (1989) reported observations of slip for a polybutadiene melt using a heat transfer technique to record deviations from fully-developed flow. Kurtz (1984), Ramamurthy (1986) and Kalika and Denn (1987) showed that the flow curves obtained CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING 25 for various polyethylenes were discontinuous and exhibited a change in slope corresponding to the occurrence of surface melt fracture. Ramamurthy (1986) therefore associated the appearance of this phenomenon with a loss of adherence at the interface between the polymer and wall material. He also observed that the onset of surface distortion was dependent on the material of construction of the die, and it could be delayed or eliminated by changing the material of the die, although this is in contrast to observations for poly(vinyl alcohof)-borax solutions (Kraynik and Schowalter, 1981). This is a clear manifestation that the nature of the interface plays a crucial role in this phenomenon. The addition of fluoropolymers to the resin eliminates surface defects in spite of the fact that it promotes wall slip (Rudin et al, 1985). Thus, it is clear that the wall slip itself is not the primary cause of sharkskin. The same conclusion was drawn by Hatzikiriakos and Dealy (1991a,b) who carried out experiments in a sliding plate rheometer and later (1992a) in a capillary rheometer to determine the effect of the presence of two fluoropolymers on the slip velocity of a HDPE. They found that in one case slip increased while in the second case it decreased, although both fluoropolymers eliminated surface defects. The mechanism of wall slip is not yet clear. One hypothesis involves the well known theory of Vinogradov (Vinogradov et al, 1972b). He argued for a transition at some critical wall stress from a melt state to a so called "forced high elastic state" in which the polymer melt could be treated as a rubbery solid, and thus adhesive failure could be understood. Another mechanism is based on the ability of polymer molecules to entangle and form a physical network. According to Brochard and de Gennes (1992), CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING .26 there exists a monolayer of a polymer next to a wall where molecules are attached to the wall through several sites along their backbone. These chains are connected with the bulk of the material through entanglements. Under flow, the polymer molecules in the bulk are stretched, and in turn, they apply forces to the molecules at the interface through the entanglements. At some critical shear stress, some of the chains detach from the interface, and as a result, a weak slip boundary condition is obtained. This process depends on the interfacial conditions, e.g. the presence of fluoropolymer coatings which reduce polymer adsorption. If the shear stress is increased further, sudden disentanglement occurs, and a strong slip close to plug flow is obtained. Consequently, the polymer chains relax and entangle again, and this alternating transition between a weak and strong slip keeps on in a continuous fashion resulting in pressure drop oscillations in capillary flow. This flow mainly depends on the molecular characteristics of the polymer, e.g. the number of entanglements. The traditional way of inferring / A\ I Al I A3 f A Figure 2-10. Flow curves under slip w a l 1 slip is the so called Mooney method condition (Mooney, 1931) based on an apparent die diameter dependence of the rheological measurements. According to this technique, the flow curves determined with a series of capillaries having the same length-to-diameter ratio (to eliminate the pressure effect) and different diameters diverge at the critical shear stress for the onset of slip as is shown in Figure 2-10. Then the apparent shear rate, yA, in a cylindrical die is given by the following formula: CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 27 rA = rA,s+*^ (2-34) where yAS is the real wall shear rate corrected for slip and us is the slip velocity. For a given shear stress, yA is linearly dependent on l/D with slope equal to 8«s. Therefore, by using dies of different radii, the slip velocity can be determined. Obviously, this technique is indirect and it does not take into account possible temperature effects on the apparent flow curve. It should also be noted that there is discrepancy in the values of slip velocity calculated by various authors. Thus the slip velocity measured by Atwood and Schowalter (1989) for FJDPE using a hot-film probe is very high compared to that reported by Ramamurthy (1986). This variation in the reported values seems to be due to differences in experimental methods and poor control of conditions at the interface. The most reliable data on the slip velocities could be obtained by direct measurements of velocity profiles near the die wall by using laser velocimetry or a radioactive tracer technique (Binnington et al., 1983). However, there is a lack of such experimental studies for polymer melt flows. Gait and Maxwell (1964) performed direct measurements of velocity profiles in capillary flows of molten branched polyethylenes using a particle tracer technique. Migler et al. (1993) used a fluorescent optical technique to measure slip velocities directly. Both studies were carried out at shear stresses, which were to small to be of much interest to polymer processing. Several attempts have been made to model the slip velocity. For this purpose, power-law expressions relating the slip velocity to the wall shear stress have been proposed by several investigators. Hill et al. (1990) developed a framework based on the theory of elastomer adhesion. Agreement between the theory and the slip velocity data reported by Kalika and Denn (1987) is remarkably good. Hatzikiriakos and Dealy CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 2 8 (1992a) formulated a theory of wall slip based on an extension of a kinetic adsorption/desorption analysis first proposed by Lau and Schowalter (1986). The theory fits their data from both capillary and plate rheometers quite well. Stewart (1993), using a rate-activation energy theory, derived an expression for the slip velocity which includes a hyperbolic sine term in place of the " o V " term. It also includes a geometric-mean approximation for the work of adhesion that incorporates the surface energetics of the polymer and presumed coating layers explicitly into the model. Agreement with the data of both Kalika and Denn (1987) and Hatzikiriakos and Dealy (1992a) is quite good. Hatzikiriakos (1993) derived a theoretical slip velocity model by using a rate activation theory similar to that used by Stewart. Leonov (1990) and later Adewale and Leonov (1997) proposed the non-monotonic wall slip model based on a statistical theory of the adhesive friction of elastomers. Their model takes into account the delay in breaking polymeric chains off the wall due to Brownian oscillations of the chain segments attached to the wall. This results in the appearance of an S-shaped dependence in the curve relating wall stress to slip velocity, and may be used to provide qualitative description of the spurt effect. It should be noted that all these proposed models are "static" models, where the slip velocity depends on the instantaneous value of the wall stress. However, Hatzikiriakos and Dealy (1991a) suggested that the slip velocity may depend on the past states of the local wall shear and normal stresses. This is similar to the concept of the fluid memory in viscoelasticity, where the local state of stress depends on the past deformation history to which the fluid particles were subjected. To incorporate such a relaxation process, the usual no-slip boundary condition is replaced by a memory function relating the slip CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 29 velocity to the history of the wall stress. Such a model can be used to describe the slip behavior of melts under transient conditions. A dynamic slip velocity model was recently developed by Hatzikiriakos and Kalogerakis (1994) and later by Hatzikiriakos (1995). The behavior of a polymer/metal interface was simulated by using a network kinetic theory. The model predictions were found to adequately represent the experimental data for HDPE. Finally, it should be noted that all proposed models require fitting of certain model parameters to experimental data. 2.6 Pressure Driven F low of Molten Polymers 2.6.1 Viscous Heating In polymer processing, pressure driven flow of molten polymers occurs in a large variety of flow geometries. The polymer is forced through a channel by a pressure gradient (flow in an extruder die) or it is dragged along a moving wall (rotating screw in a stationary barrel). Very often the channel flow is followed by a free surface flow (film blowing, coating, etc.). These flows take place at relatively high rates of deformation, temperatures, and often at high temperature gradients. Velocity and temperature fields influence each other: the temperature field affects the flow through the temperature dependence of the rheological properties, and the velocity field influences the temperature field through the mechanisms of convection heat transfer and thermal energy production by viscous dissipation. The latter represents the conversion of mechanical energy (work of deformation) into thermal energy (Winter, 1977; Cox and Macosko, 1974). This phenomenon, generally known as viscous heating, is significant in the processing of molten polymers. Most polymers have high viscosities and low thermal CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING .30 conductivities, which in combination with large process shear rates can lead to significant local increases in temperature. Thermal effects can contribute to the stability or instability of the flow of molten polymers. Lupton and Regester (1965) studied a possible effect of viscous heating and wall slip on flow instabilities in HDPE. They concluded that temperature increases were too small to cause the instability in the polymer flow, i.e., the discontinuity could not arise through viscous heating. Sukanek et al. (1973) concentrated on the effect of viscous heating for a Newtonian fluid with a temperature dependent viscosity. Their analysis for plane Couette flow showed a variety of modes of instability, but no clear interpretation was offered in the context of melt flow instability. Pearson and Shah (1973) studied the development of the temperature field due to an imposed temperature gradient between the flow and the wall and the resultant changes in the velocity field for Newtonian and power-law fluids. By using a linearized stability analysis, they concluded that an instability might arise with temperature differences of the order of 100°C. This is unlikely to be relevant in normal extrusion, and the conclusion here, in agreement with the remarks of Pearson et al. (1973), is that this mechanism for instability is not relevant to melt fracture. However, Cox and Macosco (1974) observed large temperature rises in capillary extrusion of acrylonitrile butadiene styrene which could be as high as 70°C. Reher et al. (1988) have used a specially constructed capillary die with flush-mounted thermocouples and have reported a significant rise in the temperature for the capillary flow of PVC. They concluded that this increase in temperature could be explained as a consequence of the wall slip phenomenon (local friction). Hence, it would CHAPTER 2- LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING .31 be wrong to ignore the thermal effects in polymer flow analysis if viscous heating is relevant or if there is evidence of wall slip. 2.6.2 System of Equations Heat transfer during the capillary extrusion of polymer melts has been the subject of several reviews and studies over the past decades (Winter, 1977; Warren, 1988). The problem is governed by the following equations (Bird et al., 1962), namely the equation of conservation of mass dp/& + V-(pv) = 0 (2-35) the equation of motion pD\/Dt=¥-l + Pg (2-36) and the conservation of energy equation p De/Dt = V • (kVT) + x: Vv (2-37) where d/dt denotes partial and D/Dt the substantial derivative, p and k are the fluid density and thermal conductivity, respectively, v is the velocity vector, e is the internal energy, T is the temperature, andjC is the stress tensor. Equations (2-35)-(2-37) are usually supplemented by the constitutive equation (see below) and appropriate boundary conditions. 2.6.3 Constitutive Equation and Relaxation Time Spectrum Constitutive equations are mathematical relationships that allow one to calculate the stress in liquid, given the deformation history. In general, the constitutive equation can be written as follows: CHAPTER 2- LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING .32 X = T ( C _ 1 ) (2-38) where C'l(t\t) is the Finger tensor which describes the change in shape of a small material element between times f and t (deformation history). Constitutive equations are often derived from constitutive models. A constitutive model is a set of assumptions about the molecular forces and motions that produce stress. A comprehensive review of constitutive equations and models for polymer melts and solutions can be found in Larson (1988). The classical framework of linear viscoelasticity (Ferry, 1980) describes the stress in polymers with a universal equation. A l l the material properties coalesce into a single material function, the relaxation modulus, G(r): where X is the relaxation time, and H(X) is the relaxation time spectrum. The time dependence of rheology for majority of polymeric melts is completely described by H(X), even at large strains or high strain rates. The shape of H(X) is often correlated with specific molecular architectures. The relaxation modulus, G(t), can also be expressed in terms of the Maxwell element analogy, that is the assembly consisting of a spring in series with a dashpot. If one takes the spring constant to be analogous to the initial shear modulus, go, of the polymeric liquid, and the time constant, that is a ratio of the dashpot and spring constants, to be analogous to the relaxation time of the liquid, A, then the shear relaxation modulus is: (2-39) o G(t) = g0[exp(-t/X)] (2-40) CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING 3 3 and the constitutive equation is r , (0 = \ g 0 {exp[- (t - t y x f y , (t')dt' (2-41) This is called the integral form of the Maxwell model. Actual relaxation processes cannot be described by a single exponential function. Greater flexibility can be obtained by use of the "generalized Maxwell model", which is the rheological constitutive equation analogous to the mechanical assembly shown in Figure 2-11. The forces in the various elements are additive, and the relaxation modulus is: G(0 = f>,[«P(-'/4)] (2-42) i=i where g t and Xi are the initial modulus and relaxation time corresponding to each Figure 2-11 Mechanical analog of the Maxwell element. Then the generalized generalized Maxwell model (multi-mode) Maxwell model can be written as follows: ' N (2-43) >ife=i By use of sufficient number of elements, this equation can be made to describe almost any experimental behavior within the linear viscoelastic regime. The set of (g,, X,) pairs is called the discrete relaxation time spectrum of the material. The discrete relaxation spectrum is a discrete analogue of the continuous relaxation spectrum. CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING .34 The relaxation spectrum, H(X), cannot be measured directly in an experiment. Instead, linear viscoelastic data such as the dynamic moduli G'(cy) and G"(<») are used to calculate the discrete relaxation spectrum, that is the Maxwell model parameters (g,, A,), by means of a suitable fitting procedure. Such fitting methods include least-square approximations (Baumgaertel and Winter, 1989; Laun, 1978), regularization methods (Honerkamp and Weese, 1989), the maximum entropy method (Elster and Honerkamp, 1991), and some others (Tschoegl and Emri, 1993). Some of the methods have been compared by Orbey and Dealy (1991). Baumgaertel and Winter (1989) proposed a method for representing the relaxation spectrum of a material with the fewest possible Maxwell modes while remaining within the experimental scatter of the available dynamic data. Such a representation is called a parsimonious model (PM-spectrum). Details of the method can be found elsewhere (Winter, 1997). CHAPTER 2 - LITERATURE REVIEW RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING .35 3 Objectives he primary objective of this work is a comprehensive and thorough study of the rheology of Teflon FEP resins. The processability of Teflon ® FEP resins in the extrusion through channels of different shapes is also studied. In more detail, the objectives of the thesis can be summarized as follows: 1. To conduct a thorough rheological characterization of a number of Teflon® FEP resins by means of a parallel-plate and capillary rheometers. To study their rheological properties as a function of: • Temperature • Pressure • Molecular weight • Composition • Crystallinity 2. To determine the critical conditions (wall shear stress and shear rate) for the onset of melt fracture and wall slip as functions of: • Temperature • Pressure • Molecular weight • Composition • Interface conditions 3 To develop numerical codes for solving the following problems: • Determination of relaxation time spectra from dynamic mechanical data CHAPTER 3 - OBJECTIVES RHEOLOGY AND PROCESSABILITY OF TEFLON18 FEP RESINS FOR WIRE COATING 36 • Determination of parameters of a constitutive equation from suitable experimental data • Numerical simulation of the flow of molten polymers in a capillary die accounting for thermal and wall slip effects • Calculation of wall slip velocities in capillary flow subject to thermal effects from experimental data. 4. To study the processability of a number of polymers including of Teflon® FEP resins and polyolefins in extrusion with a wire coating die as a function of: • Temperature • Interface conditions • Presence of additives 5. To study the effect of processing aids on the processability of Teflon® FEP polymers and polyolefins. To propose possible explanations of elimination of melt fracture. Thesis organization. The essential results of this thesis have been published or submitted as publications (see Rosenbaum and Hatzikiriakos, 1997; Rosenbaum et al, 1995, 1996, 1998a,b). However, additional work and results not included in these papers are presented here. Chapter 4 is based on the paper Rheological Characterization of Well-Defined Tetrafluoroethylene/Hexafluoropropylene Copolymers to be published in Rheologica Acta. It includes results obtained using linear oscillatory shear experiments in a parallel-plate rheometer with a variety of Teflon® FEP resins having different molecular weights and compositions. CHAPTER 3 - OBJECTIVES RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING .37 Chapter 5 is based on the paper Flow Implications in the Processing of DuPont Tetrafluoroethylene/Hexafluoropropylene Copolymers published in International Polymer Processing, volume X (1995) and the presentation at ANTEC'95 (Rosenbaum et al, 1995). It includes the results obtained in the capillary rheometer study of a variety of Teflon® FEP resins. Also, a few results not included in this paper, but presented at ANTEC'96 (Kazatchkov etal, 1996), are discussed in this chapter. The results of the experimental study were used for the rheological characterization of the Teflon® FEP resins presented in Chapter 6. The latter contains the portion of the paper to be published in Rheologica Acta concerned with calculation of the relaxation time spectra and estimation of the critical molecular weight based on the relaxation spectra. It also includes results on the modeling of the rheological behavior of Teflon® FEP resins by means of the Phan-Tien and Tanner constitutive equation. Chapter 7 is a comprehensive analysis of the flow of molten polymers in a capillary channel. It includes the entire paper Wall Slip in the Capillary Flow of Molten Polymers Subject to Viscous Heating published in AIChE Journal, volume 43 (1997) and the paper presented at ANTEC'96 (Rosenbaum and Hatzikiriakos, 1996). In this chapter, several aspects of the numerical simulation of nonisothermal capillary flows with a slip boundary condition are considered in detail. Specifically, a new numerical technique to calculate the slip velocity is proposed, and the results for a number of commercial resins including polyethylene, polypropylene, and Teflon® FEP are presented. In Chapter 8, the effect of various processing aids on the processability of fluoropolymers and polyolefins is studied. It is based partially on the paper published in CHAPTER 3 - OBJECTIVES RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING .38 International Polymer Processing and the paper presented at ANTEC'98 (Rosenbaum et al, 1998a). Finally, in Chapter 9, a few conclusions are drawn, recommendations for future work are given, and the contributions made to general knowledge in this field are discussed. CHAPTER 3 - OBJECTIVES RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 4 Oscillatory Flow Measurements on Teflon® FEP Resins 39 he rheology of tetrafluoroethylene/hexafluoropropylene (TFE/HFP) copolymers and tetrafluoroethylene/hexafluoropropylene/perfluoro(alkyl vinyl ether) (TFE/HFP/ PAVE) terpolymers, also known as Teflon® FEP polymers, having different molecular weight and composition (HFP and PAVE content) was studied by means of a parallel-plate rheometer. Three groups of polymers having different molecular weights and composition with nearly constant polydispersity (around 2.5) were considered; namely, Group A having a relatively low melting temperature (amorphous with a high content of HFP), Group B having a higher melting point (semi-crystalline with a lower content of HFP), and Group C with high melting point resins having a different content of PAVE. The zero-shear viscosity of the resins was found to scale with the molecular weight with the well-established scaling factor of 3.4. The critical molecular weight for the onset of entanglements, Mc, was found to be about 100,000, a value much higher than those previously reported in the literature for other polymers. The rheology of resins in the second and third groups (higher melting point) was found to exhibit a strong dependence on thermal history during oscillatory-shear measurements. The data obtained in experiments at different temperatures without a preheating to a certain value (330°C) exhibited a violation of the time-temperature superposition principle and no well-defined values of the zero-shear viscosity. This is attributed to residual crystallinity even at temperatures well above their melting point (260°C). However, the same experiments with preheating and subsequent cooling to the desired temperature resulted in a very good time-temperature scaling. The resins of the CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 40 third group were tested in an attempt to derive correlations between the rheological properties and their processing behavior in wire coating. The incorporation of PAVE in the molecules of the resin did not substantially change its rheology. However, the rheological measurements with controlled cooling revealed that the terpolymers, which are better processing resins, crystallize at higher temperatures. 4.1 Introduction Teflon® FEP resins, which are copolymers of tetrafluoroethylene (TFE) and hexafluoropropylene (HFP), are of great commercial importance. The first member of this family of Teflon® resins was Teflon® FEP 100, a commercial resin having 92 mole % TFE and 8 mole % HFP. It has a fairly high molecular weight, so its melt processing is difficult. In wire coating operations, the maximum speed at which FEP 100 can be drawn onto the wire is about 500 ft/min. In order to be able to coat wire at a higher speed, a new resin, FEP 3100, was developed. It has a slightly higher level of HFP and lower molecular weight, and it can be run at about 1300 ft/min. Recently, FEP 3100 was replaced with a new resin, FEP 4100. It has a superior stress crack resistance and can be coated onto a wire at 2000 ft/min. The outstanding performance of FEP 4100 is due to the fact that a portion of the HFP is replaced with perfluoro(alkyl vinyl ether) (PAVE). Despite their increasing commercial interest, very few studies have been published on the rheological characterization of Teflon® FEP resins. This can be partly attributed to the fact that TFE/HFP copolymers are, in general, insoluble in any known solvents. This greatly complicates determination of their molecular weights (MW) and molecular weight distributions (MWD). The few reported methods that have been used to determine CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING 4 1 MW and MWD of Teflon® polymers include end-group analysis in combination with dynamic melt rheometery (Wu, 1985, Tuminello, 1989), laser light scattering (Chu et al, 1987), and viscosity measurements (Chu and Linliu, 1995). Nevertheless, none of these methods can safely provide accurate results on the determination of the molecular characteristics of Teflon® polymers. With the introduction of the amorphous perfluoroplastics, which are soluble in selected fluorocarbon solvents, it became possible to accurately determine the MW of these resins and thus perform more reliable and systematic rheological measurements. One of the objectives of this chapter is to report results on dynamic mechanical measurements of a series of well-characterized (in terms of MW and MWD) amorphous TFE/HFP (Teflon®) copolymers. More specifically, the effect of MW on the zero-shear viscosity and relaxation spectra of these resins is studied. The latter are determined by two methods: the so-called BSW relaxation spectrum method (Baumgaertel et al, 1990) and the parsimonious method that calculates the discrete relaxation spectrum with a minimum number of Maxwell modes (Baumgaertel and Winter, 1989). This modeling study will be presented in Chapter 6 (Rheological Characterization of Teflon® FEP Resins). Another objective of the present chapter is to show some of the difficulties that may arise during rheological testing of commercial semi-crystalline Teflon® FEP polymers. It is known that crystalline polymers exhibit some unusual flow properties that can be influenced by thermal and mechanical pretreatment such as pre-heating and pre-shear (Lagasse and Maxwell, 1976). Unfortunately, many experiments carried out on FEP resins at temperatures much higher than their melting point, where one might assume the CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 42 absence of any crystals in the melt, prove that residual crystals play a significant role in determining important aspects of their rheology. Unless residual crystallinity is taken into account, it can lead to some confusion and complications in the rheological data analysis. Finally, oscillatory shear measurements were used to compare different Teflon® FEP wire coating resins in an attempt to identify correlations with their processing behavior. Specifically, the effect of the third component, PAVE, on the rheological properties of TFE/HFP/PAVE terpolymers and their ability to crystallize was analyzed. The latter was thought to potentially affect processability in the draw-down region of the wire coating process where temperatures drop rapidly, and the elongational flow would favor crystallization. 4.2 Experimental 4.2.1 Materials and Characterization Three groups of well-characterized TFE/HFP copolymers of different molecular weights and TFE/HFP/PAVE terpolymers of a different composition (courtesy of Du Pont Fluoroproducts, Wilmington, DE) were studied. The first group of resins had a high content of HFP and a relatively low melting temperature (hereinafter referred to as TFE/HFP resins of Group A, listed in Table 4-1). The second group of resins had a lower content of HFP and therefore a higher melting temperature, around 260°C (hereinafter referred to as resins FEP of Group B, listed in Table 4-2). The resins of the third group (hereinafter referred to as resins TFE/HFP/PAVE of Group C, listed in Table 4-3) were similar to those of Group B but contained a small amount of PAVE. The composition of the resins of Group A is approximately 50±5 wt. % HFP and 50±5 wt. % TFE. The CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 43 composition of the Group B resins is approximately 15 wt. % HFP and 85 wt. % TFE. The composition of the resins of Group C is approximately 11 wt. % HFP, 88 wt. % TFE, and below 1 wt. % PAVE except for the control resin (FEP-2 of Group B) which has a slightly different ratio of TFE/HFP and no PAVE. Compositions were determined by fluorine NMR in the melt state at 300-340°C. DSC analysis showed that the crystalline melting point of Groups B and C resins is about 270°C and the crystallization temperature upon cooling from the melt-state is about 249°C. The molecular weights of the Group A resins were in the range of 76,000 to 400,000 kg/kmol, Group B in the range of 165,000 to 262,000 kg/kmol, and those of Group C from 208,000 to 220,000 kg/kmol. Most resins had similar polydispersity (MJM„) of about 2.5 except for the resin TFE/HFP-1 (Group A) that had polydispersity of more than 3. The molecular weight and polydispersity were determined by GPC using Fluorinert® FC-75 (3M Corporation) solutions versus linear polyhexafluoropropylene oxide standards, one with M„=20,000 and the other with M„=70,000. The molecular weight, polydispersity, melt index, and composition of all resins are listed in Tables 4-1, 4-2, and 4-3. Table 4-1. Molecular parameters of TFE/HFP resins with lower melting temperature (Group A) Sample Composition Mw MJMn Melt index wt.% H F P / T F E kg/kmol 200 ° C , 15 kg TFE/HFP 1 45.5/54.5 76,000 3.27 -TFE/HFP 2 55.0/45.0 124,000 2.38 4 (5 kg) TFE/HFP 3 45.5/54.5 199,000 2.14 -TFE/HFP 4 51.3/48.7 327,000 2.56 0.67 TFE/HFP 5 48.0/52.0 350,000 - 0.17 TFE/HFP 6 48.0/52.0 400,000 - 0.33 CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING .44 Table 4-2. Molecular parameters of TFE/HFP (FEP) resins with higher melting Sample Composition wt.% H F P / T F E Melt index MJMn Mw kg/kmol FEP-1 15.0/85.0 44 2.5 165,000 FEP-2 15.0/85.0 18 2.5 220,000 FEP-3 15.0/85.0 9 2.5 262,000 Table 4-3. Molecular parameters of TFE/HFP/PAVE resins (Group C). Sample Composition wt.% H F P / T F E / P A V E Melt index MJMn Mw kg/kmol Control (FEP-2) 15.0/85.0/0.00 18 2.5 220,000 TFE/HFP/PAVE-1 11.05/88.26/0.69 20-24 2.5 208,000 TFE/HFP/PAVE-2 11.09/88.17/0.74 20-24 2.5 208,000 TFE/HFP/PAVE-3 10.85/88.21/0.94 20-24 2.5 208,000 4.2.2 Rheological Measurements Linear viscoelastic measurements were performed in a Rheometrics System 4 mechanical spectrometer having a parallel plate geometry (plates of diameter equal to 25 mm). Frequency sweep experiments were performed in a frequency range from 0.01 to 500 rad/s after ensuring that operation was within the linear viscoelastic region (sufficiently small shear strain). The gap between the plates was adjusted to about 1 mm. To remove residual monomers prior to testing, the Group A resins were vacuum stripped at 140°C for 24-72 hours, depending on the amount of residual monomers. The stripping duration was controlled both visually (cessation of bubble formation) and Theologically (viscosity measurements). The sample was assumed to be free of monomers when the viscosity remained essentially unchanged for at least three consecutive measurements at the same frequency. After this stripping period, the polymers were molded into disks 25 mm in diameter and 1.5 mm high and cooled quiescently to room temperature. Since CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING 45 degradation is not a factor for these stable polymers within the experimental range of temperature, no nitrogen environment was used for the rheological measurements. Measurements of the dynamic moduli of the Group A polymers were performed at 200°C and those of Groups B and C in the range from 290 to 350°C. The lower temperature limit was chosen to avoid residual crystallization, while the upper limit was secected to prevent thermal decomposition. For the polymers of Group B, two different measurement techniques were used in order to study the importance of pre-heating and residual crystals on their rheology. In the first case, after the rheometer was equilibrated at the desired experimental temperature for 10 min, the sample was placed between the plates, melted, and equilibrated again at the same temperature. Then the gap between the plates was adjusted, the edges of the sample were trimmed, and the measurements proceeded at that temperature. In the second case, all the above steps are repeated except that before starting the test, the sample was pre-heated to the higher temperature of 330°C. This temperature was maintained for at least 1 min, long enough to melt all residual crystals, and then the sample was cooled to the desired experimental temperature. The polymer was then allowed to equilibrate for 5 min prior to testing. The preheating technique was also used in characterizing the Group C resins. 4.3 Results 4.3.1 Low Melting Point TFE/HFP Resins (Group A) Figure 4-1 plots the dynamic modulus curves (G' and G" respectively) of the six TFE/HFP copolymers of Group A as a function of frequency, a>, at 200°C. The data indicate that the distinct region for flow at low frequencies, the so-called terminal zone, CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 46 106 105 h-Q. 104 CD ^ 103 D "O O E 102 CO ro ° 101 CO 10° 10-i i i i M111 i i i i 11111 i i i i 11111 i \ i 111111 i i i ^ i II TFE/HFP T=200°C § § § o * 2888 / o : o o ° o ° ° : 0 ° ° c o - ° j ° 0 ° o • • 0 • • • • • 6 • • 5 • • • • 2 1 Closed symbols correspond to terminal zone] -i i i 111111 i i i 111111 i i i 1 1 1 1 1 1 i i i 111111 i i i 11111 10": 10" 10° 101 Frequency (co), rad/s 102 103 106 105 ro CD 104 to I 103 W tn O 102 101 T 1—I I I I I 11 1 1—I I I I I 11 1 1—I I I I I I I 1 1—I I I I I I I 1 1—I I I I I M TFE/HFP T=200°C 1 ° X R O ° s8888§888888888§§88 c r , 0 ' 4 • • 3 , ' Closed symbols correspond to terminal zone \ 2 » 1» i i i 1111 i i i i ii i i i i i i 111111 i i i 11111 10": 10 •1 10° 101 Frequency {co), rad/s 102 103 Figure 4-1. The storage and loss moduli, G'(co) and G"(a>), of the TFE/HFP copolymers of Group A (Table 4-1) at 200°C. CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 47 has been reached (G' X I 103 o 102 - i — i i 111111 1—i i 1 1 1 n | 1—i i 1 1 1 1 1 | 1—i i 111 n | 1 — i i 11111 TFE/HFP T=200 °C 5AAAAAAAAAA T T T " A A . • A A T. 4 • ^ A A % 8 T h i . A # T A • • 3ooooooooooooooooooooooooo A " * 5 ' J ° o 0 ( ' 0 , ° 0 0 A» o o J L 1 OOOOOo o o o oo o oo o o o o o o oo I I I I I 1111 1 11 ll 11 I I I I I 11 10": 10' 10 ° 101 Frequency (co), rad/s 102 103 Figure 4-2. The complex viscosity \rj*(a>)\ of the TFE/HFP copolymers of Group A (Table 4-1) at 200°C. The zero-shear viscosity is clearly obtained for all resins of this group CHAPTER 4- OSCILLATORY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 4 8 Newtonian region of essentially constant viscosity at low frequencies as well as a well-defined power law region at higher ones. Figure 4-3 plots the normalized complex viscosity (dividing by the corresponding zero-shear viscosity, r/0) as a function of frequency. It can be seen that the degree of shear-thinning increases with increase in the molecular weight, and that the onset of shear thinning shifts to smaller frequencies (rates) with increase in the molecular weight. This expected behavior has also been reported for a number of other polymers (Dealy and Wissbrun, 1990). V) 8 > X I— CO . 104 103 ' I ' TFE/HFP T=200 °C 1 1 1 y • / • / - / slope=3.4 ' • slope=1.0 A -I M=2Me 1 1 1 70 100 200 300 400 500 700 Molecular weight (Mw*10 ), kg/kmol Figure 4-4. The molecular weight dependence of the zero-shear viscosity 770 of TFE/HFP copolymers (Group A) at 200°C dependence (TJQ OC MW") with n « 3.4. The small scatter in the graph can be attributed to variations in the polydispersity and the content of HFP in these samples. These findings are in agreement with previous studies on the dependence of the zero shear viscosity of CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 50 nearly monodisperse linear polymers on the molecular weight. A transition at Mc from linear to a power-law behavior with exponent of about 3.4 has been repeatedly reported (Van Krevelen, 1991). Note that the critical molecular weight, Mc that can be estimated from this set of data, lies in the range between 80,000 and 110,000 kg/kmol. This value is somewhat high compared to those previously reported in the literature. For example Wu (1985) calculated the value of Mc to be close to 12,500 kg/kmol for high melting point FEPs, while Tuminello (1989) estimated this value to be about 14,000 kg/kmol. This point of disagreement will be discussed in more detail later, in Chapter 6. It is noted that the clear deviation of the lowest molecular weight 770 from the 3.4 power low behavior was also reported by Kazatchkov et al. (1996). There, a series of similar TFE/HFP polymer melts were studied by means of a sliding-plate rheometer. The resins were not thermally treated before experimentation as in the present study. Nevertheless, a very similar relationship between r/0 and Mw was observed that resulted in about the same high Mc value. This observation leads me to believe that crosslinking, which might have taken place during vacuum stripping, is not present in the current study. 4.3.2 High Melting Point FEP Resins (Group B) Figure 4-5 depicts the master curves of the storage and loss moduli as well as that of the complex viscosity of the FEP-2 polymer (Table 2) at the reference temperature of 300°C. These experiments were performed without any preheating at a higher temperature. For a "thermorheologically simple" material (Dealy and Wissbrun, 1990), it is often found that data taken at several temperatures can be brought together on a single master curve by means of "time-temperature superposition" (TTS). According to this CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 5 1 principle, the data for different temperatures can be superposed by introducing a shift factor, ar, determined empirically. Thus, if one makes a plot of a rheological property versus time, aj is obtained from the horizontal shift necessary to bring the data for any temperature T onto the same curve as data for temperature Tref. For example, flow curves (shear stress vs. shear rate) would be plotted as shear stress versus y aj. In Figure 4-5, the time-temperature superposition principle on frequency sweep 106 ro CD CD~ TJ O E to to O T3 C CO CD CO CO CO 105 104 103 102 101 10° [FTTTj 1 1 I I I I II] 1 1 I I I I 11| FEP 2 T r e f=300°C T T • O • O TT 1 1 I I I I 111 1 1 I I I I l l | 1 1 I I I I I I O Q O oo x < co' o o CO 0) TJ * CO 103 10": 103 10-1 10° 101 102 Reduced frequency (aTa>), rad/s Figure 4-5. Master curves of the storage modulus G '(co), loss modulus G '(ca), and complex viscosity \TJ*(CO)\ of Teflon® FEP-2 copolymer at the reference temperature of 300°C. The dynamic linear viscoelastic experiments were performed without any preheating. CHAPTER 4- OSCILLATORY FLOW MEASUREMENTS OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON FEP RESINS FOR WIRE COATING .52 data obtained at temperatures varying from 290 to 350 °C was applied. It can be seen from Figure 4-5 that the superposition of the data is very good for temperatures higher than 325 °C. However, for lower temperatures, it clearly fails for the range of reduced frequencies below 10 s"1. This failure is more pronounced for G' data, where a distinctive "shoulder" appears in the low frequency region instead of approaching the typical slope of 2 in the terminal zone. The height of this "shoulder" apparently scales with temperature. Based on these data, no zero-shear viscosity can be found at least for temperatures lower than 325°C. Similar behavior was also observed for the other polymers of Group B (not shown here). Behavior such as that depicted in Figure 4-5 was previously observed for other semi-crystalline polymers (Guskey and Winter, 1991; Plazek, 1996). Such behavior normally indicates some degree of molecular association, possibly due to formation of a crystalline structure that leads to solid-like elasticity. It is believed that some residual crystallinity still exists at temperatures well above the crystalline melting point. Moreover, these residual crystals can grow with time as a result of the induced shear (shear-induced crystallization). This is clearly demonstrated in Figure 4-6. Two time sweep experiments for FEP-2 at the same temperature of 290°C were performed. The first was carried out without any pre-heating and the second with pre-heating at 330°C before switching back to 290°C (see experimental section for details). This temperature of 330°C seems to be high enough for residual crystals to completely melt since no failure of TTS was observed above 325 °C. One can see from Figure 4-6 that without preheating the storage modulus increases with time by a significant factor due to shear-induced crystallization. On the other hand, if the sample is initially pre-heated, the magnitude of CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING .53 G' remains within experimental error (±3%) throughout the test. This means that, by preheating the sample, the centers of possible crystal nucleation have been completely eliminated, thus preventing growth of crystalline structure. The experimental results plotted in Figure 4-5 were repeated for the same temperatures but this time with preheating at 330°C. The results are plotted in Figure 4-7. Clearly, the time-temperature superposition principle now applies over the whole range of temperature (290-350°C) and frequency examined in this work. For the sake of 20 15 10 5 ~1 1 1 1 1 r -FEP 2 T=290 °C (without preheating) •••• 2 O ^ . - ^ x f c P Q > -5 h E 20 p •I 15 "go CD 10 Q _i i i i L_ _ i i I i i • • 0 -5 —i 1 1 1 1 1 i 1 1 1 r 1 1 1 p-FEP 2 T=290 °C (with preheating to 330 °C) •>•) I I I • • • ' • I I I 1 1 I 1 1—I I I I I I 1 1 1„, 1, 1.1.LJ.1 10-2 10"1 10° 10 1 10 2 10 3 Reduced frequency (oo*aT), rad/s Figure 4-7. Master curves of the storage, G'(G>), and loss modulus, G'(c6), of Teflon® FEP-2 copolymer at the reference temperature of 300°C with preheating at 330°C CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING .55 for the FEP-2. The Arrhenius type equation was found to adequately describe the available data: aT = exp f R 1 1 (4-1) where Ea is the flow activation energy, R is the universal gas constant, and Tref is the reference temperature (300°C). This equation is often found to be valid as long as the temperature is at least 100 K above the glass transition temperature, Tg, which is 200 K for Teflon®. Closer to Tg, the WLF equation has been found useful (see Dealy and Wissbrun, 1990). However, at these high temperatures, either equation can be used to fit -1 1 1 1 1 1 1 1 r 1 1 p F E P 2 T r e f =300 ° C 1 0.00160 0.00165 0.00170 0.00175 0.00180 0.00185 1/T, KT1 Figure 4-8. The horizontal shift factor, a?, resulted from the application of the time-temperature superposition of dynamic linear viscoelastic experimental data for Teflon® FEP-2 copolymer CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 56 experimental values of aj. The flow activation energy was found to be equal to 50,000 kJ/kmol and essentially independent of molecular weight. This is much lower than the value of £0=84,000 kJ/kmol reported by Wu (1985) for his series of FEP resins. This can be attributed to differences in the composition of the resins used by Wu (1985) and those in the present work. Figure 4-9 depicts the dependence of the zero-shear viscosity on the molecular 10 * co D_ to O o to > i_ CO CD _c to 2 CD N 100 10 1 I I Teflon FEP A Tuminello(1989), T=300°C • Wu (1985), T=340°C • This work, T=300°C — 1 1 A / / 1 - • : A / • -A / • / • A / -* / D -/ slope = 3.4 / 1 1 1 1 1 1 , , 1 100 Molecular weight (/W *10"3), kg/kmol 1000 Figure 4-9. The dependence of the zero-shear viscosity of the TFE/HFP copolymers of Group B o n M w at 300°C (present work; Tuminello, 1989) and 340°C (Wu, 1985) CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 57 weight for the Group B resins, along with the data points reported by Tuminello (1989) and Wu (1985). A straight line having a slope equal to 3.4 also appears on the graph for reference purposes. The available data show clearly that a power-law relationship exists between r/0 and Mw. The slope turns out to be close to the value of 3.4 reported previously for many other linear polymers when the Mw is greater than a critical value, Mc (Van Krevelen, 1991). 4.3.3 Terpolymers TFE/HFP/PAVE (Group C) The viscoelastic properties of the Group C resins were measured at 300°C with preheating at 330°C as described above. Figure 4-10 plots the storage and loss moduli as well as the complex viscosity for all the resins of this group including the control resin, FEP-2. All the resins have similar viscosities except for the control whose viscosity is higher due to higher molecular weight. A slight difference in the viscosity of the terpolymers can be attributed to minor variations in the PAVE content. In general, the resins with lower viscosity process better since they are more extendable in the melt state. This is true when one compares the control resin with the other terpolymers. A comparison of the dynamic moduli revealed differences between the co- and terpolymers. Looking at the modulus curves, one can see that the G" curve and high-frequency part of the G' curve of the control resin lie above those for the three terpolymers whose dynamic moduli are virtually identical. This can be explained by a higher molecular weight of the control. However, the G' curve clearly shows that at low frequencies (below 0.2 rad/s) the storage modulus of the terpolymers is higher than that of the control resin. This means that an addition of PAVE makes a terpolymer more CHAPTER 4 - OSCILLATORY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 5 8 elastic than a copolymer. The higher elasticity of the terpolymers may be a reason for their better processability. Another reason for the better processability of the terploymers may be its enhanced ability to crystallize compared to the control copolymer. For this purpose, a series of rheological tests with controlled cooling was done to study crystallization of the resins of this group. The procedure was as follows. After preheating at 330 °C, the sample was 106 10' [±l 11[ 1—I I I II111 1—I I I 11111 1—I I I 111 lj 1—I I I I 1111 1—I—I I 1111 TFE/HFP/PAVE T=300°C w v v v v Q_ CD ; 104 CD 3 •o o E 103 GO GO O T3 CO 1 Q 2 CO 101 10° ° i vvvvvvvvvvv ^ v v V v v ^ a' ,8' ,2' Q ° 0 .V • TFE/HFP/PAVE-3 o TFE/HFP/PAVE-2 ... - „ A TFE/HFP/PAVE-1 V < "° v control (no PAVE) CD W -~ CD o CO yj O < Q_ A H 103 11"i • i 11111111 i 11111111 i i_ LLl I I I I I I 111 104 o o 3 . It can be seen that, at a critical value of the wall shear stress, the Bagley correction increases discontinuously. This is due to the fact that at this critical shear stress an oscillating melt fracture phenomenon occurs as discussed below. Similar behavior was also obtained at the other two temperatures, as well as for the other resins . 5.4 V iscos i t y In determining the viscosity, only data in the prefractured region were considered. At higher apparent shear rates where melt fracture is obtained, wall slip is present. Thus, 5000 ? 4000 co CL CO 3000 GO o o CO > 0) g 2000 •o 03 Teflon FEP ^7 V V V V 7 v • #5 A •••A FEP 4100 • T=350°C, ar=0.73 • T=325°C A T=300°C, ar=1.66 FEP 3100 v T=325°C 8 10 20 30 40 Reduced shear rate (yaT), s _1 60 Figure 5-3. The reduced viscosity of resins FEP 3100 and 4100 at 325 °C and ambient pressure CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING .67 to determine the true deformation imposed on the melt, one should apply a correction in order to account for the effects of slip. The Rabinowitch correction was also applied to the experimental data. The resulting viscosity curves for fluoropolymers FEP 4100 and 3100 are plotted in Figure 5-3 for all three temperatures. Note that the data for FEP 4100 have been reduced to the temperature of 325 °C, in order to compare its viscosity with that of resin FEP 3100 (experiments for FEP 3100 were performed only at 325 °C). The shift factors according to the time-temperature superposition principle for the other temperatures are 0.73 for 350°C and 1.66 for 300°C. Note also that all the data refer to ambient pressure (a pressure correction was applied, see below). In spite of the apparent scatter in the data for FEP 4100, the deviation of the data from the mean value is within +4%. Also the shear thinning behavior of both materials is very weak. Essentially, the melts have a Newtonian viscosity for shear rates less than about 10 s"1 and a power law one for higher shear rates with a power law exponent equal to 0.85. Finally, one may observe that the viscosity of FEP 3100 resin is higher than that of FEP 4100 by about 25%, which shows the effect of the higher molecular weight of FEP 3100. 5.5 The F low Curve Using the Bagley corrections determined previously, one can now determine the apparent flow curves for capillaries having different diameters and L/D ratios (wall shear stress vs. apparent shear rate). The wall shear stress, 0.1 CD •4—" CO l _ CO CD sz w JO l l j I I I 1 1 1 II 1 - Teflon FEP 4100 i I I I i i 111 i i i i i i i 11 T=350°C L/D=40 • • an v v • • • -• • • • -• • smooth • sharkskin - • A slip-stick V superextrusion • i i i i i • i i I I I • gross melt fracture i 101 102 10; 104 Apparent shear rate (yA), s-1 Figure 5-4. A typical flow curve of resin FEP 4100 at 350 °C using a capillary die having a diameter of 0.762 mm and a length-to-diameter ratio of 40. The various flow regions are also illustrated CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON*1 FEP RESINS FOR WIRE COATING 69 This stable regime is nearly Newtonian where the viscosity of the material appears to be slightly dependent on the apparent shear rate (see Figure 5-3). At wall shear stress of about 0.18 MPa small amplitude periodic distortions on the surface of extrudate appear (surface or sharkskin melt fracture region). A sharp change in the slope of the apparent flow curve defines the onset of the oscillating (or "stick-slip") melt fracture region, where the pressure oscillates between two extreme values and the extrudate has the appearance of alternating smooth and distorted portions. This region is obtained for apparent shear rates falling between about 100 and 700 s"1. What is plotted on Figure 5-4 for this region is the average shear stress of these two extreme values. The maximum and minimum values of stress obtained during oscillations are indicated by error bars. For shorter capillaries the slope of the flow curve in this region is distinctly negative while for longer capillaries an almost plateau-like region is obtained. It also has to be mentioned that oscillations are not always obtained within this region. For certain apparent shear rates and capillary dies, the flow becomes apparently stable but the extrudate still exhibits a stick-slip appearance. This behavior was more pronounced in the extrusion of FEP 3100. For apparent shear rates greater than about 700 s"1 and up to 2000 s"1 the pressure drop becomes stable but, most importantly, the extrudate is also smooth. This is referred to as the superextrusion flow region. It is noted that slip is present in this region, and this is discussed in a subsequent section. Finally, beyond this superextrusion region the flow is again stable but the extrudate appears grossly distorted. Note that the transition from the superextrusion region to the gross melt fracture region is fairly smooth, and the extrudate distortion gradually becomes more severe with increasing shear rate. CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 70 5.6 The Effect of Pressure on the F low Curve Figure 5-5 shows apparent flow curves for resin FEP 4100 obtained with dies having a constant diameter and various L/D ratios. It can be seen that the data for apparent shear rates less than about 80 s"1 (stable region where the extrudate appears 0.4 Q_ 0.2 CO C/) CD l _ oo CO CD sz CO J O 0.1 0.08 0.06 0.04 0.02 1 1—i—i—i—i 1 1 1 — Teflon FEP 4100 T=350°C D=0.762 mm T 1 1 1 1—I I I n 1 1—i—i—i i i V 8 • V i 101 8 V A y • L/D=10 • L/D=20 A L/D=40 V L/D=70 • L/D=100 \ I 1 1 1 ! | 1 I I 1 I 1 I I I I I I 102 103 104 Apparent shear rate (yA), s-1 Figure 5-5. The effect of pressure on the flow curves of resin FEP 4100 at 350 °C using capillary dies having a diameter of 0.762 mm and various length-to-diameter ratios CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 71 smooth) do not fall on a single curve. Instead, the apparent flow curves shift to higher values of the wall shear stress with increasing L/D ratio, thus pressure. This implies that the viscosity of FEP 4100 is a function of pressure. The pressure dependence of viscosity is typically represented by an exponential function (first order approximation) which for a given temperature can be written as: JJ=7]° exp(aP) (5-2) where 77° is the viscosity at ambient pressure, a is the pressure coefficient of viscosity and P is the absolute pressure. To obtain the pressure coefficient of viscosity, a, the data points corresponding to various values of LID ratio in the smooth region were brought together on a single curve by varying a. Note that, at very low shear rates and for small LID ratio, the wall shear stress is insensitive to the pressure coefficient, so caution should be exercised in selecting the data points. The value of a required to superpose the data reasonably well was found to be (2.25 ± 0.87) • 10"8 Pa"1 (for the 95% confidence interval and a sample of 14 points). This value is consistent with measurements reported for other polymer melts. A value of 2.9 xlO"8 Pa"1 was reported for polystyrenes by Penwell et al. (1971), but it is higher than those reported in the literature for polyethylenes: e.g., Kalika and Denn (1987) reported the pressure coefficient of viscosity for a LLDPE to be 5 • 10-9 Pa-1, while for HDPE a is believed to be less than 0.52 • 10"9 Pa-1 (Rauwendaal and Fernandez, 1985). The resulting pressure-corrected flow curves are shown in Figure 5-6. It can be observed that in the smooth region a relatively good superposition of the data results. On the other hand, the pressure correction introduces a greater separation of the data than before, particularly in the stick-slip region and beyond. However, in defining the critical CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 72 shear stress for the onset of melt flow instability, one should use the actual and not the pressure-corrected shear stress. Furthermore, due to the relatively strong effect of pressure on viscosity in this case, it may be more appropriate to define the critical shear stress for the onset of melt fracture as the shear stress at the inlet to the capillary. This is significantly higher than that at the exit for long capillaries. Thus, while it is apparent from Figure 5-5 that the critical shear stress for the onset of oscillations increases with decreasing L/D ratio, when the shear stress at the inlet is determined, oscillations occur at 0.4 CO i co m CD "55 i ro CD -C CO "TO T3 CD O i— o o CD CO CO CD 0.2 0.1 0.08 0.06 0.04 0.02 n i i i i i i i "i 1 1—i—i i i i I I I I I I T T Teflon FEP 4100 T=350°C D=0.762mm • • u • A * A A • 8 • u • A A • A ^ v v v v v v v v v v v v • L/D=10 • L/D=20 A L/D=40 V L/D=70 • L/D=100 _j i i i i i i i _i i i i i i i i _i i i i i i i i 101 102 103 Apparent shear rate (yA), s-1 104 Figure 5-6. Pressure-corrected flow curves of resin FEP 4100 at 350 °C CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N 1 8 FEP RESINS FOR WIRE COATING .73 about the same critical shear stress value, that is about 0.20 MPa (Penwell et al., 1971). As discussed before, one may see in Figure 5-5 that the absolute value of the slope in the stick slip region increases with decreasing L/D ratio and, for long enough capillaries, an almost perfect plateau region is obtained. This is somewhat surprising and in contrast to what has been reported by Hatzikiriakos and Dealy (1992a) for the oscillating melt fracture of linear polyethylenes, where the difference between the two extreme shear stress values in the oscillating flow regime scales linearly with the LID ratio of the capillary, and thus pressure. 5.7 Wall S l ip To detect the presence of slip, one may use the Mooney technique. According to this technique the flow curves determined with a series of capillaries having different diameters diverge if slip is present. In addition, to eliminate the effects of pressure on viscosity and slip velocity one should keep constant the L/D ratio of the capillary die. This technique was used in the past for a series of HDPE's and it was found that these polymers slip at critical shear stresses in the range of 0.1-0.18 MPa depending on the molecular weight and polydispersity of the resin (Hatzikiriakos and Dealy, 1992a). Ramamurthy (1986) also determined critical shear stresses in the same range for LLDPE's. Figure 5-7 shows the apparent flow curves of FEP 4100 determined with dies having different diameters but constant L/D ratio. It can be seen that these flow curves show diameter dependence for wall shear stresses beyond the oscillating flow region. This implies the presence of slip in this high shear rate branch of the flow curve. The CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON18 FEP RESINS FOR WIRE COATING 74 same behavior was obtained at the other two temperatures and also with capillaries having other LID ratios. It can also be seen that, at very high apparent shear rates, the curves seem to converge. This may be due to the effect of viscous heating which is significant at high shear rates. The effect of viscous heating is more pronounced for capillaries having a larger diameter provided that the L/D ratio is kept constant (Ybarra and Eckert, 1980; Cox and Macosko, 1974). Shidara and Denn (1993) have discussed the effect of viscous heating for a molten polystyrene in slit extrusion. To explain their re-0.4 0.2 co Q_ oo co CD i_ -*—< 00 l _ co CD sz 00 JO 0.1 0.08 0.06 0.04 0.02 11 1 1 1 1 1 1 1 1 1 1 Teflon FEP 4100 i i i 11111 I I I I I I I I I T=350°C L/D=40 • • • • • • • • • A • • D=0.508 mm • D=0.762 mm • A D=1.270 mm • A i I i i i i i i i i 1 i i i i i i i 11 i i i i i i 111 101 102 103 104 Apparent shear rate (yA), s-1 Figure 5-7. The effect of the capillary diameter on the flow curve of resin FEP 4100 at 350 °C. Wall slip is present in the regions where the flow curve becomes diameter dependent CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 75 suits, they assessed this effect to be significant. Because the effect of pressure on the viscosity of polystyrenes and FEP resins is similar, one expects that the effect of viscous heating should also be of similar significance. Shidara and Denn (1993) also pointed out that a numerical solution of the full field in capillary/slit flow incorporating pressure and temperature effects is needed. This solution is also needed in order to calculate the slip velocity as a function of the wall shear stress in the present case. The numerical simula-te Q_ co CO CD 1_ CO (0 CD . C CO "TO i 1111 i i i i i 1111 Teflon FEP 3100 I I I I I I I I I I I I I I I I I I T=325°C L/D=40 0.2 A • A 0.1 - -0.08 -0.06 & • D=0.508 mm • D=0.762 mm 0.04 A A A D=1.270mm 0.02 i i i 11 i i i i i i i 11 i i i i i i 111 1 101 102 103 104 Apparent shear rate (yA), s_1 Figure 5-8. The effect of the capillary diameter on the flow curve of resin FEP 3100 at 325 °C. Wall slip is present in the regions where the flow curve becomes diameter dependent CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 76 tion of the capillary flow subject to viscous heating will be discussed in Chapter 7. It should be mentioned that the diameter dependence of the apparent flow curves was also observed for FEP 3100 as can be seen in Figure 5-8. There, the apparent flow curves obtained by using capillaries having a fixed LID ratio and different diameters are plotted. The diameter dependence is clear in the oscillating flow region but less evident at higher shear stresses, which may be attributed to the effect of viscous heating as discussed above. 5.8 Extrudate Distort ions Samples of FEP 4100 extrudates produced at various shear rates using a capillary having a length-to-diameter ratio of 40 and diameter of 0.762 mm are shown in Figure 5-9a-e. Five extrudate samples are shown, each one corresponding to the five different flow regions discussed previously. At low rates the extrudate appears smooth (Figure 5-9a). At higher shear rates, small amplitude periodic distortions appear on the surface of extrudates (sharkskin or surface melt fracture, Figure 5-9b) and this behavior is obtained over a short range of apparent shear rates. The extrudate obtained in the unstable flow region (oscillating melt fracture) consists of two distinct zones (Figure 5-9c): a smooth section, corresponding to slip with decreasing pressure (superextrusion region), and a rough one, corresponding to stick with increasing pressure (sharkskin region). The onset of oscillating melt fracture is characterized by a sharp decrease in the slope of the flow curve (Figure 5-4). As one may see from Figures 5-5, 5-7, and 5-8, the critical shear stress for the onset of sharkskin is independent of the diameter and length-to-diameter ratio of the capillary die. At higher apparent rates in the superextrusion region, the CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N 8 FEP RESINS FOR WIRE COATING .77 Figure 5-9. Representative photographs to illustrate the extrudate appearance of FEP 4100 extrudates in the five flow regions extrudates seem to be smooth (Figure 5-9d) but not as glossy as in the prefractured region. Finally, the gross melt fracture region is characterized by severe irregularities where the distortion depth is of the order of the extrudate diameter (Figure 5-9e). The severity of distortions increases with the shear rate. The onset of gross melt fracture was detected to occur at a critical shear stress of about 0.22 MPa for capillary dies having L/D ratios from 10 to 100. The effect of temperature on the various flow regimes in the capillary extrusion of FEP 4100 is illustrated in Figure 5-10. There, the FEP4100 flow curves, obtained with a capillary die having a diameter of 0.508 mm and an L/D ratio of 40 are plotted for three different temperatures. It can be seen that in the stable region, as the temperature is increased, the flow curves shift to higher values of the wall shear stress as expected (higher viscosity). However, the onset of oscillating melt fracture occurs at smaller apparent shear rates and wall shear stresses as the temperature is decreased. As a result, the flow curves at different temperatures cross each other and, at high enough apparent shear rates, almost coincide. The superextrusion region (smooth extrudate at conditions CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 7 8 0.4 CO Q_ 0.2 ^ 0.1 CO a> 0.08 co co 0.06 CD sz CO 1 0.04 0.02 1 1 1 1 1 1 1 1 1 1 1 1 1 Teflon FEP 4100 1 i i i i i II | i i i i i i 111 D=0.508 mm L/D= =40 _ | • - A A A • f I I t *•* • • A • • A A • • A • " A • T=300°C • • A • T=325°C • A T=350°C • A • A Open symbols correspond to superextrusion region i i 111 i i i i i i i 1 i i i i i i 111 i i i i i i 111 101 102 103 104 Apparent shear rate (yA), s-1 Figure 5-10. The effect of temperature on the flow curve of resin FEP 4100. Note the strong effect of T on the superextrusion flow region beyond the oscillating melt fracture region) is also affected by temperature. It can be seen from Figure 5-10 (open symbols) that at 350°C the superextrusion region expands over a range of apparent shear rates between 700 and 2000 s"1, at 325°C this range becomes shorter, between 470 and 700 s"1, while for 300°C there is no clearly defined superextrusion region at all. CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 79 5.9 The Oscillating Melt Fracture Figure 5-11 shows the pressure drop as a function of time during a typical run in the oscillating melt fracture region. It can be seen that the pressure always oscillates between two extreme values, with the frequency of the oscillations increasing as the amount of material in the rheometer reservoir declines. Also, near the end of the run, the pressure drop amplitude decreases gradually. The oscillations are mainly due to the combined effect of the wall slip and of the compressibility of the material resin (Hatzikiriakos and Dealy, 1992a; Pearson, 1965). The effect of compressibility can be seen better in Figure 5-12, where the period 22 20 i i i i I i i i i I i i i i I i i i Teflon FEP 4100 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 T=350°C L/D=20 ^=347.2 s-1 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 0 100 200 300 400 500 600 700 800 900 1000 Time (r), s Figure 5-11. Pressure drop oscillations during capillary extrusion of resin Teflon FEP 4100 at 350 °C. Note that the frequency of pressure drop oscillations increases with decrease of the material in the barrel CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING .80 of oscillations is plotted as a function of the length of the reservoir occupied by polymer. In general, an essentially linear relationship is obtained for all three cases between these two variables, which clearly shows the effect of the compressibility of the material. In other words the period of oscillations scales linearly with the amount of polymer in the rheometer reservoir as it is pointed out by Hatzikiriakos and Dealy (1994) . 0 50 100 150 200 Length of barrel (I), mm Figure 5-12. The period of oscillations as a function of the volume of polymer (FEP 4100) in the rheometer reservoir for three capillary dies having different L/D ratios and a constant diameter at 350 °C CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 81 However, it was expected that for a fixed length of the barrel occupied by polymer, the period of oscillations should scale with the L/D ratio (Hatzikiriakos and Dealy, 1992a). This does not seem to be the case as may be inferred from Figure 5-12, i.e. the period of oscillations increases from L/D=\Q to L/D-20 but decreases from L/D=20 to L/D=40. In addition, as previously discussed, the difference between the two extreme shear stress values does not also scale with the L/D ratio as in the case of the oscillating melt fracture of HDPE's (Hatzikiriakos and Dealy, 1992a). Moreover, within this flow region, multiple "windows" of apparent shear rates were identified where the pressure drop instead of oscillating assumes a steady-state value. For example, Figure 5 -co 0-Q . O i_ T3 (D i_ ZJ GO co CD 22 20 18 16 14 12 10 8 I I I I I I I I I I I I I I I I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Teflon FEP 4100 : — I T=350°C j L/D=20 : - / ^=347.2 s-1 _I /l 1 I 1 I 1 I I I I 1 1 1 1 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 0 100 200 300 400 500 600 700 800 900 1000 Time (f), s Figure 5-13. A repeat of the experiment plotted in Figure 5-11. Instead of persisting oscillations, a stable response is obtained CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING .82 13 shows one repeat of the experiment plotted in Figure 5-11. Instead of obtaining oscillations, the pressure drop tends to assume a steady-state value. This same experiment has been repeated several times and it was found that in some cases oscillations persist throughout the experiment (Figure 5-11), while in the other cases the pressure after overshooting tends to assume a steady-state value (Figure 5-13). It is noted, however, that the steady-state value of the pressure in Figure 5-13 is about equal to the average o f the two extreme pressure values of the oscillations plotted in Figure 5-11. It seems that the pressure response is sensitive to the initial conditions which could be different in the two experiments, i.e., small fluctuations in temperature of ±1 °C. Even such a small variation in the initial temperature can give a much different response. Recently, Pudjijanto and Denn (1994) discovered a stable "island" in the slip-stick region o f a linear low-density polyethylene. This island exists only in a narrow temperature window and a small variation of temperature, i.e., of the order of 1 °C , can interchange oscillatory and stable responses. 5.10 A Comparison of the Processability of the two FEP Resins A s noted above, experiments for F E P 3100 were also carried out to identify differences in the processing between the two F E P resins. While these two resins have close molecular weight and polydispersity, a small amount of P A V E has been incorporated in the molecules of F E P 4100 (about 0.8 wt.%). As noted before, the viscosity of F E P 4100 is about 25% lower than that of F E P 3100 which can be attributed to a difference in the molecular weight (see Figure 5-8). Figure 5-14 shows the apparent flow curves of the two resins obtained at the temperature of 325°C using a capillary CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 83 having an L/D ratio of 40 and D equal to 0.508 mm. In general, FEP 3100 exhibits the same behavior as FEP 4100, and one could distinguish the same flow regions as those identified for FEP 4100. However, some of the differences observed can be summarized as follows: • The critical apparent shear rate for the onset of sharkskin melt fracture of FEP 3100 Q_ i oo oo CD •*—> 00 i _ CO CD SI 00 JO 0.2 0.1 0.08 0.06 0.04 0.02 i i M [ 1 — i — i — i — i 1 1 1 1 1 — i — i — i — i 1 1 1 1 1 — i — i — i — i 1 1 1 1 — T=325°C L/D=40 • • m ° D • • • D y • D • • 8 • • • • • Teflon FEP 3100 • Teflon FEP 4100 • i H I i i i _i i i i i 111 i i i i i M I 101 102 103 Apparent shear rate (yA), S'1 104 Figure 5-14. A comparison of the flow curves for two FEP resins (FEP 3100 and FEP 4100) at 325 °C CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING .84 was found to be about 40 s"1 while that for FEP 4100 is about 70 s"1. Thus, the presence of PAVE in FEP 4100 greatly extends the range of the stable region. • The oscillations of the pressure drop for FEP 3100 have a much smaller amplitude than for FEP 4100. In spite of this, the extrudates of both resins still exhibited the stick-slip melt fracture appearance. • The range of the superextrusion region for FEP 3100 is wider; it ranges from 250 s"1 to 700 s"1. However, the critical conditions for the onset of gross melt fracture are practically the same in both resins. • Finally, the addition of PAVE makes the molecules more flexible. This increases the melt strength, improves the stress crack resistance, and, as a result, allows higher speeds in wire coating (Stewart, 1994). 5.11 Effect of the Molecular Weight Capillary rheometer experiments were carried out with a series of TFE/HFP copolymers (Group B in Table 4-2) in order to assess their processability and its relationship with molecular weight and structure. Figure 5-15 shows the flow curves for three FEP resins having different molecular weights. It can be seen that all resins have an almost Newtonian viscosity in the prefractured region at fairly high shear rates. The onset of the sharkskin melt fracture occurs at the same value of the wall shear stress, but due to different viscosities it appears to occur at lower critical values of the apparent shear rate for resins with higher molecular weights. The superextrusion region starts approximately at the same value of the apparent shear rate for all resins. Beyond this region, the curves seem to coincide. At these high shear rates, where the flow virtually becomes plug-like, CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING .85 0.5 0.4 0.3 Q_ I 0.2 CO CO CD -i—< CO 0) | 0.08 CO i 0.06 h co B : 0.04 < 0.03 0.02 1 1 1 1 1 1 1 1 1 " Teflon FEP i i | i i i i i i 11 - T=325 °C, D=0.762 mm, L/D=40 Sharkskin Gross melt fracturea -A A A Superextrusion • - • A • • A • 1 A / " 2 M w 1>M w 2>M w 3 A 3 Open symbols correspond to stick-slip region i i i 11 101 102 10; 104 Apparent shear rate (yA), s_1 Figure 5-15. The effect of molecular weight on the flow curve of TFE/HFP copolymer resins (FEP-1, 2, and 3 of Group B in Table 4-2) the pressure drop is mainly governed by the friction between individual monomers and the wall (strong slip), and apparently the polymer properties become independent of molecular weight. Also, at these high rates, viscous heating and energy dissipation at the polymer-wall interface are high enough to also affect the shape of the flow curves. CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING .86 0.3 0.2 CL i 00 CO CD V _ -t—> CO CO CD _ c oo JO 0.1 0.09 0.08 0.07 0.06 0.05 0.04 1 1 1 1—I I I I I I I I I I I I j Teflon FEP T=325°C D=0.762mm L/D=40 "T 1 1 1 1—I I I Sharkskin t 2 a o 8 * 8 ^ 2 Stick-slip Super Gross MF A ft 0 A 0 A o c CD CO • TFE/HFP/PAVE 3 § © O A J i i i 1 1 1 _ i i i i 1 1 ' i i i i 101 102 103 Apparent shear rate (yA), s"1 104 Figure 5-16. The effect of PAVE content on the flow curve of TFE/HFP/PAVE terpolymer resins (TFE/HFP/PAVE-1, 2, and 3 of Group C in Table 4-3) 5.12 Effect of the PAVE Content The effect of the incorporation of PAVE into molecules of the copolymer was discussed in some previous sections. In this section, an attempt to assess the effect of the PAVE content on the processability of the terpolymer was made. CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING .87 Figure 5-16 plots the flow curves for three FEP terpolymers having different contents of PAVE (the resins of Group C, Table 4-3). Unfortunately, because of the small variations in the PAVE content in the resins, it was impossible to identify significant differences in their processability as it can be assessed by means of a capillary rheometer. One can see that rheology does not change much with increase in the PAVE content. A small difference in the viscosity of the resins in the prefractured region (within 10%) is consistent with the results obtained in a parallel-plate rheometer (see Chapter 4). The critical shear stress corresponding to the onset of melt fracture as well as the breadth of each flow region are about the same for all the resins and close to those of FEP 4100. However, from practical tests on wire coating, where elongational flow is dominant, it is noticed that, in general, the resins with the higher content of PAVE are processed better (Stewart, 1994). CHAPTER 5 - CAPILLARY FLOW MEASUREMENTS OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 6 Rheological Characterization of Teflon® FEP Resins .88 he rheological data for a number of Teflon® FEP polymers, obtained by ^^^J means of both a parallel-plate and capillary rheometers, were used for a ^ ^ ^ ^ ' thorough rheological modeling of the behavior of these resins. The latter includes calculation of their linear relaxation time spectra and nonlinear parameters using a multi-mode Phan-Thien and Tanner (PTT) constitutive equation. The relaxation time spectrum, H(X), calculated by use of the BSW model (developed for monodisperse linear polymers) followed a scaling relationship in the terminal zone with a scaling exponent of 0.13. However, at higher frequencies the model fails to predict adequately the experimental data. The longest relaxation time calculated from both the BSW model and the discrete relaxation spectra (Ah g,), which was determined by use of a parsimonious fitting software, depends on the molecular weight in a similar way as the zero-shear viscosity does with the well-established scaling factor of 3.4. It was found that the PTT model can represent rheological data for Teflon® FEP resins very well and may be used in relevant processing flow simulations, e.g. in wire coating. 6.1 Introduction The molecular mobility of polymeric liquids expresses itself in a relaxation time spectrum. It can be written as a continuous function, H(X), or as a sum of discrete terms, each of them having a characteristic time constant, A,, and a so called relaxation strength, gi (see Equation (2-42)). Modeling of polymer processing and analysis of processing CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING .89 experiments require knowledge of the relaxation time spectrum. It allows prediction of linear stress responses, e.g. in start-up of shear followed by relaxation, step strain, etc. Moreover, at large strains or strain rates, where some additional strain dependent perturbations of the constitutive equation are needed, the time dependent part of the rheological behavior is completely described by H(X). Therefore, it is significant to have available the means of converting dynamic mechanical data (dynamic moduli G ' and G") into the relaxation time spectrum. The determination of the relaxation time spectrum has been recognized as an ill-posed problem with degree of ill-posedness increasing as the number of relaxation times increases (Tschoegl and Emri, 1993; Honerkamp and Weese, 1989). The ill-posedness means that infinitely many parameter sets can be found that are equally satisfactory from the point of view of fitting the data. Baumgaertel and Winter (1989) showed that this problem can be avoided by simply keeping the number of relaxation modes small. They developed an algorithm for recovering the discrete relaxation spectrum from linear viscoelastic data known as parsimonious spectrum (PS) (Baumgaertel and Winter, 1992). The corresponding numerical code is commercially available and known as IRIS. The basic idea of this method is to find the spectrum with the smallest number of Maxwell modes that still represents the data within the experimental error margin. This can be obtained by a simultaneous adjustment of h and gt, which are treated as freely adjustable material parameters during the fitting procedure. The right choice of the number of relaxation modes, N, is essential for the success of the algorithm. For small values of A7, the spectrum is too coarse, and model calculations using the spectrum appear wavy. As more and more modes are considered, the waviness and the deviation between the fitted CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 90 spectrum and the data decrease. This can be shown in Figure 6-1 where the minimized standard deviation, SD, is plotted. It is defined as 1 M S D 2 = — y 1-1 £g,(a>M 2 G ' K ) 7 ^ 1 + K A , . ) 2 + 1 1 G ' t o ) & l + K 4 ) a "|2 (6-1) where M is the number of data points. The noise in the data set yields a natural limit to this improvement since the fit cannot be better than the standard deviation due to the noise. Taking more modes is meaningless because the fitting does not improve significantly with the extra modes and the values of gt fluctuate erratically. The resulting spectrum is claimed to be unique since various very differently looking discrete spectra recovered by this procedure reduce to the same continuous spectrum H(X). Details of the 10° I 10 to CD 1 ro cr co co S 10-2 -1 L 10" 1 1 1 r 1 1 1 r "i i 1 r n 1 1 r Result of fit \ \ Optimum range \ v _i i i i_ 0.5 1.0 1.5 2.0 2.5 N/decade Figure 6-1. The standard deviation between the best possible fit and data. The fit improves when the number of Maxwell modes increases. Above a certain number of modes, the fit does not improve much further and the problem becomes ill-posed (from Winter et al, 1993) CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 91 method can be found elsewhere (Winter et al., 1993; Winter, 1997). An alternative way to describe the relaxation time spectrum is to define correlations between the molecular parameters and macroscopic properties such as the longest relaxation time, plateau modulus, etc. Unfortunately, this can be done only for limiting cases. Baumgaertel et al. (1990) found that the relaxation spectrum of linear flexible polymers with molecules of (nearly) uniform length can be very well represented as H(X) = + vAnax J for X < X„ for X > X„ (6-2) where GN° is the plateau modulus, X^^ is the longest relaxation time, ne and ng are the slopes of the spectrum in the entanglement and glass transition zones, respectively, and Xc is the crossover time to the glass transition. The first term in the brackets represents the high frequency glass transition region, while the second term describes the entanglement and flow region. Equation (6-2) was tested using data for narrowly distributed polybutadienes and polysterenes and gave excellent results. Later, Baumgaertel and Winter (1992) modified this spectrum to suit broadly distributed polymers by replacing the abrupt cut-off at the longest relaxation time with a stretched exponential cut-off, as follows: H(X) = H, f X v"< + »EG°N rX^ exf>(-X/Xmaxy for MW»MC (6-3) where Hg is the glass-transition constant, Mw and Mc are the molecular weight and critical molecular weight, respectively, and /? is the cut-off exponent. CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING .92 In this chapter, the effect of MW on the relaxation spectra of Teflon® FEP resins was studied. The spectra are determined by use of both the method employing the BSW relaxation spectrum and the parsimonious method. For this purpose, a numerical code capable of recovering the discrete relaxation spectra from dynamic mechanical data was developed. The Phan-Thien and Tanner (PTT) constitutive model (Phan-Thien and Tanner, 1977) was also used to fit the experimental data from both capillary and parallel-plate rheometers to identify the additional nonlinear parameters that are necessary to carry out numerical simulation of complex viscoelastic flows. 6.2 Method of Evaluating Relaxation Time Spec t rum The method of calculating the relaxation time spectrum is similar to that described in Winter (1997). The discrete relaxation spectrum corresponds to a discrete relaxation modulus with a sum of exponential decays (Maxwell modes): G(t) = fjgi[exp(-t/Xi)] (2-42) i=i where gy=//,A,(ln/l).A finite number of Maxwell modes, A7, has to be determined: (gy, X,) with i=\,2,...,N. To calculate gy, one must know the step size A,(liU). A variable size is used in this work since this allows a closer fit of the data with fewer parameters. Both gy and Xi are variable in the spectrum calculation. The range of frequencies of the small amplitude oscillatory shear tests, a>min CD •o CO c to -*-• CO l O 2 I I I I I I I I Dowlex 2049 -_ S D scatter -" I I I I i i i i -3 4 5 6 7 8 9 10 11 Number of relaxation modes (N) 106 CO 0. io5 o>104 tz £ 102 101 1 1 1 lllllj 1 1 l l l l l l j 1 1 l l l l l l j 1 1 l l l l l l j 1 1 l l l l l l j 1 1 l l l l l l • Dowlex 20491 - • T=200 °C 1 E • Mini : • : linn i • i mill - • • i 11in linn i i i • i i i mill 1 Ill i i I I mil i mini i 11 mi l l i 1 i i m m 10-4 10-3 10-2 10-1 10° 101 Relaxation time (A), s 102 Figure 6-3. Dependence of the standard Figure 6-4. Relaxation time spectrum for deviation on the number of Dowlex 2049 at 200°C (8 relaxation mode modes) Comparative test 2: model polybutadiene star polymer. The data for the second test is taken from Vlassopoulos et al. (1997). In this case, the shape of the mastercurves for the loss and storage moduli is significantly more complex than that in the previous case (see Figure 6-5). Nevertheless, the fit obtained by the UBCFIT software is still very good (plotted in the same figure). Figure 6-6 plots the dependence of the standard error on the number of relaxation modes. One can see that acceptable accuracy is achieved with 14 relaxation modes. The fit does not improve significantly for iV>14. The IRIS software resulted in 16 relaxation modes with a standard deviation higher than that obtained by UBCFIT with 14 modes (see Figure 6-6). Figure 6-7 depicts the resulting relaxation spectrum. Overall, the developed software for evaluating relaxation time spectra produces results not worse than those obtained by commercial software such as IRIS. CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON 1 " FEP RESINS FOR WIRE COATING .96 10M0^10-M0M0-310-210-1 10° 101 102 103 104 105 106 107 Frequency (coaT), rad/s Figure 6-5. Storage and loss moduli for star polymer polybutadiene 12807 (Vlassopoulos et al, 1997). Solid lines represent the fit obtained by means of UBCFIT software. 0.26 h F~l 1 1 1 1 1 1 Polybutadiene 12807_ o w .1 024 to '> CD 10.22 T 3 C CD w 0.20 SD IRIS (16 modes) SD UBCFIT (14 modes) J I I I L _ _L 8 10 12 14 16 18 20 Number of relaxation modes (N) Figure 6-6. Dependence of the standard deviation on the number of relaxation mode for star polymer PB 12807 1011 gn^ IIII^ niq iiiiq IIII^ IIII^ IIU^ IIII^ IIII^ IIII^ IIII^ IIII^ IIII^ in^ una "(0 101° D. 109 c 108 c 107 o +3 CO X 106 OS CU Dl 105 104 t o Polybutadiene 12807: Tref=-83°C 1 o A IRIS (16 modes) ° ^ E O UBCFIT (14 modes) - u J l l l l j l l l J l l l l J l l l l J llllJ l l l l J l l l l J l l J l l l l j l l l l J MI l J llll M -10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 Relaxation time (log A), s Figure 6-7. Relaxation time spectrum for PB 12807 at -83°C. Comparison of the UBCFIT and IRIS spectra CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING .97 6.3 Rheological Characterization Using Relaxation Spectra 6.3.1 A Method to Estimate the Critical Molecular Weight In Chapter 4, the value of the critical molecular weight, ME, for TFE/HFP copolymers was experimentally obtained that seems to be quite high compared to those previously reported in literature. Below, a method to calculate ME, which seems to support the conclusion drawn in that chapter is presented. For linear flexible polymers, the entanglement molecular weight, ME, can be calculated from (Van Krevelen, 1991; Larson, 1988) K = g „ ^ <«> where gN is a numerical factor (close to 1 for flexible polymers), p is the polymer density, and GN is the plateau modulus. In general, the plateau modulus is independent of the molecular weight and its distribution, for polymers with MW greater than ME. Knowing GN, it is possible to calculate the critical molecular weight as M<&2Me, where ME can be calculated from Equation (6-6). Unfortunately, the plateau modulus is a difficult, sometimes impossible quantity to measure. Usually, it is calculated from dynamic mechanical data for monodisperse polymers where a well-defined plateau in the G' plot or a maximum in G" appears (Ferry, 1980). Using this approach, Wu (1985) found the value of GN for a series of FEP resins to be equal to 1.2xl06 Pa. Similarly, Tuminello (1989) reported a value of l . l x lO 6 Pa. However, in most cases, this approach is not applicable, because the dynamic moduli curves do not exhibit a plateau or a maximum. For example Figure 4-1 shows neither a plateau nor a maximum in the G', G" curves, thus making calculation of GN problematic. Moreover, when the dynamic moduli do CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING .98 exhibit such behavior, it does not assure the accuracy in the GN determination. This is the high frequency range where spectrometers exhibit the highest experimental error. As an alternative way to calculate GN, one can make use of the empirical BSW relaxation time spectrum. Referring back to Figures 4-1 and 4-2, one can see the well-defined terminal zone in both dynamic moduli curves. The terminal zone can be clearly identified by the characteristic slope of the moduli in the low frequency region. Thus, neglecting the contribution of the glassy region in the BSW spectrum (Equation (6-3)), one can calculate its parameters (including GN) by fitting the contribution of the flow region to experimental points in the terminal zone by means of the following formulae: The fitting procedure is similar to that described by Jackson et al. (1994). The BSW fitting for the terminal zone is shown in Figures 6-8 and 6-9. The value of GN found from this analysis turned out to be equal to 1.41 xlO5 Pa. Using Equation (6-6), the critical molecular weight recovered from GN is equal to 101,000 kg/kmol. This result is found to be much higher than the values reported by Wu (1985) and Tuminello (1989). However, the value of GN calculated in this work results in a value for the critical molecular weight that is remarkably close to that determined from the experimental data plotted in Figure 4-4 (a value forM c between 80,000 and 110,000 kg/mol). As mentioned above, this result for Mc seems to be quite high compared to those for other polymers. Indeed, for most polymers, the critical molecular weight lies in the due to the fact that the relevant experimental data points for the GN determination are in (6-7) (6-8) CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING .99 range between 3,000 for polyethylene and 35,000 for polystyrene (Porter, 1995) with a few exceptions that can have a much higher Mc. The same source reports a value of about 12,000 for the Mc of PTFE. This seems to be reasonable only if one compares the molecular weights of the repeating units in the molecules of PE and PTFE. However, for FEP, Mc should beat least about 1.5 times higher if the number of carbon atoms per Frequency fa>), rad/s Figure 6-8. The storage modulus G '(GO) of the TFE/HFP copolymers of Group A at 200°C. The solid lines represent the fit with the parsimonious (PM) spectrum. The dash-dotted lines are the fit with the BSW spectrum with stretched exponential cut-off calculated from the full set of experimental data. Finally, the dotted lines are the fit with the BSW spectrum to the terminal zone data points (closed symbols). The plateau modulus determined from the data analysis is also drawn as reference CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N 1 8 FEP RESINS FOR WIRE COATING 100 entanglement is the same because of the incorporated HFP copolymer, whose molecular weight is twice that of TFE (content of HFP in the copolymer is about 50 wt. %). Moreover, Teflon® or FEP molecules cannot exhibit the planar zigzag formation of the crystalline regions as PE macromolecules do. The large fluorine atoms restrict the Z 1 I I I I I I 11 I I I I I I I 11 1 I I I I I I 11 I I I I I I I I j 1 I I M i l l -: TFE/HFP T=200 °C : Frequency (oS), rad/s Figure 6-9. The loss modulus G"(a>) of the TFE/HFP copolymers of Group A at 200°C. The solid lines represent the fit with the parsimonious (PM) spectrum. The dash-dotted lines are the fit with the BSW spectrum with stretched exponential cut-off calculated from the full set of experimental data. Finally, the dotted lines are the fit with the BSW spectrum to the terminal zone data points (closed symbols) CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON18 FEP RESINS FOR WIRE COATING 101 flexibility of the molecule due to the nature of C-F bond and the repulsion between the negative fluorine atoms. As a result, the FEP molecule is a very stiff one, thus requiring a much higher molecular weight to be able to form entanglements. Therefore based on the experimental results that were also explained in terms of relevant modeling, it is believed that the critical molecular weight, Mc, for FEP resin should be several times higher than 12,000 (Wu, 1985) or 14,000 (Tuminello, 1989) and equal to about 100,000 kg/mol. An attempt to fit Equation (6-3) to the entire set of experimental data for the whole range of frequencies was also made. The results from this procedure are plotted in Figures 6-8 and 6-9. One can see that the fit was satisfactory only for the high molecular weight resins (ASp>300,000). On the other hand, it clearly fails for the resins with M»<200,000. This provides additional support to the conclusion that Mc should be very high as was observed experimentally. It is noted that Equation (6-3) is valid only for MW»MC (Baumgaertel and Winter, 1992). The value of Mc recovered by this fitting procedure turned out to be even higher, namely 136,000 kg/kmol. 6.3.2 The Relaxation Spectrum of TFE/HFP Copolymers The experimental data were also analyzed by means of a discrete relaxation spectrum (parsimonious model). The results of the parsimonius (PM) fit are also plotted in Figures 6-8 and 6-9. It can be seen that it describes all the available experimental data well. Figure 6-10 shows the calculated parsimonius (PM) relaxation spectra for the TFE/HFP resins (Group A in Chapter 4) together with the continuous BSW spectra. One can see that the discrete gi-values do not fall on the continuous curves. However, the CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 102 10 6 2 10 5 104 c 00 rz o c 10 3 CO X CO 10' TTTI 1 1 1 I I I I I I 1 1 1 I I I I I I 1 1 1 I I I I I I 1 1 1 I I I I I r T F E / H F P T = 2 0 0 ° C J I I I U I i i i\ i i 11 I O 3 10": i o - 1 10° 10 1 Relaxation time (X), s Figure 6-10. Comparison of the continuous B S W (continuous lines) and the discrete parsimonious (PM) spectra of the T F E / H F P copolymers o f Group A oo | 10i CD E c o 1 10° L-CO CD OO CD O) o 10"1 k T F E / H F P T=200 ° C O PM spectrum O slope=3.4 O O 100 200 300 400 500 Molecular weight ( M W ^ 0 ), kg/kmol Figure 6-11. The molecular weight dependence o f the longest relaxation time of the T F E / H F P copolymers of Group A calculated from the parsimonious ( P M ) model CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 103 ro Q_ '5> 106 105 104 |r C D J 103 CO c g 'co 102 X _(0 d) * 101 10° I T — i i i 111 1 i — i — T ~ r : A • A f # r™rr| 1 1 A T • i I I I I I I T A T 1 1—' I"I I | 1 1 1 — r T T T Teflon FEP 1 | 1 1 1 I I I 1 L T=300 °C ; • • T A -• f A 1 2 -• CO -i 1 J 1 » ' 1 ' ! i i i i 1 I 1 • 10-: 10": 10-1 10° 101 102 Relaxation time (A), s Figure 6-12. The discrete parsimonious (PM) spectra of the TFE/HFP copolymers of Group B (FEP resins) shape of the discrete spectra corresponding to the high molecular weight TFE/HFP is about the same as that of the continuous. The regular shift between the two types of spectra can be explained by discretization (Baumgaertel and Winter, 1992) and does not violate their equivalency. On the contrary, the shape of the spectra calculated by both methods for the low molecular weight resins is very different, thus supporting presented results forM c . Figure 6-11 depicts the values of the maximal relaxation time determined from the P M model as a function of the molecular weight Mw. One can see that the values of /Imax obtained in this way follow the expected power-law relation with a slope of 3.4. CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON* FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 104 Figure 6-12 represents the P M relaxation spectra obtained for the series of high melting point FEP resins (Group B in Chapter 4). The P M fit, together with the BSW fit, is shown in Figures 6-13 and 6-14. Note that the BSW fit is not as accurate as the PM. This is due to the much more complicated morphology of these melts that can not be described by this particular empirical spectrum which requires the existence of a terminal zone. While it can be seen from Figure 6-14 that the terminal zone seems to be reached (slope equal to 1), the G' curves in Figure 6-13 extend to lower frequencies without 10-2 10"1 10° 101 102 103 Frequency (co), rad/s Figure 6-13. The storage modulus, G'(co), of the TFE/FfFP copolymers of Group B at 300°C. The dashed lines represent the fit with the parsimonious (PM) spectrum, while the solid lines are the fit with the BSW spectrum using stretched exponential cut-off CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 105 attaining the limiting slope of 2. This suggests that either the terminal zone is not reached yet or crystallinity still plays a role in spite of the fact that pre-heating has been used. T 1 1—f—I I I I ] 1 1 1—I—I I 1 1 | 1 1 1—I—I 1 I I | 1 1 1—1 " T T I T ' I 1 1 1—I 1 F I 1J Teflon FEP T=300°C 10-2 10"1 10° 101 102 103 Frequency (co), rad/s Figure 6-14. The loss modulus, G"(co), of the TFE/HFP copolymers of Group B (FEP resins) at 300°C. The dashed lines represent the fit with the parsimonious (PM) spectrum, while the solid lines are the fit with the BSW spectrum using a stretched exponential cut-off CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING '. 106 6.4 Constitutive Modeling The Phan-Thien and Tanner model is a constitutive equation based on the network theory of concentrated polymer solutions and melts. In general, it can be written as follows: 1=1 — Zitrxfa +Af%+^Al(y-TL + V Y ) = -rj, % (6-10) where Z - exp —trx. ,x_ i^s the stress tensor, x, is the contribution of the z'-th ^ Si =) relaxation mode to the total stress, At and gt are the relaxation time and relaxation strength of the z'-th mode, respectively (relaxation spectrum), rj,=Argi is the viscosity of the z'-th mode, and y is the rate-of-deformation tensor. The particular form of Z was chosen because the exponential term results in a maximum in the steady-state extensional viscosity in accordance with experimental data on polymer melts (Hatzikiriakos et al, 1997a). In addition to the constants defining the relaxation time spectrum, this model involves two non-linear parameters per mode, si and £ . The former characterizes the rate of destruction of polymer segments in the network model and the latter, the rate of "slip" (non-affine) deformation. The term involving £. is most important in shear flows, and the parameter e, is dominant in shear-free (e.g. elongational) flows. The caret in Equation (6-10) denotes the upper convected derivative of r{, and is defined by: ^ = ^ + v - V x 4 - ^ - x 4 + x4-y) (6-11) CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 107 Fitting data by means of the PTT model requires knowledge of both the shear and extensional viscosities. The shear viscosity is readily obtained using a parallel-plate (low shear rates) and capillary (high shear rates) rheometers. The extensional viscosity can be estimated from capillary rheometry data by means of the Cogswell analysis (see Equations (2-31)-(2-33)). Using Equations (2-3)-(2-5) and (2-9)-(2-ll), the components of the matrix Equations (6-9)-(6-ll) can be rewritten for each mode as follows (Bird et al., 1987): • Simple shear: exp g (6-12) exp g "far + 0 ^ +^rfa, +ryy)-Xfryy = -ijf (6-13) ryy' exp g -far+O Tyy+^fTxy=0 (6-14) Simple extension exp - f a x + ^ + r J g (6-15) Tyy-. exp ' - f a + ^ + ^ J g yy yy (6-16) exp — far+^+O g rzz - 2Xezzz + 2%XSTZZ = -2ns (6-17) Equations (6-12)-(6-17) define 6xiV coupled algebraic equations for the stress tensor components in shear and shear-free flows, where N is the number of relaxation modes. They are solved with respect to the stress components in order to obtain the CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 108 values of the shear and extensional viscosities, rf = respectively. In turn, these calculated values are fitted to experimental data. The fitting algorithm works as follows. The linear parameters of the relaxation spectrum (Aj, g,) are first estimated by means of the UBCFIT software. They are used as an initial guess for the PTT fitting code. Then all the parameters are fitted simultaneously by means of an iterative minimization procedure in order to minimize the squared deviation between the Fi nl i i i 111 nl i i i 111 nl i i i 111 i l l i i i i 11 i l l i i i I 3 10-2 10"1 10° 101 102 103 Frequency {co*aT), rad/s Figure 6-15. The dynamic moduli mastercurves for Teflon® FEP 4100 at Tref=300°C. Solid lines represent the relaxation spectrum fit CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 109 calculations and the experimental data. The minimization method used for this purpose is the constrained BFGS method (Zhu et al, 1997). The PTT model parameters are subject to the following constraints: ei > 0 and 0 < ^ 1 (Phan-Thien and Tanner, 1977). As an example, let us consider Teflon® FEP 4100. The relaxation spectrum was recovered by means of the UBCFIT software and resulted in 7 relaxation modes (Table 6-2). The experimental data points for the dynamic moduli of FEP are plotted in Figure 6-15 along with the model predictions (solid lines) obtained using the calculated spectrum. Figure 6-16 shows the complex, shear, and extensional viscosity of FEP 4100 as a function of frequency, shear, and extensional rate respectively. All the data are reduced to 300°C. It can be seen that the complex viscosity (parallel plate rheometer) agrees very well with the shear viscosity (capillary rheometer) up to the point corresponding to the onset of melt fracture. Only the data from the prefractured region only were taken into account in this fitting procedure. The solid lines in Figure 6-16 represent the predictions of the PTT model with 7 modes for the rheological properties of this polymer. The parameters of the model are listed in Table 6-2. This example shows that the multi-mode PTT model can represent the rheological behavior of Teflon FEP resins quite well, and therefore such a model can be used effectively in process simulation such as wire coating. Tab! le 6-2. Parameters in the PTT constitutive equation for Teflon FEP 4100 i A(s) #(Pa) Vi (Pas) 6 £i 1 1.1470E-03 4.9050E+05 5.6260E+02 2.2040E-02 7.5680E-01 2 6.0390E-03 2.2702E+05 1.3710E+03 1.4960E-01 4.0030E-01 3 2.9410E-02 6.6202E+04 1.9470E+03 2.273 0E-01 8.1920E-01 4 1.9110E-01 4.8231E+03 9.2170E+02 2.0270E-01 8.2170E-02 5 1.6600E+00 1.7241E+02 2.8620E+02 5.6530E-02 1.9230E-03 6 1.0130E+01 1.8628E+01 1.8870E+02 6.8470E-02 8.2600E-02 7 5.6520E+01 3.6235E+00 2.0480E+02 5.0100E-02 1.6320E+00 CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF T E F L O N * FEP RESINS RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 110 10-2 10"1 10° 101 102 103 Frequency (coaT), rad/s; shear rate (yaT), s"1; elongational rate {eaT), s"1 Figure 6-16. The complex, shear, and extensional viscosity of Teflon® FEP 4100. The solid lines represent the fit obtained by means of a 7-mode PTT constitutive equation. CHAPTER 6 - RHEOLOGICAL CHARACTERIZATION OF TEFLON® FEP RESINS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 7 Modeling of Capillary Flow of Molten Polymers in he traditional way of determining the slip velocity of molten polymers is the classical Mooney technique which utilizes experimental data obtained from a capillary rheometer. However, measurements of the rheological properties of polymer melts in capillary flow at high shear rates are often complicated by viscous heating which is not taken into account by this method. A data analysis procedure based on a mathematical model for nonisothermal capillary flow of molten polymers is developed. Conduction, convection, and viscous heating are included, together with the effect of wall slip. The technique provides detailed velocity and temperature fields in the die and can be used to determine the slip velocity at high shear rates corrected for the effect of viscous heating. It is tested for the capillary flow of several polymers including polystyrene, polypropylene, high density and linear low density polyethylenes, and Teflon® FEP. 7.1 Introduction It is generally accepted that polymer melts, unlike Newtonian fluids, may violate the classical no-slip boundary condition of Newtonian fluid mechanics and slip over solid surfaces when the wall shear stress exceeds a critical value (Ramamurthy, 1986; Kalika and Denn, 1987; Hatzikiriakos and Dealy, 1991a). In several polymer processes, the melts are subject to very large shear stresses which often exceed this critical value (usually about 0.1 MPa). To simulate these processes realistically, a reliable slip velocity model is needed that adequately describes the interfacial behaviour of polymer melts. CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 112 It is also well known that whenever a viscous material is deformed in a flow field, some of the work of deformation is converted into thermal energy by means of viscous dissipation (Winter, 1977; Cox and Macosko, 1974). This phenomenon, generally known as viscous heating, is typical in the processing of molten polymers. Most polymers have high viscosities and low thermal conductivities, which in combination with large process shear rates can lead to significant temperature increases. One of the common tools used to study the rheological behaviour of molten polymers as well as the wall slip phenomenon is a capillary rheometer. The traditional way to detect the presence of wall slip and quantify it, is by using experimental data from a capillary rheometer and the classical Mooney method (Mooney, 1931). This technique requires the performance of capillary experiments with a series of dies having the same length-to-diameter ratio, L/D, in order to keep constant the effect of pressure and different diameters, D. If slip occurs, the flow curves (wall shear stress versus apparent shear rate) start diverging (become diameter dependent) at a certain value of wall shear stress. This value is taken to be the critical shear stress for the onset of slip. The Mooney method has been used for a variety of polymers by several authors in the past to determine their slip velocity as a function of the wall shear stress (Lupton and Regester, 1965; Blyler and Hart, 1970; Ramamurthy, 1986; Hatzikiriakos and Dealy, 1992a). One of the basic assumptions of the Mooney method is that the temperature and pressure effects (see Section 2.3.3) can be neglected. However, it is reasonable to expect that the effect of viscous heating can be quite significant at sufficiently high shear rates at least for some types of polymers. Thus, one would expect that the Mooney method cannot be applied in all cases. Indeed, many researchers have pointed out that CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF T E F L O N 1 8 FEP RESINS FOR WIRE COATING 113 experimental data points on the Mooney plot (apparent shear rate versus inverse of capillary diameter) often do not fall on a straight line as this technique presumes (Lupton and Regester, 1965; Shih, 1979; Hatzikiriakos et al, 1995). Instead, the data define curves exhibiting a tendency to bend towards the higher apparent shear rates with increase in the die diameter (convex downwards). Usually such anomalies are ignored by researchers in the field, which may lead to inaccurate slip velocity calculations. Viscous heating in the capillary extrusion of polymer melts has been the subject of several reviews and studies over the past decades (Winter, 1977; Warren, 1988). Essentially, most of the previous investigators solved the mass, momentum, and energy equations which describe laminar flow in a capillary or slit under conditions where viscous heating is important (Ybarra and Eckert, 1980; Dinh and Armstrong, 1982; Milthorpe and Tanner, 1987; Ko and Lodge, 1991). However, very few of them considered the combined effects of viscous heating and wall slip in their numerical analyses. An attempt to do this was made by Lupton and Regester (1965). They carried out an analysis of the combined effects of slip velocity and viscous heating by using a simplified mathematical model for the flow of a power law fluid, in an attempt to explain the origin of melt fracture. In this chapter, the results of a numerical simulation of the capillary flow for polymer melts are presented in order to assess the effect of viscous heating on the slip velocity measurements. Moreover, using the mathematical model, a new data analysis procedure is proposed which is found to be suitable for slip velocity calculations corrected for the effect of viscous heating. The method is applied successfully to CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 114 experimental data for several polymers, including polypropylene, high density and linear low density polyethylenes, and Teflon® FEP. 7.2 Mathematical Model Consider flow of a non-Newtonian fluid in a capillary of radius R and length L where r and z are the coordinates in the radial and axial directions respectively. The relevant nonzero velocity components are vr and vz, and the relevant physical properties of the fluid under consideration are its density, p, heat capacity, Cp, and thermal conductivity, k. For the mathematical model one can make the following assumptions: • Steady laminar axisymmetric flow prevails. • Flow is assumed to be fully-developed at z=0. This assumption is based on laser velocimetry measurements showing that the velocity profile approaches its fully developed form within a distance of about O.W (Dealy and Wissbrun, 1990). • The radial velocity is sufficiently small to be neglected in the momentum and energy equations, and is included only in the continuity equation. • Pressure variations in the radial direction are small compared to those in the axial direction. • The effects of inertia and gravity are negligible. • Axial heat conduction is negligible compared to axial convection. • The heat capacity and thermal conductivity are considered to be temperature dependent and the fluid density is pressure and temperature dependent. The relevant CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 115 equations to calculate these properties are taken from Van Krevelen (1991) and given later in this chapter. Fluid viscosity is a function of temperature and pressure and the fluid follows a "power-law" model. The re-component of the stress tensor may be written as follows: Tr2=KexV[aP + A(T^-T)]-^ \dr j (7-1) where Tn is the rz component of the stress tensor, P is the absolute pressure, T is the temperature, T^/is a reference temperature, K and n are the consistency index and the power law exponent of the power-law model, respectively, and a and A, are the pressure and temperature dependence coefficients of the viscosity respectively. • There is a finite slip velocity at the wall us. With these assumptions the equations of continuity, momentum and energy reduce to: 1 d(rpvr) d(pvz) r dr dz 0 dz r dr = 0 _ dT Id y dz r dr f rk— \ + T V rz ydr j rp OP + lev.— 2 dz R The mass flow rate constancy equation is: 2n^pvzrdr = m 0 Boundary conditions: (7-2) (7-3) (7-4) (7-5) (7-6) 2=0: T=T0 z=L: P=Pa r=0: dT/dr=0 dvzldr=0 vr=0 CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 116 r=R: vz=u. vr=0 cJT k. 1 (T~T0) •s cr kR ln(l + t/R) where kw and t are the thermal conductivity and thickness of the wall respectively, 7o=const is the temperature of the surroundings (at the outer surface of the die) taken to be equal to that of the polymer at the die inlet. The second term on the right side of Equation (7-4) is the viscous heating term while the last term allows for the effect of expansion cooling due to fluid compressibility. that Equation (7-4) is valid for both purely viscous and viscoelastic materials and independent of the choice of the constitutive equation (Astarita and Sarti, 1974). The thermal boundary condition at the wall is not known in general, and one has to guess this condition. Most of the studies prescribe idealized conditions (without heat generation due to slip) such as: • constant wall temperature (7V=const) • adiabatic wall ( dTjdr - 0 ) • constant heat flux at the wall (dTjdr = const) The latter condition was successfully used in previous studies (e.g. Winter, 1977) and is believed to be the most realistic one. Only this thermal boundary condition will be used in numerical calculations. For the sake of simplicity, the local slip velocity is modeled at this point by a modified power-law expression (no pressure and temperature dependence): The parameter sis the coefficient of thermal expansion defined as s = — . Note P\ST)r a m (7-7) 10 CT w CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 117 where Tg: k(T) = k(Tg) -(1.2- 0.2 -T/Tg) (7-12) where Tg is the glass transition temperature (K), and k(T) is in W/(m-K). All constants for the four resins studied (polyethylene, polypropylene, polystyrene, and Teflon® FEP) are tabulated in Table 7-1. Table 7-1. Physical properties of the studied polymers Type of polymer TV, bar m, cnrVg M, g/mol Cp29*, J/(mol-K) Tg,K k(Tg), W/(m-K) Polypropylene 2470 0.83 42.1 91 260 0.144 Polyethylene 3290 0.88 28.1 63 195 0.326 Polystyrene 1870 0.82 104.1 178 373 0.172 Teflon® FEP 1680 0.495 100 96 200 0.100 7.4 Numerical Ana lys i s and Results To study the combined effect of viscous heating and wall slip, numerical simulations for the flow of a hypothetical polymer melt having physical properties similar to those of a typical polystyrene melt, were performed. These constants were found in Van Krevelen (1991) and are listed in Table 7-2. Three cases were analyzed numerically CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 120 in order to understand the relative significance of the viscous heating and slip flow effects on the flow curve (wall shear stress X a b l e 7 _ 2 Constants in Equations (7-1)-(7-7) for a hvDOthetical oolvstvrene fluid versus apparent shear rate): • No v iscous heating with slip • Viscous heating with no slip • Viscous heating with slip For the sake o f simplicity, no Equation (7-1) 0.02 K, Pas" 35000 Tref, °C 190 a, Pa 3.5-10"9 n 0.4 Equation (7-7) a 1.2 , T, and P. In short capillaries where the temperature rise is relatively small, it increases nearly linearly along the die. As the LID ratio increases, the pressure becomes a factor and the average slip velocity decreases. However, since the effect of viscous heating is more pronounced for longer capillaries, the slip velocity is not constant throughout the die any more, thus decreasing with increase of temperature. The dip in the slip velocity profile becomes larger and deeper as the LID ratio increases. At the die exit the reduction of pressure causes the slip velocity to increase, thus diminishing the effect of temperature. Figure 7-8 presents predicted slip velocity, wall shear stress, pressure and temperature rise profiles (axial) for capillaries having LID=40 and different diameters. The same trend can be observed in this case; that is, the slip velocity first decreases due to viscous heating, then passes through a minimum, and increases close to the die exit as a result of pressure reduction. The curvature of the slip velocity profile depends on the temperature rise which is greater for capillaries having a larger diameter. CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 137 I— i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 20 ^. CO 16 -Z I I I I I I I I I I I I I I I I I I I I I I I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 0.35 1 T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r i ' i i I i ' i i I i i i i I i i i i I i i i i 3 0.0 0.2 0.4 0.6 0.8 1.0 Axial position (z/L) Figure 7-8. Calculated axial slip velocity, wall shear stress, pressure and average temperature rise in the capillary flow of a polypropylene resin for three dies having the same L/D ratio and various diameters CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON* 1 FEP RESINS FOR WIRE COATING 138 8 4 0 -4 -8 K 8 < -4 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r Polypropylene T=200 °C, D=1.27 mm, z/L=1 - — L/D=10 L/D=40 - — L/D=70 j i i i _ j i i i _ _ i i i L_ _] i i i _ ~ i — i — i — i — | — i — i — i — i — Polypropylene T=200 °C, L/D=40, z/L=1 D=0.508 mm D=0.762mm D=1.270 mm i 1 1 i 1 1 1 1 r n 1 1 r \ V J I I I I I I I I I I I I I I I I I I I I I L 0.0 0.2 0.4 0.6 Radial position (r/R) 0.8 1.0 Figure 7-9. Calculated radial temperature profiles at the die outlet in the capillary flow of a polypropylene resin for dies having various LID ratios and diameters The average temperature rises plotted in Figures 7-7 and 7-8 are, in general, more pronounced for longer dies having the same diameter and for larger dies having a constant LID ratio. In a long die the residence time of the melt is higher and thus the melt is subject to larger heat dissipation amounts. However, for long enough capillaries this trend may be reversed due to the fact that expansion cooling becomes significant. Indeed, as can be seen in Figure 7-7, the average temperature rise is higher in the capillary having CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON18 FEP RESINS FOR WIRE COATING 139 an Z/D=40 than that in the capillary having an L/D=70. While energy dissipation is higher for the L/D=70 capillary, expansion cooling drops the temperature in the core region of the melt significantly and, as a result, the average temperature rise is kept small. In general, it can be seen in Figures 7-7 and 7-8 that the calculated average temperature rises are small and one would expect that viscous heating is not significant. However, the maximal temperature rise close to the wall may exceed the average value by several times, reaching quite significant values. It is this temperature rise which significantly influences the rheological measurements and always increases with LID (D=const) and D (LID=const). Figure 7-9 plots the radial temperature profiles at the die outlet for two cases described in Figures 7-7 and 7-8. It can be seen that the higher temperature rise occurs in the region close to the wall. This is the region of high shear and thus that of the largest temperature rise. At the same time this is the region where temperature has the strongest influence on the rheological measurements as well as the slip velocity. In the core region of the die, however, expansion cooling is dominant thus causing the temperature to drop significantly. Expansion cooling caused by the small but finite polymer compressibility is strongly affected by the pressure, hence it is more pronounced for the capillaries having larger LID ratios. From the slip velocity model used and the numerical results presented in Figures 7-7 and 7-8, it is obvious that the slip velocity is a function of the wall shear stress, wall normal stress and temperature, and thus it varies with the axial position along the die. However, it is often desirable to know the average slip velocity as a function of the average wall shear stress for capillaries having various length-to-diameter ratios. This can be obtained by first assuming that pressure changes linearly in a capillary (a good CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 140 approximation). Secondly, one can express the normal stress, a„, in terms of L/D, and substitute the results into Equations (7-15)-(7-16) (for more details see Hatzikiriakos and Dealy, 1992a). The following expression for the slip velocity can thereby be obtained: u = ZMT) 1 - c, tanh E*+c*L/D V RT w v - / 1 / 4 y (7-17) where E*-E+50c2/l2, and c*2=2c2. The significance of this equation is that the obtained slip velocity values can now be compared directly with the experimentally determined ones. Figure 7-10 plots the slip velocity of PP as a function of wall shear stress for various capillary L/D ratios. The optimum values of the parameters in Equations (7-15) co E o to O o cu > CO 10 8 Polypropylene / / / -t T=200°C / / / : III-L/D=10 / / / L/D=20 / / / / L/D=40 / / / / L/D=70 / / /'' y 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 0.10 0.15 0.20 0.25 Wall shear stress (o~J), MPa 0.30 Figure 7-10. Calculated slip velocity of a polypropylene resin as a function of wall shear stress for capillary dies having various L/D ratios CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 141 and (7-17) calculated from the minimization algorithm are listed in Table 7-4. It can be seen from Figure 7-10 that despite the apparent absence of slip from the experimental data of Figure 7-5, the slip velocity of PP is considerable. At high enough shear stresses, it exceeds that calculated for a HDPE (Hatzikiriakos and Dealy, 1992a). In addition, the calculated slip velocities scale with the LID ratio indicating the same trend as that observed experimentally. 101 102 103 Apparent shear rate (jA), s"1 Figure 7-11. Experimental flow curves and those calculated in the absence of wall slip for a polypropylene resin for three capillary dies having the same L/D ratio of 40 and various diameters CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 142 Figure 7-11 shows a comparison of the experimental results presented in Figure 7-5 with the model predictions in the absence of wall slip. It is clear that viscous heating is significant due to the presence of diameter dependence and the overall description of the data in the absence of wall slip becomes poor. Thus, the inclusion of wall slip is a necessary ingredient of the model in order for it to adequately describe the capillary flow of polypropylene at high shear rates where the effects of viscous heating and wall slip become significant. 7.6.2 Linear Low Density Polyethylene The case of PP demonstrates how the slip velocity of a polymer can be calculated when the macroscopic experimental data imply the absence of slip (no diameter dependence of the flow curves). For such cases, the Mooney method is obviously not applicable. However, it would be interesting to examine a case where the capillary data were actually used to determine the slip velocity. In this example, by using the mathematical model, it should be possible to estimate the error that results from the curvature of the lines in the Mooney plot. To answer this question, the experimental data for a linear low density polyethylene (LLDPE, Dowlex 2049) reported by Hatzikiriakos et al. (1995) were used to calculate the parameters of the slip velocity model for this polymer (Equation 7-15). The authors reported that the Mooney plots were severely curved and identified this as a viscous heating effect. In spite of this, straight lines were fitted to the data and thus the slip velocity was calculated as a function of the wall shear stress for a number of capillaries having various L/D ratios. CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 143 The values of the parameters used in Equations (7-1) and (7-15) are tabulated in Table 7-5. The number of experimental points was 46. The optimal parameter values of the slip velocity model calculated by the optimization technique are listed in Table 7-6. The average deviation from the experimental data was about 5.9%. Figure 7-12 shows the experimental and predicted flow curves for capillaries having the same LID ratio and different diameters. As can be seen, the 5.9% deviation can be largely attributed to experimental error and comes primarily from the fitting of the data corresponding to the capillary die having the smallest diameter. Table 7-5. Constants for LLDPE LLDPE Polydispersity I 3.9 Thermal conductivity of the wall kw, W/(m-K) 17.0 Equation (7-1) 0.0075 K, Pas" 8100 Tref, °C 200 a, Pa 4-10"9 n 0.674 WLF equation Ci 2.552 C 2 , K 83.61 Table 7-6. Calculated parameters of the slip velocity model, Equations (7-15) and (7-17) for LLDPE Parameter Polyethylene Equation (7-15) Equation (7-17) m/s 0.1227-10-1 0.1227-10"1 Cl 0.988 0.988 ci, cal/mol 15.27 30.54 E, cal/mol 1203.0 1266.6 oc, Pa 0.807-105 0.807-105 m 4.312 4.312 CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 144 CD Q_ 0.7 0.5 0.4 0.3 0.2 h 0.1 * 0.07 GO GO CD CO CD - C CO JO 0.05 0.04 0.03 0.02 0.01 ~t—i—i—i—i i i n 1 — i — i — i i i i -i 1 — i — i — i i i i Dowlex 2049 T=200°C L/D=40 _i i i i ' 1 1 Hatzikiriakos er al. (1995) _i i i i i i 11 D =0.508 mm D =0.762 mm D =1.270 mm o D =0.508 mm A D =0.762 mm • D =1.270 mm _1 I I I ' I 101 102 Apparent shear rate (yA), s 10 ; -1 Figure 7-12. Experimental and calculated flow curves for a linear low density resin (Dowlex 2049) for three capillary dies having the same L/D ratio o f 40 and various diameters Figure 7-13 compares the slip velocities calculated by use of Equation (7-17) using the values o f the parameters listed in Table 7-6 with those calculated directly from the macroscopic experimental data reported by Hatzikiriakos et al. (1995). One may identify quite significant differences between the slip velocity values predicted by the present procedure (continuous lines) and those calculated by using the graphical Mooney CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 145 technique (symbols). These differences become more significant at relatively high wall shear stress values (where viscous heating effects dominate). The agreement between the predicted values and the experimental data obtained for the special case of L/D=0 is remarkably good. These data correspond to the slip velocity obtained from a sliding plate rheometer operated at ambient pressure. This is due to the fact that viscous heating effects are negligible in a sliding-plate rheometer compared to those in a capillary Wall shear stress (=0.762 mm and Z/D=100 at an apparent shear rate of yA=549 s"1. Agreement with Hatzikiriakos and Dealy (1992a) is remarkably good in spite of the fact : Sclair 56B D=0.762 mm L/D=100 T=180°C ^=549 s oo E o -co 0.25 CL £ 0.20 i i i r " i 1 1 r i 1 1 r " i 1 1 r - i 1 1 r -1 J i i I i i i i I i i i i I i i i i I i i i i _ "i 1 1 1 1 1 1 1 r H i i i i i i i i i i r j i i i _ l 1 1 r _ i i i i _ "l 1 1 1—q Axial position (z/L) Figure 7-14. Slip velocity, wall shear stress, and pressure profiles along a capillary die CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 148 that, in their study, the effect of viscous heating was neglected. At these moderate apparent shear rates, the effect of viscous heating is insignificant. Figure 7-15 plots the calculated and experimental apparent flow curves for HDPE. As a result of an overestimation of the slip velocity due to neglecting viscous heating in Hatzikiriakos and Dealy (1992a), there is some disagreement between the calculated and experimental apparent flow curves. This is due to the combined effect of wall slip and viscous heating which shifts the calculated flow curves to higher values of the apparent 1 0 1 102 103 Apparent shear rate yA, s"1 Figure 7-15. Apparent flow curves for Sclair 56B at 180 °C with capillaries of various diameters and I/£>=40; experimental and calculated CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS 149 RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING shear rate. However, in general, this example demonstrates a case where the Mooney technique can be safely used to obtain in a fairy good estimate of the slip velocity. 7.6.4 Teflon FEP The final polymer that studied was Teflon® FEP 4100. The flow curves for this polymer are plotted in Figure 5-7. Looking at this figure, one can see that the slip model represented by Equation (7-15) is not applicable in this case, since it implies that the slip velocity is a monotonic function of the wall shear stress. However, there is a distinct maximum and minimum in the flow curve of Teflon® FEP 4100 (spurt flow). Modeling of this phenomenon requires a special slip model which results in a non-monotonic, S-shaped behavior of the slip velocity as a function of o>. Such a model was recently presented by Leonov (1990) who developed a molecular model for the adhesive friction of elastomers. It can be presented in a non-dimensional form as: where cr£ and u°s are scaling factors for the shear stress, ow, and slip velocity, us, respectively, while m and k are parameters related to the molecular characteristics of the elastomer/wall interfce. These four parameters are considered to be adjustable. The plot of fiu) is sketched in Figure 7-16. It exhibits a non-monotonic behavior with a maximum and minimum and thus can be used to simulate the spurt effect (oscillating melt fracture). Initially, the slip velocity increases with shear stress. This increase is due to the stretching l - ( l + /w + l/«)exp(-/w-l/tt) l + km- exp(-/w - l/u) (7-18) CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 150 of the bonds. On this branch, the slip velocity is microscopic. The second, decreasing branch is due to the rapidly decreasing average concentration of attached bonds that facilitates slip significantly. The third, upper increasing Figure 7-16. Sliding friction curve b n m c h . g d u g t Q & d d a y Q f b o n d detachment from the wall. Starting with the second branch, the increasing slip velocity is macroscopic. This would correspond to an almost plug flow. The values of the parameters used in Equation (7-1) are tabulated in Table 7-8. Table 7-8. Constants for Teflon® FEP 4100 u FEP 4100 Thermal conductivity of the wall km W/(m-K) 17.0 Equation (7-1) 0.01 K, Pas" 3350 Tref, °C 350 a, Pa 1,2-10"* n 0.827 The number of experimental points was 44. The optimal values of the parameters of the slip velocity model calculated from the optimization technique are listed in Table 7-9. Figure 7-17 shows experimental and Table 7-9. Calculated parameters of the slip velocity model, Equation Parameter Teflon FEP cr° ,MPa u° , m/s k m Equation (7-18) 0.4698 9.74-10"4 3.082 0.01 predicted flow curves for capillaries having the same LID ratio and different diameters. As can be seen, the fit is good for the first increasing and decreasing branches of the flow curve. However, for CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING 151 the second increasing flow rate branch, the fit deteriorates with decrease in the diameter of the die. It is believed that the problem is related to the slip velocity model used. The model considers mainly adhesive failure as the causative mechanism of wall slip. While this may be true for weak slip (the lower branch of the flow curve), the spurt effect involves cohesive failure through the disentanglement of chains bonded at the interface from the bulk flow rather than adhesive failure at the interface (Hatzikiriakos et al, 0.4 CO 0.2 2 0.1 (U t 0.08 CO -5 0.06 CO 0.04 0.02 I I 1 1 1 1 I 1 1 1 1 Teflon FEP 4100 T=350°C L/D=40 1 1 1 1 1 II | ^ O / i i i i i i 111 A A / / A ' A " * A A A — jf A D=0.508 mm / • D=0.762 mm O D=1.270 mm i I i i i i i i i i 1 I i i i i i 1111 10 1 102 103 104 Apparent shear rate (yA), s Figure 7-17. Experimental and calculated flow curves for Teflon® FEP 4100 for three capillary dies having the same L/D ratio of 40 and various diameters CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 152 1997b; Wang et al, 1996). As a result, the slip model (Equation (7-18)) underestimates the slip velocity for the upper branch of the flow curve, especially for capillaries having smaller diameters where the effect of wall slip is more pronounced. Thus, to describe the stable steady flow of a polymer at high flow rates, a more detailed slip model is required. However, Equation (7-18) is good in predicting the slip velocity up to moderate values of shear rates and suitable for a semi-quantitative description of the flow at high shear rates. CHAPTER 7 - MODELING OF CAPILLARY FLOW OF MOLTEN POLYMERS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 153 8 Extrusion of Molten Polymers with Processing Aids he extrusion of fluoropolymers and polyolefins with various processing aids is studied and discussed in this chapter. First, it was found that polyethylene in small amounts of up to 0.1 wt. % works well as a processing aid in the extrusion of Teflon® FEP resins in the same way as fluoropolymers do in the extrusion of polyolefins. It dramatically reduces the pressure drop along the capillary die and eliminates extrudate distortion over the whole range of apparent shear rates up to the superextrusion region. Second, the influence of a new processing additive (fine particles of boron nitride) on the processability of polyolefins and fluoropolymers in extrusion is studied. The equipment used includes both an Instron capillary rheometer with two types of dies, namely capillary dies and special annular dies (Nokia Maillefer wire coating crosshead) attached to the rheometer, and an extruder. A metallocene polyethylene and several Teflon® fluoropolymers were tested using these two pieces of equipment. The additive had no or very little effect on the extrudate appearance in the capillary geometry (both capillary and orifice dies with a different entrance angle were tested). The greatest influence of the additive occurs in crosshead dies and tips with a streamlined flow, where the additive particles seem to enhance melt slippage and relieve internal stresses. This action eliminates surface melt fracture and postpones the critical shear rate for the onset of gross melt fracture to significantly higher values depending on resin type, temperature, and additive content. To explain the possible mechanism for the effect of the additive on the processability of the resins, rheological measurements using both a parallel-plate and CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 154 sliding-plate rheometers were carried out. The rheology of the resins did not seem to change significantly with the addition of boron nitride except for the low-shear-rate (low-frequency) range where the behavior of the filled resin was found to be similar to that of a crosslinked polymer. Practical wire coating and tubing extrusion studies for these resins were also carried out. Finally, the combined effect of the boron nitride and Teflon® particles was found to result in even better processability of the metallocene polyethylene. 8.1 Introduction It is well known that the rate of production of many polymer processing operations including fiber spinning, film blowing, extrusion, and various coating flows, is limited by the onset of flow instabilities (Petrie and Denn, 1976; Larson, 1992). In particular, as was discussed in Chapter 2, in extrusion processes where the throughput exceeds a critical value, small amplitude periodic distortions appear on the surface of extrudates (surface melt fracture or sharkskin) and at higher throughput rates these take a more severe form of larger irregular distortions (gross melt fracture) (Tordella, 1969). The surface melt fracture is believed to originate in the land of the die next to the die exit (Piau et al, 1990), and gross melt fracture to be initiated at the die entry (Tordella, 1969; Vinogradov and Malkin, 1980). To increase the rate of production by eliminating or postponing the melt fracture phenomena to higher shear rates, processing additives/aids must be used. These are mainly fluoropolymers that are widely used in the processing of polyolefins (HDPE, LLDPE) and other commodity polymers. They are added to the base polymer at low CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 155 concentrations (approximately 0.1%), and they essentially act as die lubricants, modifying the properties of the polymer-wall interface (increasing slip of the molten polymers). As a result of this lubrication effect, the onset of instabilities is postponed to much higher output rates and the power requirement for extrusion is significantly reduced. Note that these additives can eliminate only sharkskin and the so called stick-slip (oscillating or cyclic) melt fracture. To the best of author's knowledge, they do not appear to have an effect on the extrudate appearance in the gross melt fracture region. One of the objectives of this chapter is to examine the use of polyethylene as a processing aid for Teflon® resins. It is interesting to note that Teflon® has been already been successfully used as a processing aid in polyethylene extrusion to eliminate sharkskin melt fracture (Hatzikiriakos et al., 1994). Therefore, it would also be interesting to examine the opposite case, that is the possible use of polyethylene as a processing aid for Teflon® FEP resins. Another objective of this chapter is to study the effect of boron nitride (BN) based compositions as a processing aid in the extrusion of a number of fluoropolymers and polyolefins. It is shown that compositions containing B N can be successfully used as processing aids to eliminate not only sharkskin melt fracture but also substantially postpone gross melt fracture to significantly higher shear rates well within the gross melt fracture region in the extrusion of polyolefins and fluoropolymers (Buckmaster et al., 1997). The successful use of the boron nitride additives in two commercially important extrusion processes, namely tubing extrusion and wire coating, are also demonstrated. Finally, the combined effect of the boron nitride and Teflon® APA particles on the processability of polyolefins is examined. CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON18 FEP RESINS FOR WIRE COATING 156 8.2 Polyethylene as a P rocess ing A id in the Extrus ion of Tef lon® F E P 8.2.1 Experimental Evidence FEP copolymers may act as processing aids in the extrusion of linear low density polyethylene, when added at amounts as little as 0.01 % weight. It has been observed that during extrusion, FEP particles that are finely dispersed in polyethylene come into contact with metal dies and displace the polyethylene from the surface. During extrusion, the fluoropolymer particles spread as a result of the shear stress and, as shown by ESCA analysis, eventually form a very thin layer that completely coats the die surface. Due to the poor adhesion characteristics between the polyethylene and the fluoropolymer, the polyethylene slips over the thin fluoropolymer coating. This enhanced slip significantly reduces the pressure required to extrude the polyethylene at a particular flow rate and eliminates sharkskin melt fracture (Figure 8-1). Optimum processing aid performance occurs when the melt viscosities of the polyethylene and the FEP additive are approximately equal. Moreover, to be more effective, the FEP must be dispersed into the polyethylene as very fine particles 0.2 pm in diameter or less. 0.01 LLDPE 200°C y PE+ fluoropolymer 101 TA, s" 10' Figure 8-1. Flow curve of linear polyethylene (PE) and that of polyethylene containing 250 ppm fluoropolymer (from Stewart et al, 1993) CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N 1 8 FEP RESINS FOR WIRE COATING 157 It is perhaps surprising to discover that polyethylene can be used in a similar manner as a processing aid in FEP resins to reduce extrusion pressure and eliminate sharkskin melt fracture. Figure 8-2 shows the apparent flow curves obtained at 350°C for pure FEP 4100 and that of a blend of FEP 4100 with 0.1% by weight of a finely dispersed linear low density polyethylene (GRSN/7047). The capillary die used had an L/D ratio of 40 and diameter of 0.762 mm. No Bagley correction was applied in this plot. It can be seen that the presence of the polyethylene dramatically decreases the shear stress co 0.2 c Q O 2 i — 8 0.1 >» c? 0.08 00 I 0.06 V) 0.04 co CD JZ CO 0.02 T= i i i =350°C i i i i 11 L/D=40 D= 1 1 l l l l l l j 1 1 l l l l l l 0.762 mm ^ A A A • • V — • V V • V V - V -V A V - V -V A Teflon FEP 4100 • V Teflon FEP 4100 + 0.1% PE V V i i i 1 1 1 1 1 1 1 i i i i i 111 i 101 102 103 104 Apparent shear rate (yA), s -1 Figure 8-2. The effect of the addition of 0.1 % of polyethylene on the flow curve of resin FEP 4100 at 350 °C CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 158 practically over the whole range of apparent shear rates up to those in the superextrusion region (see Chapter 5). The polyethylene eliminates the sharkskin melt fracture, pressure oscillations and oscillating (stick-slip) melt fracture. Thus, the extrudates appear relatively smooth up to the shear rates of 1000 s'1. 8.2.2 Mechanism In the above experiment, polyethylene particles would tend to diffuse through the bulk of FEP towards the die wall due to its lower viscosity. However, it is the work of adhesion, i.e., the energy required to remove the polymer from the metal surface, that determines which component will eventually coat the die wall. Polyethylene has a greater affinity to metal surfaces than do FEP resins. Therefore, it is not surprising, in this experiment, that the metal die surface eventually becomes coated with a very thin layer of polyethylene. Since there is very little adhesion between FEP and polyethylene, at sufficiently high shear stress values it appears that FEP slips over the thin polyethylene layer on the die wall. This then raises the question as to why a very small quantity of FEP resin, when finely dispersed in polyethylene, will completely coat the die wall during extrusion. The answer again lies in the relative values of the work of adhesion. Although the work of adhesion of FEP to base metal is less than the work of adhesion of polyethylene to metal, the work of adhesion of polyethylene to FEP is much less than either of these. Thus, if a very small FEP particle that is dispersed in polyethylene comes into contact with the metal die surface during extrusion, there will be very little force at the FEP/polyethylene interface acting to pull the particle off the surface. The polyethylene will slip over this CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING 159 interface and will cause the particle to spread. On the other hand, the force acting to pull the polyethylene off the surface is the result of the wall shear stress during extrusion. The overall result is that the FEP particles accumulate, spread, and eventually form a very thin coating on the die over which the polyethylene can slip. A similar behavior of other polymer blends was observed by Shih (1979). Examination of a broad range of fluorocarbon/hydrocarbon blends has led to the following general observations. To be effective, the minor component must be in a finely divided state, having particle diameter less than about 0.2 u.m. It must also be at a very low concentration of less than about 1% by weight. For optimum performance, the viscosities of the two polymers should be approximately equal. The relative work of adhesion between the two polymers and the metal surface and between the polymers themselves determine the final performance. For example, fluoropolymers will displace nonpolar hydrocarbons with low work of adhesion, but will not displace polar polymers such as nylon, polyesters or poly(methyl methacrylate) from metal surfaces because of the very high value of the work of adhesion of these polymers with metals. 8.2.3 Transient Coating Experiments The following transient experiments illustrate the process of wall coating by the polyethylene additive. In Figure 8-3 a the apparent shear stress transient is plotted for the capillary extrusion of pure FEP 4100. The shear stress builds up rapidly until it assumes a steady-state value. When the blend of FEP 4100 + 0.1% PE is extruded through a clean die (Figure 8-3b), the shear stress passes through a maximum and as the polyethylene coats the interface, slip becomes a factor, and, as a result, the shear stress decreases. The CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 160 steady-state value is obtained after filling the reservoir several times (5 times). It should be noted, however, that this response is not due to the degradation of polyethylene. Pure polyethylene was extruded several times at these high temperatures for about one hour, and in all cases the apparent shear stress remained practically constant. The time required to obtain steady-state operation (steady shear stress) depends on the apparent shear rate, the LID ratio, and the diameter of the capillary die. The effects 0.20 co 0.16 co 0.12 CO CD -«—• co CO CD w 0.08 CD CO C L C L < 0.04 0.00 ~i—m—[-r a ' ' I I I T l I I | I I I I | l I I I | I I I I | I I I I ] I I I I | I I l I [~ b T=325°C ^=104.2 s-1 L/D=40 D=.762 mm a. Teflon FEP 4100 b. Teflon FEP 4100+0.1% PE Run 1 Run 2 Run 3 i i i i i i i i i Run 4 Run 5 i i i i i i i 'i i i i i i i i i i i i i i 1 50 0 50 100 150 200 250 300 350 Time (r), min Figure 8-3. The effect of the addition of 0.1 % of polyethylene on the transient response in the capillary extrusion of FEP 4100 at 325 °C, ?^ =104.2 s"1, L/D=40 and £>=0.762 mm. CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON18 FEP RESINS FOR WIRE COATING 161 of these parameters on the time required to obtain a steady-state response are illustrated in Figures 8-4, 8-5, and 8-6, respectively. Specifically, Figures 8-4a, 8-5a, and 8-6a illustrate the transient response in the absence of polyethylene, while Figures 8-4b, 8-5b, and 8-6b illustrate the corresponding response with the addition of 0.1% polyethylene. These figures should be compared with Figure 8-3 in order to observe the relative effect. It can be seen that the time required to obtain steady state operation decreases with increase in the apparent shear rate, and decreases with a decrease in the L/D ratio and diameter of the capillary die. This should be expected if one interprets this time as the time required to obtain a complete uniform coverage of the interface with polyethylene. Thus, this time should be proportional to the area being coated. This means that decreas-0.20 0.00 i—n i—i—I—i—i—i—r i—i—i—i—|—i—i—i—rn—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—r T -1 T=325°C ^=347.2 s L/D=40 D=0.762mm a. Teflon FEP 4100 b. Teflon FEP 4100+0.1% PE Run 1 Run 2 ' i i ' i i i i i i i i Run 3 ] i i I i i i i 0 10 200 10 20 30 40 50 60 Time (f), min Figure 8-4. The effect of the apparent shear rate on the time required to obtain steady state operation in the capillary extrusion of FEP 4100 with the addition of 0.1 % of polyethylene ( 7=325 °C, ^=347.2 s"1, L/D=40 and 7>0.762 mm). To see the effect compare with Figure 8-3 CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 162 £ 0.28 b* 0.24 F-w 0 20 CO CD to 1_ CO CD J = CO 0.16 0.12 CO £ 0.08 -*-> c CD co 0.04 Q . < 0.00 0.20 1 0.16 0.12 0.08 0.04 ~ i i i i | i i i i | i i i i | i i i i | i i i r b T=325°C ^=104.2 s-1 L/D=10 D=0.762mm a. Teflon FEP 4100 b. Teflon FEP 4100+0.1% PE 0.00 40 0 _l I L_ l I I I I L_ l I I ' I I l I I J I I I L_ 40 80 120 160 200 Time (f), min Figure 8-5. The effect of the L/D ratio of the capillary die on the time required to obtain steady state operation in the capillary extrusion of FEP 4100 with the addition of 0.1 % of polyethylene ( 7=325 °C, ^=104.2 S'\ L/D=10 and/>0.762 mm) 0.12 co 0.20 Q_ t? 0.16 -1 1 1 : b • 1 1 1 1 i 1 i i i i 1 i i i i 1 i i T=325°C ^=104.2 s"1: - L/D=40 D=0.508mm -a. Teflon FEP 4100 I v: Teflon FEP 4100+0.1% PE ~ Run 1 Run 2 -1 1 1 i i i i i • i i ' i i i i i i i i i i i 0 100 200 300 400 Time (/), min Figure 8-6. The effect of the diameter, D, of the capillary die on the time required to obtain steady-state operation in the capillary extrusion of FEP 4100 with the addition of 0.1 % of polyethylene ( 7=325 °C, ^=104.2 s1, L/D=40 andZ>=0.508 mm) CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N 1 8 FEP RESINS FOR WIRE COATING 163 ing the L/D ratio or diameter, D, and keeping all the other variables fixed decreases this area, and, therefore, the time required to obtain steady state operation decreases. On the other hand, increasing the apparent shear rate, the rate of the coating process increases, while the required time for steady-state operation decreases. 8.3 Extrus ion of F luoropolymers and Polyolef ins with Boron Nitride as a P rocess ing A id 8.3.1 Experimental Evidence The present section discusses the use of boron nitride as a processing aid for the extrusion of fluoropolymers and polyolefins (Buckmaster et al., 1997). In polymer processing, it is used as a foam nucleating agent, and when added to the polymer melt acts as a very effective processing aid as will be seen in the present chapter. Boron nitride is a solid lubricant whose structure resembles that of graphite (see Figure 8-7). In polymer processing, it is used as a Key • Boron O Nitrogen 2.5 A Figure 8-7. Structure of B N foam nucleating agent in most commercial applications for fluoropolymer foams such as heat insulation, foamed tubing, etc. In the presence of a blowing agent added to the molten resin during extrusion, it nucleates the formation of voids in polymer extrudate. In this study, B N particles are used without a blowing agent, so that the extruded polymer is CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 164 unfoamed. The amount of boron nitride effective in providing improved extrusion performance can be as little as 0.001 wt %, preferably about O.Olwt %. It is used in combination with some other inorganic nucleating agents such as calcium tetraborate in amounts from 0.002 to 0.04 wt %. During the extrusion of fluoropolymers or polyolefins with B N particles, the maximal shear rate at which the extrudate appears smooth is usually orders-of-magnitude higher than can ordinarily be achieved in the absence of this additive. More importantly, this maximal shear rate is usually much higher than that at which the virgin resin exhibits gross melt fracture. This means that BN, unlike fluoropolymers in the extrusion of polyethylene, can eliminate not only surface and stick-slip melt fracture but also significantly delay the onset of gross melt fracture to much higher shear rates. Specific examples of its use can be found below. Another requirement of the process is that the extrusion experiments be carried out with a special crosshead die of the type used for wire coating. The significance of this statement is that similar experiments with BN repeated in a capillary rheometer do not result in a significant improvement of the processability of the resins. In other words, B N has little or no effect on melt fracture in a capillary die. 8.3.2 Extrusion Experiments The two groups of polymers studied are polyolefins and fluoropolymers. The former includes two metallocene catalyzed poly ethylenes, Exact® 3128 and Exceed® 116 (Exxon), and the latter involves the following DuPont Teflon® fluoro-copolymers of tetrafluoroethylene/hexafluoropropylene (Teflon® FEP) resins: type 100 (melt flow rate is CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 165 6.9), 3100 (17), 4100 (22), 5100 (20), and the following copolymers of tetrafluoro-ethylene/perfluoro-(propyl vinyl ether) (Teflon® PFA): type 340 (14.7), 345, and 350 (1.8). Both rheometer and extrusion equipment were used to determine the shear rate at which smooth extrudates can be produced. The rheometer is the standard Instron piston-driven constant-speed capillary unit described previously. Two types of dies were used, namely circular dies having a 90° entrance angle, and a special annular crosshead die attached to the rheometer to simulate the wire coating process (see Figure 8-8). The crosshead was a Nokia Maillefer 4/6 that included dies and tips of various diameters ("tip" is the wire guide) with equal entry cone angles of 60° and the die land length of 7.62 mm. The molten polymer enters the die 2 via port 11 and is forced around the wire guide 16 towards the die orifice 8. The wire guide serves as a mandrel for the molten polymer, giving the extrudate 10 a tubular shape. The die passage 4 forms the exterior surface of the tubular shape, and the exterior surface of the cylindrical extension 24 forms 22 ^12 ^2 Figure 8-8. Crosshead die for wire coating (from Buckmaster et al., 1997) CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 166 the interior surface of the tubular shape. The greater speed of the wire compared to the polymer extrusion rate causes the polymer coming into contact with the wire at a point remote from the orifice 8 to draw down to a thinner cross-section, forming a thin polymer coating 26 on the wire. This is a melt draw-down extrusion process with draw down ratio (DDR), which is the ratio of die orifice area to cross-sectional area of the polymer insulation, of at least 5:1. However, in the present study the pressure extrusion makes no use of wire and therefore DDR is irrelevant. The extrusion equipment involved a 31.725 mm Entwistle extruder having a 31:1 length to diameter ratio and equipped with the same crosshead extrusion die. The Entwistle extruder with the Maillefer crosshead was also used for producing polyethylene tube, and a 45 mm extruder was used for a practical wire coating test with fluoropolymers. The working temperature was 163°C (325°F) and 204°C (400°F) in the case of polyethylene, 371°C (700°F) for FEP resins, and 385°C (725V) for PFA resins. Composition resins with B N content varying from 0.01 to 2.5 mass %, along with virgin resins, were tested over a wide range of apparent shear rates from 10 to 7000 s"1. All compositions were prepared by extrusion of the boron nitride/resin mixture in a 28 WP twin screw extruder. 8.3.3 Polyolefins Figure 8-9 shows the flow curves of the virgin and filled Exact® 3128 (metallocene LLDPE) obtained using the capillary rheometer with a capillary die having D=0.762 mm and L/D=0 at 7=163°C. The Bagley correction was determined by using an orifice die of CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING 167 equal diameter and subsequently was applied to the raw data in order to get accurate values for the wall shear stress. In the case of the virgin resin, sharkskin appears at about 35 s'1 followed by stick-slip and gross melt fracture at higher shear rates. The addition of 0.05% B N to the resin does not seem to noticeably change the rheology since the two flow curves almost coincide. However, it has an effect on the extrudate appearance, eliminating extrudate distortions in the range of shear rates corresponding to transition from sharkskin to stick-slip melt fracture. This was the only case where a difference in 1 co Q_ GO GO to 1 CO CD - C to "co c CD CO Q . Q . < 1 h 0.1 h 102 103 Apparent shear rate (yA), s"1 Figure 8-12. The effect of the boron nitride concentration on the processability of PE Exact 3128 in an extruder with the crosshead having 3.00 mm die and 1.52 mm tip at 204 °C CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON8 FEP RESINS FOR WIRE COATING 172 Figure 8-13 shows photos of the extrudate samples obtained in the extrusion of PE Exact 3128 with and without BN. One can see that an addition of 0.01 wt.% BN results in smooth extrudate at shear rates where the extrudate would normally exhibit gross melt fracture. Figure 8-13. The extrudate samples of metallocene PE Exact 3128 at 163°C: a) sharkskin for pure PE at ^=80 s"1; b) gross melt fracture for pure PE at yA =800 s"1; c) smooth extrudate for PE with 0.01% BN at yA =800 s"1 Finally, a practical tubing test was carried out with Exact resin using the Maillefer crosshead at a melt temperature of 163 °C. The die and tip diameters are 3.1 mm and 1,53 mm. Smooth surfaced tubing was processed having a 2.13 mm outer diameter and 0.94 mm inner diameter at 600 s"1. The loading of the BN was less than 0.05%. 8.3.4 Fluoropolymers The rheological performance of FEP 100 resin was studied using the crosshead die mounted on the capillary rheometer. The maximum shear rate limit for achieving a smooth surface of extruded virgin FEP 100 resin was about 90 s" . The same resin with CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 173 the addition of 0.25% B N could be run without extrudate defects up to 140 s"1 and from 550 to approximately 1000 s"1. The tests using the extruder with the same crosshead die showed that in the presence of small amount of BN, smooth extrudate can be obtained for the entire range of shear rates up to 4000 s"1, which is well beyond the onset of gross melt fracture for the extruded pure resin (Figure 8-14). It is believed that the difference in performance between the rheometer and the extruder with the same crosshead die is due to the much better mixing in the barrel of the latter. A decrease in the B N content to CL to CO CD -4—» to CO CD - C to "co c CD i _ CO CL CL < 0.1 1 1 1 1 I I I 1 1 1 Teflon FEP 100 1 1 1 1 1 1 i i i I I I T=371 °C Crosshead: D=3.0 mm, d= 1.524 mm -V -i • • -A • virgin resin • A 0.05% BN T 0.25% BN Open symbols correspond to smooth extrudate _ . O i i i i i i I i i i i i i i i 1 i i i i i i 102 103 Apparent shear rate (yA), s"1 Figure 8-14. The effect of boron nitride on the processability of Teflon FEP 100 in an Entwistle extruder with the crosshead Nokia Maillefer having 3.00 mm die and 1.52 mm tip at 371 °C CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON9 FEP RESINS FOR WIRE COATING 174 0.05% resulted in a drop in the maximum shear rate for the onset of flow instabilities to about 3200 s . Figure 8-15 shows photos of the extrudate samples of FEP 100 obtained in an extruder at 371°C. The detailed rheological study of the FEP 4100 and 3100 resins using a capillary rheometer can be found in Chapter 5. In the superextrusion region, where the virgin extrudate is smooth, extrusion through the crosshead die does not produce as pronounced a supershear range as that through a circular die at 371°C. The extruder and Maillefer crosshead studies with the FEP 4100 filled with 0.17% of BN and dried overnight at 150°C yielded smooth extrudates at shear rates as high as 6000 s (Figure 8-16). At 0.035% BN content, the maximum shear rate was 3200 s". A similar performance was observed with FEP 3100 and FEP 5100. The PFA fluoropolymers have higher melting points than FEP resins, so they were studied at the increased temperature of 385°C. Extrusion tests with the crosshead and the virgin PFA 340 resulted in melt fracture at a shear rate of about 100 s", while the resin Figure 8-15. Extrudate samples of Teflon® FEP 100 at 371°C: a) sharkskin for pure PE at yA=320 s ; b) gross melt fracture for pure PE at ^=4000 s"1; c) smooth extrudate for PE with 0.25% BN at yA =4000 s"1 CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 175 with 0.25% B N could be processed without melt fracture up to 2000 s'1. To summarize the results obtained for all the resins studied, the maximum shear rate at which the inner and outer surfaces of the tubing were smooth are shown in Table 8-1. Finally, wire coating tests on FEP 4100 were carried out in the 45 mm Nokia Maillefer extruder with the crosshead having a 3.81 mm die and 1.905 mm tip. The screw speed was 11.6 rpm, and the melt temperature 388°C. The composition with 0.1% B N 1 h co CL i CO OO CD -»—« oo CO CD J C 00 "co c CD CO C L C L < 0.1 "i 1 1 1—i—i—i—r Teflon FEP 4100 T=371 °C Crosshead: D=3.0 mm, d=1.524 mm -i 1 1 1 1—r 9 V o 2 • virgin resin • 0.035% BN A 0.055% BN T 0.17% BN Open symbols correspond to smooth extrudate O 102 103 Apparent shear rate (jA), s"1 Figure 8-16. The effect of boron nitride on the processability of Teflon FEP 4100 in an Entwistle extruder with the crosshead Nokia Maillefer having 3.00 mm die and 1.52 mm tip at 371 °C CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON" FEP RESINS FOR WIRE COATING 176 was successfully run to obtain smooth inner and outer insulation surfaces at 100 m/min which corresponds to shear rates of approximately 800 s'1. This shear rate was several times greater than that at which smooth interior surface insulation could be obtained for the virgin resin. Figure 8-17 compares the tightness of the insulation obtained with and without B N at the above conditions. Table 8-1. Influence of boron nitride concentration upon tubular extrudate surface smoothness (extrusion tests in the Entwistle extruder with Nokia Maillefer crosshead 3.0 mm die and 1.52 mm tip) T , ° C BN concentration, mass% Maximum shear rate to yield smooth extrudate, s"1 Polyethylene Exact® 3128 163 0 50 0.01 960 0.05 800 0.5 640 204 0 100 0.01 200 0.05 1280 0.1 1440 0.5 1600 FEP 100 371 0 40 0.05 3200 0.25 4000 FEP 4100 (FEP 5100) 371 0 350 0.035 3200 0.055 4000 0.17 5600 FEP 3100 371 0 250 0.25 6000 PFA 340 385 0 50 0.25 2000 CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 177 crosshead having a 3.81 mm die and 1.905 mm tip: a) virgin resin; b) with the addition of 0.1% BN 8.3.5 Mechanism To explain the effect of BN on the performance of fluoropolymers and polyolefins during the extrusion in a wire coating crosshead die, the following possible mechanisms will be discussed: • Change in the rheology • Effect of die geometry • Wall slip There may be some other explanations for this phenomenon; however, only these possible scenarios are considered below. In the following discussion, we concern ourselves only with metallocene PE. It is believed that the mechanism of the BN effect is CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 178 the same regardless of the nature of the polymer. It is noted that PE is a material that is much easier to work with compared to Teflon® FEP. This is mainly due to the lower operating temperature of the former. 8.3.5.1 Change in Rheology To study possible effects of the B N addition to the resin on the rheology of a 106 105 \r co - 104 CD Z3 I 103 oo oo o "O g 102 X Q) C L E o O 10"; 10"1 10° 101 102 Frequency {co), rad/s Figure 8-18. Dynamic moduli and complex viscosity of metallocene PE Exact 3128 (with and without BN) at 163 °C CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 179 polymer melt, linear oscillatory shear experiments were carried out for the metallocene PE Exact 3128 with and without BN in a Rheometrics System IV parallel-plate rheometer. The frequency sweeps were carried out at 163°C for the virgin resin as well as for resins containing 0.05 and 0.5 wt. % BN. Figure 8-18 depicts the dynamic moduli of the three resins along with their complex viscosities. In the case of the virgin resin there is no change in slope at low frequencies. However, for the filled resins and particularly at low frequencies, there is a characteristic shoulder similar to those observed for crosslinked and phase-separated polymers (Kapnistos et al, 1996). This is because of form relaxation that occurs when the motion of polymer chains is slower than that of the B N particles at low frequencies. Thus longer relaxation times are seen in the latter case. Obviously, the viscosity of the filled resins is higher than that of the virgin one because of reinforcement. At higher frequencies above 1 rad/s, the curves coincide, since the motion of small portions of polymer chains dominates rheology (length scales involved are small at higher frequencies), and the B N has almost no effect. Although it is clear that the morphology of the resin is affected by the addition of BN, it is believed that this difference at low frequencies cannot explain the effect on the extrudate appearance, which one can see in the extrusion with a crosshead die. Another series of experiments with this resin involved cessation of steady shear and relaxation carried out in an Interlaken sliding plate rheometer. Figure 8-19 shows the normalized shear stress decay coefficient for PE Exact 3128 with and without B N at different shear rates. The shear stress decay coefficient is defined as (Dealy and Wissbrun, 1990) r?'(t,f)^r-(t,r)/r (8-3) CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 180 where T~(t,y)is the shear stress decay function (stress as a function of time during relaxation) and y is the shear rate prior to cessation. One can see that there is difference in the relaxation process between the virgin and the filled resins at low shear rates. An addition of BN seems to slow down the relaxation. This is in agreement with the previous findings that the filled resin has some additional 10° 10"1 h 10-i i 111 r — i — i i i i 11 PE Exact 3128 L T=180°C j i i i 11111 i i i i 1111 10° d 10-0.01 0.1 l O " 2 1 0.01 0.1 10° 10 •1 L 10-0.01 0.1 1 0.01 0.1 1 Figure 8-19. Shear stress decay coefficient, rf (t,y)/7j(j), for metallocene PE Exact 3128 as a function of time (s) at 180°C and different shear rates. Solid lines correspond to the virgin resin, dashed lines to the resin with 0.05 wt. % BN, and dotted lines to 0.5 wt. % BN. CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 181 long relaxation modes (see Figure 8-18). However, at higher shear rates the curves are almost indistinguishable which means that the resin relaxes in the same way regardless of whether the B N is present or not. At this point, one can say that BN at small concentrations has a very small effect on the rheology of the molten polymers. The almost identical shape of the flow curves of the pure and filled resins (see figures in the previous section) support this conclusion. It is believed that the insignificant hardening and somewhat more complex morphology at low shear rates cannot solely explain the dramatic effects that B N has on resin processability during extrusion in a crosshead die. 8.3.5.2 Effect of the Die Geometry The fact that the effect of B N is more pronounced in a crosshead die rather than a capillary die implies that the die geometry is a factor in this phenomenon. Indeed, as can be seen in Figure 8-8, the crosshead die provides a very streamlined flow of the polymer. This is achieved by substantial conformation of the die inlet angle 14 and the included angle 28 of the conical surface 22 of the wire guide with the conical surfaces 12 and 22 being substantially parallel to one another. The annular gap between the conical surfaces is of uniform width along the pathway of the polymer. The result of this conformation of the conical surfaces is that the polymer entering the die through port 11 flows along the conically converging annular channel defined by surfaces 12 and 22 to enter the die inlet essentially without turbulence. It is known that the region of the die inlet is the site of the origin of gross melt fracture (see Section 2.5.2). That is why a streamlined flow at the die entrance is so important in this phenomenon. CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 182 An attempt to model such a streamlined flow was made by use of a capillary rheometer. For this purpose, a series of orifice dies (L/D=0) with a different entrance angle varying from 15 to 90° was used. The idea behind this experiment was to see how the entrance angle affects the extrudate appearance in the presence of BN. Figure 8-20 plots the end pressure as a function of the apparent shear rate for four orifice dies having different entrance angles. As can be seen, in spite of a significant difference in the shape of the pressure drop curve for each die, the entrance angle has co Q_ <, CD zz GO CO CD LU i i i 11 i i i i i i i 11 i 1—i—i i i i 11 1 1—i—i i i i 11 PE Exact 3128 + 0.5% BN h T=163°C 101 10° the onset of sharkskin 101 o v O V I I I I I I I L / / / / o o o v O partially smooth Melt fracture i 1111 i i I I I I I I Entrance angle • 90° o 60° A 30° v 15° i i I I i 1111 102 103 104 Apparent shear rate (yA), s"1 Figure 8-20. The effect of the die entrance angle on the extrudability of PE Exact 3128 in the presence of 0.5% B N CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 183 virtually no effect on the extrudate appearance. For all dies, sharkskin started at about 50 s'1. This was expected because at this concentration B N does not completely eliminate sharkskin at low shear rates (see Figure 8-11). However, after the onset of melt fracture, the surface roughness persisted with increase in the apparent shear rate regardless of the die entrance. This means that a streamlined inlet region is a necessary but not a sufficient condition for the B N effect to be noticeable at this concentration. In fact, it is a combination of the slowly converging entrance and the annular geometry of the crosshead die that seem to provide the best conditions for the repression of melt fracture. 8.3.5.3 Wall Slip As was mentioned before, wall slip is a primary cause of the enhanced processability of polyolefins in the presence of fluoropolymers. That is why it would be reasonable to assume that BN particles also enhance the slip behavior of molten polymers. However, it is unlikely that slip at the wall caused by the adhesion failure at the polymer-wall interface is a significant factor in this case. This wall interface slip is usually accompanied by a significant shift in the flow curve towards lower shear stress values (see Figure 8-1). However, such shifts are never observed with the BN-modified resins. In fact, while there is some deviation between the flow curves of virgin and filled resins, it is small compared to that caused by slip. To prove this point, let us consider Figure 8-21. It shows the flow curves obtained for the metallocene polyethylene Exceed 116 at 204°C with a crosshead die attached to a rheometer. One can see that an addition of 0.2% B N has a very little effect on the flow curve compared to the virgin resin. On the other hand, an addition of 0.05% Viton , a fluoropolymer widely used as a processing aid in the extrusion of polyolefins, causes the CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 184 flow curve to shift significantly towards lower shear stress values. Since the mechanism of the Viton® action is purely based on a lubrication effect, one can conclude that the mechanism of the B N effect is not associated with wall slip. Thus, at this stage of investigation, the mechanism of the effect of B N on the processability of molten polymers is not well understood. A possible explanation could be the following. Different local concentrations of B N particles in the bulk flow could lead to the generation of zones with different viscosity. This may result into a fluid layer 1 1—i—i—i i i 11 1 1—i—i—i i i i | 1 1—i—i—i i i i PE Exceed 116 " T=204°C (400°F) I 1 — i — i — i — i i 111 1 i i i ' ' ' i i ' I I I i i 111 101 102 103 104 Apparent shear rate (yA), s"1 Figure 8-21. Comparison of the effect of B N and Viton® on the flow curves of the metallocene PE Exceed 116 obtained with a crosshead die at 204°C. CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N 1 8 FEP RESINS FOR WIRE COATING 185 next to the die surface that has a much lower viscosity than the bulk. In a sense, this picture gives rise to an apparent slip and to deformations of the bulk of the molten resin that are smaller than any encountered by the virgin resin run at comparable throughputs. At the same time, the B N particles may act to nucleate tiny cracks in the bulk of the melt, thus releasing stress and leading to a much more homogeneous extrudate. A final a possible explanation may lie in the shape of the die entrance. It seems that the annular entrance of the crosshead die provides much smoother streamlines than the plain capillary die. The fact that there is not much difference between the processing of virgin and filled resins in capillary extrusion is supportive of the last speculation. At any rate, the observed phenomenon requires additional studies such as visualization techniques in order to determine the specific mechanism of the effect of B N particles on the processability of various polymers. 8.4 The C o m b i n e d Effect of BN and Tef lon® on the Processabi l i ty of Polyolef ins At this point, it is reasonable to assume that, since the mechanisms of the action of fluoropolymers as a processing aid and BN are essentially different, they might supplement each other if they were used together. Indeed, the fluoropolymer could work in the sharkskin and stick-slip fracture region, eliminating melt fracture and reducing the pressure drop. On the other hand, B N could work in the gross melt fracture region, where fluoropolymers have no effect, thus delaying the onset of melt fracture to even higher shear rates. The examples below demonstrate the possible use of such combined processing aids. CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N ' F E P RESINS FOR WIRE COATING 186 The first example involves the metallocene polyethylene Exact 3128. Figure 8-22 shows four flow curves obtained using a crosshead die attached to a capillary rheometer for the pure resin and for blends of PE with 0.05% by weight of a finely dispersed Teflon® APA-II, 0.05% BN, and 0.05% Teflon® APA-II and 0.05% BN. It can be seen that the presence of the B N particles has only a small effect on the flow curve. However, the onset of melt fracture with the addition of BN can be postponed from 60 to 1850 s'1. CO Q_ 10° Jo to to CD -»—< to CO CD .£= to "co It c CD v_ CO Q . QL < 1 1 1—i—i—n -] r PE Exact 3128 L T=204°C (400°F) Rheometer with crosshead d/D=0.06070.122" • virgin O 0.05% Teflon APA A 0.05% BN A 0.05% BN, 0.05% Teflon APA 10"1 ~i 1 1—i—i—r~r f 2 o 2 • O 6 0.05% Teflon ^ 0.05% BN 0.05% BN and 0.05% Teflon. _ _l I I I 102 103 Apparent shear rate (yA), s"1 Figure 8-22. The effect of B N and Teflon APA additives on the processability of PE Exact 3128 obtained in a rheometer with Nokia Maillefer crosshead at 204°C CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 187 The addition of Teflon® particles decreases the shear stress practically over the whole range of apparent shear rates up to those in the gross melt fracture region regardless of the presence of BN. More important is the effect of the combination of the two processing aids (Teflon® and B N particles) on the onset of melt fracture. For this case, the critical shear rate is 2250 s"1. Note that neither BN nor Teflon® added separately to this resin yielded such a high shear rate. co Q_ oo in CD I— ~t6 l _ CO CD sz oo "co c CD CO CL CL < 0.1 i i i i i I r q PE Exceed 116 T=204°C (400°F) Crosshead o7D=0.0670.122" — • — virgin PE PE+0.1% BN - O - PE+0.1% BN+0.05% Teflon T I 1 1 1 I I I Onset of sharkskin Onset of MF: PE+BN Onset of MF: PE+BN+teflon j i i i i i i i _i i i_ _L 101 102 103 Apparent shear rate (yA), s" Figure 8-23. The effect of BN and Teflon APA additives on the processability of PE Exceed 116 obtained in a rheometer with a Nokia Maillefer crosshead at 204°C CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 188 The second example involves the metallocene polyethylene Exceed 116. Figure 8-23 shows the flow curves obtained for the pure resin and that with 0.1% B N and 0.1% BN+0.05% Teflon APA-II. The addition of BN allows an increase in the maximal shear rate yielding a smooth extrudate from about 100 s"1 for the virgin resin to almost 1000 s'1. The combined processing aid containing both BN and Teflon® results in the maximal shear rate of 2000 s"1 before melt fracture occurs. In summarizing the combined effects of B N and Teflon® on the extrusion of polyolefins, it is necessary to emphasize that each of the two processing aids works in a different flow region. Teflon® eliminates sharkskin and stick-slip melt fracture while B N seems to postpone gross melt fracture to higher shear rates where Teflon® has no effect. Obviously, additional experiments are required to find the optimal concentration of each processing aid needed to obtain the best extrusion performance. CHAPTER 8 - EXTRUSION OF MOLTEN POLYMERS WITH PROCESSING AIDS RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 9 Conclusions and Contributions to Knowledge 189 9.1 Conclusions Experiments were carried out in both parallel plate and capillary rheometers for a variety of tetrafluoroethylene/hexafluoropropylene (TFE/HFP) copolymers and TFE/HFP/perfluoro(alkyl vinyl ether) (TFE/HFP/PAVE) terpolymers, also known as Teflon® FEP polymers, having different molecular weights and compositions (i.e., HFP and PAVE contents). Dynamic linear viscoelastic data have shown that the critical molecular weight for the onset of entanglements, MC, is about 100,000, a value much higher than those previously reported. The rheology of the high melting point resins (low content of HFP) was found to exhibit a strong dependence on thermal history during oscillatory-shear measurements because of residual crystallinity at temperatures well above their melting points. The processability of the wire coating Teflon® FEP resins was found to correlate with their composition, viscosity, ability to crystallize, and melt elasticity. The capillary rheometer experiments revealed that surface melt fracture (sharkskin) appeared at critical shear stresses greater than about 0.18 MPa, practically independent of temperature in the range of 300 to 350 °C. At higher apparent shear rates, oscillating melt fracture was observed due to the presence of wall slip and compressibility of the melt. Furthermore, a superextrusion region was identified at apparent rates greater than those where oscillating melt fracture was obtained. In this region, the extrudate appears again smooth. This region was found to be wider at higher temperatures. CHAPTER 9 - CONCLUSIONS AND CONTRIBUTIONS TO KNOWLEDGE RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 190 The rheological data obtained by means of both parallel-plate and capillary rheometers were used for a thorough rheological modeling of the behavior of these resins. The latter includes calculation of their linear relaxation time spectra and nonlinear parameters using a multi-mode Phan-Thien and Tanner (PTT) constitutive equation. The values of Mc recovered from the fitting procedure were close to the experimentally determined ones. The longest relaxation time was found to depend on the molecular weight in a similar way as the zero-shear viscosity does with a scaling factor of about 3.4. It was shown that the PTT model can represent rheological data for Teflon® FEP resins well and may be used in flow simulation of relevant processing, e.g. wire coating. The problem of evaluating the slip velocity in the capillary flow of molten polymers based on experimental results (diameter dependence of flow curves) was studied in detail. It was found that in cases where viscous heating effects are significant, the traditional methods used to estimate the slip velocity (for example Mooney's technique) often fail to give accurate or even physically meaningful results. A new data analysis procedure based on a mathematical model for the nonisothermal capillary flow of polymer melts coupled with heat transfer is developed. The computer simulations can be used for two purposes: first, to provide detailed velocity, temperature, and pressure distributions, which can be useful in designing dies and, secondly, to recover the parameters of the employed slip velocity model corrected for the effect of viscous heating. The method was used to correct capillary experimental results obtained for various polymers, including PP, high and low density PE and Teflon® FEP. The results corrected for viscous heating effects were found to be consistent with the experimental data. CHAPTER 9 - CONCLUSIONS AND CONTRIBUTIONS TO KNOWLEDGE RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 191 Finally, the effect of various processing aids on the processability of fluoropolymers and polyolefins in extrusion and wire coating was studied. First, it was found that polyethylene in amounts up to 0.1 wt. % works well as a processing aid in the extrusion of Teflon® FEP resins in the same way that fluoropolymers do in the extrusion of polyolefins. Second, the processing additive based on the boron nitride (BN) composition was found to eliminate sharkskin melt fracture and postpone gross melt fracture to significantly higher shear rates for a variety of polymers including a metallocene polyethylene, as well as several FEP and PFA resins. The degree of the effect was found to depend on the resin type, additive concentration and temperature. The combined addition of boron nitride and Teflon® particles resulted in an even better processability of the metallocene polyethylene. 9.2 Contr ibut ions to Knowledge Several significant contributions to knowledge resulted from this research. These are as follows: • For the first time, a thorough rheological characterization of well-defined TFE/FfFP copolymers was performed. The critical molecular weight for the onset of entanglements determined for these polymers turned out to be much higher than previously reported values. Agreement was found between the values of the critical molecular weight obtained by means of relaxation time spectra and those found from direct experiments. CHAPTER 9 - CONCLUSIONS AND CONTRIBUTIONS TO KNOWLEDGE RHEOLOGY AND PROCESSABILITY OF T E F L O N " FEP RESINS FOR WIRE COATING 192 • The critical conditions for the onset of melt fracture as a function of temperature, molecular weight, artd composition of Teflon® FEP resins were determined from capillary rheometer experiments. • A new data analysis procedure based on a mathematical model for the nonisothermal capillary flow of polymer melts coupled with heat transfer is developed. The proposed technique can be used for two purposes. First, to provide detailed velocity, temperature, and pressure distributions which can be useful in designing dies and, secondly, to recover the parameters of the employed slip velocity model corrected for the effect of viscous heating. A reliable slip velocity model is crucial for numerical simulation and polymer process modeling. • It is shown that polyethylene can be used as a processing aid in the extrusion of Teflon® in the same way that fluoropolymers are used as processing aids for polyolefins. A mechanism, based on the relative work of adhesion between the components of the polymer blend and the material of the die, is proposed to describe this phenomenon. • Boron nitride was found to act as an effective processing aid in the extrusion of both fluoropolymers and polyolefins. For the first time,' the processing aid was shown to not only eliminate sharkskin and stick-slip (oscillating) melt fracture, but also to postpone gross melt fracture to significantly higher shear rates. The critical conditions and the influence of operating parameters such as the temperature and B N concentration were determined. CHAPTER 9 - CONCLUSIONS AND CONTRIBUTIONS TO KNOWLEDGE RHEOLOGY AND PROCESSABILITY OF TEFLON® FEP RESINS FOR WIRE COATING 193 9.3 Recommendations Based on the experience gained during this study, the following recommendations for future work can be made. • In Chapter 4, it was found that the critical molecular weight of low melting point TFE/HFP copolymers is close to 100,000, a value much higher than those previously reported for other polymers. However, for the group of the high melting point resins, there were insufficient experimental data to allow a similar conclusion to be drawn. It is desirable to carry out additional experiments with the low molecular weight FEP resins in order to see clearly the discontinuity in the relationship between zero-shear viscosity and molecular weight. • In Chapter 7, a detailed technique to calculate the slip velocity from the capillary rheometer data is proposed that accounts for the thermal effects in viscoelastic flow. However, the thermal boundary condition at the wall did not include the thermal effect due to friction at the polymer-wall interface as a result of wall slip. This local temperature rise may be significant, and it should be taken into account at high slip velocity values. • In Chapter 6, the PTT constitutive equation was used to model the rheological behavior of Teflon® FEP resins. It was found to describe well the rheological properties of these resins. In future, it may be used in numerical simulation of a capillary flow using the numerical procedure described in Chapter 7. Also a universal slip velocity model describing the polymer behavior in all flow regions should be developed. CHAPTER 9 - CONCLUSIONS AND CONTRIBUTIONS TO KNOWLEDGE RHEOLOGY AND PROCESSABILITY OF T E F L O N 1 8 FEP RESINS FOR WIRE COATING 194 • A numerical code suitable for modeling the wire coating process should be developed. It should include the equations of mass, motion, and energy for the shear and shear-free flows coupled with the PTT equation, the wall slip model, and other proper boundary conditions. The numerical simulation of the process under all operating conditions is needed for design purposes. • Additional experiments should be carried out with boron nitride processing aid. These should include the extrusion of polymers at various concentrations of B N to find its optimal concentration as a function of the processing temperature and type of polymer. Experiments with dies of various geometry are also desirable to see how the die geometry affects the resin processability. • A visualization study involving, e.g., the laser-speckle technique, is needed to identify the mechanism by which B N affects the extrusion of molten polymers. 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REFERENCES RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 205 Notation A temperature coefficient of viscosity, K"1 a parameter in the slip velocity equation (Eq. 7-7), MPa""1 • m/s ar shift factor b Rabinowitsch correction C Cauchy tensor c P heat capacity, J/(kg • K) C\, c2 constants in the slip velocity model, Equation (7-15) D capillary diameter, m D tip diameter, m EA activation energy for flow, J E* constant in the slip velocity model, Equation (7-17) e Bagley end correction or energy in Equation (2-37) G shear modulus, Pa G' storage modulus, Pa G" loss modulus, Pa G* complex modulus, Pa GD amplitude ratio in oscillatory shear GN° plateau modulus, Pa gi relaxation strength of the /'-th Maxwell mode, Pa gN constant in Equation (6-6) H(X) relaxation time spectrum glass transition constant in Equation (6-3) h gap between plates, m I melt polydispersity K power-law consistency index, MPa • s" NOTATION RHEOLOGY AND PROCESSABILITY OF T E F L O N * FEP RESINS FOR WIRE COATING 206 k heat conductivity, W/(m • K ) kw wall thermal conductivity, W/(m • K ) L capillary length or length of sample, m U initial length of sample, m M molecular mass o f the interacting unit, g/mol Mc critical molecular weight for entanglement, kg/kmol Me average molecular weight between entanglements, kg/kmol Mn number average molecular weight, kg/kmol My, weight-average molecular weight, kg/kmol m parameter in the slip velocity equation (Eq. 7-7) n power-law exponent ne slope o f B S W spectrum in the entanglement zone ns slope o f B S W spectrum in the glass transition zone P absolute pressure, Pa Pa ambient pressure, Pa Pd driving pressure, Pa ^end Bagley correction, Pa APex exit pressure drop, Pa APent entrance pressure drop, Pa Q volumetric flow rate, m3/s R capillary radius, m or universal gas constant SD standard deviation T absolute temperature, K t time, s or wall thickness, m Tg glass transition temperature, K Tgel gel temperature, K Tref reference temperature, K NOTATION RHEOLOGY AND PROCESSABILITY OF TEFLON* 1 FEP RESINS FOR WIRE COATING 207 Tw temperature at the wall, K u melt velocity, m/s us slip velocity, m/s v velocity vector Vx, Vy, vz velocity components in x, y, and z direction, respectively, m/s vr velocity component in radial direction, m/s Ax plate displacement, m Z parameter in the PTT model, Equation (6-10) G r e e k Letters a pressure coefficient of viscosity, Pa"1 B constant in BSW spectrum, Equation (6-3) 8 mechanical loss angle e parameter of the Phan-Thien and Tanner model or coefficient of thermal expansion or Hencky strain £ parameter of the Phan-Thien and Tanner model £o coefficient in the slip velocity model, Equation (7-15) e Hencky strain rate y(i) shear strain Yv rate of deformation tensor, s"1 y shear rate, s"1 y A apparent shear rate, s"1 yAs apparent shear rate, corrected for slip, s"1 y w wall shear rate, s'1 y0 strain amplitude in oscillatory shear j] viscosity, Pa • s r/o zero-shear viscosity, Pa • s NOTATION RHEOLOGY AND PROCESSABILITY OF TEFLON* FEP RESINS FOR WIRE COATING 2 0 8 rf viscosity at ambient pressure, Pa • s dynamic viscosity, Pa • s out-of-phase component of complex viscosity, Pa • s 77* complex viscosity, Pa • s VA apparent viscosity, Pa • s VE extensional viscosity, Pa • s A relaxation time, s Amax longest relaxation time, s Ac critical relaxation time, s K internal pressure, bar, Equation (7-8) P density, kg/m3 critical shear stress for the onset of melt fracture, Pa