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Thermorheology and processing of polyethylene blends : macromolecular structure effects Velazquez, Omar Delgadillo 2008

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THERMORHEOLOGY AND PROCESSING OF POLYETHYLENE BLENDS: MACROMOLECULAR STRUCTURE EFFECTS. by OMAR DELGADILLO VELAZQUEZ Master of Chemical Engineering, UNAM, Mexico, 2003. Diploma of Chemical Engineering, UNAM, Mexico, 2001. A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies (Chemical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (VANCOUVER) April 2008 ©2008 Omar Delgadillo Velazquez  ABSTRACT Rheological and processing behavior of a number of linear low-density polyethylene (LLDPE)/low-density polyethylene (LDPE) blends was studied with emphasis on the effects of long chain branching. First, a linear low-density polyethylene (LL3001.32) was blended with four LDPE's having distinctly different molecular weights. At high LDPE weight fractions, DSC melting thermograms have shown three different polymer phases; two for the pure components and a third melting peak of co-crystals. Different rheological techniques were used to check the thermorheological behavior of all blends in the melt state and the effect of long chain branching. It was found that all blends are miscible in the melt state at small LDPE concentrations. The elongational behavior of the blends was studied using a uniaxial extensional rheometer, SER. The blends exhibit strain hardening behavior at high rates of deformation even at LDPE concentrations as low as 1%, which suggests the strong effect of branching added by the LDPE component. On the other hand, shear rheology was found to be insensitive to detect addition of small levels of LDPE up to lwt%. The second set of blends prepared and studied consisted of two ZieglerNatta LLDPE's (LL3001.32 and Dowlex2045G) and two metallocene LLDPE's (AffinityPL1840 and Exact 3128) blended with a single LDPE. In DSC melting thermograms, it was observed that blends with metallocence LLDPE's exhibit a single melting peak at all compositions; whereas the Ziegler-Natta blends exhibit three melting peaks at certain compositions. It was found also that the metallocene LLDPE's are miscible with the LDPE at all concentrations. On the other hand, the Ziegler-Natta LLDPE's were found to be miscible with LDPE only at small LDPE concentrations. The processing behavior of all blends with emphasis on the effects of long chain branches was also studied in capillary extrusion. The critical shear stresses for the onset of sharkskin and gross melt fracture are slightly delayed with the addition of LDPE into LLDPE. Furthermore, the amplitude of the oscillations in the stick-slip flow regime, known as oscillating melt fracture, were found to scale with the weight fraction of LDPE. Amounts as low as 1 wt% LDPE have a significant effect on the amplitude of pressure oscillations. These effects are clearly due to the presence of LCB. It is suggested that the  ii  magnitude of oscillations in the oscillating melt fracture flow regime can be used as a method capable to detect low levels of LCB. Finally, the sharkskin and stick-slip polymer extrusion instabilities of a linear low-density polyethylene were studied as a function of the type of die geometry. The critical wall shear stress for the onset of flow instabilities, the pressure and flow rate oscillations, and the effects of geometry and operating conditions on the instabilities are presented for a LLDPE. It was found that sharkskin and stick-slip instabilities were present in the capillary and slit extrusion. However, stick-slip and sharkskin in annular extrusion are absent at high ratios of the inside to outside diameter of the annular die. This observation also explains the absence of these instabilities in polymer processing operations such as film blowing. These phenomena are explained in terms of the surface to volume ratio of the extrudates.  iii  TABLE OF CONTENTS  ABSTRACT ^ii TABLE OF CONTENTS ^iv LIST OF TABLES ^vii LIST OF FIGURES ^ ix ACKNOWLEDGEMENTS xv xvi DEDICATION ^ CO-AUTHORSHIP STATEMENT ^ xvii 1. LITERARURE REVIEW  1.1. Introduction 1.2. Structure of polyethylenes 1.3. Elements of rheology 1.3.1. Linear viscoelasticity 1.3.2. Material functions 1.3.3. Temperature effects in viscoelastic properties 1.4. Viscometric flows and rheometers 1.4.1. Capillary flow 1.4.2. Flow in a narrow slit 1.4.3. Flow through an annulus 1.4.4. Small amplitude oscillatory shear 1.4.5. Uniaxial extension 1.5. Shear thinning and strain Hardening 1.6. Rheological criteria for miscibility of polyethylene blends 1.7. Melt fracture phenomena 1.8. Scope of the work^ 1.8.1 Thesis objectives 1.8.2. Thesis organization 1.9. References  ^1 ^1 ^3 ^5 ^6 ^7 ^10 ^12 ^12 ^14 ^15 ^16 ^18 ^20 ^21 ^24 26 ^26 ^27 ^29  2. THERMORHEOLOGICAL PROPERTIES OF LLDPE/LDPE BLENDS... 33  2.1. Introduction 2.2. Materials and methodology 2.2.1. Polyethylene resins and blends 2.2.2. Thermal analysis 2.2.3. Rheological techniques 2.3. Results and discussions 2.3.1. Rheological characterization of pure resins 2.3.2. Thermal analysis: DSC Thermograms  ^33 ^35 ^35 ^36 ^36 ^37 ^37 ^40  iv  2.3.3. Linear viscoelastic measurements 2.3.4. Extensional measurements 2.3.5. Activation energy 2.3.6. Rheological criteria for miscibility 2.4. Conclusions 2.5. References  ^42 ^49 ^50 ^52 ^59 ^61  3. THERMORHEOLOGICAL PROPERTIES OF LLDPE/LDPE BLENDS: EFFECTS OF THE PRODUCTION TECHNOLOGY OF THE LLDPE ' S ^65 3.1. Introduction ^65 3.2. Materials and methodology ^68 3.2.1. Polyethylene resins and blends ^68 3.2.2. Thermal analysis ^69 3.2.3. Rheological techniques ^69 3.3. Results and discussions ^70 3.3.1. Rheological characterization of pure resins ^70 3.3.2. Thermal analysis: DSC Thermograms ^73 3.3.3. Linear viscoelastic measurements ^75 3.3.4. Extensional measurements ^82 3.3.5. Activation energy ^83 3.3.6. Rheological criteria for miscibility ^84 3.4. Conclusions ^90 3.5. References ^92 4. SHARKSKIN AND OSCILLATING MELT FRACTURE: WHY IN SLIT AND CAPILLARY DIES AND NOT IN ANNULAR DIES? ^ 96 4.1. Introduction ^96 4.2. Materials and methodology ^98 4.3. Results and discussion ^100 4.3.1. Linear viscoelastic measurements ^100 4.3.2. Extensional measurements ^101 4.3.3. Flow curves ^102 4.3.3.1. Capillary flow ^104 4.3.3.2. Slit flow ^109 4.3.3.3. Annular flow ^113 4.3.4. Discussion ^115 4.4. Conclusions ^116 4.5. References ^118 5. PROCESSABILITY OF LLDPE/LDPE BLENDS: CAPILLARY EXTRUSION STUDIES ^ 5.1. Introduction 5.2. Experimental  121 ^121 ^122  5.2.1. Polyethylene resins and blends 5.2.2. Rheological techniques 5.3. Results and discussion 5.3.1. Capillary rheometry 5.3.2. Stick-slip flow regime 5.4. Conclusions 5.5. References 6. CAPILLARY EXTRUSION STUDIES OF LLDPE/LDPE BLENDS: EFFECT OF MANUFACTURING TECHNOLOGY OF LLDPE AND LONG CHAIN BRANCHING ^  6.1. Introduction 6.2. Experimental 6.2.1. Polyethylene resins and blends 6.2.2. Rheological techniques 6.3. Results and discussion 6.3.1. Capillary rheometry 6.3.2. Stick-slip flow regime 6.4. Conclusions 6.5. References  7. CONCLUSIONS, CONTRIBUTION TO THE KNOWLEDGE AND RECOMMENDATIONS ^  7.1. Conclusions 7.2. Contribution to the knowledge 7.3. Recommendations for future work 7.4. References  ^122 ^122 ^123 ^123 ^134 ^139 ^141  143 ^143 ^144 ^144 ^145 ^146 ^146 ^154 ^157 ^158 160 ^160 ^161 ^162 ^164  APPENDIX A. SHIFT FACTORS FOR POLYETHYLENE RESINS AND THEIR BLENDS ^  165  APPENDIX B. DSC MELTING PEAKS BY DIFFERENT CALORIMETERS ^  168  vi  LIST OF TABLES Table 2-1. Properties of polyethylene resins used in this study  ^35  Table 2-2. Relaxation spectra of polyethylene resins @ 150 ° C  ^38  Table 2-3. Thermodynamic behavior of LLDPE (LL3001)/LDPE-I (LD200) blends, at 150 ° C, as concluded by various methods  ^57  Table 2-4. Thermodynamic behavior of LLDPE (LL3001)/LDPE-II (EF606A) at 150 ° C, as concluded by various methods  ^  57  Table 2-5. Thermodynamic behavior of LLDPE (LL3001)/LDPE-III (6621) at 150 ° C, as concluded by various methods  ^  58  Table 2-6. Thermodynamic behavior of LLDPE (LL3001)/LDPE-IV (1321) at 150 ° C, as concluded by various methods  ^58  Table 3-1. Properties of polyethylene resins used in this study  ^68  Table 3-2. Relaxation spectra of polyethylene resins @ 150 ° C  ^72  Table 3-3. Thermodynamic behavior of ZN-LLDPE I (LL3001)/LDPE (6621) at 150 ° C, as concluded by various methods  ^88  Table 3-4. Thermodynamic behavior of ZN-LLDPE II (Dowlex)/LDPE (6621) at 150 ° C, as concluded by various methods  ^89  Table 3-5. Thermodynamic behavior of m-LLDPE I (Exact)/LDPE (6621) at 150  ° C, as concluded by various methods  ^89  Table 3-6. Thermodynamic behavior of m-LLDPE II (Affinity)/LDPE (6621) at 150 ° C, as concluded by various methods  ^89  Table 4-1: Different die geometries used in this study along with their dimensions  ^99  Table 4-2. Critical shear rates and stresses for LLDPE (LL3001) in capillary flow at 150 ° C  ^105  Table 4-3. Critical shear rates and stresses for LLDPE (LL3001) in capillary flow at 190 ° C  ^106  Table 4-4. Critical shear rates and stresses for LLDPE (LL3001) in slit flow at 150 ° C  ^109  Table 4-5. Critical shear rates and stresses for LLDPE (LL3001) in slit flow at  vii  190 ° C  ^110  Table 4-6. Critical shear rates and stresses for LLDPE (LL3001) in annular flow at 150 ° C  ^114  Table 4-7. Critical shear rates and stresses for LLDPE (LL3001) in annular flow at 190 ° C  ^114  Table 5-1. Critical shear rates and stresses for Blend System I (LL3001/LD200) at 150 ° C and 190 ° C  ^125  Table 5-2. Critical shear rates and stresses for Blend System II (LL3001/EF606) at 150 ° C and 190 ° C  ^127  Table 5-3. Critical shear rates and stresses for Blend System III (LL3001/6621) at 150 ° C  ^  129  Table 5-4. Critical shear rates and stresses for Blend System IV (LL3001/1321) at 150 ° C  ^  129  Table 6-1. Critical shear rates and stresses for Blend System II, ZN-LLDPE II (DOWLEX)/LDPE(662I) at 150 ° C  ^  147  Table 6-2. Critical shear rates and stresses for Blend System III, m-LLDPE I (Exact 3128)/LDPE(662I) at 150 ° C  ^149  Table 6-3. Critical shear rates and stresses for Blend System IV, m-LLDPE II (Affinity)/LDPE(662I) at 150 ° C  ^150  Table A-1. Horizontal shift factors for LL3001/LD200 blends at Tre f = 150 ° C.....^165 Table A-2. Horizontal shift factors for LL3001/EF606 blends at Tref = 150^165 Table A-3. Horizontal shift factors for LL3001/662I blends at Tref = 150 ° C  ^165  Table A-4. Horizontal shift factors for LL3001/132I blends at Tref = 150 ° C  ^166  Table A-5. Horizontal shift factors for Dowlex/662I blends at Tref = 150 ° C  ^166  Table A-6. Horizontal shift factors for Exact/662I blends at Tref = 150 ° C  ^166  Table A-7. Horizontal shift factors for Affinity/662I blends at Tref = 150 ° C  ^166  viii  LIST OF FIGURES Figure 1-1.. Schematic representation of the microstructure of HDPE, LLDPE ^4  and LDPE Figure 1-2. Schematic representation of simple shear flow  ^7  Figure 1-3. Schematic representation of uniaxial extension  ^9  Figure 1-4: Schematic diagram of a typical cylindrical capillary die along with ^13  the definition of the design parameters  Figure 1-5. Schematic diagram of the rectangular flow geometry and the slit die ^14  showing the land zone Figure 1-6.. Schematic of the die and the insert for annular flow. For the external die, Db=25.4mm, D o =2.54mm; for the different mandrels (inserts), D oi=5mm, Dr-1.542mm, 2.167mm and 2.415 mm  ^15  Figure 1-7. Set-up of the Instron extruder  ^16  Figure 1-8. Parallel plate rheometer  ^17  Figure 1-9. Schematic of Sentmanat Extensional Rheometer (SER)  ^19  Figure 1-10. Strain Hardening behavior for LDPE (LD200) and LLDPE (LL3001.32) at 150 °C, and different extensional rates, s =0.1, 1, 10 and 20 s" 1  21  Figure 1-11. A typical apparent flow curve for a linear polyethylene. 1. Smooth; 2. Sharkskin; 3. Stick-slip; 4. GMF  ^26  Figure 2-1. The complex viscosity curves of LLDPE (LL3001), and those of all four LDPE resins (132i, 662i, EF606A and LD200) at 150 °C  ^37  Figure 2-2. The tensile stress growth coefficient for the LLDPE resin (LL3001) and the four LDPE resins (LD200, EF606A, 662i and 132i), at three different Hencky strain rates: 0.1, 1 and 10 s 1 ; at 150 °C  39  Figure 2-3. DSC thermograms for the LLDPE/LDPE blend systems: (a) LL3001/LDPE I (LD200); (b) LL3001/LDPE II (EF606A); (c) LL3001/LDPE III (6621); (d) LL3001/LDPE IV (1321) 41 Figure 2-4. Mastercurves of a) elastic modulus, G', and b) complex viscosity, 177 * (co)1 , for blend system I (LL3001/LD200)  ^44  ix  Figure 2-5. Mastercurves of a) elastic modulus, G', and b) complex viscosity,lq * (co)1, for blend system II (LL3001/EF606)  ^46  Figure 2-6. Mastercurves of a) elastic modulus, G', and b) complex viscosity, 17 * (w) , for blend system III (LL3001/6621)  ^47  Figure 2-7. Mastercurves of a) elastic modulus, G', and b) complex viscosity,lq * ( 01 , for blend system IV (LL3001/6621)  ^48  Figure 2-8. Tensile stress growth coefficient curves for 0.1, 1 and 10 s-1 Hencky strain rates at 150 °C for LLDPE/LDPE blend systems: (a) LL3001/LDPE I (LD200); (b) LL3001/LDPE II (EF606A); (c) LL3001/LDPE III (6621); (d) LL3001/LDPE IV (1321)  50  Figure 2-9. Tensile stress growth coefficient curves at Hencky strain rates of 0.1, 1 and 10 s-1 for LLDPE/LDPE blend systems containing 1 wt% LDPE at150  51  Figure 2-10. Activation energy, E a (KJ/mol), as a function of weight fraction of LDPE for all blend systems at 150 °C  ^52  Figure 2-11. Van Gurp-Palmen plots for all four LLDPE/LDPE blend systems using linear viscoelastic data at 130 °C, 150 °C, 170 °C, 190 °C and 210 54  Figure 2-12. Zero shear viscosity, 11 0 , versus LDPE weight fraction, w, for all four LLDPE/LDPE blend systems at 150 °C  ^55  Figure 2-13. Weighted relaxation spectra for all four LLDPE/LDPE blend systems at 150 °C  ^56  Figure 3-1. The complex viscosity curves of LDPE (6621), and those of all four LLDPE resins (LL3001, Dowlex, Exact and Affinity) at 150 °C  ^71  Figure 3-2. The tensile stress growth coefficient for the LDPE resin (6621) and the four LLDPE resins (LL3001, Dowlex, Exact and Affinity), at three different Hencky strain rates: 0.1, 1 and 10 s-1 ; at 150 °C  73  Figure 3-3. DSC thermograms for the LLDPE/LDPE blend systems: (a) ZNLLDPE I/LDPE; (b) ZN-LLDPE II/LDPE; (c) m- LLDPE I/LDPE; (d) mLLDPE II/LDPE  75  Figure 3-4. Mastercurves of a) elastic modulus, G', and b) complex viscosity, n*, ^78  for blend system I (ZN-LLDPE I/LDPE)  Figure 3-5. Mastercurves of a) elastic modulus, G', and b) complex viscosity, 11 * , ^79  for blend system II (ZN-LLDPE II/LDPE)  Figure 3-6. Mastercurves of a) elastic modulus, G', and b) complex viscosity, T1 * , ^80  for blend system III (m-LLDPE I/LDPE)  Figure 3-7. Mastercurves of a) elastic modulus, G', and b) complex viscosity, n*, ^81  for blend system IV (m-LLDPE II/LDPE)  Figure 3-8. Tensile stress growth coefficient curves for 0.1, 1 and 10 s -1 Hencky strain rates at 150 ° C for LLDPE/LDPE blend systems: (a) ZN-LLDPE I (LL3001)/LDPE; (b) ZN-LLDPE II (Dowlex)/LDPE; (c) m-LLDPE I (Exact)/LDPE; (d) m-LLDPE II (Affinity)/LDPE  82  Figure 3-9. Activation energy, E a (KJ/mol), as a function of weight fraction w of LDPE for all blend systems at 150 ° C  ^84  Figure 3-10. Van Gurp-Palmen plots for all four LLDPE/LDPE blend systems using linear viscoelastic data at 130 ° C, 150 ° C, 170 ° C, 190 ° C and 210  °C  86  Figure 3-11. Zero shear viscosity, n o , versus LDPE weight fraction, w, for all four LLDPE/LDPE blend systems at 150 ° C  ^87  Figure 4-1. A picture of the annular die showing the various inserts that are used to change the gap  ^100  Figure 4-2. The master viscoelastic moduli and complex viscosity of LLDPE (LL3001) at 150 ° C  ^101  Figure 4-3. The tensile stress growth coefficient curves for the LLDPE resin (LL3001) at three different Hencky strain rates: 0.1, 1 and 10 s -1 ; at 150  ° C.  102  Figure 4-4. Typical flowcurves of LLDPE in capillary, slit and tube extrusion at 150 ° C  ^103  Figure 4-5. Photographs of extrudates from capillary, slit and annular extrusion experiments at 150 ° C  ^103  Figure 4-6. Flow curves of LLDPE in capillary extrusion at 150 ° C for three  xi  different capillary dies with L/D=14-16 and diameters ranging from 0.43 to 2.34 mm. Discontinuities in the flow curve are clear that indicate the presence of stick-slip (oscillating) flow 105 Figure 4-7. Flow curves of LLDPE in capillary extrusion at 190 ° C for three different capillary dies with L/D=14-16 and diameters ranging from 0.43 to 2.34 mm. Discontinuities in the flow curve are clear that indicate the presence of stick-slip (oscillating) flow 106 Figure 4-8. Typical pressure oscillations in capillary flow using a die having D=0.762 mm, L/D=16 at various apparent shear rates and 150 ° C  107  Figure 4-9. Typical pressure oscillations in capillary flow using a die having D=0.762 mm, L/D=16 at various apparent shear rates and 190 ° C  108  Figure 4-10. Flow curves of LLDPE in slit die extrusion at 150 ° C using the three different slit dies. Discontinuities in the flow curve are clear in all cases indicating the presence of stick-slip (oscillating) flow 109 Figure 4-11. Flow curves of LLDPE in slit die extrusion at 190 ° C using the three slit dies. Discontinuities in the flow curve present in all dies indicating the presence of stick-slip (oscillating) flow 110 Figure 4-12. Typical pressure oscillations in slit flow at 150 ° C  111  Figure 4-13. Typical pressure oscillations in slit flow at 190 ° C  112  Figure 4-14. Flow curves of LLDPE in annular extrusion at 150 ° C using three reduction ratios: RR=152, 350 and 1000 — No discontinuity (no stick-slip) was  obtained  113  Figure 4-15. Flow curves in annular extrusion at 190 ° C using three reduction ratios: RR=152, 350 and 1000 — No discontinuity (no stick-slip) was obtained  114  Figure 5-1. The apparent flow curves of blends in Blend System I (LL3001/LD200) at 150 ° C  ^  123  Figure 5-2. The apparent flow curves of blends in Blend System II ^(LL3001/EF606) at 150 ° C  126  Figure 5-3. The apparent flow curves of blends in Blend System III  xii  (LL3001/6621) at 150 ° C  128  Figure 5-4. The Apparent flow curves of blends in Blend System IV ^  (LL3001/1321) at 150 ° C  128  Figure 5-5. Images of extrudates for Blend system I (LL3001/LD200) extruded at ^130  150 ° C  Figure 5-6. Images of extrudates for Blend system II (LL3001/EF606) extruded at ^131  150 ° C  Figure 5-7. Images of extrudates for Blend system III (LL3001/6621) extruded at ^132  150 ° C  Figure 5-8. Images of extrudates for Blend system IV (LL3001/1321) extruded at ^  150 ° C  133  Figure 5-9. Pressure oscillations in capillary extrusion of LL3001/EF606A blends at rA = 350s -1 and 150 °C  ^  135  Figure 5-10. Pressure oscillations in capillary extrusion of LL3001.32/EF606 blends at 2' A = 400s 1 and 150 °C ,  ^136  -  Figure 5-11. Pressure oscillations in capillary extrusion of LL3001/662I blends at YA = 350s ' and 150 °C  ^137  -  Figure 5-12. Pressure oscillations in capillary extrusion of LL3001/132I blends at )% ii = 350s -1 and 150 °C  ^138  Figure 5-13. The amplitude of pressure oscillations as a function of w% of LDPE for blends in the four systems extruded at 150 ° C  ^139  Figure 6-1. The apparent flow curves of blends in Blend System II (Dowlex/662I) at 150 ° C  ^147  Figure 6-2. The apparent flow curves of blends in Blend System III (Exact/662I) at 150 ° C  ^148  Figure 6-3. The apparent flow curves of blends in Blend System IV (Affinity/662I) at 150 ° C ^  149  Figure 6-4. Images of extrudates for Blend system II (Dowlex/626I) extruded at 150 ° C  ^151  Figure 6-5. Images of extrudates for Blend system III (Exact/662I) extruded at  150 ° C ^  152  Figure 6-6. Images of extrudates for Blend system IV Affinity/132I) extruded at 150 ° C  ^  153  Figure 6-7. Pressure oscillations in capillary extrusion of Dowlex/6621 blends at  y A = 700s and 150 °C ^  155  Figure 6-8. Pressure oscillations in capillary extrusion of Exact/662I blends at  y A = 400s ' and 150 °C -  ^  156  Figure 6-9. The amplitude of pressure oscillations as a function of w% of LDPE for blends in the four systems extruded at 150 ° C  ^157  Figure A-1. Horizontal shift factor, al., as a function of (1/T — VT„ f ), in IC I for LLDPE (LL3001) and all LDPE resins ^  167  Figure A-2. Horizontal shift factor, aT, as a function of (1/T —1/Tref ), in IC I for LDPE (6621) and all LLDPE resins ^  167  Figure B-1. DSC melting thermograms of 90:10 LL3001/662I blend obtained with a Shimadzu DSC 60 and TA Q1000 calorimeters ^  168  Figure B 2. DSC melting thermograms of 25:75 LL3001/662I blend obtained with a -  Shimadzu DSC 60 and TA Q1000 calorimeters ^  169  Figure B 3. DSC melting thermograms of 25:75 Exact/662I blend obtained with a -  Shimadzu DSC 60 and TA Q1000 calorimeters ^  169  xiv  ACKNOWLEDGEMENTS  I would like to acknowledge the following people and organizations that helped me in various ways throughout the duration of this project. Firstly, I am very grateful to my supervisor, Prof. Savvas G. Hatzikiriakos for his support, skilful guidance and encouragement throughout my Ph.D studies. Thanks to Dr. Martin Sentmanat for his assistance with SER rheometry, his thoughtful discussions and ideas. Dr. Stephan Costeux's comments were also helpful and constructively used in this research. I would also like to thank Prof. James J. Feng for his encouragement throughout this work. I am grateful to Natural Sciences and Engineering Research Council of Canada for providing financial support. The National Council of Science and Technology (CONACyT) has generously awarded me with a scholarship. The materials used in this research have been generously donated by Dow Chemical Company and ExxonMobil. I would also like to extend this acknowledgement to my colleagues and friends from RHEOLAB: Isaias, Ed, Jorge, Pramod, Anne, Christo, and Babak for their help and support. Finally, I would also like to thank my dear friends Nohra and Jacqueline who supported in various ways.  xv  Dedicated to my wife And To Irma, Rafael and Juana, in memoriam  xvi  CO-AUTHORSHIP STATEMENT  The work of this thesis consists of five different manuscripts which correspond to chapters two to six. During all this work, my research supervisor Prof Savvas Hatzikiriakos and I, participated in the identification and the design of the research work All of the experimental work was carried out by me as part of my PhD. research project. The data analysis was performed by me after several insightful discussions with my supervisor, Dr. Sentmanat and Dr. Georgiou in chapters two, three and four. The data analysis for chapters five and six was done by me with the skillful guidance of my research supervisor. Finally, I did the final preparation for each manuscript after careful revision and approval of my research supervisor.  xvii  1. LITERATURE REVIEW. 1.1. Introduction. Polyolefin resins (POs) are produced worldwide in a very large volume of about 100 x 10 6 metric tons in 2006, which corresponds to more than 50% of the total production of all plastic materials. Ethylene polymers and copolymers account for 5055% of the total PO production and propylene polymers for the rest 45%. The 2006 world capacities were about 4.9 x 10 7 tons (Bauman, 2007). The largest application of PE is thin film production and this can be made from LDPE, HDPE, and LLDPE. The film is mostly used for bags and packaging. However, there are many non-packaging applications especially for LLDPE, such as industrial sheeting, injection molding, blow molding or rotational molding, pipe/tubing extrusion and wire coating. The reason for this wide range of applications is that LLDPE macromolecules are able to crystallize in solid state. Therefore, its properties in solid state are superior to its counterpart, LDPE. However, the processability of linear resins and particularly LLDPE is limited as it is subjected to melt instabilities such as sharkskin, stick-slip or gross melt fracture at high rates of production (Hatzikiriakos and Migler, 2005). On the other hand, LDPE resins possess a unique molecular structure in its own right: large amounts of long-chain branching. This molecular characteristic of LDPE is the origin of two particular rheological phenomena: enhanced shear thinning, which is a significant decrease in melt viscosity with shear rate; and strain hardening, which is an increase in elongational viscosity with strain (Dealy and Wissbrun, 1990). Shear thinning provides better processability at high shear rates, whereas the effect of strain hardening effect is most clearly seen through the stability of bubble in blown film extrusion. A polymer that exhibits strain hardening will become more rigid as it is drawn to a greater extent or drawn at faster rates. Unlike LDPE, LLDPE resin never strain hardens. In order to improve the processability of LLDPE, this resin is blended with other PO resins. However, due to structural differences between resins, many undesirable effects may occur that are related to the thermorheological and processing behavior of the  1  final blends. The origins of the effects are not well understood and therefore need to be studied. As detailed further in the next sections of this chapter, the miscibility between linear and branched polyethylenes using rheological characterization has been the subject of many studies (Yamaguchi, et. al., 1999; Lee and Denn, 2000; Liu, et. al., 2002; Hussein, et. al., 2003; Hameed and Hussein, 2004; Hussein and Williams, 2004a, 2004b; Fang, et. al., 2005). There has been reported that the thermorheological and processing properties of polyethylenes are largely determined by molecular parameters, which include: (i). Long Chain Branching Content (LCB): This is the length of the long branches along the polymer backbone (Wood-Adams and Costeux, 2001; Gabriel and Miinstedt, 2002; Vega, et al., 2002; Sentmanat et al., 2004) (ii). Compositional distribution (CD): The composition means the number and length of long chain branching for a given macromolecule. A uniform compositional distribution means that all the molecules have the same number of branches of similar length (Gabriel and Mtinstedt, 1999, Wei et al., 2007). (iii). Molecular weight, M. This is the average molecular weight of the polymer (Wood-Adams et al., 2000) (iv). Molecular weight distribution MWD: This is the distribution of the various molecular sizes (Hatzikiriakos, 2000; Wood-Adams et al., 2000). Rheology has become an important tool in the determination of miscibility of polyethylene blends (Utracki, 1989; Lee and Denn 2000). In spite of many studies on the thermorheological behavior of polyethylene blends, there are several questions related to the effect of LCB and the molecular structure on the rheology and the processability of polyethylene blends; how miscibility of various polyethylenes changes with composition, with emphasis on the miscibility of LDPE with LLDPE; how rheology and processing are influenced by adding small amounts of LDPE into LLDPE; how rheology and processing are influenced by the thermodynamics of the polyethylene blends. These questions are part of the objectives of the present work.  2  1.2. Structure of Polyethylenes. Polyolefin resins (PO), is the generic name for a large family of homopolymers and copolymers derived from olefins (chemical name "alkenes"), unsaturated hydrocarbons with one or several C C double bonds. Most of the olefins used for the synthesis of PO resins are a-olefins of the general formula CH2 = CH —R, where according to the chemical structure of the R group, this could be a hydrogen atom (—H), as the case of ethylene , CH 3 in propylene, or — C2H 5 in 1-butane. Polyethylene resins are subdivided in different classes, which include: lowdensity polyethylene (LDPE), linear-low density polyethylene (LLDPE), and highdensity polyethylene (HDPE). The general chemical structure of a polyethylene macromolecule is (CH2 - CH2) —, where side branches are possible. Figure 1 illustrates the microstructure of the above listed types of polyethylenes. These vary from a linear structure (HDPE) to linear with small side branches (LLDPE) and finally to linear with long side branches (LDPE). The LLDPE resins are produced in industry with various classes of catalysts. These include Ziegler catalysts based on titanium compounds and several types of catalysts utilizing metallocene complexes. Copolymers obtained via Ziegler catalysis differ from metallocene ones in terms of the uniformity of branching distribution of the macromolecule; that is, using metallocenes, all the macromolecules have approximately the same branching composition. On the contrary, Ziegler catalysts yield a pronounced non-uniform compositional distribution given by a mixture of two types of polymer chains: high molecular weight macromolecules having linear structure (low a-olefin content); and low molecular weight chains with more branched structure (high a-olefin content. As a result, non-uniformly branched LLDPE possesses high linear, crystallizable chains, which give rigidity and stiffness, and amorphous chains which are flexible. This structural characteristic provides strength and toughness to the LLDPE.  3  HDPE Molecule  LLDPE Molecule  LDPE Molecule  Figure 1 1. Schematic representation of the microstructure of HDPE, LLDPE and LDPE. -  4  1.3. Elements of Rheology. Rheology is defined as the science of flow and deformation of matter as result of an applied force. From the continuum mechanics point of view, the stress tensor, a, which describes the state of stresses in the material at any point, is expressed by  o =^ -  were p is the hydrostatic pressure, and the second term,  1',  (1 -1)  is the extra stress tensor which  contains all the effects of deformation in the material. There are two general fundamental physical laws that describe the relation between the stress and the deformation, or rate of deformation. First, Hooke's Law, describes the rheological behavior of a perfectly (ideal) elastic solid. The shear stress is related to the deformation or strain tensor, y, via the modulus of elasticity, E, which is constant for an isotropic material. = Gy^  (1 2) -  Where G is the shear modulus and is equal to E/3 for an incompressible, isotropic perfectly elastic body. In index notation, the elements of the strain tensor y are defined as Y,,=  1 au, aui ^ 2 ax ax,  (1-3)  In Equation 1-3, uf is the component of the displacement field in the direction of xf (x, y or z, in Cartesian coordinates). On the other hand, Newton's law applies to a viscous fluid, where the shear stress tensor is proportional to the rate of deformation tensor, y , given by: 1- = 2,uy^  (1-4)  The viscosity, p, of the fluid is independent of the applied level of deformation rate. The rate of deformation tensor y is defined as: = —1 {Vv + Vv T 1^  (1-5)  Where v is the velocity field and Vv T is the transpose of Vv .  5  1.3.1 Linear Viscoelasticity. The above mentioned equations, Hooke's and Newton's laws, correspond to limiting cases of material response. Any material whose behaviour falls in between those of a purely viscous and a purely elastic behavior is said to be viscoelastic. Such materials will not deform instantaneously when a stress is applied, or the stress does not respond instantaneously to any imposed deformation. Viscoelasticity is typical for polymeric materials. In some polymer melts when the applied force is instantaneously removed, part of the deformation recovers with time, so it is said that the material possesses "memory" of his previous state, prior to deformation. The principal relation of linear viscoelasticity is the Boltzmann superposition principle, which states that the stress exerted to a material is related with of the sum of all infinitesimal deformations experienced in the past: u  (t) = G - Ody,i  (t')  (1-6)  or in terms of the rate of the rate of strain this can be expressed as:  J  (t) = G(t  (e)dt'  (1 7) -  where G(t-t) is the relaxation modulus. The principle expressed by Equations 1-6 and 17 tell us that the relaxation modulus depends only on the elapsed time, t-t', between the past and present states. The relaxation modulus is commonly represented by a generalized Maxwell model. This is a discrete relaxation spectrum and is represented as a sum of weighted exponentials (Dealy and Wissbrun, 1990). G(t) =E exp(— 21 ) 1+1  (1 8) -  For each node i, correspond a relaxation time and a modulus G 1 . If the number of Maxwell nodes (G i , Xi ) increase to infinity, then the relaxation modulus can be represented in terms of a continuous function of relaxation times, i.e. the relaxation spectrum H(2). This function accounts for the contribution to the modulus which relaxation times fall between 1n(2) and ln(X) + dln(A). In this case the relaxation modulus, G(t), is given by:  6  G(t) = IH(.1)exp(— t 2,)dln(1)^  (1-9)  When substituting Equation 1-8 into Equation 1-7, the general linear viscoelastic model is obtained: I  N  =^G exp[— (t — 0/2122, (e)dt'  (1-10)  The parameters G, and X, can be determined from experimental results of small amplitude oscillatory shear that are explained in section 1.4.4.  1.3.2. Material Functions. There are two types of deformations that are used to characterize the rheological properties of polymers, namely shear and extension. Material functions related to these two types of flow will be reviewed in this section. In steady simple shear flow represented in Figure 1-2, the shear rate across the field is constant. The viscosity is defined by: 1  1(11  (  )^  1-11)  In Equation 1-11, o is the shear stress and ji is the shear rate.  AX V  F  // //  ///////)  22 =^o- = F/A Figure 1-2. Schematic representation of simple shear flow.  7  The viscosity of molten polymers decreases with increase of shear rate, although it approaches a constant value at diminishingly small shear rates. This limiting value of viscosity is known as the zero-shear viscosity, observed in a log-log plot of viscosity 1  ti  ti o ,  and corresponds to the plateau  as a function of y :  70 = ittip(r)  ^  (1-12)  The zero-shear viscosity is related to the relaxation modulus of linear viscoelasticity by: 770 = f G(t)dt  (1-13)  0  In simple shear flow, the rate of deformation tensor, y has the following form:  =  0  y  ))  0 0  0  0  0 (1-14)  0  In transient experiments, the stress relaxation is a fundamental way to define the relaxation modulus, G(t). In this test, the shear stress is measured as a function of time after a constant strain y o is applied instantaneously. If the strain is small enough (linear viscoelasticity) G(t) is independent of y o . However, for larger strains, the relaxation modulus becomes a function of y o as well: G(t,7 0 ) =  r(t) 70  (1-15)  Creep experiments are used to measure the recovery of the material as a function of time, after a constant shear stress,r o , is applied. Creep is defined in terms of the compliance J(t): J(t) = y(t)  (1 -16)  To  8  Start up of steady shear is a test that determines the growth of shear stress with time as a function of shear rate,7 0 . The relevant material function is the shear stress growth coefficient, 17+ (t), defined as: (t)=  r (t) Yo  (1 -1 7)  Using the linear viscoelastic model, (Equation 1-10), the stress growth coefficient, if' is expressed as: i E+  (t) =  r  E i=1  where /7, =^. There are several types of extensional flows. The one mostly used in the laboratory is the uniaxial elongational flow depicted in Figure1-3. A certain rate of extension is imposed in direction 1 and the force is measured as a function of time.  Figure 1 3. Schematic representation of uniaxial extension -  It can be shown that the deformation tensor has the following form (Dealy and  Wissbrun, 1990): 2e = 0 0  0  0  —E 0  0 —  (1-19)  9  The elongational rate of deformation, s , is related to the velocity field by Equations 1-20 that gives the kinematics of the flow. In this special flow, the material is stretched in direction 1, and compressed in directions 2 and 3. The kinematics of the flow are given by: V  1 =V 2  ——x 2 2 , V 3 = — —x 3^ 2  (1-20)  The elongational viscosity or stress growth coefficient, 7 , is thus related to the normal stresses, ail and a 22 by: +^ 0' 11  —  6 22^r11 T 22  E  (1-21)  In uniaxial elongation T22= 0 and therefore: 11E+ (t) =  Z ll  (1-22)  1.3.3. Temperature Effects on Viscoelastic Properties. Rheological properties depend on temperature. This means that to obtain a complete picture of the rheological behaviour, experiments must be carried out at several temperatures. It is often found that rheological data measured at several temperatures can be brought together on a single master curve by means of "time-temperature superposition" (TTS). This greatly simplifies the description of the effect of temperature. Furthermore, it makes possible the display on a single curve of material behaviour covering a much broader range of time or frequency than can ever be measured at a single temperature. Materials whose behaviour can be displayed in this way are said to be "thermorheologically simple" (Dealy and Wissbrun, 1990). As discussed above rheological data at different temperatures can often be superposed by introducing a shift factor, aT, determined empirically. Thus, if one makes a plot of a rheological property versus time, a T is obtained from the horizontal shift necessary to bring the data for any temperature T onto the same curve as data for reference temperature Tref. For example, mastercurves of G' and G" should be plotted versus coa l to  10  reduce to a mastercurve. The shift factor is a function of temperature, and the WLF Equation has been found useful (Ferry, 1980): log(a r  - Citp (T- To ) C23 + (T - To ) 1  (1-23)  where C 1° and C2° are constants determined at To for each material. This equation holds at temperatures very close to glass transition temperature, Tg . At temperatures at least 100 K above Tg, an empirical relationship, the Arrhenius Equation for the shift factors is frequently used: 10,Ya 7') .=  H  r 1 _1 (1-24)  T Tref  where EH is called "horizontal activation energy", and R is the constant of gases. The horizontal shift factor, aT reflects the temperature dependence of relaxation time .1(aT co,T)=.1.,(co,Tro  (1-25) Therefore aT, shifts rheological quantities related with time dimensions, such as rate of shear, or extension, frequency, or viscosity. )  In the same way, a vertical shift factor, br, is often required to superpose data for polymers with LCB (Mavridis and Shroff, 1992). These authors proposed a similar expression for b y- , given by: log(b T ) =7-;  1^1 T Tref j  (1-26)  where E, are the "vertical activation energy", R is the gas constant, and Tref is the reference temperature. The vertical shift factor reflects the temperature dependence of the plateau modulus G,°,„ : bTGN° (ot r co,T)= GN° (co,Trei  )  (1-27)  Hence, in analogy to horizontal shifting, b T can be used to shift rheological quantities along the vertical axis, such as G', G", or q*. In their analysis, Mavridis and Schroff (1992) have shown that polymers with long chain branching, such as LDPE and EVA, still can be considered as thermorheologically simple materials, if a vertical shift is applied. The feasibility of time temperature superposition can be made by inspection of 11  ^  the so-called Van-Gurp Palmen plots (Van-Gurp and Palmen, 1998). These can be constructed by plotting tan(6) as a function of G* at different temperatures. If the resulted lines are parallel lines, separated by a distance determinated by aT , TTS is to be obeyed. This analysis have been used to detect LCB in polyethylene blends (Liu, et. al., 2002; Peon, et. al., 2003; Perez, et. al., 2005). The observance of time-temperature superposition is suggested to be an indication of blend miscibility (Mavridis and Shroff, 1992; Van-Gurp Palmen, 1998).  1.4. Viscometric Flows and rheometers. 1.4.1. Capillary Flow. The simplest and most popular type of rheometer is the capillary rheometer shown in Figure 1-4 (Dealy, 1990). In its simplest configuration, the capillary rheometer consists of a small tube of diameter D through which the polymer melt is made to flow, either by means of an imposed pressure or by means of a piston moving at a fixed speed. The quantities normally measured are the volumetric flow rate Q, and the driving pressure, Pd. If the flow is generated by a moving piston, it is usually the piston force, Ed, that is measured. This is related to Pd as follows:  P = 4 dd ^i  F,d ^2 "  (1-28)  l^ b  where Rb is the radius of the barrel or reservoir (Dealy, 1990). It can be shown that the absolute value of the shear stress at the wall, cr w , is related to the pressure drop, AP, over a length of tube, L, as follows (Bird, et al., 2002):  a. .---- r ml,R= —  AP • R 2L^  (1-29)  The pressure drop, AP, is always a negative quantity, because the flow is in the direction of the axial coordinate, z. As this is a partially controllable flow, the velocity profile depends on the rheological properties of the fluid under study, and a general expression relating the volumetric flow rate, Q, to the wall shear rate cannot be derived.  12  Barrel diameter Db  Capillary land zone L  Capillary diameter D  Figure 1-4: Schematic diagram of a typical cylindrical capillary die along with the definition of the design parameters.  It is known that for a Newtonian fluid in laminar flow, the velocity distribution is given by the familiar parabolic law (Bird et al., 2002): v = 2 ^ [1 7ER 2^(R  (1-30)  This is the velocity profile for "fully developed flow" in which the effects of the entrance and exit are assumed negligible and there is thus no velocity component in the radial direction. The absolute magnitude of the shear rate at the wall, 2%,„ , can be determined from Equations 1-30, as follows: dv)4Q w —( dr 3 ^ r . R^7TR  (1-31)  For non-Newtonian fluids, Equation 1-31 is no longer the wall shear rate, instead it is referred to as the apparent shear rate, 2% A .  13  1.4.2 Flow in a narrow slit. Equations 1-29 and 1-31 apply for a flow in a cylindrical channel. When a fluid flows through a rectangular channel in which the width, W, is much larger than the thickness, H, the edges make a negligible contribution to the pressure drop and this geometry can effectively be used for rheological measurements (see Figure 1-5). For the steady flow of an incompressible fluid in such a channel, the absolute value of the shear stress at the wall, aiv , is given by (Dealy, 1990): -  6w ---  AP - H  (1-32)  2L^  where AP is the pressure drop over a length of channel, L. The apparent shear rate in a slit, which is the true wall shear rate for a Newtonian fluid is given by: .^6Q TA = H2w  (1-33)  The schematic of the slit dies used in this work is depicted in Figure 1-5  Figure 1 5. Schematic diagram of the rectangular flow geometry and the slit die showing the land zone. -  14  1.4.3. Flow through an annulus.  In this case, the polymer melt flows through an annular region between two coaxial cylinders having an inside diameter Di, and outside diameters D o , respectively. When the annulus is very thin, then it becomes to a slit die. The expression for the shear stress at the wall, g„, is then given by:  AP • (Do — D, ) criu  (1-34)  2L  and the expression for the apparent shear rate becomes:  48Q17r(D„  —  De ) 2  (D + D.^(1-35)  The annular flow for a LLDPE melt was studied in this work using a combination of a die and three different inserts, with different Di, as depicted in Figure 1-6  • C •  Z=0^  •  Z=L  Annular Zone  Figure 1-6. Schematic of the die and the insert for annular flow. The dimensions for the die are: D b=25.4mm, D o =2.54mm, while for the different mandrels (inserts) are, D m=5mm, D,=1.542mm, 2.167mm and 2.415 mm.  All the capillary/slit/annular extrusions were performed by using an Instron tensile tester model 1123. As shown in Figure 1-7, the instrument consists of the barrel, the motor drive, the load cell and the data acquisition system. Two interchangeable barrels of 9.525 mm and 25.4 mm inner diameter were available. The dies for capillary 15  and slit flow studies were used in conjunction with the small barrel, while the dies for annular flow were used in conjunction with the big barrel. Both barrels include heating bands and temperature controllers. A load cell of 2270 kg with a plunger attached to it, is mounted on a mobile stage. The motor drive allows moving the stage at a specific speed entered in the computer controlled board. The load cell senses the resistance to flow applied by the melt contained in the barrel through the plunger. It sends it to the data acquisition system, which allows the experimental results to be recorded automatically and stored in the computer.  Load Cell Plunner  Temperature Controllers  Barrel  El  Data Acquisition System  Control Panel  El  ^  000  Thermocounle  Die  IBM Co  Figure 1 7 Set up of the Instron capillary rheometer. -  -  1.4.4. Small amplitude oscillatory shear. One of the most widely used rheological tests is the Small Amplitude Oscillatory Shear (SAOS). In this test, the sample contained between two parallel plates is deformed at an angular frequency co, and strain amplitude, y o , as shown in Figure 1-8 (parallel plate rheometer).  16  The strain in the upper plate is sinusoidal as described by: y =y o sin(w t)^  (1-36)  where 7 0 is the strain amplitude, usually much less than one in order to be within the limits of linear viscoelasticity. It can be proven that the measured shear stress signal varies sinusoidally as:  Fluid sample  Pressure transducer  Figure 1 8. Parallel plate rheometer -  T = r o sin(w t + 8)^  (1-37)  The stress amplitude is cr o and 8 is the phase angle. The stress wave is decomposed into two contributions, one in-phase with stress, and the other out-of-phase with the strain as follows: T =1 .  -  0  cos 8 sin cot + 6 0 sin 8 cos cot = y o [G' sin cot + G" cos cod^(1 38) -  where G' and G" are given by:  zG = =' cos 8,^ = sin 8, tan 8 =^(1-39) 70^70 From this decomposition the two dynamic moduli are obtained: the storage modulus, G', and the loss modulus, G ". From these two expressions a complex moduli, G* can be defined: G* = G'+iG"  ^  (1-40)  17  Therefore =^*  ^  (1-41)  Alternatively, performing a similar analysis, the time derivative of the strain rate allow us to work in terms of a complex viscosity, as follows. ^ 77 * =  , G"^, G'  (1-42) (1-43)  = ^; 71 1 = — co co  The magnitudes of the complex modulus and viscosities are then related by  G*  77*  (1-44)  a)  If the general linear viscoelastic model is used, the following expressions can be obtained from the relaxation moduli:  co2  G' (co) =E G, ^ 1.1^1 + co 2  (1-45)  G" (co) =IG  (1-46)  i=1  1 ± co 2 /112  1.4.5. Uniaxial extension. The Sentmanat Extensional Rheometer (SER) is suitable to perform extensional rheology studies of strip shape samples (Sentmanat, 2004). A schematic of this rheometer is shown in Figure 1-9. This rheometer is attached to concentric disk rheometer described in section 1.4.4. The rheometer consists of paired master and slave wind up drums mechanically coupled by a gear (Figure 1-9). The rotational motion of the Bohlin VOR motor results in a rotation of the master drum and an equal but opposite rotation of the slave drum. As a result, the sample, which is secured on the drums by mean of a pair of clamps, is subjected to a uniform extensional deformation. The Hencky strain in an extensional flow is defined as: (  c H =1n  \ Lo  ^  (1-47)  18  where EH is the Hencky strain, L is the length of the specimen at any time, and Lo is the initial sample length. The Hencky strain rate is then obtained by taking the derivative of the Hencky strain with respect to time .^dc H 1 dL ^ dt^L dt  (1-48)  8H  For small deformations, the change of length with time can be approximated to the initial length and Equation 1-48 becomes 1 dL L^ o dt  (1-49)  8 H =7—  For a constant Hencky strain rate,i' H , the tensile stress growth function,  77E  (t), of  the stretched sample can be expressed as: F(t)^F(t) 77; (t)= ^ = A(t)E H A o exp(—E H t)i.„^(1-50)  The force F(t) measured by the instrument is related to the torque, and A o is the initial cross-sectional area of the specimen. Lo  Master Drum  Slave Drum  Clips  Sample  Intermeshing Gears  Figure 1 9. Schematic of the Sentmanat Extensional Rheometer (SER). -  19  1.5. Shear Thinning and Strain Hardening. Polyethylene processing technologies involve resin melting and flow. The main factors that affect melt viscosity are the molecular weight of a resin, its distribution and temperature. Polymer melts are non-Newtonian liquids and their viscosity is significantly reduced with increase of shear rate (flow rate). This phenomenon is called shear thinning; it plays a very important role in processing. The resins with enhanced shear-thinning capability have greatly decreased viscosities at a high speed melt flow typical for industrial processing conditions, and hence call for a reduced energy demand. Although LDPE shows a higher melt viscosity at low shear rate values, this decreases significantly at higher shear rates due to its high degree of shear thinning, and becomes smaller than that of LLDPE. Furthermore, the zero-shear viscosity for LDPE is difficult to be meassured, as it can only be reached at extremely low shear rates (less than 10  4  s -1 ). On  the other hand, the zero-shear viscosity of LLDPE is lower than that of LDPE and can be reached typically at rates of the order of 10 -2 -10 -1 s -1 . It is worthwhile to mention that shear thinning also increases with broadening of the molecular weight distribution (MWD). Strain hardening behavior is a typical behavior obtained for LDPE due to the presence of long-chain branches (Wagner et. al., 1998; MUnstedt and Kurzbeck, 1998; Gabriel and MUnstedt, 2003; Sentmanat et. al, 2005; MUnstedt et. al., 2005). It is observed in tensile stress growth experiments. Typical results for a LDPE and a LLDPE are depicted in Figure 1-10. The tensile stress growth coefficients or transient elongational viscosities are plotted versus time, at several Hencky strain rate values, s for both resins. In the case of LDPE, it can be observed that at low elongational rates, the stress growth coefficient follows the linear viscoelastic envelope indicated by the relation 7/ 4- E = 377 + , where ii + E can be calculated from the analysis of small amplitude oscillatory experiments. This is exceeded at higher Hencky strain rates and longer times; this behavior is referred to as strain hardening. On the other hand, the transient elongational viscosity of linear polyethylene (LLDPE) never exceeds the linear viscoelastic envelope of 31/ + .  20  1.0E+06 ^  T = 150°C  0.1 S -1  s'  U) 1.0E+0 : I Ca^E L 0 1.32  20 s'^  10 s. " 1  0...  4 ^  I LVE: 31.1 1.0E3 ^ ' ^ ^ 0.01 0.1  +  from Cone Pla te  10  t [SI Figure 1-10. Strain Hardening behavior for LDPE (LD200) and LLDPE (LL3001.32) at  150 °C, and different extensional rates, s =0.1, 1, 10 and 20 s -1 .  1.6. Rheological criteria for immiscibility of polyethylene blends. The physical approach of blending polymers to develop or improve new polymeric products has been an extremely active area of polymer research. Fundamental issues that affect the properties of blends include equilibrium phase, phase morphology and rheology; their interrelation is of fundamental importance in the processing and the characteristics of the final product. Rheology has been a useful method in the determination of miscibility between polyethylenes (Utracki and Schlund, 1987; Utracki, 1989; Cho et. al. 1998). Differential scanning calorimetry (DSC) is an alternative way to determine the miscibility, since polymer components crystallize at different ways, (Puig, 2001; Arnal, et.al , 2000; Wignal, et. al. 2000). The occurrence of two peaks in a heating DSC graph is indicative of phase segregation, due to independent melting of the crystallites of the components in the blend.  21  Recently, many authors have combined both, rheological and calorimetrical techniques to elucidate the miscibility of polyethylenes (Yamaguchi, et. al, 1999; Lee and Denn, 2000; Liu, et. al., 2002; Fang, et. al., 2005; Hussein, 2005). Cole-Cole plots (77" vs  71 in linear scale) are often used to determine miscibility of the blends (Cho, et. al., 1998; Ho, et. al., 2002; Hussein, 2005). A smooth semicircular plot, suggests polymer compatibility (Utracki, 1989). The effect of temperature on the rheology of the blends can be quantified in terms of the time-temperature superposition principle (TTS). A material is said to be thermorheologically simple if TTS is obeyed. Thermorheological complex behavior arises by the presence of LCB, as well as the different temperature sensitivity of the relaxation times of a polymer (Mavridis and Shroff, 1992; Wood-Adams and Costeux, 2001). This leads to failure of TTS. Failure of time-temperature superposition can be interpreted as an immiscibility criterion in polymer blends (Van Gurp and Palmen 1998; Peon, et. al., 2003; Wagner et al., 2004; Perez et al., 2005, Delgadillo-Velazquez, et al., 2007). Other rheological indication of two phase system is the behavior of the linear viscoelastic moduli, as a function of frequency, which resemble the behavior of an emulsion system; that is G ' (co) and G "(co) of the blend may exceed the corresponding values of the matrix phase or dispersed phase due to the interfacial tension exerted by the presence of droplets of the dispersed phase (Choi and Schowalter, 1975). In addition to the criteria discussed above, several mixing rules are used to decide whether a polymer system is miscible or not. Many of them are based on the dependence of the zero-shear viscosity, /7 0 , on the volume fraction, 0 . The simplest mixing rules applied are the linear additivity rule, and the log-additivity rule (Utracki, 1989). Thus, a blend is said to be miscible, if 77 0 follows either of the following equations: 170 =  Eoh,o 1=1  log ri o = 0, log 77,, 0 i=1  (1-51)  (1-52)  22  For ZN-LLDPE and m-LLDPE blended with LDPE the compositional dependence of rh o is found to have a positive deviation behavior (PDB) from the mixing rule (Hussein, et. al., 2003; Hussein and Williams, 2004a; 2004b), whereas the mLLDPE/HDPE system, has been found to follow log-additivity rule and suggested to be miscible (Liu, et. al., 2002; Hussein, 2005). Other mixing rules have been used, such as taking the complex viscosity, 1*, or the dynamic viscosity,  n ', at a fixed low frequency  (Hussein, 2003; Hussein, et. al., 2003; Hussein and Williams, 2004b; Fang, et. al., 2005). To capture the curvature of the log (i) curve, Haley and Lodge (2004) proposed an approach to calculate miscible blend viscosities as a function of composition for monodisperse systems; although the model has been corrected for polydisperse systems, its predictions are only qualitative (Haley and Lodge, 2004; 2005). Finally, Utraki (1991) proposed a model to describe the positive (PDB) and negative (NDB) deviations form the log-additivity rule and have been used for mLLDPE/LDPE blends (Fang, et.al , 2005) and HDPE/LDPE (Liu, et. al., 2002); however, the phase inversion concentrations for components 1 and 2 are needed. The double reptation model (Tsenoglou, 1988; 1991; des Cloizeaux, 1990), Equation 1-53, is used to describe the dynamic data of miscible linear polymer blends: N  G(t) =[EO,G,V ^2 2 (t)1  (1 53) -  where N is the number of components in the blend. To fit the dynamic data of linear and branched polymer blends, Groves and coworkers (1996) modified the double reptation model, as shown in Equation 1-54:  i r  N^C  G(t) =[Z(bi G (t)  (1 54) -  where C is an empirical exponent. Lee and Denn (2000) applied both theories to describe the viscoelastic behavior of miscible blends of linear and branched polyethylenes. The description of dynamic behavior for blends of linear and branched polyethylenes (LLDPE/LDPE) was extended for a partially miscible system by means of a hybrid model (Lee and Denn, 2000). It was suggested that a fraction X of the minor component is miscible with the major component. The matrix properties are determined  23  from the double reptation theory, and the properties of the blend are defined by the Palierne's emulsion model with a dispersed phase of 1-X of the minor component. This approach has also been used for m-LLDPE/LDPE (Peon, et. al., 2003). Partially miscibility has also been observed in m-LLDPE/LDPE blends (Fang, et.al , 2005) and mLLDPE/HDPE (Hussein, 2003, 2004a). Most of these rheological methods are used and explained in detail in Chapters 3 and 4, where the miscibility of several LLDPE/LDPE blends is studied.  1.7. Melt fracture phenomena. Common operations for the manufacture of polymeric products like bottles, rods, tubes, sheets, or coating are based on extrusion. In such processes the polymer melt is conveyed by a screw and then forced to flow through a shaping die. Depending on the shear stress at the wall, polymer melts exhibit flow instabilities that manifest themselves as extrudate distortion. Such instabilities, limit the rate of production in many polymer processes. Comprehensive reviews of the instabilities observed for polymer melts have been published (Denn, 2001; Hatzikiriakos and Migler, 2005). These phenomena are known collectively as melt fracture. The term melt fracture was introduced by Tordella (1956) because of the audible tearing noises which accompanied the distortion of the extrudate. The phenomena of melt fracture and the accompanied instabilities can be best explained by making reference to the apparent flow curve of the polymer, this is a plot that relates the volumetric flow rate, Q, to the pressure required to generate capillary flow. In fundamental quantities, this can be presented in terms of wall shear stress cr,„ versus apparent shear rate 22 A . A typical flow curve of linear polyethylene of narrow MWD, is shown in Figure 1-12. Four distinct flow regimes are observed: at sufficiently low extrusion rates, the surface of the extrudate is smooth as it exits the die and therefore, it is considered to be a stable regime. At progressively higher extrusion rates, and wall shear stresses greater than a critical value, cra , usually of the order of 0.1 MPa, the extrudate's surface exhibits small-amplitude periodic distortions known as sharkskin. In many cases, this phenomenon has been accompanied by the occurrence of slip. In this  24  regime, there is a frequently change of slope of the flow curve at .7, 1 . At higher extrusion rates, when the wall shear stress is above a second critical value, 0, 2 , of approximately 0.3 to 0.4 MPa, stick-slip or oscillating melt fracture is obtained. This regime is characterized by oscillations in pressure and flow, and the extrudate changes between sharkskinned and smooth sections. Finally, at higher apparent rates, the distortions become gross and therefore this regime is known as gross melt fracture (GMF). Typical extrudate appearances in these flow regimes are shown in Figure 1-12, for a LLDPE (LL300.32) extruded through a cylindrical die. Capillary flow is a good way of examining the processability of polymers, i.e., determine the critical shear stress or shear rate for the onset of flow instabilities. It is known that LDPE does not exhibit sharkskin and oscillating melt fracture as opposed to LLDPE, where sharkskin is a major processing problem (Denn, 2001; Hatzikiriakos and Migler, 2005). It would be interesting to examine how the processability of LDPE and LLDPE are influenced by blending; in other words, to study the effect of the presence of long chain branching on the onset and occurrence of flow instabilities in the blends. Therefore, it would be of primary importance to see whether sharkskin and oscillating melt fracture can be eliminated by adding small amounts of LDPE into LLDPE. In addition, it would be of importance to examine whether or not changes observed in the processability of blends are reflected in changes in their rheological properties. Furthermore, since crystallinity influences the mechanical properties of final products, it would be also of importance to examine the effect of blending LDPE with LLDPE into rheological, processing and mechanical properties of the final products. Finally, melt fracture phenomena should also be examined by means of slit and annular flows (apart form capillary flow) in order for these studies to be relevant to real processing operations. An important question is how the critical stresses for the onset of these phenomena depend on die geometry. This is examined in Chapter 5 of this thesis.  25  1. ...  logy. Figure 1-11. A typical apparent flow curve for a linear polyethylene. 1. Smooth; 2. Sharkskin; 3. Stick-slip; 4. Gross melt fracture.  1.8. SCOPE OF THE WORK. 1.8.1. Thesis objectives. This project is devoted to the study of the thermorheology and flow instabilities of several LLDPE and LDPE resins and their blends. An effort has been made to understand the relation between the long chain branching and miscibility and their effects on the rheology and processing of LLDPE/LDPE blends. The central hypothesis is how addition of LDPE into various types of LLDPE's influence their processability. The objectives of this work can be summarized as follows: 1. To measure systematically the thermorheological behaviour of different types of LLDPE and LDPE resins and their blends. 2. To evaluate the effect of long chain branching on the thermorheological behaviour of LLDPE/LDPE blends. 3. To determine the miscibility of various blends using differential scanning calorimetry (DSC) and linear viscoelastic measurements (time-temperature superposition, Van GurpPalme plots, Cole-Cole plots, zero-shear viscosity versus composition plots, and relaxation spectrum plots).  26  4. To compare the thermorheological behaviour of Ziegler-Natta with that of metallocene LLDPE resins when blended with LDPE, using various techniques (listed in objective 3). 5. To evaluate the processability of all blends in capillary rheometry in order to determine the effects of long chain branching on the onset of sharkskin, stick-slip oscillations and gross melt fracture. 6. To study the onset of sharkskin and stick-slip (oscillating) melt fracture of a linear lowdensity polyethylene in extrusion by using different flow geometries (capillary, rectangular slit and annular)  1.8.2. Thesis organization.  This chapter of the thesis discusses the basic motivation of the present work. It includes basic information related to the different macromolecular structure of polyethylenes, as well as presents a review of the rheological concepts used in this thesis. This chapter also includes a review of the different flows that are utilized to study rheologically all the resins and their blends. The rheological criteria for polyethylene miscibility, definitions of shear thinning and strain hardening and melt fracture phenomena are also discussed. Chapter 2 is a study of the thermorheological properties of a Ziegler-Natta LLDPE and its blends with four different LDPE, having different molecular weights. The effect of long chain branching on the thermorheological properties of the blends, their miscibility and extensional rheology is examined thoroughly. This chapter is based on a journal paper that has already been published (Delgadillo-Velazquez, 0.; Hatzikiriakos, S.G.; Sentmanat, M., Rheologica Acta, 43: 19-31, 2007). Chapter 3 presents the analysis of two Ziegler-Natta and two metallocene LLDPE resins that are blended with a single LDPE. The effect of the manufacturing technology of LLDPE on the thermorheology, miscibility and extensional rheology using techniques described in Chapter 2 is discussed. This chapter is based on a paper that was submitted for publication (Delgadillo-Velazquez, 0.; Hatzikiriakos, S.G.; Sentmanat, M, submitted to J Polym Science Part B: Polymer Physics, 2008).  Chapter 4 is a study of flow instabilities such as sharkskin and stick-slip melt fracture of a LLDPE as functions of the die geometry. Experimental observations  27  concerning the flow curves, the critical wall shear stress for the onset of the various flow instabilities, the pressure and flow rate oscillations, and the effects of geometry and operating conditions on the phenomena are presented. This chapter is based on a journal paper that has been accepted for publication (Delgadillo-Velazquez 0, Georgiou G., M. Sentmanat, and Hatzikiriakos, S.G, Polym. Eng. Sci., 48: 405-414, 2008). Chapter 5 contains the processing behavior of polyethylene resins and their blends studied in chapter 2. The effect of long chain branching on the onset of sharkskin, stickslip and gross melt fracture is discussed. Special attention is paid to the suppression of pressure oscillations with LDPE content in stick-slip flow regime. This chapter is based on a journal paper that has been published (Delgadillo-Velazquez, 0.; Hatzikiriakos, S.G., Polym Eng Sci, 47, 1317-1316,47: 1317-1326, 2007). Chapter 6 presents a capillary extrusion study, similar to that presented in chapter 5, for the blend systems whose thermorheology is examined in Chapter 3. These results were accepted for publication (Delgadillo-Velazquez, 0.; Hatzikiriakos, S.G., International Polymer Processing, 2008). Finally, the conclusions, contributions to knowledge and recommendations for future research are summarized in Chapter 7. A general summary of the most significant findings resulted from this work is presented.  28  1.9. References. Arnal ML, Sanchez JJ, Muller AJ, (2001) Miscibility of linear and branched polyethylene by thermal fractionation: use of the successive self-nucleation and annealing (SSA) technique. Polymer 42: 6877-6890. Bauman, RJ (2007), Polyolefins: Globalization and beyond, Polyolefins 2007 Conference (SPE), February, Houston, Tx, 2007. Bird RB, Stewart WE, Lightfoot EN, (2002) in Transport Phenomena. J Wiley, New York. Cho K, Lee BH Hwang K, Lee H, Choe S (1998) theological and mechanical properties in polyethylene blends. Polym Eng Sci 38: 1969-1975 Choi, SJ, Schowalter WR (1975), Rheological Properties of Nondilute Suspensions of Deformable Particles, Phys. Fluids 18: 420-427. Dealy, J. M., in .Rheometers forMolten Plastics. A practical Guide to Design and Properly Measurement. Van Nostrand Reinhold, New York, 1982. Dealy, JM and Wissbrun KF (1990) in Melt Rheology and its Role in Plastics Processing. Theory and Applications. Van Nostrand Reinhold, New York Delgadillo-Velazquez 0, Hatzikiriakos SG, Sentmanat M (2007) Thermorheological properties of LLDPE/LDPE blends. Rheol Acta 47: 19-31 Delgadillo-Velizquez, 0.; Hatzikiriakos, S.G.; Sentmanat, M. (2008), Thermorheological properties of LLDPE/LDPE blends: Effects of the production technology of T.I.DPE, submitted to J Polym Science Part B: Polymer Physics. Delgadillo-Velazquez 0.; Georgiou, G.; Sentmanat, M.; Hatzikiriakos, S.G. (2008), Sharkskin and oscillating melt fracture: Why in slit and capillary dies and not in annular dies?, Polymer Engineering and Science., 48: 405-414. Delgadillo-Velizquez, 0.; Hatzikiriakos, S.G. (2007), Processability of LLDPE/LDPE blends: Capillary extrusion studies, Polymer Engineering and Science, 47, 1317-1326. Delgadillo-Velazquez, 0.; Hatzikiriakos, S.G. (2008), Capillary extrusion studies of LLDPE/LDPE blends: Effects of manufacturing technology of LLDPE and long chain branching, International Polymer Processing, in press. Denn, MM (2001) Extrusion Instabilities and Wall Slip, Ann. Rev. Fluid Mech. 33: 265-287. des Cloizeaux, J (1990) Relaxation of Entangled Polymers in Melts, Macromolecules, 23, 3992-4006. Fang Y, Carreau PJ, Lafleur PG (2005) Thermal and theological properties of mLLDPE/LDPE blends. Polym Eng Sci 45: 1254-1269 Ferry, J. D., in VzIrcoelastic Properties of Polymers, John Wiley and Sons, New York, 1980. Gabriel C, Miinstedt H (1999) Creep recovery behavior of metallocene linear low-density polyethylenes. Rheol Acta 38: 393-403 Gabriel C, Miinstedt H (2002) Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear. Rheol Acta 41: 232-244 Gabriel C, Miinstedt H (2003) Strain hardening of various polyolefins in uniaxial elongational  29  flow J Rheol 47: 619-630 Groves DJ, McLeish TCB, Chohan RK, Coates PD (1996) Predicting the Rheology of Linear with Branched Polyethylene Blends, Rheol. Acta. 35: 481-493. Haley JC Lodge TP (2005) Viscosity predictions for model miscible polymer blends: including self-concentration, double reptation, and tube dilation. J Rheol 49: 1277-1302 Haley JC, Lodge TP (2004) A framework for predicting the viscosity of miscible polymer blends. J Rheol 48: 463-486 Hameed T, Hussein IA (2004) Effect of short chain branching of LDPE on its miscibility with linear HDPE. Macromol Mater Eng 289: 198-203 Hatzikiriakos, S.G (2000), Long chain branching and polydispersity Effects on the Rheological Properties of Polyethylenes. Polym Eng Sci 40: 2279-2287 Hatzikiriakos, SG, Migler, KB (2005) in Polymer Processing Instabilities. Control and Understanding. Marcel Dekker, New York. Ho K, Kale L, Montgomery S (2002) Melt strength of linear-low density polyethylene/low density polyethylene blends. J Appl Polym Sci 85: 1408-1418 Hussein IA (2003) Influence of composition distribution and branch content on the miscibility of m-LLDPE and HDPE blends: theological investigation. Macromolecules 36: 20242031 Hussein IA, Hameed T, Sharkh BFA, Khaled M, (2003) Miscibility of hexene-LLDPE and LDPE blends: influence of branch content and composition distribution. Polymer 44: 4665-4672 Hussein IA, Williams MC (2004a) Rheological study of heterogeneities in melt blends of ZNLLDPE and LDPE: influence of Mw and comonomer type, and implications for miscibility. Rheol Acta 43: 604-614 Hussein, IA (2005) Melt Miscibility and Mechanical Properties of Metallocene Linear-lowDensity Polyethylene Blends with High-Density Polyethylene: Influence of Comonomer Type, Polym. hit. 54: 1330-1336. Hussein, IA, Williams MC (2004b) Rheological study of the influence of branch content on the miscibility of octene m-LLDPE and ZN-LLDPE in LDPE. Polym. Eng Sci., 44: 660672 Lee HS, Denn MM (2000) Blends of linear and branched polyethylenes. Polym Eng Sci 40: 1132-1142 Liu C, Wang J, He J (2002) Rheological and thermal properties of m-LLDPE blends with mHDPE and LDPE. Polymer 43: 3811-3818 Mavridis H, Shroff RN (1992) Temperature dependence of polyolefin melt rheology. Polym Eng Sci 32: 1778-1787 Miinstedt H, Steffl T, Malmberg A (2005) Correlation between rheological behavior in uniaxial elongation and film blowing properties of various polyethylenes. Rheol Acta 45: 14-22 Miinstedt, H., Kurzbeck, S., Elongational Behavior and Molecular Structure of Polymer Melts; in Progress & Trends in Rheology. Proceedings of the V Eur. Rhea Conference. Emri, Ed., 30  Portoz, Slovenia, Sept. 1998. Peon, J, Dominguez C, Vega JF (2003) Viscoelasticity behavior of metallocene-catalyzed polyethylene and low-density polyethylene blends: use of the Double Reptation and Palierne viscoelastic models. J Mater Sci 38: 4757-4764 Perez R, Rojo E, Fern6ndez M, Leal V, Lafuente P, Santamaria A (2005) Basic and applied rheology of m-LLDPE/LDPE blends: miscibility and processing features, Polymer 46: 8045-8053 Puig CC (2001) Enhanced crystallization in branched polyethylenes when blended with linear polyethylene. Polymer 42: 6579-6585 Sentmanat M, Muliawan, EB, Hatzikiriakos SG(2004) Fingerprinting the Processing Behavior of Polyethylenes from Transient Extensional Flow and Peel Experiments in the Melt State, Rheol. Acta 44: 1-15. Sentmanat M, Wang BN, McKinley, GH (2005) Measuring the Transient Extensional Rheology of Polyethylene Melts using Extensional Rheology of Polyethylene Melts using the SER universal Testing Platform," Rheol., 49: 585-606. Sentmanat, M (2004) Miniature universal testing platform: from extensional melt theology to solid state deformation behavior. Rheol Acta 43: 657-699 Tordella JP (1956) Fracture in the extrusion of amorphous polymers through capillaries. J. Appl. Phys. 27: 454-458 Tsenoglou C (1988) Network architecture and Modulus of Miscible Heteropolymer Blends. J Polym Sci Polym Phys 26: 2329-2339 Tsenoglou C (1991) Molecular weight polydispersity effects on the viscoelasticity of entangled linear polymers. Macromolecules 24: 1762-1767 Utracki LA (1991) On the Viscosity-Concentration Dependence of Immiscible Polymer Blends, J. Rheol. 35: 1615-1637. Utracki LA, Schlund B (1987) Linear-low Density Polyethylenes and Their Blends: Part 4. Shear Flow of LLDPE Blends with LLDPE and LDPE Polym. Eng. and Sci. 27: 1512-1522. Utracki, L.A., in Polymer Alloys and Blends. Thermodynamics and Rheology, Hanser, Munich, Vienna, New York, 1989. Van Gurp M, Palmen J (1998) time-temperature superposition for polymer blends. Rheol Bull 67: 5-8 Vega JF, Aguilar M, PeOn J, Pastor D, Martinez-Salazar J (2002) Review: Effect of long chain branching on linear-viscoelastic melt properties of polyolefins e-Polymers 46: 1-35 Wagner MH, Kheirandish S, Yamaguchi M (2004) Quantitative analysis of melt elongational behavior of LLDPE/LDPE blends. Rheol Acta 44: 198-218 Wei X, Collier JR, Petrovan S (2007) Shear and elongational rheology of polyethylenes with different molecular characteristics I. Shear rheology. J App Polym Sci 105: 309-316 Wignall GD, Alamo RG, Londono JD, Mandelkern L, Kim MH, Lin JS, Brown GM (2000) Morphology of blends of linear and short-chain branched polyethylenes in the solid state by small-angle neutron and x-ray scattering, differential scanning calorimetry, and 31  transmission electron microscopy. Macromolecules 33: 551-561 Wood-Adams P, Costeux, S (2001) Thermorheological behavior of polyethylene: Effects of microstructure and long chain branching. Macromolecules 34; 6281-6290 Wood-Adams P, Dealy JM, de Groot AW, Redwine David 0 (2000) Effect of molecular structure on the linear viscoelastic behavior of polyethylene. Macromolecules 33: 74897499 Yamaguchi M, Abe S (1999) LLDPE/LDPE blends I. Rheological, thermal and mechanical properties. J Appl Polym Sci 74: 3153-3159  32  2. THERMORHEOLOGICAL PROPERTIES OF LLDPE/LDPE BLENDS. 1 2.1. Introduction. The thermodynamic behavior of linear and branched polyethylene blends using rheological methods has been the subject of many studies (Yamaguchi, et. al., 1999; Lee and Denn, 2000; Liu, et. al., 2002; Ho et al., 2002; Hussein, et. al., 2003; Hussein and Williams, 2004a, 2004b; Fang, et. al., 2005). It has been reported that the thermorheological and processing properties of the blend are largely determined by molecular parameters, which include: (1) long chain branching content (LCB), which is the number of long branches, typically having a number of carbon atoms more than thirteen (Wagner et al, 2004; Kissin, 2005), (2) compositional distribution (CD) that is the number and length of long chain branches for a given LCB macromolecule, or the amount and type of comonomer in the case of LLDPE (Gabriel and Munstedt, 2003; Hussein and Williams, 2004b; Fang et al., 2005; Kissin, 2005) (3) molecular weight, M  w  (Hussein and Williams, 2004b; Gabriel and Lilge, 2006), and (4) molecular weight distribution (MWD) (Dealy and Wissbrun, 1990). Most studies agree that LLDPE/LDPE are miscible blends at low LDPE contents, which become immiscible at higher ones (Lee and Denn, 2000; Ho et al., 2001). Hexanecomonomer promotes immiscibility (Hussein et al., 2003; Hussein and Williams, 2004b), whereas octane-comonomer promotes miscibility (Fang et al., 2005). In addition, low molecular weight LLDPEs promote miscibility better than high M, ones (Hussein and Williams, 2004a). In a recent review, Zhao and Choi (2006) have reported that LLDPE/LDPE blends were immiscible in the melt state, with LCB being the determining factor of their immiscibility behavior. Recently Wagner et al. (2004) performed a quantitative analysis of the melt elongational behavior of LLDPE/LDPE blends. They have reported that the complex behaviour of these blends can be understood by assuming the existence of two phases; one phase composed of the highly branched low M w chains of both polyethylenes and a I A version of this chapter has been published. Delgadillo-Velazquez 0, Hatzikiriakos SG, Sentmanat M (2007) Thermorheological properties of LLDPE/LDPE blends. Rheol Acta 47: 19-31.  33  second phase composed of the high M, chains (mostly linear) of both polyethylenes. DSC thermograms of LLDPE/LDPE blends reported by Fang et al. (2005) support the existence of a third phase composed of chains from the two polyethylenes that have the ability to co-crystallize; additionally, enhancement in the crystallization behavior of branched polyethylene (BPE) blended with linear polyethylene (LPE) was explained in terms of co-crystallization due to the incorporation of the linear segments of BPE into rich-LPE lamellae, and the segregation of the most branched chains (Puig, 2001). The LLDPE/LDPE blend miscibility studies mentioned above make use of thermal techniques such as differential scanning calorimetry (DSC) and rheometrical techniques such as linear viscoelasticity of blends at different temperatures (Van Gurp and Palmen 1998; Mavridis and Shroff, 1992; Hatzikiriakos, 2000). Failure of timetemperature superposition can be interpreted as an immiscibility criterion (Van Gurp and Palmen 1998; Peon, et. al., 2003; Wagner et al., 2004; Perez et al., 2005). Positive deviation of zero shear rate viscosity from the log additivity mixing rule is also an indication of immiscibility (Lee and Denn, 2000; Liu et al., 2002, Hussein, et. al, 2003). The Cole-Cole plot, representation between the imaginary (n") and real part (n') of the complex viscosity, has been used by several authors as criteria for miscibility in polyethylene blends (Kim, et. al., 2000; Ho, et. al., 2002). The determination of the weighted relaxation spectra based on linear viscoelasticity is another method used to infer the thermorheological behavior of polyethylene blends. The spectra have been used to determine whether the blend components are immiscible due to an additional relaxation mechanism associated with interfacial tension (Gramespacher and Meissner, 1992; Lacroix, et. al., 1997; Fang, et. al., 2005). In this chapter, we study systematically the thermorheological behavior of a LLDPE with four LDPEs that have viscosity curves which lie above, about the same and below that of the LLDPE. The miscibility of the various blends is studied with DSC and linear viscoelastic measurements with the application of several thermorheological complexity criteria (TTS, Van Gurp plot, Cole-Cole plot, zero-shear viscosity versus composition, and relaxation spectrum). All the methods are compared to check  34  consistency of the results. The extensional rheological properties of the blends are also studied in order to examine the effects of LCB.  2.2. Materials and methodology. 2.2.1. Polyethylene resins and blends. The LLDPE resin used in this study was a Ziegler-Natta, hexene copolymer, supplied by ExxonMobil (LL3001). The LDPE resins used in this work are LD200 by ExxonMobil, EF606A by Westlake Polymers; 6621 and 1321, provided by Dow Chemicals. Table 2-1 lists all the polymers used along with their melt indices and densities. The LDPE resins have been labeled as LDPE-I to IV in order of decreasing Melt Index value. The LLDPE resin was melt blended respectively with each LDPE resin in order to create LLDPE/LDPE blends having weight compositions of 99/1, 95/5, 90/10, 80/20, 50/50 and 25/75. The blending was performed as follows: the original components were mixed and grinded in a Brabrender mixer in order to reduce their pellet size and ensure good mixing. Then, the mixture in the form of flakes was blended into a single screw extruder, at a processing speed of 20 rpm, using a screw having mixing elements near to the end of the metering zone. The temperature of the die was kept at 160 ° C. The extrudates were then pelletized for easy handling. The blend 99/1 was produced in two dilution steps, the first being the 95/5.  Table 2-1. Properties of polyethylene resins used in this study. Melt Index (g/10min)  Density (g/cc)  tio (Pa.^)  (190 ° C)  (25 ° C)  150 ° C  1  0.917  17,448  LDPE I (LD200)  7.5  0.915  8,272  LDPE II (EF606A)  2.2  0.919  44,234  LDPE III (6621)  0.47  0.919  72,780  LDPE IV (1321)  0.22  0.921  132,065  Resin  LLDPE (LL3001.32)  35  2.2.2. Thermal Analysis  A Shimadzu DSC-60 calorimeter was used to study the thermal behavior of the pure components and their blends. Measurements were made on samples of about 1-2 mg sealed in aluminum pans and nitrogen flow. The samples were heated from 30 ° C to 180 ° C, at a heating rate of 10 ° C/min, in order to determine the melting temperature (TO and heat of fusion (A 11,0 . The calorimeter was calibrated periodically for melting temperature and heat flow using Indium and Zinc as standards. 2.2.3. Rheological Techniques.  Parallel-plate rheometry was performed to determine the linear viscoelastic properties of the pure components and their blends. The measurements were performed using a Rheometrics System IV (controlled-strain) and a Bohlin—CVOR (controlledstress) rheometers. Experiments performed at different temperatures, namely, 130°C, 150°C, 170°C, 190°C, and 210°C. Mastercurves were obtained and most results are presented at the reference temperature of 150°C. Finally, the blends were rheologically characterized in simple extension using an SER Universal Testing Platform (Sentmanat, 2003; 2004) from Xpansion Instruments (see Figure 1-9). As described by Sentmanat (2003, 2004), the SER unit is a dual windup extensional rheometer that has been specifically designed for use as a fixture on a variety of commercially available rotational rheometer host platforms. The particular SER model used in this study, a model SER-HV-B01, was designed for use on a VOR Bohlin rotational rheometer host system. Specimens were prepared by compression molding the polymer samples between polyester films to a gage of about 1 mm, under 20 MPa and 170 ° C, using a hydraulic press. Individual polymer specimens were then cut to a width of 6.4-12.7 mm. Typical SER extensional melt rheology specimens range from 40-150 mg in mass. Measurements were conducted at the reference temperature of 150°C, over 25 degrees above the peak melting point of the polymers.  36  2.3. Results and discussions.  2.3.1. Rheological characterization of pure resins.  Figure 2-1 depicts the complex viscosity of all polymers listed in Table 2-1 as a function of frequency at 150°C. For the case of LLDPE (LL3001) the viscosity curve approaches its zero-shear viscosity value at small frequencies and exhibits a certain degree of shear thinning at higher frequencies, a behavior that is typical of LLDPEs. The zero-shear viscosity values of the four LDPEs were not reached experimentally, as can be seen from Figure 2-1. These were calculated by determining their relaxation spectrum of the resins using the linear viscoelastic mastercurves at the reference temperature of 150  ° C. The parsimonious relaxation spectra of all polymers are listed in Table 2-2. Note that while LDPE-III (6621) and LDPE-IV (1321) possess a much higher zero-shear viscosity than that of LL3001, the presence of LCB causes significant shear thinning and thus their viscosity becomes considerably smaller at high frequencies.  1 06 T = 150 °C  2E11_1 1(1E 10Fj026:06  10 5  :7000000 00000^^  U)  Cu 10 4  4.610,2A  LDPE III (6621) ^ LDPE EIV V (2 00000 ^  AAAAAAAAA222222 410,41# 14 • • al" ^ 8217 27:6:6 Cl  10 3 P"  000000,3000000000000000000 )4x.22222.6e, 411444414414 iD0:70:1:( 0 ,_1741 x 01  L- 3.0:111  10 2  0  )  10 1 ^ ^ .1 ^ 1 0 - 1^10° 10' 1 02 1 03 1^1.1111  I^•^111111  co (rad/s) Figure 2-1. The complex viscosity curves of LLDPE (LL3001), and those of all four LDPE resins (132i, 662i, EF606A and LD200) at 150 ° C.  37  Table 2-2. Relaxation spectra of polyethylene resins @ 150 ° C Gi (Pa)  ki (s) LLDPE (LL3001)  143450  0.0035  119070  0.0104  75470  0.0526  15222  0.3962  1369  3.7790  LDPE I (LD200) 96117  0.0020  29041  0.0182  9593  0.1369  2475  0.9859  465.4  7.3490  LDPE II (EF606A) 127420  0.002  50141  0.021  22337  0.167  8262  1.301  2459  11.320  LDPE III (6621) 87067  0.0045  39698  0.0349  19764  0.2390  8638  1.5990  3915  13.6700  LDPE IV (1321) 88407  0.0044  42334  0.0367  23534  0.2651  11979  1.8470  6509  17.3300  The extensional rheological behavior of the pure resins is depicted in Figure 2-2 at 150 ° C. In all cases the tensile stress growth coefficients, /I are plotted for three 38  different Hencky strain rates, namely 0.1, 1 and 10s -1 . For the sake of clarity, the material functions 77 E+ have been multiplied by an appropriate factor (for convenience, a power of 10), as indicated on the plot. The LLDPE(LL3001) does not exhibit any degree of strain hardening at any extension rate, an observation consistent with polymers of linear architecture, and displays very little deviation from the linear viscoelastic envelope (LVE), 377 + . The latter was calculated from the spectra in Table 2-2, and is plotted as a dashed line in Figure 2-2. On the other hand, the four LDPEs show significant strain hardening (deviation from the linear viscoelastic envelope, 377 ÷ , also indicated for all resins by dashed lines) which is typically an indication of the presence of LCB. It is worth noting that the onset of strain hardening at a given rate occurs at approximately the same Hencky strain for all four LDPE resins, independent of the molecular weight of the resin. Also LDPE-I (LD200) shows a significantly higher deviation form LVE behavior, an indication of the presence of a higher degree of branching which is a characteristic of coating LDPE resins.  10"  Factor  10 1 °  xio  10°  lLt  4  x10 3  10 8  Q. io7  x10 2  + W10 6  x10  1 0$  xl  10 4 10 3 10 2  10-2  ^  10-'  ^  100  ^  101  ^  102  t (S) Figure 2-2. The tensile stress growth coefficient for the LLDPE resin (LL3001) and the four LDPE resins (LD200, EF606A, 662i and 132i), at three different Hencky strain rates: 0.1, 1 and 10 s -1 ; at 150 ° C.  39  2.3.2. Thermal analysis-DSC Thermograms. Figures 2-3a to 2-3d depict the melting thermograms of all blends obtained from Differential Scanning Calorimetry (DSC). For the LLDPE (LL3001)/LDPE-I (LD200) system and all other three systems, the melting peaks of LDPEs are lower than that of LL3001. At low weight fractions of LDPE, 5%, 10% and 20% the melting is dominated by the linear polyethylene, LL3001 and as such the melting peak for these blends is the same as that of the pure LL3001. For the blends containing 50% and 75% LDPE-I, multiple melting peaks are observed denoting an immiscible system, with one peak corresponding to the melting of the LL3001 component, another corresponding to the melting of the LDPE-I component, and a third peak suggesting the existence of a transitional phase. Co-crystallization was first proposed by Clampitt (1963), to explain the presence of an intermediate peak in Differential Thermal Analysis (DTA) of linear and branched polyethylene blends. This is formed with chains segregated from the two polymers (linear and branched), which have the ability to co-crystallize and thus form distinct lamellae morphologies and thicknesses (Wignall, et. al., 2000; Puig, 2001; Fang et al., 2005,). This leads to multiple melting behavior (Zhang et al., 2002; Mirabella et al., 1988). The formation of a third melting peak for LLDPE/LDPE blends has also been observed by Hussein and Hameed (2005) and Xu and coworkers (Xu, et. al., 2001). As they have suggested, it is possible that the co-crystalline phase is formed from LLDPE and LDPE chains which segregate selectively from their individual components. It is well known that Ziegler-Natta LLDPE resins segregate in fractions ranging from high molecular weight chains with low short chain branching content, and low molecular weight chains with high amounts of short chain branching (Mirabella, et. al., 1987 and 1988; Schouterden, at. al., 1987; Karbashewski, et. al., 1992; Wignall, et. al., 1996 and 2001; Zhang, et. al., 2001). Lee and Denn (2000) have suggested a hybrid system, in which a small fraction of LDPE is miscible with LLDPE, forming the matrix phase; more recently, Wagner (2004) explained the strain hardening of a LLDPE/LDPE system by assuming the existence of a phase composed of high molecular weight molecules from both LLDPE (linear) and LDPE (branched) segregated together to form a matrix phase.  40  The second set of blends, LL3001/LDPE-II (EF606A) exhibits similar behavior to the aforementioned blend; that is, dominated melting by the linear component up to a 20% LDPE-II blend composition, while the higher blend systems exhibit multiple melt peaks characterized by a second peak corresponding to the LDPE-II component and the occurrence of a third peak, likely resulting from the co-crystallization of chains from both polyethylene components and the possible formation of the third phase. Finally, the same behavior can be observed with regard to the third and fourth set of blends, namely LL3001/LDPE-III (662i), and LL3001/LDPE-IV (132i). The melting thermograms plotted in Figures 2-3a-d support the observation that LLDPE/LDPE blends are generally immiscible systems at high LDPE weight fractions, typically more than 20 wt%. On the other hand, DSC is unable to resolve the thermodynamic behavior of blends at low LDPE concentrations, as the dominant melting peak at these compositions appears to be only that of the LLDPE component. These DSC results will be compared with several rheological techniques below.  LLDPE (LL30011 LLDPE (LL3001)  5% LDPE I  6% LDPE II  10% LDPE I  10% LDPE II 20% LDPE I 0 LL  20% LDPE II  50% LDPE I 60% LDPE II  75% LDPE I  76% LDPE II  LDPE I (LD200)  LDPE II (EF606A)  80^90^100  ^  110^120  T ( ° C)  130^140^150 80^90^100^110^120^130^140^150  T ( ° C)  (a)  (b)  Figure 2-3a to 2-3d. DSC thermograms for the LLDPE/LDPE blend systems: (a) LL3001 /LDPE I (LD200); (b) LL3001/LDPE II (EF606A)  41  LLDPE LL3001) LLDPE (LL3001) 5% LDPE IV 5° LDPE III  ------„,_/—^10% LDPE IV  10% LDPE III ---',.../.--^20% LDPE III 50% I DPE19 -  ---V--^  0  I  20% LDPE IV 50% LDPE IV ^  75% LDPE III  75% LDPE IV  ,......-------------7—  LDPE III (DOW 66211  LDPE IV (DOW 1321)  -------/80^90^100^110^120^130^140^150  80^90^100^110^120^130^140^150  T ( ° C)  (c)^  T ( °C)  (d)  Figure 2-3a to 2-3d Contd. DSC thermograms for the LLDPE/LDPE blend systems: (c) LL3001/LDPE III (6621); (d) LL3001/LDPE IV (1321).  2.3.3. Linear Viscoelastic Measurements. The linear viscoelastic behavior of pure components and all their blends was studied in detail over a wide range of temperatures 130-210 ° C. Time-temperature superposition (TTS) was applied to shift the data horizontally and vertically (whenever necessary) in order to obtain a master curve at a reference temperature, T„f, in the present case 150 ° C. Horizontal shift factors, a T, which reflect the temperature dependence of the relaxation times, were obtained following the procedure proposed by Mavridis and Shroff (1992), where aT is described by an Arrhenius equation, as follows, ( \ E 1^1 log(a T ) = a R ‘,, T Tref  (2-1)  where Ea is the "horizontal activation energy", and R is the universal gas constant. Due to the presence of LCB in the macromolecular structure of all LDPE resins, it was necessary to apply vertical shift factors (bT) on the viscoelastic moduli in order to obtain better superposition (Mavridis and Shroff, 1992). Failure of TTS in the presence of LCB is typical (Malmerg et al., 1999; Wood-Adams and Costeaux, 2001; present work). Mavridis and Shroff (1992) proposed the following expression for bT, similar to Equation 2-1.  42  1^ E, 1 log(b, ) =— — – R T Tref (  ■ (2-2)  where E, is the "vertical activation energy". Materials showing high E, values are said to be thermorheologically complex systems (Mavridis and Shroff, 1992, Wood-Adams and Costeux, 2001). In most cases, the superposition to obtain mastercurves was not perfect and may be attributable to two factors: (1) presence of LCB and (2) immiscibility of the blend systems studied (see DSC results above) which can both contribute to thermorheological complexity. Figures 2-4a and 2-4b show the shifted storage modulus, bTG', and complex viscosity, (b' aT )171* (co,I versus reduced frequency, ago, for the pure resins and their -  blends with 10%, 20%, 50% and 75% of LDPE for the LL3001/LDPE I (LD200) system. LL3001 possesses a higher viscosity than that of LDPE-I (LD200) due to the inherently lower M,„, of the LDPE. LL3001 apparently dominates the shear rheology of the blend with noticeable changes in shear viscosity only seen at 50% of LDPE and higher. Regarding TTS, no perfect master curve could be built for the 50% and 75% LDPE blends, which indicates thermorheologically complex behavior due to immiscibility. At smaller concentrations, mastercurves were obtained for the blends containing up to 20% of LDPE. This latter observation suggests that the lack of TTS for the blends with a higher LDPE concentration is not necessarily due to the presence of LCB, but it is rather due to immiscibility of the blend. In the low frequency region, for the higher LDPE blend compositions, the values of the shifted storage modulus, brG ' were observed to be higher than those of the pure components (elasticity enhancement). This implies the existence of an interface between two distinct phases, pointing to the conclusion that the system is immiscible at the high LDPE compositions. This elasticity enhancement also suggests that lack of TTS is not necessarily due to the presence of the LCB but rather to the complex thermodynamic behavior of the blend.  43  1 06  1 05  Tcr a  6  .0  104 LLDPE (LL3001) 10% LDPE I 20% LDPE I 50% LDPE I 75% LDPE I LDPE I (LD200)  10 3  10 2 ^ 10 -2^10 -1^100^101^102 1 0'^104  a T co (rad/s)  (a) 1 06  a- 10 4  °7— 10 3  LLDPE (LL3001 ) 10% LDPE I 20% LDPE I 50% LDPE I 75% LDPE I LDPE I (LD200)  10 2 ^ 1 03 10 -2^10 -1^10°^101^102  ^  1 04  a T co (rad/s) (b) Figure 2-4a and 2-4b. Mastercurves of a) elastic modulus, G', and b) complex viscosity, 177 *  (0)1,  for blend system I (LL3001/LD200).  44  Figures 2-5a and 2-5b depict the mastercurves of the LL3001/LDPE-II (EF606A) blends, including the pure components. The shifted complex viscosity curves, * (c01 versus reduced frequency,  arco, of the two components of the blend are  closer compared to those in the previous blend. Lack of good superposition particularly for 50% and 75% LDPE blends indicates that the systems are thermorheologically complex. In addition, elasticity enhancement can be seen for 50% and 75% LDPE blends. Similar observations of elasticity enhancement were reported by Hussein and Williams (2004) for ZN-LLDPE/LDPE blends at 90% and 70% LDPE compositions. Elasticity enhancement implies the existence of interface and thus immiscibility of the blends at these compositions. For the third set of blends, LL3001/LDPE-III (662i), the storage modulus, b i G', and complex viscosity,  (b/  aT  ) I j * (0, mastercurves are plotted in Figures 2-6a and 2-6b,  respectively. Due to its high  Ad , the values of N )1/7 * (a w  T  for LDPE-III (662i) at low  frequencies, are higher than those of the LL3001. Again failure of TTS implies that the systems are immiscible at high LDPE compositions. No elasticity enhancement is seen for this system due to the much higher viscosity of LDPE-III. Similar conclusions can be drawn for the fourth set of blends LL3001/LDPE-IV (132i), where the viscosity and elasticity of LDPE-IV dominates the properties of these series of blends (see Figs 2-7a and 2-7b). For example, with the addition of 10% of LDPE-IV into the LLDPE, significant changes are seen in the complex viscosity of the blend.  45  10 6 = 150 ° C I  •-  " 02N•7 44 \  tkA* \ M*V7  1 05  -41.4 •  4■%  a  104 • ^ ^ O  CD 10 3  A  ■  LLDPE (LL3001) 10% LDPE II 20% LDPE II 50% LDPE II 75% LDPE LDPE II (EF606)  10 2 ^ ^ 10 -2^10-1^10°^101^102 103 104  a T co (rad/s) (a) 10 5 Tref = 150 ° C  • • ^ o • ■  LLDPE (LL3001) 10% LDPE II 20% LDPE II 50% LDPE II 75% LDPE II LDPE II (EF606)  10 2 ^ ^ ^ 10-2 10 -1^10°^101^102 103 1 04  a T co (rad/s) (b) Figure 2-5a and 2-5b. Mastercurves of a) elastic modulus, G', and b) complex viscosity, Ir * (co)I , for blend system II (LL3001/EF606).  46  10 6 Tref = 150 ° C 10 5  il  a.  ---  e  10 4  LI — 10 3 .12  LLDPE (LL3001) • v 10% LDPE III o 20% LDPE III o 50% LDPE III A 25% LDPE III ■ LDPE III (6621)  10 2  10 1 10 -2^10-1^10°^101^102  a T co (rad/s)  1 03  ^  1 04  (a)  10 6 Tref = 150 ° C  • ^ o o A  ■  LLDPE (LL3001) 10% LDPE III 20% LDPE III 50% LDPE III 75% LDPE III LDPE III (6621)  10 1 10 -2^10-1^10°^101^102  10 3  1 04  a T 03 (rad/s) (b) Figure 2-6a and 2-6b. Mastercurves of a) elastic modulus, G', and b) complex viscosity,  ig * (co)1, for blend system III (LL3001/662I).  47  10 6 Tref = 150 ° C  10 5  10 4 • ^ o o  LLDPE (LL3001) 10% LDPE IV 20% LDPE IV 50% LDPE IV A^75% LDPE IV ■ LDPE IV (1321)  10 3  10 2  10 1 10 -2  I^1^I^A ....I^, ^1^. . II. .1^, ^1^. ^I ...,1  .^.^■^. ....I^■^.^. . ....I^.^.^■^. . , ..  10 -1^10°^101^102 ar a) (rad/s)  10 3  10 4  (a)  10 6  Tref = 150 ° C  • LLDPE (LL3001) 10% LDPE IV ^ o 20% LDPE IV o 50% LDPE IV ,n, 75% LDPE IV ■ LDPE IV 10 2 10 -2^10-1^10°^101^102  103  1 04  a l- co (rad/s) (b) Figure 2-7a and 2-7b. Mastercurves of a) elastic modulus, G', and b) complex viscosity, Iii * (co)! , for blend system IV (LL3001/6621).  48  2.3.4. Extensional Measurements Extensional rheological measurements were conducted for all blends at 150 ° C. The tensile stress growth curves are plotted in Figures 2-8a to 2-8d, using scaling factors as before (powers of ten). As observed in Figures 2-8a to 2-8d, the strain hardening behavior is a function of LDPE content with the degree of strain hardening increasing with LDPE weight fraction in the blend, becoming more evident at higher Hencky strain rates. In addition, at similar Hencky strain rates the onset for strain hardening (deviation from the relation 77; = 377 + ) occurs at smaller Hencky strains with increasing LDPE content. Note that the presence of LDPE at a weight content of just 5% is clearly evident from the strain hardening behavior witnessed in the tensile stress growth curves of the blends. Comparatively, differences in the linear viscoelastic shear rheology behavior of the polymer blends were only evident for LDPE weight contents greater than 20%. Figure 2-9 contains plots of the tensile stress growth coefficient curves for each blend with a LDPE weight of 1%. Although no strain hardening behavior is observed with the LDPE-I and LDPE-II blends because of their inherently lower molecular weight, note that significant strain hardening behavior is clearly evident with the LDPE-III and LDPE-IV blends at high rates of extension, an observation that could not be elucidated from the shear rheology data. It is therefore concluded that the extensional rheology is an extremely sensitive tool to describe and detect subtle macro-structural features in polymer blends.  49  ▪^  10,2 loll 1010 log  1 0 17  lo" 1 0 10 10 (ET.  x 1 05 LOPE II (EF606) 20% LDPE II  X10 3^03 10 8  10 7  ."."- 10 7  10 °  10 °  X100  10  10 5  x1  x102  ,- -  104  10 4  --- 3 ri ÷(1)  10 3 0.01  10  0.1  10 3 ^ 0.01^0 . 1^1^10^100  100  t (s)  t (s)  (a) LLDPE/LDPE I (LD200)  ^  10 12  (b) LLDPE/LDPE II (EF606)  ^1011 Factor  1011  1 010  0.1s 1 3-  6- = 1 0  10 10 -  co CL  e=10s-1  108  to  us  Factor  X10' _ LDPE1111.6i2k. --  log -  20% LOPE III  108 -  10% LDPE fll  44 10 1 r  •  x103  1 07 w  10  ,  105  LLDPE (LL3001)  los  10,  a  x102  5% LDPE III^c ^ x10  10 6  109  10,  10 ,  311 * (t)  10 3 ^ 0.01  0.1  10  t (s)  100  10 3 0.01 ^0 . 1^1^10^100  t ( s)  (c) LLDPE/LDPE III (6621) (d) LLDPE/LDPE IV (1321) Figure 2-8a to 2-8d. Tensile stress growth coefficient curves for 0.1, 1 and 10 s -1 Hencky strain rates at 150 °C for LLDPE/LDPE blend systems: (a) LL3001/LDPE I (LD200); (b) LL3001/LDPE II (EF606A); (c) LL3001/LDPE III (6621); (d) LL3001/LDPE IV (1321).  2.3.5. Activation Energy  The presence of LCB in the blend can also be reflected by its effect on the activation energy, Ea (Mark et al., 1986). This is seen in Figure 2-10, where the activation energy is plotted as a function of weight fraction of LDPE, for all four systems (For individual values Arrhenius function is plotted in Appendix A). The activation energy of each LDPE resin is higher than that of LL3001. The value for LL3001 is 33.5 kJ/mol, a 50  value typical for LLDPEs, whereas the LDPEs range from 46.6 to 64.9 kJ/mol, values typically reported for LDPEs. In general, it can be seen that the activation energy increases monotonically with LDPE concentration in the blend systems with the exception of the blend systems I and IV at composition 75% LDPE that exhibit an activation energy higher than the corresponding value for pure LDPE (existence of maximum). The differences in these values are 9% and 6% respectively, which might be due to elasticity and in general shear viscosity enhancement due to the presence of the interface (note that the blends are immiscible at these high LDPE compositions). However, since these effects are relatively small (less than 10% for a difference in composition of over 25%) experimental error might also play a role. It is noted that the vertical shift factors, bT, applied to obtain the master curves for the various blend systems were small ranging from 0.72 to 1.14 with the higher values corresponding to the blends having higher amounts of LDPE. The corresponding calculated vertical activation energies, E„, ranged from 1.76 to 8 kJ/mol for the various compositions of all four blend systems with no particular trends worthy of reporting. 10 0  Factor  10 8  x10 2  x1 0  x1  104 10 3  10 -2^10-1^10°  ^  10 1^1 02  t (s) Figure 2-9. Tensile stress growth coefficient curves at Hencky strain rates of 0.1, 1 and 10 s -I for  LLDPE/LDPE blend systems containing lwt% LDPE atl 50 ° C.  51  70 * LLDPE/LDPE I 0 o^ LLDPE/LDPE II E^ LLDPE/LDPE III 0 60 o o LLDPE/ LOPE IV^o 0 O  °  WTref = 150 C  50 2^ N C  W  • •  i  o 0  o^• CO .4--, 40 el o > -4^ -,^o• (..)^ oFi < -  30 . ^ 0.0^0.2^0.4^0.6^0.8 1.0  Weight fraction of LDPE Figure 2-10. Activation energy, E a (KJ/mol), as a function of weight fraction of LDPE for all blend systems at 150 °C.  2.3.6. Rheological Criteria for Miscibility In this section several rheological criteria for miscibility will be examined for the various blends systems. First, time-temperature superposition (TTS) has already been used as a method to assess miscibility in LLDPE/LDPE blends (Yamaguchi and Abe, 1999; Perez, et.al , 2005). As discussed before, the blends rich in LDPE composition have shown difficulty in applying TTS principle. This is an indication of different relaxation times, possibly due to the existence of different phases comprised by linear and branched chains, respectively. In addition, elasticity enhancement for certain blends was observed, pointing to the conclusion that these blends were immiscible as well (see Tables 2-3 to 26). A possible third phase exists in these blends composed of chains from both pure components that have the ability to co-crystallize i.e. high M W branched chains from LDPE with high M w of linear chains from LLDPE. Use of the Van Gurp-Palmen plots has been used in the past to infer miscibility of the blends. These are phase angle (6 ° ) versus complex modulus  (13  G*) plots. Figures 2-  11 a to 2-11 d depict such plots for all four sets of blends. First, it is clear that timetemperature superposition for the pure LL3001 is excellent. Similarly for low LDPE 52  blend compositions (10%), in all the blend systems of this study, TTS is obeyed. For Systems III and IV, failure of superposition was clearly observed at 20% LDPE composition, perhaps due to the higher molecular weights of LDPE III and IV compared to that of LLDPE. For high LDPE composition, i.e. 50% and 75% of LDPE, all blend systems exhibit lack of superposition. Hence, these blends are thermorheologically complex fluids. Another criterion commonly used to check the miscibility/immiscibility of blends is the zero shear viscosity, loge o, vs. weight fraction plot. The graphs shown in this study compare experimental data of zero-shear viscosity determined by calculating the parsimonious relaxation spectra of all blends from fitting the linear viscoelastic data (Baumgaertel and Winter, 1989; Baumgaertel et al., 1990, 1992). The graphs are shown in Figures 2-12a to 2-12d. The log-additivity and Tsenoglou mixing rules (Tsenoglou, 1988; 1991) are also plotted in Figure 2-12. Positive deviation behavior (PDB) from the log-additivity rule means immiscibility, while the opposite implies miscibility (Utracki, 1989). In most cases, positive deviation is clearly observed for LDPE compositions of 20% and higher, which means immiscibility, an observation also drawn from DSC and failure of TTS, as well as from the van Gurp-Palmen plots. Small negative deviation can only be seen at small LDPE concentrations and perhaps it is reasonable to assume that at small LDPE compositions the blends are miscible with LLDPE (also concluded by Lee and Denn, 2000). Similar plots at 130 ° C, 170 °C, 190 ° C, and 210 ° C (not shown here) show similar behavior for all blend systems. Positive deviations from the log-additivity mixing rule of blends of linear and branched PP have been recently reported by Stange et al., (2005), also concluding immiscibility of these blends. Weighted relaxation spectra, rH(r) as a function of log (r), were constructed to extract further information on the miscibility of the blends. The relaxation spectrum, H(r) was determined by fitting experimental G'(w) data, following a numerical differencing procedure developed by Ninomiya and Ferry (Ferry, 1980). All spectra were calculated from linear viscoeasltic data at 150 ° C. Figure 2-13a shows the weighted relaxation spectra of LL3001/LDPE-I (LD200). Pure LLDPE (LL3001) shows a very broad spectrum as well as a "shoulder" at the high 1\4„, end.  53  90  8 (°)  LLDPE (LL3001; 10% LDPE1 20% LDPEI 50% LDPE I 75% LDPE I LDPEI(LD200)  80 70 60  90 80 70 60  50  50  40  40  30  30  20 10 3  10 4  LLDPE (LL3001) 10% LDPE II 20% LDPE II 50% LDPE II 75% LDPE 11 LDPE II (EF606)  8 (°)  20 10 3  10 6  b T G* (Pa)  104  105  106  b.r G*(Pa)  (a) LL3001/LDPE I (LD200)  (b) LL3001/LDPE II (EF606) 90  90  8 (°)  LLDPE (LL3001) 10% LDPE III 20% LDPE III 50% LDPE HI 75% LDPE III LDPE III (6621)  80 70 60  8 (°)  LLDPE (LL3001) 10% LDPE IV 20% LDPE IV 50% LDPE IV 75 % LOPE IV LDPE IV (1321)  80 70 60  50  50  40  40  30  30 20  20 10 3  1 04  1 05  106  10 3  104  10 6  105  G* (Pa)  b T G* (Pa)  (c)  LL3001/LDPE III (6621)  (d) LL3001/LDPE IV (1321)  Figure 2-11a to 2-11d. Van Gurp-Palmen plots for all four LLDPE/LDPE blend systems using linear viscoelastic data at 130 ° C, 150 °C, 170 ° C, 190 ° C and 210 ° C.  This is possibly due to phase separation that results from non-uniform branch content distribution previously observed in Ziegler-Natta LLDPE resins (Mirabella, et. al., 1987 and 1988; Schouterden, et. al., 1987; Karbashevski, et. al., 1992). On the other hand, weighted relaxation spectrum for LDPE-I (LD200), shows a much smaller peak than LL3001, which is due to their apparent difference in molecular weight. The weighted spectra for 5% and 10% LDPE blends were observed to be identical as those of pure LLDPE, which indicates that the relaxation of the blends is dominated by the major component.  54  los  103  ^•^  U)  ct, 0.  0 10 4  •  •• •  • Exp. Data - Tsenoglou ^ Log-additivity  Exp. Data • - Tsenoglou Lug-addnivity^  10 3 ^ ^ 00 0.2 0.4^0.6  0.8  ^  10  10 4 ^  00  ^  0.2  w LDPE I  ^  0.4^0.6  w LDPE  (a) LL3001/LDPE I (LD200)  ^  0.8  ^  10  II  (b) LL3001/LDPE II (EF606) 10 3  10 5  • • .. 4..^  a. _•• Exp. Data • - Tsenoglou ^ Log-additivity  ♦ Exp. Data Tsenoglou  •••• Log-additivity 10 4 00  ^  0.2  ^  0.4^0.6  0.8  ^  w LDPE III  (c) LL3001/LDPE III (6621)  10  10 4 ^ ^ 00 0.2  0.4^0.6  ^  0.8  ^  w LDPE IV  (d) LL3001/LDPE IV (1321)  Figure 2-12a to 2-12d. Zero shear viscosity, 1 0 , versus LDPE weight fraction, w, for all four LLDPE/LDPE blend systems at 150 ° C.  For the rest of the blends, (20%, 50% and 75% compositions in LDPE), the  distribution of the spectrum is narrower; however, they do not show single peak and smooth peak transitions from one pure component to the other, conditions required for a blend to be considered as miscible as discussed by Gramespacher and Meissner, (1992). Similar observations can be drawn for the rest of blends LL3001/LDPE-II (III) (IV). As calculation of the relaxation spectrum H(r) is from oscillatory shear data, the reliability of  55  10  the spectrum decreases rapidilty at values of time i approaching  1/(Amax  and 1/o),,,„, where  (0max and co n i n correspond to the limit frequencies in the experimental window. 12000 • • 10000 - • • • 8000 • •  T =150 ° C  LLDPE (LL3001) 5% LDPE I 10% LDPE I 20% LDPE I 50% LOPE I 75% LDPE I  20000  15000 -  LDPE I (LD200)  • o • • • • •  T=150°C  LLDPE (LL3001) 5% LOPE II 10% LDPE II 20% LDPE II 50% LDPE II 75% LDPE II LDPE II (EF606A)  q  2.: 6000  10000 -  \ 4000  V  0 0.001^0.01  0.1  1^10 ti  (a)  5000 -  6  2000  0  100^1000 10000  4:• 20000  0.1  10  (s)  100  1000 10000  (s)  LL3001/LDPE I (LD200)  (b) LL3001/LDPE II (EF606) 80000  40000  30000 -  0.001^0.01  LLDPE (LL3001) —0---- 5% LDPE III 10% LDPE III 20% LDPE III 50% LDPE III 75% LDPE III LDPE (6621)  T = 150 ° C 60000 -  17: •—• 40000  LLDPE (LL3001) 5% LDPE IV 10% LDPE IV 20% LOPE IV 50% LDPE IV 75% LDPE IV LDPE IV (1321)  20000 -  10000  0  0 0.001^0.01  • q • • • • •  0.1  1^10  100^1000 10000  (c) LL3001/LDPE III (6621)  0.001^0.01  0.1  1^10  100^1000 10000  (d) L3001/LDPE IV (1321)  Figure 2-13a to 2-13b. Weighted relaxation spectra for all four LLDPE/LDPE blend systems at 150 °C.  Finally, Cole-Cole plots,^vs if , were constructed for all blend systems to check for immiscibility. It is said that for a miscible blend, Cole-Cole plots give semicircular relationships of almost identical radii (Utracki, 1989; Cho, et. al., 1998; Kim, et. al., 2000; Kwag, et. al. 2000). Cole-Cole plots were constructed for the four blend systems,  56  using the reduced values of^vs.^at all temperatures by applying their respective vertical shift factors VaT 77 .  b/ T %7,  ) The Cole-Cole plots for LL3001 gave a semi  circular shape demonstrating its thermorheological simplicity (also concluded from other rheological methods). On the other hand, Cole-Cole plots for all the LDPE resins did not result semicircular shapes, suggesting a different signature due to the presence of LCB (thermorheological complexity). Regarding the blends systems, for 1%, 5%, 10% and 20% LDPE compositions, Cole-Cole plots (not shown here for the sake of simplicity) observed circular relationships, thus suggesting miscible blends. However, for 50% and 75% LDPE compositions, the behavior is similar to the LDPE resin and thus suggesting immiscibility. This was observed to be the case for all four blend systems. The results of all the methods for examining miscibility are shown in Tables 2-3 to 2-6, for the different blend systems: All methods agree that at high LDPE composition the blends are immiscible. At low LDPE composition the agreement is only partial among the various methods; in fact the relaxation spectrum does not agree with the others since the calculated times, i (s), fall outside the experimental regime of frequencies, as discussed above, hence it is reasonable to conclude that this method is not reliable to infer miscibility/immiscibility for this blend systems; therefore, this method is not used in the next chapter. Nevertheless, all other methods appear to indicate a transition from miscibility to immiscibility for all the blend systems studied and therefore we can conclude miscibility at smaller LDPE concentrations exist which changes to immiscibility at higher LDPE concentrations (essentially higher than 20%). As failure of TTS might be due to the presence of LCB, TTS is not a good indicator for miscibility unless elasticity enhancement is observed which points towards immiscibility (blend systems I and II). Overall it is reasonable to conclude that LDPEE (hexane)-LDPE blends are immiscible at high LDPE concentrations (Lee and Denn, 2000).  57  Table 2-3. Thermodynamic behavior of LLDPE (LL3001)/LDPE-I (LD200) blends, at 150 ° C, as concluded by various methods. 10% 20% 50% 5% LDPE LDPE LDPE LDPE I U U DSC U M I I M ilo vs w M' M' M1 I TTS  75% LDPE I I  I  van Gurp-Palmen  M  M  M  I  I  Relax. Spectrum  I  I  I  I  I  M M I M I Cole-Cole *U: unable to resolve, M: miscible system, I: Immiscible system. M'. Elasticity enhancement of G'(co) observed.  Table 2-4. Thermodynamic behavior of LLDPE (LL3001)/LDPE-II (EF606A) at 150 ° C, as concluded by various methods. 5% 10% 20% 50% LDPE LDPE LDPE LDPE  75% LDPE  DSC lo vs w TTS  U I M'  U I M1  U M M'  I I I  I I I  van Gurp-Palmen  M  M  M  I  I  Relax. Spectrum  I  I  I  I  I  I M M M Cole-Cole *U: unable to resolve, M: miscible system, I: Immiscible system M 1 . Elasticity enhancement of G'(a) observed.  I  58  Table 2 5. Thermodynamic behavior of LLDPE (LL3001)/LDPE-III (6621) at 150 ° C, as concluded by various methods. 5%^10%^20%^50%^75% -  LDPE LDPE ^LDPE^LDPE^LDPE DSC^U^U^U^I^I ilo vs w^M^M^M^I^I TTS^M^M^M^I^ I van Gurp-Palmen^M^M^M^I^I Relax. Spectrum ^I^I^I^I^I Cole-Cole^M^M^M^I^I 1^.^ - *TT . unable ^ o resolve, M: miscib l e system, I: Immiscible system  Table 2 6. Thermodynamic behavior of LLDPE (LL3001)/LDPE-IV (1321) at 150 ° C, as concluded by various methods. 5%^10%^20%^50%^75% LDPE^LDPE^LDPE^LDPE^LDPE DSC^U^U^U^I^I llo vs w^M^M^M^I^I TTS^M^M^M^I^I -  van Gurp-Palmen^M^M^M^I^I Relax. Spectrum ^I^I^I^I^I Cole-Cole^M^M^M^I^I . unabl e to resolve, M : miscible system, I: Immiscible system  4e77^1 I^  .^•• -^•  2.4. Conclusions.  The rheological effects of LCB was studied using several LDPE resins as pure and as blends with a hexane copolymer of LLDPE by means of linear viscoelastic measurements and tensile stress growth measurements (strain hardening). While LLDPE essentially follows the envelope of 3r1 + , the LLDPE/LDPE blends exhibit clearly strain hardening which is found to be a function of LDPE concentration; moreover, strain  59  hardening was observed even for some blends with only a 1% LDPE weight fraction for blends with the higher 1v1,, LDPE's. At these low compositions of LDPE, linear viscoelastic experiments in simple shear have shown no effect; hence, the theological characterization of polymers in uniaxial extension could be used as a very sensitive tool for detecting and describing subtle differences in blend composition and morphology. DSC thermograms for high LDPE compositions have shown the presence of a third melting peak, possibly due to the existence of co-crystallization. At low LDPE compositions the thermograms exhibit a single melting peak suggesting that the LLDPE is dominating the melting, thus yielding inconclusive results with regard to the issue of miscibility. Several rheological criteria were applied to all blends for assessing polymer miscibility. First, by inspection of viscoelastic moduli mastercurves, failure of TTS was observed for all blends at high LDPE compositions. The same behavior was corroborated with van Gurp-Palmen plots. Therefore, it can be concluded that LCB promotes thermorheologically complex behavior at high compositions of LDPE. Positive deviation behavior (PDB) from log-additivity rule was observed, in the whole range of temperatures, for all blend systems with LDPE compositions of 20% and higher. Finally, the broad distribution of the weighted relaxation spectrum in pure LLDPE suggests an inherent and non-homogeneous chain composition, and immiscibility for all blends. In general, all blends of hexene-LLDPE were immiscible with amounts of LDPE greater than 20%, regardless of the molecular weight.  60  2.5. References. 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Korea Polym J 8: 34-43 Kissin YV, (2005) Polyethylene, linear-low density Kirk-Othmer Encyclopedia of Chemical Technology, Wiley, New York Kwag H, Rana D, Cho K, Rhee J, Woo T, Lee BH, Choe S (2000) binary blends with conventional polyolefins: theological and morphological properties. Polym Eng Sci 40: 1672-1681 Lacroix C, Aressy M, Carreau, PJ (1997) Linear viscoelastic behavior of molten polymer blends: a comparative study of the Palierne and Lee and Park models. Rheol Acta 36: 416-428 Lee HS, Denn MM (2000) Blends of linear and branched polyethylenes. Polym Eng Sci 40: 1132-1142 Liu C, Wang J, He J (2002) Rheological and thermal properties of m-LLDPE blends with mHDPE and LDPE. Polymer 43: 3811-3818 Malmberg A, Liimatta J, Lehtinen A and L45fgren B, (1999) Characteristics of long chain branching in ethane polymerization with single site catalysts. Macromolecules 32: 6687-6696 Mark HF, Bikales NM, Overberger CG, Menges, G (1986) in Encyclopedia of polymer science and engineering, 2nd Edition, Vol. 6, Wiley, New York, p. 477. Mavridis H, Shroff RN (1992) Temperature dependence of polyolefin melt rheology. Polym Eng Sci 32: 1778-1787 Mirabella FM, Westphal SP, Fernado PL, Ford EA, Williams JG (1988) Morphological explanation of the extraordinary fracture toughness of linear low density polyethylene. J Polym Sci Polym Phys Ed 26: 1995-2005 Mirabella FM, Ford EA (1987) Characterization of linear low-density polyethylene: crossfractionation according to copolymer composition and molecular weight. J Polym Sci Polym Phys Ed 25: 777-790Miinstedt H, Steffl T, Malmberg A (2005) Correlation between theological behavior in uniaxial  62  elongation and film blowing properties of various polyethylenes. Rheol Acta 45: 14-22 Peon, J, Dominguez C, Vega JF (2003) Viscoelasticity behavior of metallocene-catalyzed polyethylene and low-density polyethylene blends: use of the Double Reptation and Palieme viscoelastic models. J Mater Sci 38: 4757-4764 Perez R, Rojo E, Fertthndez M, Leal V, Lafuente P, Santamaria A (2005) Basic and applied rheology of m-LLDPE/LDPE blends: miscibility and processing features, Polymer 46: 8045-8053 Puig CC (2001) Enhanced crystallization in branched polyethylenes when blended with linear polyethylene. Polymer 42: 6579-6585 Schouterden P, Groeninckx G, Van der Heijden B, Jansen F (1987) Fractionation and thermal behavior of linear low density polyethylene. Polymer 28: 2099Sentmanat ML (2003) Dual windup extensional rheometer. US Patent No. 6,578,413 Sentmanat, M (2004) Miniature universal testing platform: from extensional melt rheology to solid state deformation behavior. Rheol Acta 43: 657-699 Stange J, Uhl C, Munstedt H (2005) Rheological behavior of blends from a linear and a longchain branched polypropylene. J Rheol 49:1059-1079 Tsenoglou C (1991) Molecular weight polydispersity effects on the viscoelasticity of entangled linear polymers. Macromolecules 24: 1762-1767 Tsenoglou C (1988) Network architecture and Modulus of Miscible Heteropolymer Blends. J Polym Sci Polym Phys 26: 2329-2339 Utracki LA (1989) Polymer alloys and blends. thermodynamics and rheology. Hanser Publishers Van Gurp M, Palmen J (1998) time-temperature superposition for polymer blends. Rheol Bull 67: 5-8 Wagner MH, Kheirandish S, Yamaguchi M (2004) Quantitative analysis of melt elongational behavior of T.T DPE/LDPE blends. Rheol Acta 44: 198-218 Wignall GD, Alamo RG, Londono, JD, Mandelkern L, Stehling FC (1996) Small-angle neutron scattering investigations of liquid-liquid phase separation in heterogeneous linear low-density polyethylene. Macromolecules 29: 5332-5335 Wignall GD, Alamo RG, Ritchson EJ, Mandelkern L, Schwahn D (2001) SANS studies of liquid-liquid phase separation in heterogeneous and metallocene-based linear-low density polyethylene, Macromolecules 34: 8160-8165 Wignall GD, Alamo RG, Londono JD, Mandelkern L, Kim MH, Lin JS, Brown GM (2000) Morphology of blends of linear and short-chain branched polyethylenes in the solid state by small-angle neutron and x-ray scattering, differential scanning calorimetry, and transmission electron microscopy. Macromolecules 33: 551-561 Wood-Adams P, and Costeaux S (2001) Thermorheological behavior of polyethylene: Effects of microstructure and long chain branching. Macromolecules 34: 6281-6290. Xu J, Xu X, Chen L, Feng L, Chen W (2001) Effect of composition distribution on miscibility and co-crystallization phenomena in the blends of low density polyethylene with 63  conventional and metallocene-based ethylene-butene copolymers. Polymer 42: 38673874 Yamaguchi M, Abe S (1999) LLDPE/LDPE blends I. Rheological, thermal and mechanical properties. J Appl Polym Sci 74: 3153-3159 Zhang FJ, Liu F, Xie Q,F, He T, J (2002) Polym Sci Polym Physics Ed 40: 822-830 Zhang MD, Lynch T, Wanke SE (2001) Effect of molecular structure distribution of melting and crystallization behavior of 1-butene/ethylene copolymers. Polymer 42: 3067-3075 Zhao L, Choi P (2006) A review of the miscibility of polyethylene blends. Mat Man Processes 21: 135-142  64  3. THERMORHEOLOGICAL PROPERTIES OF LLDPE/LDPE BLENDS: EFFECTS OF THE PRODUCTION TECHNOLOGY OF THE LLDPE'S. 2  3.1. Introduction. The flow behavior of polyolefin melts is dictated by their macromolecular architecture, namely long chain branching content (LCB), compositional distribution of the branches (CD), molecular weight and its distribution (MWD) (Dealy and Wissbrun, 1990; Wood-Adams and Dealy, 2000, Vega et al., 2002, Malmberg et al., 2002; Gabriel and Miinstedt, 2002; Gabriel and Lilge, 20060). Polyethylene resins, in particular linear ones, are subject to a number of melt flow instabilities (Hatzikiriakos and Migler, 2005), hence it is a common practice to blend them with highly branched ones to improve their processability (Aguilar et al., 2002; Delgadillo-Velazquez and Hatzikiriakos, 2007). However, the final improvement in the processability is heavily dependent on the thermorheological properties of the blends. Rheological methods to determine the thermodynamic behavior of linear and branched polyethylene blends have been the subject of many studies (Yamaguchi and Abe, 1999; Lee and Denn, 2000; Liu et al., 2002; Ho et al., 2002; Hussein et al., 2003; Hussein and Williams, 2004a, b; Fang et al., 2005). It has been reported that the thermorheological and processing properties of the blend are largely determined by the levels of Long Chain Branching (LCB) (Wagner et al, 2004; Zhao and Choi, 2006), molecular weight, M W and its distribution (MWD) (Hussein and Williams, 2004b). In the case of linear-low density polyethylene (LLDPE), the miscibility • with low-density polyethylene (LDPE) is greatly influenced by the distribution of branches (Hussein and Williams, 2004b; Hussein, 2004; Fang et al., 2005). Most studies agree that LLDPE/LDPE are miscible blends at low LDPE compositions, which become immiscible at higher ones (Lee and Denn, 2000; Ho et al.,  A version of this chapter has been submitted for publication. Delgadillo-Velazquez, 0.; Hatzikiriakos, S.G.; Sentmanat, M. (2008), Thermorheological properties of LLDPE/LDPE blends: Effects of the production technology of LLDPE, submitted to J Polym Science Part B: Polymer Physics.. 2  65  2002). Hexane-comonomer in LLDPE promotes immiscibility (Hussein et al., 2003; Hussein and Williams, 2004b), whereas octane-comonomer promotes miscibility (Fang et al., 2005). In addition, low molecular weight LLDPEs promote miscibility better than high molecular weight ones (Hussein and Williams, 2004a). The LLDPE/LDPE blend miscibility studies above make use of thermal techniques such as differential scanning calorimetry (DSC) and thermorheology analysis (Mavridis and Shroff, 1992; Van Gurp and Palmen, 1998; Hatzikiriakos, 2000; WoodAdams and Costeux, 2001). Failure of time-temperature superposition can be interpreted as an immiscibility criterion (Van Gurp and Palmen, 1998; Peon et al., 2003; Wagner et al., 2004; Perez et al., 2005). Positive deviation of zero shear rate viscosity from the log additivity mixing rule is also an indication of immiscibility (Lee and Denn, 2000; Liu et al., 2002; Hussein et al., 2003). The Cole-Cole plot, representation between the imaginary (f') and real part (ii') of the complex viscosity, has been used by several authors as criteria for miscibility in polyethylene blends (Kim et al., 2000; Ho et al., 2002; Hameed and Hussein, 2004). The determination of the weighted relaxation spectra based on linear viscoelasticity is another method used to infer the thermorheological behavior of polyethylene blends. The relaxation spectra have been used to determine whether the blend components are immiscible based on detecting an additional relaxation mechanism associated with interfacial tension (Gramespacher and Meisssner, 1992; Lacroix et al., 1997; Fang et al., 2005). However, use of this technique made difficult to draw definite conclusions for LLDPE/LDPE blends and therefore it will not be used in the present chapter (Delgadillo- Velazquez et al., 2007). In the last chapter, all of the aforementioned techniques where used to assess the miscibility of a number of LLDPE/LDPE blends. A single Ziegler-Natta LLDPE (ethylene-hexene comonomer) blended with four LDPE's of distinctly different molecular weight was studied. It was concluded that all blends were immiscible and that immiscibility is induced by the thermorheological complex behavior as a consequence of the presence of LCB and the heterogeneous structure of ZN-LLDPE. In fact, it has been demonstrated by Temperature Rising Elution Fractionation (TREF) (Mirabella and Ford, 1997; Mirabella et al., 1998) and rheology (Gabriel et al., 1998) that ZN-LLDPE's segregate in fractions ranging from high molecular weight chains, almost linear and low  66  molecular weight chains with high amounts of LCB. Therefore in ZN-LLDPE is always difficult to isolate the effects of LCB from those of Mw and MWD on rheology and processing. With the development of a particular type of single-site catalyst (SSC), it is possible to synthesize completely linear polyethylenes of narrow MWD and introduce controlled LCB distributions as well; such resins are known as metallocene polyethylenes (m-LLDPE's) (Soares and Hammielec, 1998). Hence the macromolecular structure of a metallocene LLDPE is different from a Ziegler-Natta LLDPE providing different rheological effects (Wood-Adams and Dealy, 2000; Wood-Adams et al., 2000; WoodAdams, 2001; Malmberg et al., 2002; Hussein et al., 2006; Wei et al., 2007). In addition, it has been reported that m-LLDPE possesses quite different thermodynamic behavior when blended with linear and branched polyethylenes compared to that of ZN-LLDPE. Some authors have found that low LCB in m-LLDPE promotes miscibility with HDPE (Hussein, 2003; Hammed and Hussein, 2004); besides, miscibility was found by increasing length of LCB in m-LLDPE when blended with LDPE (Hussein et al., 2003; Hussein and Williams, 2004b; Fang et al., 2005). In this chapter, we study systematically the thermorheological behavior of a single LDPE blended with four different LLDPE's produced with two different types of catalysts. The effect of the macromolecular structure was evaluated by using two ZieglerNatta copolymers (one hexane and one octene comonomers) and two metallocene (one butane and one octane comonomers). The miscibility of the various blends is studied with DSC and linear viscoelastic measurements with the application of several thermorheological complexity criteria including the time-temperature superposition principle (TTS), van Gurp plot and zero-shear viscosity versus composition plot. All the methods are compared to check consistency of the results. The extensional rheological properties of the blends are also studied in order to examine the effects of LCB on their extensional rheological properties.  67  3.2. Materials and methodology. 3.2.1. Polyethylene resins and blends. The metallocene LLDPE resins used in this study were an octene-copolymer (Affinity PL1840G), supplied by DOW Chemicals and a butene-copolymer supplied by ExxonMobil (Exact 3128); in addition, two Ziegler-Natta LLDPE were used; namely a hexene-copolymer, supplied by ExxonMobil (LL3001) and an octane-copolymer (Dowlex 2045G), supplied by DOW Chemicals. The LDPE resin used in this work is 6621 provided by Dow Chemicals. All of the above LLDPE's have a similar Melt Index value (MI) of about 1. The metallocene LLDPE resins have been labeled as m-LLDPE I and m-LLDPE II for the butane- and octane-copolymers, respectively; likewise the Ziegler Natta LLDPE's has been labeled as ZN-LLDPE I and ZN-LLDPE II for the hexane- and octane-copolymers respectively. Table 3-1 lists all the polymers used along with their melt indices, densities at room temperature and their zero-shear viscosities at 150 ° C. Table 3-1. Properties of polyethylene resins used in this study.  Sample ID  Resin Type  Melt Index  Density (g/cc)  rlo (Pa.^)  (g/10min) (190 °C)  (25 °C)  150 °C  m-LLDPE I  Exact 3128  1.3  0.9  11,383  m-LLDPE II  Affinity PL1840G  1  0.920  34,116  ZN-LLDPE I  LL3001.32  1  0.917  17,448  ZN-LLDPE II  Dowlex 2045G  1  0.920  16,994  DOW 6621  0.47  0.919  127, 910  LDPE  The LDPE resin was melt blended respectively with each LLDPE resin in order to create LLDPE/LDPE blends having weight compositions of 99/1, 95/5, 90/10, 80/20, 50/50 and 25/75. The blending was performed as follows: the original components were mixed and grinded in a Brabender mixer/grinder in order to reduce their pellet size and assure good mixing conditions. Then, the mixture in the form of flakes was blended and  68  fed into a single screw extruder, at low processing speed (20 rpm), using a screw having mixing elements near to the end of the metering zone. The temperature of the die was kept at about 160 ° C. The extrudates were then pelletized for easy handling. The blend 99/1 was produced in two dilution steps, the first being the 95/5. The final blends between the different LLDPE's with the LDPE (6621) are labeled as follows: two Zigler Natta blend systems, ZN-LLDPE I/LDPE and ZN-LLDPE II/LDPE, and two metallocene blend systems, m-LLDPE I/LDPE and m-LLDPE II/LDPE.  3.2.2. Thermal analysis. A Shimadzu DSC-60 calorimeter was used to study the thermal behavior of the pure components and their blends. Measurements were made on samples of about 1-2 mg sealed in aluminum pans and nitrogen flow. The samples were heated from 30 ° C to 180  ° C, at a heating rate of 10 ° C/min, in order to determine the melting temperature (T.) and heat of fusion (AHm ). The calorimeter was calibrated periodically for melting temperature and heat flow using Indium and Zinc as standards. Additional determinations for the melting thermograms were carried out using a calorimeter form TA Instruments (model Q1000) by applying the sample to two heating cycles in order to eliminate thermal history. In this case, the sample was heated from 50 ° C to 150 ° C at a rate of 40 ° C/min under nitrogen atmosphere. The sample was held at 150 ° C for 5 minutes. Next the sample was cooled from 150 ° C to 50 ° C at a rate of 40 ° C/min. Finally, a second heating cycle similar to the previous one was applied to the sample. We considered the second heating endotherm for analysis. In Appendix B we present for selected cases, the comparison of the melting peaks obtained for both calorimeters where can be observed that the results are similar.  3.2.3. Rheological techniques. Parallel-plate rheometry was performed to determine the linear viscoelastic properties of the pure components and their blends. The measurements were performed using a Bohlin—CVOR (controlled-stress rheometer) at various temperatures, namely, 130°C, 150°C, 170°C, 190°C, and 210°C. Mastercurves were obtained using the time-  69  temperature superposition principle (TTS) and the results are presented at the reference temperature of 150°C in most cases. The blends were rheologically characterized in simple extension using the SER Universal Testing Platform from Xpansion Instruments (Sentmanat, 2003, 2004). Details of sample preparation and operating principle of this rheometer are given in DelgadilloVeldzquez et al. (2007). Uniaxial extension tests at the reference temperature of 150 °C were performed for all blends.  3.3. RESULTS AND DISCUSSION 3.3.1. Rheological Characterization of Pure Resins Figure 3-1 depicts the complex viscosity for the all resins listed in Table 3-1 as a function of frequency at 150 °C. The zero-shear viscosity of the four polyethylenes listed in Table 3-1 were determined by creep experiments performed at 150 ° C to obtain the zero-shear viscosity value. The measurements were carried out in an MCR 501 rheometer by Anton Paar using parallel plate geometry and at a constant shear stress of 10 Pa to attain very low shear rates. The parsimonious relaxation spectra of all polyethylenes are listed in Table 3-2. For the case of LDPE (6621) the zero-shear viscosity value is high. This suggests its high molecular weight and the presence of high amounts of long chain branching. Moreover, its significant shear thinning that causes its viscosity to become smaller than those of all LLDPE resins at high frequencies is due primarily to the presence of LCB and secondarily to its broad MWD. The shear rheology of both Ziegler Natta LLDPE resins, ZN-LLDPE I and ZNLLDPE II, is very similar, if not identical, i.e. the viscosity curve approaches its zeroshear viscosity value at small frequencies and exhibits a certain degree of shear thinning at higher frequencies, a behavior observed in LLDPE melts. In the case of the metallocene-LLDPE, butene-copolymer (m-LLDPE I), a Newtonian plateau is reached over a wide range of frequencies; this behavior is typical of linear polymers of narrow molecular weight distribution (MWD). Furthermore, for this polymer, the frequency at which the onset of shear thinning is observed is the highest with respect to the other resins, which is another suggestion of its linear structure and  70  narrow MWD. The zero-shear viscosity of m-LLDPE-I is the lowest which is due to the lower molecular weight of this resin compared to all other LLDPE's.  1 05  T=150 ° C in^04  a. 103  • o • o A  LDPE (6621) ZN-LLDPE I (LL3001) ZN-LLDPE II (Dowlex) m-LLDPE I (Exact) m-LLDPE II (Affinity)  1 02 ^ ^ 10 -2^10-1^10°^101^102 104 1 03  (radis) Figure 3-1. The complex viscosity curves of LDPE (6621), and those of all four LLDPE resins (LL3001, Dowlex, Exact and Affinity) at 150 ° C.  The extensional rheological behavior of the pure resins is depicted in Figure 3-2 at 150 ° C. In all cases the tensile stress growth coefficients,^, are plotted for three different Hencky strain rates, namely 0.1, 1 and 10s -1 . For the sake of clarity, the material functions 771' have been multiplied by an appropriate factor (for convenience, a power of 10), as indicated on the plot. The linear viscoelastic envelope (LVE),377 + , was calculated from the relaxation spectra listed in Table 3-2 and is plotted as a dashed line in Figure 32. The LDPE shows significant strain hardening (deviation from the linear viscoelastic envelope, 377 + ) which is typically an indication of the presence of LCB in LDPE resins (Gabriel and Miinstedt, 2003). On the other hand, the LLDPE's resins do not exhibit any degree of strain hardening at any extension rate, an observation consistent with polymers of linear architecture.  71  Table 3-2. Relaxation spectra of polyethylene resins @ 150 ° C li (s)  G. (Pa) m-LLDPE I 218360 178110 82421 9380 323  154000 122810 61289 14414 2869  143450 119070 75470 15222 1369  212320 99295 31243 5878 802  87067 39698 19764 8638 3915  m-LLDPE II  ZN-LLDPE I  ZN-LLDPE II  LDPE  0.0041 0.0127 0.0526 0.2831 2.6360  0.0033 0.0094 0.0526 0.5478 5.3870  0.0035 0.0104 0.0526 0.3962 3.7790  0.0051 0.0278 0.1449 0.7884 4.5220  0.0045 0.0349 0.2390 1.5990 13.6700  72  10 11  °c^  Factor  1  s ^1^0.13 ^=-10 10 10 -  2 x10 4  10 8  LDPE (6621) - - ....-•ek"4"1--a-1°.ads."..""Imm- =ET(LL3001)  "'6;;` 10 8  a. 10 7 11.1  10 3  10 2 171-L1 77 ELOPE )PE II (Dowlex):  10 6  --^•,°41..°....".--....."-.11"--1"n-LLDPE I (Exact)  10  10 5 m-LLDPE II (Affinity)  10 4 ---  10 3 10-2  10 -1  100 Time (s)  101  1 02  Figure 3-2. The tensile stress growth coefficient for the LDPE resin (6621) and the four LLDPE resins (LL3001, Dowlex, Exact and Affinity), at three different Hencky strain rates: 0.1, 1 and 10 s'; at 150 ° C. 3.3.2. Thermal Analysis — DSC Thermograms Figures 3-3a to 3-3d depict the melting thermograms of all blends obtained from Differential Scanning Calorimetry (DSC). In the blends containing the Ziegler Natta resins, ZN-LLDPE I (LL3001)/LDPE (Figure 4-3a) and ZN-LLDPE II (Dowlex)/LDPE (Figure 3-3b), the melting peak of LDPE is lower than those of ZN-LLDPE I and ZNLLDPE II. At low weight fractions of LDPE, 5%, 10% and 20% the melting is dominated by the hexene linear polyethylene, LL3001, and as such the melting peak for these blends is the same as that of the pure LL3001. For the blends containing 50% and 75% LDPE, multiple melting peaks are observed denoting an immiscible system, with one peak corresponding to the melting of the LL3001 component, another corresponding to the melting of the LDPE component, and a third peak suggesting the existence of a transitional phase of co-crystals. For the ZN-LLDPE II/LDPE blend system (Figure 4-3b) at 5%, 10% and 20% wt. of LDPE, the formation of two distinct peaks is observed, one corresponding to linear LLDPE-rich crystals (Dowlex), and the second one shifted toward the peak of LDPE, which probably contains a high fraction of branched chains. At 50% and 75% wt of  73  LDPE, three different melting peaks are observed: two peaks corresponding to pure components and a third peak probably due to co-crystallization. Comparing Figures 3-3a and 3-3b, one may conclude that octene-comonomer LLDPE's are more compatible with LDPE's, due to the formation of a co-crystallized phase at smaller LDPE fractions. The formation of a third melting peak for ZN-LLDPE/LDPE blends has been observed previously (Xu et al., 2001; Hussein and Hameed, 2005; Delgadillo- VelAzquez et al., 2007). Co-crystallization takes place when chains segregate from the two polymers (linear and branched), forming distinct lamellae morphologies and thicknesses (Wignall et al., 2000; Puig et al., 2001; Fang et al., 2005). On the other hand, it is well known that Ziegler-Natta LLDPE resins segregate in fractions ranging from high molecular weight chains with low short chain branching content, and low molecular weight chains with high amounts of short chain branching (Mirabella, 1987; Mirabella et al., 1988; Schouterden, 1987; Karbashewski, 1992; Wignall et al., 1996; Wignall et al., 2001; Zhang et al., 2001). Lee and Denn (2000) and Wagner and co-workers (2004), suggested that the complex rhelogical behavior of this blends can be understood by assuming that linear and branched chains segregate from both polyethylenes and form a homogenous phase with chains of similar structure. The thermograms plotted in Figures 3-3a and 3-3b support the observation that Ziegler Natta LLDPE/LDPE blends are generally immiscible systems at high LDPE weight fractions (Lee and Denn, 2000; Wagner et al., 2004). The melting behavior of blends of metallocene polyethylenes, m-LLDPE I (Exact) and m-LLDPE II (Affinity) with LDPE is depicted in Figures 3-3c and 3-3b respectively. From Figure 3-3c it is observed that the melting peak of m-LLDPE I is lower than that of LDPE, by almost 10 ° C. This is due to the low M W of this butane mLLDPE. This is different from the octane m-LLDPE, as seen in Figure 3-3d; the melting peak for this m-LLDPE is slightly lower than that of LDPE. Blend systems m-LLDPE I/LDPE and m-LLDPE II/LDPE show a single peak at all LDPE compositions studied; additionally, the position of the peaks for all blends shift toward the LDPE peak, as its weight fraction increases in the blend. This observation suggests miscibility by cocrystallization in the blends of LDPE and m-LLDPE studied here; hence, the macromolecular structure of LLDPE strongly dictates the miscibility with LDPE. Other  74  authors have observed co-crystallization in blends of m-LLDPE/LDPE blends and concluded miscibility (Yamaguchi et al., 1999; Lee and Denn, 2000; Fang et al., 2005). ZN-LLDPE II (Dowlex)  ZN-LLDPE I (LL3001)  7-  6% LDPE  6% LDPE 10% LOPE  10% LDPE 20% LDPE  20% LDPE  w  el  50% LDPE  50% LDPE 76% LDPE  75% LDPE  LDPE (DOW 662i)  LDPE (DOW 6621)  90  ^  100^  °  110 T ( e)^120  ^130^140^90^100^110  (a)  T (°C)^120^130^140  (b)  m-LLDPE I (Exact )  0  LL ^  11 (Affinity)  5% LDPE  6% LOPE (6621)  10% LDPE  10% LDPE (6621) 20% LDPE (6621)  20% LDPE  60% LDPE (6621)  50% LDPE  LDPE (6621)  76% LDPE LDPE (6621)  80^90^100^110 ( ° O)  120  130  80^90^100  (c)  110  120  ( ° O)  (d)  Figure 3-3a to 3-3d. DSC thermograms for the T.T DPE/LDPE blend systems: (a) ZN-LLDPE I/LDPE; (b) ZN-LL II/LDPE; (c) m- IL I/LDPE; (d) m-LL II/LDPE.  3.3.3. Linear Viscoelastic Measurements The linear viscoelastic behavior of pure components and all their blends was studied in details over a wide range of temperatures 130-210 ° C. Time-temperature superposition (TTS) was applied to shift the data horizontally and vertically (whenever necessary) in order to obtain a master curve at a reference temperature,  T„f, .  in the present  case 150 ° C. To achieve the superposition, the temperature dependence of viscoelastic  75  behavior is described by using a time (horizontal) shift factor, a T, that was assumed to follow the Arrhenius equation (Mavridis and Shroff, 1992). E 1 l^1 R \ T T„./^(3-1)  log(ara ) =  The horizontal activation energy (Ea) is obtained by regression of the experimental data. In some cases it was necessary the use of a vertical shift factor (bT) on the viscoelastic moduli in order to obtain better superposition (Mavridis and Shroff, 1992; Wood-Adams and Costeux, 2001). In this case vertical shift, bT, could be calculated. In our case it was necessary to apply vertical shift for the rheological data of LDPE and some blends having a high weight fraction of LDPE. Mavridis and Shroff (1992) proposed an Arrhenius equation (similar to Equiation 4-1) to model the vertical shift factor bT. log(bT )  T Tref  (4-2)  Where E is the "vertical activation energy". Materials showing high E, values are said to ,  be thermorheologically complex systems (Mavridis and Shroff, 1992). Thermorheological complex behavior typically arises in the presence of LCB, as well as due to the different temperature sensitivity of the relaxation times of a polymer (Mavridis and Shroff, 1992; Wood-Adams and Costeux, 2001). This leads to failure of TTS principle. In cases where the superposition to obtain mastercurves was not perfect, failure may be attributable to two factors: (1) presence of LCB and (2) immiscibility of the blend systems studied (see DSC results above) which can both contribute to thermorheological complexity. Figures 3-4a, and 3-4b show the shifted storage modulus, bTG', and complex viscosity, (bT aT,* versus reduced frequency, a7 a for the pure resins and their blends -  with 10%, 20%, 50% and 75% of LDPE for the ZN-LL I/LDPE blend. In the terminal zone, the values of the storage modulus for the LDPE are higher than those of the Ziegler Natta LLDPE, ZN-LLDPE I (Figure 3-4a); whereas the storage modulus values are lower for LDPE in the high frequency region, a typical characteristic of the presence of LCB  76  (Vega et al., 2002). Blends with LDPE compositions of 20% and below follow TTS principle; however, mastercurves of blends with 50% and 75% of LDPE composition lack superposition. This implies that the system is immiscible at rich-LDPE compositions (in view also of Figure 3-4a). A similar behavior is plotted in Figures 3-5a and 3-5b for the ZN-LLDPE II/LDPE blends. However, immiscibility due to TTS failure appears at lower LDPE composition compared to the previous blend system discussed above. Only blends with 1% and 5% LDPE composition obey TTS (not shown here), whereas for 10% LDPE and higher compositions, superposition fails. Figure 3-6a shows the storage modulus mastercurve b TG'for the third blend system, m-LLDPE I/LDPE. The behavior is similar as before. As the LDPE is more elastic than the LLDPE, the storage modulus of the blends increase proportionally with LDPE content. Thermorheological complex behavior was found at compositions in LDPE of 50% and higher. Figure 3-6b shows pretty much the same history regarding the complex viscosity. Finally, similar conclusions can be drawn for the fourth set of blends m-LLDPE II/LDPE, where the viscosity and elasticity of LDPE dominates the properties of this series of blends (see Figs 3-7a and 3-7b).  77  10 6 Tres = 150 ° C  • ^ ^ O • ■  10 2  ZN-LLDPE I (LL3001) 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE (6621)  10 1 ^ ^ 10 -2^10-1^100^101^102 103 10 4 a T co (radls) 1^11111/1  (a) 10 5 Tr ef = 150 ° C  10  -  10 4  3  4  c  —  o3  • ^ ^ o A  ■  ZN-LLDPE I (LL3001) 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE (6621)  10 2 1 0 -2^10-1^100^101^102  • 10 3  104  a T co (raclis) (b) Figure 3-4a and 3-4b. Mastercurves of a) elastic modulus, G', and b) complex viscosity, vi*, for blend system I (ZN-LLDPE I/LDPE).  78  10 6  Tres = 150 ° C 10 5  10 4  • • O •  1- 103 .0  A  10 2  ■  ZN-LLDPE II (Dowlex) 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE (6621)  10 1 10-2^10-1^10°^101^102  103  104  a T co (radis) (a) 10 5 Tr e f = 150 *C  •  • • ^ o A  ■  ZN-LLDPE II (Dowlex) 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE (6621)  10 2 10-2^10-1^• 10°^101^102  10 3  104  a T cL (rad/s) (b) Figure 3-5a and 3-5b. Mastercurves of a) elastic modulus, G', and b) complex viscosity, yl*, for blend system II (ZN-LLDPE II/LDPE).  79  10 6  '^  10 5 (Ts^104  ca  m-LLDPE I (Exact) 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE (6621)  103  .0  102  10-3  10-2  ■  10-1  100^101  102  10 3  10 4  a T (rad/s) (a) 10 5 Tref = 150 ° C  0-  104  8 7 4- 10 2 .13  •  m-LLDPE I (Exact)  ^ • o • ■  10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE (6621)  vO. v  •  10 2  10-2^10-1^10°^101^1 02  ^  10 3  ^  104  a T (radls) (b) Figure 3-6a and 3-6b. Mastercurves of a) elastic modulus, G', and b) complex viscosity, 71*, for blend system III (m-11,DPE I/LDPE).  80  10 6 Tref =  150 °C  10 6  2  104 • • O •  10 3  10 2  A  ■ 10 1 10-2  10-1  m-LLDPE II (Affinify) 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE (6621)  1 0°^101^1 02  103  104  a T (rad/s) (a)  10 6 ^ T re f =  • • O o • ■  m-LLDPE II (Affinity) 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE (6621)  10 2 ^ 10-2 10r1^10°^101^102  150 °C  A  •■ 103  ^  104  a T o (rad/s) (b) Figure 3-7a and 3-7b. Mastercurves of a) elastic modulus, G', and b) complex viscosity,^for blend system IV (m-LLDPE II/LDPE).  81  ^  3.3.4. Extensional Measurements Extensional rheological measurements were conducted for all blends at 150 ° C. The tensile stress growth coefficient curves of selected blends are plotted in Figures 3-8a to 3-8d, using scaling factors as before (powers of ten) for the sake of clarity. As observed in Figures 3-8a to 3-8d, the strain hardening behavior of the various blends is a function of LDPE content. The degree of strain hardening increases with LDPE weight fraction in the blend and becomes more evident at higher Hencky strain rates. 10"  150 °C  1 0 10  = I Os ' -  _ _____•10 4 LDPE (6621) 1  17. 108  10 7  106  ^5%  105 10 4  _ — — — — 1.2x10 ° LDPE (6621) — — 1 03 10% LDPE 10 LDPE 1 ZN-ELOPE II (Dowlex) •  — — 317  10 3  102^10.1^100^101^102 Time (s)  10-1  ^  10°  ^  10 10 1.2 x10 4  (b) ZN-LLDPE II/LDPE  150 °C e= 10s  Factor -1  __--- 1.2 x10 4 LDPE (6621)  10 9  10 9  — — — : 10 3 10 %LDPE ^ , 10 2 5 % LDPE --- — 10 1 % LDPE  108 1 03  MI 10 2  102  la 106  10 10 5  1  10 4  102  1 01 '  10 10  1 06  1 01  Time (s)  Factor  .  1 02  LDPE  104  10"  10 3  -  10 9  10 3^lo' 10% LDPE^ to 102 fi ^ 1102^ LDPE io . 10^+^10 8 1% LDPE _ _ _.! 1^105 ZN-LLDPE I (LL3001)  (a) ZN-LLDPE I/LDPE  (.7)  U. 1  10s 1^I s  10 8  )  10 3  Factor  150 °C^-1  10 10  109  co  1 011  Factor  0:1 10 7 o_ + W  10 6 10 6  m-LLDPE II (Affinity) 104 10 3  10 -2  10-1  100 Time (s)  1 01  (c) m-LLDPE I/LDPE  102  10-2  ^  10-1  10 0  10 1  10 2  Time (s)  (d) m-LLDPE II/LDPE  -1 Hencky strain rates at 150 °C for LLDPE/LDPE blend systems: (a) ZN-LLDPE I (LL3001)/LDPE; (b) ZN-T I DPE II (Dowlex)/LDPE; (c) mLLDPE I (Exact)/LDPE; (d) m-LLDPE II (Affinity)/TDPE.  Figure 3 8a to 3 8d. Tensile stress growth coefficient curves for 0.1, 1 and 10 s -  -  82  At similar Hencky strain rates the onset for strain hardening (deviation from LVE behavior) occurs at smaller Hencky strains with increasing LDPE content. In the particular case of the first blend system, ZN-LLDPE I/LDPE, at 1% LDPE weight fraction, a significant strain hardening behavior is clearly evident at high rates of extension, an observation that could not be elucidated from the shear rheology data. Extensional rheology is a sensitive tool to describe and detect subtle macro structural features in polymer blends.  3.3.5. Activation Energy The presence of LCB in the blend can also be reflected by its effect on the activation energy, Ea (Individual plots of the Arrhenius equation can be seen in Appendix A). This is seen in Figure 3-9, where the activation energy is plotted as a function of weight fraction of LDPE, for all four blend systems. The activation energy value obtained for the LDPE is 64.14 (kJ/mol). It is well known that polymers with LCB exhibit rather high values of Ea (Hatzikiriakos, 2000; Vega et al, 2002; Gabriel et al., 1998). The values for LL3001, Dowlex and Exact range from 28.5 to 33.5 kJ/mol, values very typical for LLDPE's (Wood-Adams and Costeux, 2001). On the contrary, the metallocene octene copolymer, m-LLDPE II (Affinity) exhibits an unusual high value of Ea (58.7 kJ/mol) and a vertical activation energy E v of about 10 kJ/mol, in contrast to 8.0 kJ/mol for the LDPE used in this work. This might be due to the low level of LCB that is present. For the rest of the LLDPE's the vertical activation energy ranges from 0.0 to 3.0 kJ/mol; hence, the magnitudes of E a and E v can be used as indication of thermorheologically complex behavior. The activation energy increases monotonically with LDPE concentration in all blend systems with the exception of the blend system IV (m-LLDPE II/LDPE) which at compositions of 50% and 75% LDPE exhibit a maximum. The differences in the values before and after the maximum are 1.5% and 6% lower than the maximum value respectively. The existence of a maximum might be due to elasticity and shear viscosity enhancement due to the presence of an interface. It is noted that the blends are immiscible at these high LDPE compositions and that the m-LLDPE II (Affinity) has a small degree of LCB as was concluded above from its high E a value.  83  (7) E W  80  k Tref = 151 °C  70 60  A  as  A  A  6  50  0 473  4:(  40 30  0 • o •  ZN-LLDPE I (LL3001)/LDPE ZN-LLDPE II (Dowlex)/LDPE m-LLDPE I (Exact)/LDPE A m-LLDPE II (Affinity)/LDPE  20 ^ ^ ^ ^ 0 0^0.2 0.4 0.6 0.8 1.0  w LDPE Figure 3-9. Activation energy, Ea (KJ/mol), as a function of weight fraction w of LDPE for all blend systems at 150 ° C.  3.3.6. Rheological Criteria for Miscibility  In this section several rheological criteria for miscibility will be examined for the various blends systems. First, time-temperature superposition (TTS) has already been used as a method to assess miscibility in LLDPE/LDPE blends (Yamaguchi and Abe, 1999; Perez et al., 2005). As discussed before, the thermorheological behavior of the blends rich in LDPE composition were observed to be complex, i.e. they have shown difficulty in applying the TTS principle. This is an indication of different relaxation times, possibly due to the existence of different phases comprised by linear and branched chains, respectively (see Tables 3-3 and 3-4). A possible third phase exists in these blends composed of chains from both pure components that have the ability to co-crystallize i.e. high M,„, branched chains of LDPE with high M w, linear chains of LLDPE. Another method to assess miscibility from rheology by plotting the data as phase angle (6°) versus complex modulus (b T G*). This is known as the Van Gurp-Palmen .  method. Figures 3-10a to 3-10d depict such plots for all four sets of blends. First, it is clear for the pure hexane Zieger Natta polyethylene, ZN-LLDPE I (LL3001) that the  84  time-temperature superposition is excellent (Figure 3-10a). This correlates well with the relatively low value of E. The shape of the curve for this resin is characterized by a concave curve and that at low frequencies; the value of loss angle is close to 90 ° . On the other hand, the LDPE exhibits thermorheologically complex behavior (Figure 3-10a). The shape of these curves compared to that of ZN-LLDPE I, shows a shift to lower phase angles at high bTG* values (Wood-Adams and Dealy, 2000; Hatzikiriakos, 2000). At low LDPE compositions, TTS is obeyed. Failure of superposition was clearly observed at 20% and higher LDPE composition. Hence, these blends are thermorheologically complex fluids. Similar observations were made by Wagner and co-workers (Wagner et al., 2004). The determination of miscibility is thus difficult if the blend is thermorheologically complex Similar conclusions can be drawn for the blend system II, ZN-LLDPE II/LDPE as depicted in Figure 3-10b. For blend systems III, m-LLDPE I/LDPE, and IV, m-LLDPE II/LDPE the blends show better superposition, as depicted in Figures 3-10c and 3-10d. It is worth to note, nevertheless, that in the case of the pure butane metallocene-LLDPE (mLLDPE I), the shape of the plot shows a well defined plateau in the low bTG* region, consistent with typical behavior of linear, narrow MWD polyethylene (Wood-Adams and Dealy, 2000; Malmberg et al., 2002). However, this is not the case for m-LLDPE II, which has a shape similar to LDPE. This clearly tells us the existence of a small degree of LCB as also inferred by its Ea and Ev values above. Another criterion commonly used to check the miscibility/immiscibility of blends is the zero shear viscosity, rl o, versus weight fraction in semilog-plot. The zero-shear viscosity values for pure components and blends were determined by shear experiments in creep at 150 ° C. The measurements were carried out in an MCR 501 rheometer by Anton Paar using parallel plate geometry and at a constant shear stress of 10 Pa to attain very low shear rates. Figures 3-11a to 3-11d compare the experimental data against the log-additivity and Tsenoglou (Tsenoglou 1988, 1991) mixing rules. Positive deviation behavior from the log-additivity rule means immiscibility, while the opposite implies miscibility (Utracki, 1989). In all cases, positive deviation is clearly observed for LDPE compositions of 50% and higher, which means immiscibility, an observation also drawn from failure of TTS, as well as from the van Gurp-Palmen plots. For the particular case of  85  blend system IV m-LLDPE II/LDPE), the 50% LDPE blend exhibits the strongest deviation from the mixing rule, this also correlates with the high values of Ea for at LDPE-rich compositions observed for this blend system in Figure 3-9.  8 (°)  90  90  ZN-LLDPE I 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE  80 70 60  8 (o)  70 60  50  50  40  40  30  30  20 10'^104^105  20 10 3  106  b T G* (Pa)  (a) ZN-LLDPE I/LDPE  (1  70  70 60  60  50  20 10  m-LLDPE H 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE  80  80  30  106  90  5 (°)  90  40  104^105 b T G* (Pa)  (b) ZN-LLDPE II/LDPE  100 8  ZN-LLDPE II 10% LDPE 20% LDPE 50% LDPE 75% LDPE LDPE  80  50  m-LLDPE I 7 10% LDPE 20% LDPE * 50% LDPE 75% LDPE ■ LDPE  40 30  '  0 10 3  104^105  b T G* (Pa)  (c) m-LLDPE I/LDPE  20 10 6^103^104^105  10 6  b T G 6 (Pa s)  ^  (d) m-LLDPE II/LDPE  Figure 3 10a to 3 10d. Van Gurp-Palmen plots for all four LLDPE/LDPE blend systems using linear viscoelastic data at 130 °C, 150 0C, 170 0C, 190 °C and 210 °C. -  -  86  10 6  106  fn  0_ •  •r•r•'•  .•Ball  10 6 :r."- •  0  -••••  ---.  l  vorgli.b f ♦  Exp. Data  10 4 00  ^  0.2  ^  0.4^0.6  w LDPE  ^(a)  ^  0.8  ^  10  00  ^  ^  ZN-LLDPE I/LDPE  — Tsenoglou  le"  104 ^  ^  0.4^0.6  • •• • Log additivity ■  ^  0.8  ^  10  w LDPE  ^  106  .^,^,^.......  0.2  Exp. Data  ♦  •••••••41e....  - Tsenoglou ••• • Log additivity  (b) ZN-LLDPE II/LDPE  10 6  ♦ • ..-..  "  -7-..  •• ..,".  .....  •  .-. .. • • •-"•..  __,......f..  ........•••  ♦ Exp. Data - Tsenoglou • • • •^Log additivity  ♦ Exp. Data - Tsenoglou • •••^Log additivity  .........^, .104 10 4 ^ ^ ^ ^ ^ ^ ^ 0 0^0.2^0.4^0.6 0.8 10 00 0.2 0.4^0.6 0.8 10  w LDPE  ^  (c) m-LLDPE I/LDPE  ^  w LDPE  (d) m-LLDPE II/LDPE  Figure 3-11a to 3-11d. Zero shear viscosity, 1„, versus LDPE weight fraction, w, for all four LLDPE/LDPE blend systems at 150 °C.  Positive deviations from the log-additivity mixing rule of blends of both, Ziegler Natta and metallocene LLDPE with LDPE were also reported by Hussein and co-workers (Hussein and Hameed, 2003; Hussein and Williams, 2004a); according to these authors, immiscibility occurs at rich-LDPE blends, due to conformational mismatch from the chains of both components. On the other hand, this group also concluded that LCB improves miscibility at low LDPE compositions which agrees with what we have 87  observed here. It is possible that thermorheological complexity would be another effect of having macromolecules of different structures mixed together in different configurations, leading to immiscibility. Positive deviation behavior from additivity rule, PDB, in linear and branched polypropylene have been also reported by Stange and coworkers (Stange et al., 2005), also concluding immiscibility of these blends. Similar plots at 130 ° C, 170 ° C, 190 ° C, and 210 ° C (not shown here) show similar behavior for all blend systems. The results of all the methods for examining miscibility are shown in Tables 3-3 to 3-6, for the different blend systems: All methods agree more or less enabling us to draw conclusions. For the blends with the ZN-LLDPE's, the various methods imply that at high LDPE compositions the blends are immiscible. At low LDPE composition most methods appear to indicate a transition from miscibility to immiscibility for these blend systems. Therefore, we can conclude miscibility at smaller LDPE concentrations which changes to immiscibility at higher LDPE concentrations (essentially higher than 20 wt%). Since failure of TTS might be due to the presence of LCB, TTS is not a good indicator for miscibility unless elasticity enhancement is observed (indication of immiscibility). However, overall it is reasonable to conclude that Ziegler-Natta LLDPEs blended with LDPE are immiscible blends at high LDPE compositions in view also of the DSC melting thermograms (Hussein and Williams, 2004a, b). For the blends with the metallocene LLDPE's all methods agree that these blends are essentially miscible blends even at high LDPE compositions. This can be acceptable in view also of DSC analysis that has shown the continuous shift of a single peak. Table^3-3.^Thermodynamic^behavior^of^ZN-LLDPE^I (LL3001)/LDPE (6621) at 150 ° C, as concluded by various methods. 50% 75% 5% 10% 20% LDPE LDPE LDPE LDPE LDPE I I U U U DSC I M I M M rio vs w I M I M TTS M I M I M M van Gurp-Palmen *U: unable to resolve, M: miscible system, I: Immiscible system  88  Table 3-4. Thermodynamic behavior of ZN-LLDPE II (Dowlex)/LDPE (6621) at 150 ° C, as concluded by various methods. 5% 10% 20% 50% 75% LDPE LDPE LDPE LDPE LDPE DSC^I^I^I^I^I I rlo vs w^M^M^M^I^ I I^ TTS^M^M^I^ van Gurp Palmen ^M^M^I^I^I *U: unable to resolve, M: miscible system, I: Immiscible system  Table 3-5. Thermodynamic behavior of m-LLDPE I (Exact)/LDPE (6621) at 150 ° C, as concluded by various methods. 5% 10% 20% 50% 75% LDPE LDPE LDPE LDPE LDPE DSC^M^M^M^M^M I^I 'o vs w^M^M^M^ TTS^M^M^M^I^I  van Gurp-Palmen ^M^M^M^I^I *U: unable to resolve, M: miscible system, I: Immiscible system  Table 3-6. Thermodynamic behavior of m-LLDPE II (Affinity)/LDPE (6621) at 150 ° C, as concluded by various methods. 75% 50% 5%^10%^20% LDPE LDPE LDPE^LDPE^LDPE M M M U U DSC I I M M M lo vs w I I M M M TTS M M . ^... r • *U: unable to resolve, M: miscib l e system, : mmi  van Gurp-Palmen  M  I I •, ,_^___-____  89  3.4. Conclusions The rheological effects of LCB were studied using four different LLDPE resins; two Ziegler Natta (one hexene and one octene-comonomer) and two metallocene (one butene and one octene). These were studied thermorheologically as pure polymers and as blends with an LDPE. Linear viscoelastic measurements and tensile stress growth behavior experiments were performed. The extensional stress growth coefficient of all four LLDPE's follows the envelope of linear viscoelasticity, 31-1f . The LDPE and its blends with all LLDPE's exhibit clearly strain hardening which is found to be a function of LDPE concentration; moreover, strain hardening was observed even for some blends having only 1 at % LDPE weight fraction, particularly at higher Hencky strain rates. At these low compositions in LDPE, linear viscoelastic experiments in simple shear show no effect; hence, the rheological characterization of polymers in uniaxial extension could be used as a tool for detecting and describing subtle differences in blend composition and morphology. For the blend systems with Z-N-LLDPE resins at high LDPE fractions, DSC thermograms have shown the presence of a third melting peak, possibly due to the existence of co-crystallization. At low LDPE compositions the thermograms exhibit a single melting peak suggesting that the LLDPE is dominating the melting, thus yielding inconclusive results with regard to the issue of miscibility. The other two blend systems having the metallocene LLDPE, show a single melting peak. Even at rich-LDPE concentrations, the peak shifts towards the peak of pure LDPE suggesting miscibility. Several rheological criteria were applied to all blends for assessing polymer miscibility. First, by inspection of viscoelastic moduli mastercurves, failure of TTS was observed for all blends systems at high LDPE compositions. The same behavior was corroborated with van Gurp-Palmen plots. Positive deviation behavior (PDB) from logadditivity rule was observed, in the whole range of temperatures, for all blend systems with LDPE compositions in LDPE of 50% and higher. Therefore, the ZN- LLDPE/LDPE blends are miscible at low LDPE compositions and become immiscible at higher. The mLLDPE/LDPE has shown a different behavior. In view also of the DSC analysis, these blends are miscible even at higher LDPE compositions. However, failure of TTS principle at very high LDPE compositions is mainly due to the thermorheological  90  behavior as observed for the LDPE and m-LLDPE II resins; therefore, the determination of miscibility using TTS and van Gurp-Palmen plots is difficult by the thermorheological complexity of the sample.  91  3.5. References. 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Macromolecules 24: 1762-1767 Utracki LA (1989) Polymer alloys and blends. thermodynamics and theology. Hanser Publishers Van Gurp M, Palmen J (1998) time-temperature superposition for polymer blends. Rheol Bull 67: 5-8 Vega JF, Aguilar M, Peon J, Pastor D, Martinez-Salazar J (2002) Review: Effect of long chain branching on linear-viscoelastic melt properties of polyolefins. e-Polymers 46: 1-35 Wagner MH, Kheirandish S, Yamaguchi M (2004) Quantitative analysis of melt elongational behavior of LLDPE/LDPE blends. Rheol Acta 44: 198-218 Wei X, Collier JR, Petrovan S (2007) Shear and elongational theology of polyethylenes with different molecular characteristics I. Shear theology. J App Polym Sci 105: 309-316 Wignall GD, Alamo RG, Londono JD, Mandelkern L, Kim MH, Lin JS, Brown GM (2000) Morphology of blends of linear and short-chain branched polyethylenes in the solid state by small-angle neutron and x-ray scattering, differential scanning calorimetry, and transmission electron microscopy. Macromolecules 33: 551-561 Wignall GD, Alamo RG, Londono, JD, Mandelkern L, Stehling FC (1996) Small-angle neutron scattering investigations of liquid-liquid phase separation in heterogeneous linear low-density polyethylene. Macromolecules 29: 5332-5335 Wignall GD, Alamo RG, Ritchson EJ, Mandelkern L, Schwahn D (2001) SANS studies of liquid-liquid phase separation in heterogeneous and metallocene-based linear-low density polyethylene, Macromolecules 34: 8160-8165 Wood-Adams and Dealy, JM (2000) Using theological data to determine the branching level in metallocene polyethylenes. Macromolecules 33: 7481-7488  94  Wood-Adams P (2001) The effect of long chain branching on the shear flow behavior of polyethylene. J Rheol 45: 203-210 Wood-Adams P, Dealy JM, de Groot AW, Redwine David 0 (2000) Effect of molecular structure on the linear viscoelastic behavior of polyethylene. Macromolecules 33: 74897499 Wood-Adams P, Costeux, S (2001) Thermorheological behavior of polyethylene: Effects of microstructure and long chain branching. Macromolecules 34; 6281-6290 Xu J, Xu X, Chen L, Feng L, Chen W (2001) Effect of composition distribution on miscibility and co-crystallization phenomena in the blends of low density polyethylene with conventional and metallocene-based ethylene-butene copolymers. Polymer 42: 38673874 Yamaguchi M, Abe S (1999) LLDPE/LDPE blends I. Rheological, thermal and mechanical properties. J Appl Polym Sci 74: 3153-3159 Zhang MD, Lynch T, Wanke SE (2001) Effect of molecular structure distribution of melting and crystallization behavior of 1-butene/ethylene copolymers. Polymer 42: 3067-3075 Zhao L, Choi P (2006) A review of the miscibility of polyethylene blends. Mat Man Processes 21: 135-142  95  4. SHARKSKIN AND OSCILLATING MELT FRACTURE: WHY IN SLIT AND CAPILLARY DIES AND NOT IN ANNULAR DIES? 3  4.1. Introduction. The instabilities that occur in the extrusion of molten polymers are fascinating from the scientific perspective but troublesome and frequently catastrophic from the industrial one (Ramamurthy, 1986). Over the past 50 years, there has been a sustained interest in the understanding and control of these instabilities (Hatzikiriakos and Migler, 2005). They can occur in common extrusion operations such as in the manufacture of polymeric rods, tubes, sheets, profiles, films and wire coating. Since its onset occurs at relatively low rates of production, sharkskin which is characterized by small amplitude periodic surface distortions is the most troublesome of these instabilities and is often one of the first processing-related issues to be addressed in extrusion (Migler, 2005). Two frequently cited contributions from the eighties are the articles by Ramamurthy (1986) and Kalika and Denn (1987) who studied the sharkskin of linear low-density polyethylenes (LLDPEs) and the effects of different die materials on these instabilities. Subsequently, El Kissi, Piau and co-workers (1989, 1990) have studied extensively the extrusion instabilities for moderately and highly entangled polydimethylsiloxanes (PDMS), LLDPEs and PBs. Stick-slip flow, or oscillating melt fracture, is a processing instability that is characterized by pressure and flow rate oscillations during controlled throughput extrusion and manifested by periodic, alternating rough and smooth regions on the surface of the extrudate (Tordella, 1956). The stick-slip instability has been the subject of experimental studies since the late 1950s and has been given many different names such as stick-slip, cyclic, bamboo, cork flow and oscillating melt fracture by researchers studying polymer extrusion instabilities (Tordella, 1956; Bagley, 1958). Systematic 3  A version of this chapter has been published. Delgadillo-Velazquez 0.; Georgiou, G.; Sentmanat, M.; Hatzikiriakos, S.G. (2008), Sharkskin and oscillating melt fracture: Why in slit and capillary dies and not in annular dies?, Polymer Engineering and Science., 48: 405-414.  96  observations on the oscillating melt fracture behaviour of HDPEs have been reported by Lupton and Regester (1965) and Myerholtz (1967). Vinogradov and co-workers, (1970, 1972, 1984) investigated thoroughly the flow of narrow molecular-weight-distribution (MWD) polyisoprenes (PIs) and polybutadienes (PBs) in both pressure- and flow-ratecontrolled experiments, and introduced the term spurt flow for the stick-slip instability. In the early 1990s, Hatzikiriakos and Dealy (1992) studied the stick-slip instability of HDPEs for which they used the term cyclic melt fracture. Important contributions on the origin of this instability were made by Wang and Drda (1996a, 1996b, 1997) who studied systematically the extrusion of linear PE melts and the molecular origins of the stick-slip instability. Recent work on the subject concerns the use of direct pressure drop measurements and their relation with local velocity distributions (Mtinstedt et al, 2000; Robert et al., 2002; Merten et al., 2002). Recent publications discuss thoroughly the origin of this type of flow and provide important literature reviews (Georgiou, 2005; Malkin, 2006). Most of the experimental studies cited above involved extrusion through capillary dies with the exception of those studies incorporating the use of local velocity measurements (Miinstedt et al., 2000; Robert et al., 2002 Merten et al., 2002) which involved extrusion through orthogonal channels. To date, few observations have been reported in the literature on the occurrence of oscillating melt fracture and sharkskin melt fracture involving extrusion through annular dies. Since many common polymer processing operations such as film blowing, blow moulding, wire coating, pipe extrusion and specialty profile extrusion operations involve extrusion through annular dies, an experimental study identifying the conditions under which sharkskin and oscillating melt fracture occur during annular die flow would be of great practical importance. Rosenbaum (1988) and Rosenbaum et al (2000) have reported experimental data for a linear metallocene PE in capillary extrusion and identified clearly the occurrence of stickslip instability. However, their data for a crosshead die (annular die) showed a continuous flow curve with no hint of stick-slip. Moreover the reported critical shear rate for the onset of sharkskin melt fracture was much higher than that obtained in capillary extrusion. It is the objective of this work to study systematically this phenomenon by using several capillary, slit and annular dies. Moreover, an attempt will be made to  97  identify the origin of this different behaviour of linear polymers in capillary, slit and annular dies with regard to sharkskin and stick-slip instabilities. In addition, this study can be used as a guide for assessing the processability of polymers using a capillary/slit/annular rheometer and inferring their processing behaviour in industrial applications.  4.2. Materials and methodology. The LLDPE resin used in this study was a Ziegler-Natta, hexane copolymer, supplied by ExxonMobil (LL3001). It has a melt index of about 1 at 190 ° C, a density of 0.917 at 25  ° C and a zero shear viscosity of 24,56 kPa.s at 150 ° C. Parallel plate rheometry was performed to determine the linear viscoelastic properties of the LLDPE resin at several temperatures. The measurements were performed using a Rheometrics System IV (controlled-strain) and a Bohlin—CVOR (controlled-stress) rheometers. Experiments were performed at different temperatures, namely, 130°C, 150°C, 170°C, 190°C, and 210°C. Mastercurves were obtained and most results are presented at the reference temperature of 150°C. The extensional rheological characterization of the LLDPE was performed using the SER Universal Testing Platform (Sentmanat, 2003; 2004) as described in Chapters 3 and 4. Measurements were conducted at the reference temperature of 150°C, over 25 degrees above the peak melting point of the polymer. Extrusion experiments in a capillary rheometer using various dies were used to assess the processability of the LLDPE and the critical parameters for the onset of flow instabilities such as sharkskin and oscillating melt fracture. Table 4-1 summarizes the dimensions of the dies corresponding to the different geometries used in this study. First, capillary extrusion measurements were conducted at 150°C and 190 ° C using three different capillary dies having diameters, D, equal to 0.43, 0.762 and 2.34 mm; and a length-to-diameter ratio, L/D, from 14 to 16. The onset of oscillating melt fracture was determined from the pressure signal as well as from the alternate relatively smooth and distorted sections along the extrudates using an Olympus MIC-D microscope. The same microscope was used to detect sharkskin melt fracture.  98  Second, similar experiments were performed with three slit dies having different height, H, width, W, length-to-height ratios, L/H, and entrance angles, 2a, of 180 ° for two dies, and 60 ° for the other one. The aspect ratio of their cross section was near 10 and thus the calculated shear stress based on a typical analysis of slit flow to produce rheological data is valid (Dealy and Wissbrun, 1990). Finally, three annular dies were used to determine the flow curve of the LLDPE in annular flow using different inside to outside ratios, D/D o , ranging from 0.607 to 0.951 (see Table 4-1 for details), with reduction ratios RR (ratio of cross sectional areas), equal to 152, 350 and 1000 correspondingly. It is noted that an annular die having a D/D0 ratio approaching zero becomes similar to a capillary die, whereas a D/D O approaching 1 becomes similar to a slit die. A picture of a typical annular die appears in Figure 4-1, where the different inside pieces are also shown.  Table 4-1: Different die geometries used in this study along with their dimensions Capillary D (mm)  L/D  2a  0.432  15  180°  0.762  16  180°  2.34  14  180°  Slit die H (mm)  W (mm)  L/H  2a  0.305  2.6  34  180°  0.324  2.45  31  60°  0.47  2.54  44  180°  Tube extrusion RR  Do (mm)  Di (mm)  Di/Do  L/(Do-DO  152  2.54  1.542  0.607  10  350  2.54  2.167  0.853  27  1000  2.54  2.415  0.951  80  99  Figure 4-1. A picture of the annular die showing the various inserts that are used to change the gap.  4.3. Results and discussion. 4.3.1. Linear Viscoelastic Measurements. The linear viscoelastic behavior of pure LLDPE was studied in detail over the temperature range 130-210 ° C, as discussed above. Time-temperature superposition (TTS) was applied to shift the data horizontally in order to obtain a master curve at a reference temperature, T„f----150 ° C, using the procedure proposed by Mavridis and Shroff (1992), as described in previous chapters. Figure 4-2 shows the master storage modulus, G",, and loss modulus, G", as well the master complex viscosity, 77*/a r , versus reduced frequency, a T co for the pure LLDPE. The superposition is satisfactory, typical for linear polymers. The resulting energy of activation was about 8 kcal/mol that is typical for a LLDPE as reported by Mavrides and Shroff (1992) and Hatzikiriakos (2000).  100  10 6  1 06  LLDPE (LL3001) T ref = 150 ° C  10 5  ca 0_  2  10 4  (5,  .0 _9_ .0  10 3  10 2  1 01 1 0 -3  1 0 -2^10-1  10°^101^102^1 03 a T co (s " 1 )  ^  10 2  Figure 4.2. The master viscoelastic moduli and complex viscosity of LLDPE (LL3001) at 150 ° C.  4.3.2. Extensional Measurements Extensional rheological measurements were conducted at 150 ° C for the pure LLDPE. The extensional rheological behavior of pure resin is depicted in Figure 5-3 at 150 ° C. The tensile stress growth coefficients, 7 IE1 , are plotted for three different Hencky -  strain rates, namely 0.1, 1 and 10s -1 as functions of time. It can be observed that the LLDPE (LL3001) does not exhibit any degree of strain hardening at any extension rate, an observation consistent with polymers of linear architecture. In addition the tensile stress growth curves display very little deviation from the linear viscoelastic envelope (LVE), 377 + , that was determined independently from linear viscoelastic shear rheology measurements, plotted as a continuous line in Figure 4-3, an indication of the consistency of the experimental data.  101  n  ca 10 5 a. w  c.)  a)  0  2  10 4  Na) ct) N a) 10 -2  10-1  10°  101  1 02  time (s)  Figure 4 3. The tensile stress growth coefficient curves for the LLDPE resin (LL3001) at three -  different Hencky strain rates: 0.1, 1 and 10 s -1 ; at 150 °C. The absence of strain hardening is typical for a linear polymer.  4.3.3. Flow curves. Plots of wall shear stress (calculated from the time average) versus apparent shear rate, known as flowcurves, at 150 ° C are depicted in Figure 4-4 using three different geometries; namely, a capillary die (D=0.762cm, L/D=16), a slit die (H=0.305mm, L/H=34) and a tube extrusion die (D i/D 0 0.607, RR=152). For shear rates below 100 s -1 , slit die extrusion exhibits a flowcurve higher than the rest of the geometries. This is mainly due to the fact that the wall shear stress was calculated without measuring the Bagley correction. Moreover, an additional error in slit rheometry' originates from the finite aspect ratio of the die. Discontinuities in the flowcurves can be observed for capillary and slit flow which is mainly due to the occurrence of oscillating flow (stick-slip flow); however, in the case of annular extrusion, there are no discontinuities, and thus no stick-slip has been observed. As will be discussed later this is the case with all three tube extrusion dies.  102  LLDPE (LL3001)  ^^^^  T = 1 50 ° C  ^  o°  • 0 • 0 jOk  a^ 0  ^  0  00 • •  0 0000  ^  0  411:3^ 5  8u  0  0 Capillary die L/D=16 • Slit die LA-1=34 ^ Annular die RR=152  0.01  10 1^102^  103  Apparent shear rate, 7A ( .1 Figure 4 -4. Typical flowcurves of LLDPE in capillary, slit and tube extrusion at 150 °C.  Figure 4-5 shows typical photographs of the extrudates taken from the three different geometries used in this study. Extrudate pictures of samples collected during extrusion in the smooth, sharkskin, stick-slip and gross melt fracture flow regimes can be seen, depending on the individual cases.  Capillary flow L/D=15, D=0.762 mm  15 s 4 smooth^175 s- 1 sharkskin^350 stick slip  103  Slit flow L/H = 31  15 s- 1 smooth  ^  150 s 4 sharkskin  ^  350 5 -1 stick slip  Annular Flow RR=350  100 s -1 smooth  ^  500 s- 1 sharkskin  ^  1300 s- 1 Gross melt fracture  Figure 4 5. Photographs of extrudates from capillary, slit and annular extrusion experiments at 150 °C. -  4.3.3.1. Capillary flow. Figure 4-6 shows the flowcurves of LLDPE obtained in capillary flow at 150 ° C using all three capillary dies. The critical shear rates and wall shear stresses for the onset of sharkskin and oscillating melt fracture are listed in Tables 4-2 and 4-3. First, at 150 ° C, the critical shear stress for the onset of sharkskin is in the range of 0.17-0.19 MPa consistent with values reported previously in the literature (Ramamurthy, 1986). Discontinuities in the flowcurves, which define the stick-slip flow regime, were observed  104  only for the dies having smaller diameters, i.e, 0.432 and 0.762 mm; For the larger diameter die, this flow regime should appear at higher apparent shear rates not accessible with our capillary rheometer. Furthermore, the onset of these discontinuities with the smaller diameter capillaries were obtained at apparent shear rate values of 300 and 230 s- 1 , respectively, and shear stress oscillations of 0.31-0.40 and 0.43-0.44 MPa respectively (see Table 4-2). The amplitude of these oscillations depends on the diameter of the die (Hatzikiriakos and Dealy, 1992). 1 LLDPE (LL3001) L/D = 14-16 T = 150 °C  A A ^ ^  0  ^  A 0  0.1  •  D=0.432 mm ^ D=0.8 mm A D=2.34 mm  0.01 10  ^  100  ^  Apparent shear rate,  1000  7A (s-1)  Figure 4 6. Flow curves of LLDPE in capillary extrusion at 150 ° C for three different capillary dies with L/D=14-16 and diameters ranging from 0.43 to 2.34 mm. Discontinuities in the flow curve are clear that indicate the presence of stick-slip (oscillating) flow. -  Table 4-2. Critical shear rates and stresses for LLDPE (LL3001) in capillary flow at 150 ° C.  Stick-slip  Sharkskin MF D (mm)  crw (MPa)  YA (s4)  aw (MPa)  f',4 (s 4 )  0.432  0.19  30  0.44-0.43  300  0.80  0.19  50  0.40-0.31  230  2.34  0.17  25  -  Not accessed  105  Table 4-3: Critical shear rates and stresses for LLDPE(LL3001) in capillary flow at 190 ° C. Sharkskin MF  Stick-slip  D (mm)  aw (MPa)  )2,4^(s-i)  crw (MPa)  f/A (s -1 )  0.432  0.16  70  0.41-0.4  600  0.80  0.17  90  0.42-0.39  850  2.34  0.15  50  -  Not accessed  At 190 ° C, stick-slip was also present in the dies with 0.762 mm and 0.432 mm diameter, as observed from the discontinuity on the flowcurves on Figure 4-7. In both cases, the onset of the oscillations is shifted to higher apparent shear rates (600 s -1 and 850 s -1 ) with respect to the flow curves at 150 ° C. Typical pressure oscillations obtained with the die having a diameter of 0.762 mm are shown in Figures 4-8 and 4-9, at 150 °C and 190 ° C, respectively. Moreover, for all the three capillary dies, the onset of sharkskin melt fracture is shifted to higher shear rates when the temperature is increased from 150 ° C to 190 ° C. 1  LLDPE (LL3001)  •  - L/D = 14-16 T = 190 ° C  EIO 0  8 84[0^  °Aefin^  A  0.1  6 6 ';  A  • D=0.432 mm ^ D=0.762 mm A D=2.34 mm  0.01 10^  100  ^  1000  Apparent shear rate, /A (s 4 ) Figure 4-7. Flow curves of LLDPE in capillary extrusion at 190 °C for three different capillary dies with L/D=14-16 and diameters ranging from 0.43 to 2.34 mm. Discontinuities in the flow curve are clear that indicate the presence of stick-slip (oscillating) flow  106  LLDPE (LL3001)  22, = 400s -1 24 16  0. 2  P2 = co Cl)  a) 0.  22  L/D = 16 D= 0.762 mm T =150 ° C  24 it'  a. 2  a) L  =  0  Cl)  a)  0  22  0^25^50^75  ^  100  ^  125  ^  150  Time (s) Figure 4-8. Typical pressure oscillations in capillary flow using a die having D=0.762 mm, L/D=16 at various apparent shear rates and 150 °C.  107  27  =1 0 3  LLDPE (LL3001)  s'  I 1 01  II  II It l l l^11^I L/D = 16 D = 0.762 mm T = 190 ° C  25 LLDPE (LL3001)  26  ea  0. 2  II 21: 25  L/D = 16 D= 0.762 mm T = 190 ° C  ^ =850s -1  LLDPE (LL3001)  26  25  L/D = 16 D = 0.762 mm T = 190 ° C 0^25^50^75^100  125  150  Time (s)  Figure 4-9. Typical pressure oscillations in capillary flow using a die having D=0.762 mm, L/D=16 at various apparent shear rates and 190 ° C.  108  4.3.3.2. Slit flow. The flowcurves for slit flow for LLDPE at 150 ° C using the three different slit dies are shown in Figure 4-10. Sharkskin and stick-slip is present in all cases, as is evident from the discontinuity depicted in the flowcurves; the critical shear stresses for the onset of sharkskin are in the range 0.16-0.22 MPa and in general much higher than the corresponding ones in capillary extrusion. The critical apparent shear rates and stresses for the onset of instabilities are listed in Tables 4-4 and 4-5.  LLDPE (LL3001) T=150 °C ••• • • • t^0 6  •  • 4 6 46  • • a  Zli■F  iz 0 A  o •  Slit die L/H=44 Slit die L/H=34 A Slit die LIH=31 2a=60 °  0.01  10  ^  100  ^  •  1000  Apparent shear rate, 2> ii (s") Figure 4 10. Flow curves of LLDPE in slit die extrusion at 150 °C using the three different slit dies. Discontinuities in the flow curve are clear in all cases indicating the presence of stick-slip (oscillating) flow. -  Table 4-4: Critical shear rates and stresses for LLDPE (LL3001) in slit flow at 150 ° C. Sharkskin MF  Stick-slip Ow (MPa)  (s  L/H  acv (MPa)  34  0.20  60  0.38-0.32  150  44  0.16  40  0.28-0.26  175  31  0.22  70  0.34-0.29  200  2  ?  A  (S4)  2.1,4^  -1 )  109  Table 4-5: Critical shear rates and stresses for LLDPE (LL3001) in slit flow at 190 °C. Sharkskin MF  Stick-slip  L/H  crw (MPa)  f',4 (s-1)  aw (MPa)  f',4 (s 4 )  34  0.25  150  0.34-0.33  300  44  0.1  40  0.33-0.34  550  31  0.21  125  0.38-0.39  700  Figure 4-11 depicts the flowcurves for LLDPE in slit extrusion at 190 ° C. Stickslip is also present in the three slit die geometries however the critical shear rates for its onset are grater than those obtained at 150 ° C. In general, the critical shear stresses for the onset of sharkskin are again higher (0.12-0.25MPa) than the corresponding values obtained in capillary extrusion (0.15-0.17MPa). Typical pressure oscillations obtained with the slit die having a height of 0.305 mm are shown in Figures 4-12 and 5-13, at 150 ° C and 190 ° C, respectively. 1 LLDPE (LL3001) T = 190 ° C  0.1  •  2  zI  *2 I  1111  A 666 a ° • a 6 0• 0• o  o Slit die LA-I=44 • Slit die LA-1=34 A Slit die L/H=31 2a=60°  0.01  10  ^  100  ^  1000  Apparen Shear rate,YA (s 4 ) Figure 4 11. Flow curves of LLDPE in slit die extrusion at 190 ° C using the three slit dies. Discontinuities in the flow curve present in all dies indicating the presence of stick-slip (oscillating) flow. -  110  W = 0.26 cm H = 0.03 cm LJH = 34 T = 150 °C  W = 0.26 cm H = 0.03 cm LJH = 34 T = 150 °C  W = 0.26 cm H = 0.03 cm L/H = 34 T = 150 °C  0^20^40^60^80^100^120^140^160^180  Time (s) Figure 4-12. Typical pressure oscillations in slit flow at 150 °C.  111  500s-1 31  W= 0.26 cm H = 0.03 cm L/H = 34 T = 190 ° C  y  A  = 450s - '  Ili^lll l ^,^ll  31 ea  I I I I^1 1^I II I'^Ill'^II^f t  L  0 30 -  W= 0.26 cm H = 0.03 cm L/H = 34 T = 190 ° C  2%, = 400,s -1  /IN /I/ lliiiiilitIONIN  31 as  1z a) 0  Nill  W = 0.26 cm H = 0.03 cm L/H = 34 T = 190 ° C  30  0^20^40^60^80^100^120^140^160^180  Time (s)  Figure 4 13. Typical pressure oscillations in slit flow at 190 °C. -  112  4.3.3.3 Annular flow. For the case of annular flow, the flowcurves at 150 ° C and 190 ° C, using all the available annular dies are depicted in Figures 4-14 and 4-15 respectively. No stick-slip flow regime was observed, at any temperature, as can be observed by the monotonous increase of wall shear stress vs. apparent shear rate relationships. Regarding the onset of sharkskin, Tables 4-6 and 4-7 summarize the critical shear rates and wall shear stresses for the onset of this instability for the three annular dies. At the higher temperature only for the smallest reduction ratio (RR-152) that corresponds to higher annular gap of Di/D o-0.607 sharkskin was observed. At 150 ° C the critical shear stress values increased with Di/D o from 0.36 MPa to about 1 MPa. These values and the corresponding apparent shear rate values are much higher than the corresponding critical values obtained in capillary and slit extrusion. Therefore, in annular flow sharkskin is delayed.  LLDPE (LL3001) -^T = 150 °C  2  ui 0  0  0.1  •  •• ••  v(T,  r  • !Or  L  0  • • ^ 0.01  10^  100  RR=1000 RR=350 RR=152  ^  Apparent shear rate,  1000  IA (S -1 )  Figure 4 14. Flow curves in annular extrusion at 150 ° C using three reduction ratios: RR=152, 350 -  and 1000 — No discontinuity (no stick-slip) was obtained.  113  LLDPE (LL3001)  •  T=190°C  ••• 0.1  •  •  •  •v 5  • V  • O •  RR=1000 RR=350 RR=152  0.01 10^ 100^ 1000 Apparent shear rate, ) (A (s 1 ) -  Figure 4-15. Flow curves in annular extrusion at 190 °C using three reduction ratios: RR=152,  350 and 1000 —No discontinuity (no stick-slip) was obtained.  Table 4-6. Critical shear rates and stresses for LLDPE (LL3001) in annular flow at 150  °C. Sharkskin MF  Stick-slip  RR  ow (MPa)  2.1 A (s -1  152  0.36  350 1000  aw (MPa)  ff,4 (s -1)  200  -  -  0.47  400  -  -  1  150  -  -  )  Table 4-7. Critical shear rates and stresses for LLDPE (LL3001) in annular flow at 190  °C. Sharkskin MF  Stick-slip  RR  aw (MPa)  i',1^(s-11)  crw (MPa)  152  0.37  500  -  -  350  -  -  -  -  1000  -  -  -  -  )  A  (s -1 )  114  4.3.4. Discussion. As presented above in our study of sharkskin through capillary, slit and annular dies, it was found that the melt undergoes sharkskin in annular dies at considerably higher shear rates compared to those in slit dies and these in turn are higher than the ones obtained in capillary extrusion. As has been described in earlier studies (Cogswell, 1987; Migler et al., 2002; Sentmanat & Hatzikiriakos, 2004; Sentmanat et al., 2004; Migler, 2005), the onset of sharkskin is believed to be due to a localized melt rupture phenomenon initiated at the free surface of the extrudate and propagated inward upon exiting the die. The singularity that occurs at the die exit as the melt abruptly transitions from a fixed boundary to a free surface, results in high extensional flow deformations isolated to the region of the melt nearest the outermost layer of the extrudate. The periodicity of the sharkskin melt fracture comes as a result of the intermittent elastic energy storage via tensile modulus increase and elastic energy dissipation via transverse crack propagation along the surface region of the extrudate. Although highly branched materials have an inherent means of rapidly dissipating this free surface stress condition via branch mobility (in which the lower molecular weight branches are able to rapidly reconfigure themselves towards a lower stress state condition while the large molecular backbone hardly participates in this rapid energy dissipation process), linear materials must dissipate this stress by only one means - along their large molecular backbone. Consequently, linear polyethylenes are prone to this type of sharkskin melt fracture phenomenon due to the fact that at high extensional flow rates they exhibit both a rapid increase in elastic tensile modulus and a brittle-type mode of failure at rupture, factors that inherently contribute to crack propagation (Sentmanat et al., 2004; Muliawan et al., 2005). Slip promoters also alleviate this critical stress condition at the free surface by reducing the extensional deformation witnessed by the material at the extrudate surface immediately upon exiting the die (Migler, 2005). Hence with sharkskin, the critical factor in determining the onset of melt fracture is how rapidly the material at the free surface of the extrudate can dissipate energy and assume a lower stress state configuration at the free surface. It is believed that the primary reason that the annular extrusion die yields a delayed onset for sharkskin melt fracture lies in the fact that the material exiting the die  115  has the largest surface area to volume aspect ratio at the die exit. This increased surface area ratio coupled with the fact that an annulus has no edges allows the material at the free surfaces additional degrees of freedom to rapidly assume a lower stress state as it exits the die. Unlike a slit that is confined by its edges, an annular geometry can allow for a subtle spiraling flow (three-dimensional flow) as it exits the die thereby benefiting from an additional degree of freedom than material exiting a slit die where the flow over a majority of the web is primarily a 2-D flow. Although a capillary die can also allow for spiraling flow, it has the lowest surface area to volume ratio of the three geometries and only a single free surface over which a lower stress state configuration must be rapidly achieved upon exiting the die. One can think of this as a critical surface stress condition per unit surface area that must be achieved for sharkskin to occur. Hence, the increased free surface area and ability to allow for 3-D flows enable materials extruded from an annular die to exhibit a delayed onset to sharkskin melt fracture when compared to capillary and slit die geometries. Regarding the lack of an observable stick-slip flow regime with annular die flow, it is believed to be due to an inherent difference in the converging flow section in the entrance region of the die when compared to the slit and capillary die geometries. Additionally, due to the presence of the central mandrel support in the entrance region of the annular die, the vortex-like flow in the die entrance region that would otherwise accompany the onset of the stick-slip instability is inherently stifled.  4.4. Conclusions. The sharkskin and oscillatory melt fracture behavior of a LLDPE was studied at two different temperatures, 150 ° C and 190 ° C in capillary, slit and annular flows. Oscillatory melt fracture was observed only in capillary and slit flows, in both cases, the onset of the pressure oscillations is delayed to higher apparent shear rates as the temperature is increased from 150 ° C to 190 ° C. As for the annular flow three different reduction ratios (RR) were used, 152, 350 and 1000. It was observed that the critical shear rate and stress for the onset of sharkskin in annular flow is considerably higher than those detected in slit extrusion and those higher than the ones determined in capillary flow. These results were explained in terms of a critical surface stress condition per unit  116  surface area that must be achieved for sharkskin to occur. It was also argued that the annular flow allows for a three dimensional spiraling flow that provides additional degrees of freedom for the stress concentration at the exit to be relieved.  117  4.5. References. Bagley, EB; Cabott, IM;z DC West. Discontinuity in the flow curve of polyethylene. J Applied Phys 29:109-110, 1958. Cogswell. Streching flow instabilities at the exits of extrusion dies. J Non-Newtonian Fluid Mech 2:37-47, 1977 Dealy, JM and Wissbrun KF (1990) Melt Rheology and its Role in Plastics Processing. Theory and Applications. Van Nostrand Reinhold, New York Georgiou, SG "stick-slip instability," in Polymer Processing Instabilities: Control and Understanding, Eds SG Hatzikiriakos and K Migler, Marcel Dekker, New York (2004) Hatzikiriakos, SG; Dealy. JM. (1992) Role of slip and fracture in the oscillating flow of HDPE in a capillary. J Rheol 36:845-884. Hatzikirikos, S.G., (2000), Long chain branching and polydispersity Effects on the Rheological Properties of Polyethylenes. Polym Eng Sci 40: 2279-2287 Hatzikiriakos S.G, Migler KB (ed) (2005) Polymer processing instabilities. Control and understanding. Marcel Dekker, New York Kalika, DS; Denn. MM (1987) Wall slip and extrudate distortion in linear low-density polyethylene. J Rheol 31:815-834. El Kissi, N ; Piau. JM (1989) Ecoulement de fluides polyrneres enchevetres dans un capillaire Modelisation du glissement macroscopique a la paroi. CR Acad Sci Paris 309, Serie 11:7-9, 1989. El Kissi, N; Piau. JM (1990) The different capillary flow regimes of entangled polyclimethylsiloxane polymers: Macroscopic slip at the wall, hysteresis and cork flow. J Non-Newtonian Fluid Mech 37:55-94. Lupton, JM; Regester. JW (1965) Melt flow of polyethylene at high rates. Polym Eng Sci 5:235-245. Malkin AY. (2006), Flow instability in polymer solutions and melts. Polym. Sci. Series C 48:21-37. Mavridis H, Shroff RN (1992) Temperature dependence of polyolefin melt theology. Polym Eng Sci 32: 1778-1787 Merten, A; Schwets, M; Miinstedt, H. (2002) Simultaneous measurements of pressure and velocity oscillations during spurt flow of a high-density polyethylene. Procs 6th European Conf Rheol, Erlangen, pp 147-148. Migler, KB; Son, Y; Qiao, F; Flynn, K (2002) Extensional deformation, cohesive failure, and boundary conditions during sharkskin melt fracture. J. Rheol. 46:383-400. Migler K.B (2005), Sharkskin Instability in extrusion, in Polymer Processing Instabilities: Control and Understanding, S.G. Hatzikiriakos and Migler K.B. (Eds), 121-160, Marcel Dekker, NY.  118  Miinstedt, H; Schmidt, M; Wassner, E. (2000) Stick and slip phenomena during extrusion of polyethylene melts as investigated by laser-Doppler velocimetry. J Rheol 44:413-427. Muliawan, EB; Hatzikiriakos, SG;. Sentmanat M (2005) "Melt Fracture of linear polyethylenes: A critical study in terms of their extensional behaviour" Intern. Polym. Processing, XX, 60-67. Myerholtz. RW (1967) Oscillating flow behavior of high-density polyethylene melts. J Appl Polym Sci 11:687-698. Ramamurthy, AV (1986) Wall slip in viscous fluids and influence of materials of construction. J Rheol 30:337-357. Robert, L; Vergnes, B; Demay, Y (2002) Experimental investigation during the stick-slip flow of a HDPE with Laser-Doppler velocimetry and flow birefringence. Procs 6th European Conf Rheol, Erlangen, pp 145-146. Rosenbaum, EE; Randa, S; Hatzikiriakos, SG; Stewart, CW (2000) "Boron Nitride as a Processing Aid for the Extrusion of Polyolefins and Fluoropolymers," Polym. Eng. Sci., 40, 179-190. Rosenbaum, E.E (1998) "Rheology and processability of FEP Teflon resins for wire coating," PhD thesis, UBC. Sentmanat ML (2003) Dual windup extensional rheometer. US Patent No. 6,578,413 Sentmanat, M (2004) Miniature universal testing platform: from extensional melt rheology to solid state deformation behavior. Rheol Acta 43: 657-699. Sentmanat, M; Hatzikiriakos (2004) Mechanism of gross melt fracture elimination in the extrusion of polyethylenes in the presence of boron nitride Rheol. Acta. 43: 624-633 Sentmanat, M; Muliawan, EB; Hatzikiriakos, SG (2005) Fingerprinting the processing behavior of polyethylenes from transient extensional flow and peel experiments in the melt state. Rheol Acta 44: 1-15 Tordella. JP (1956) Fracture in the extrusion of amorphous polymers through capillaries J Appl Phys 27:454-458. Vinogradov, GV; Driedman, ML; Yarlykov, NV; Malkin AY (1970) Unsteady flow of polymer melts: polypropylene. Rheol Acta 9:323-329. Vinogradov, GV; Malkin, AY; Yanovskii, YG; Borisenkova, EK; Yarlykov, BV; Berezhnaya. GV (1972) Viscoelastic properties and flow of narrow distribution polybutadienes and polyisoprenes. J Polym Sci Part A2, 10:1061-1084. Vinogradov, GV ; Protasov, VP ; Dreval, VE (1984) The rheological behavior of flexiblechain polymers in the region of high shear rates and stresses, the critical process of spurting, and supercritical conditions of their movement at T>T g . Rheol Acta 23:4661 Wang, SQ; Drda. PA; (1996a) Superfluid-like stick-slip transition in capillary flow of linear Polyethylene. 1. General features. Macromolecules 29:2627-2632. Wang, SQ; Drda. PA (1996b) Stick-slip transition in capillary flow of linear polyethylene. 2. Molecular weight and low-temperature anomaly Macromolecules 29:4115-4119.  119  Wang, SQ; Drda. PA (1997) Stick-slip transition in capillary flow of linear polyethylene. 3. Surface conditions, Rheol Acta 36:128-134.  120  5. PROCESSABILITY OF LLDPE/LDPE BLENDS: CAPILLARY EXTRUSION STUDIES. 4 5.1. Introduction. The processability of linear low-density polyethylenes (LLDPEs) can be improved by blending with a small amount of a low-density polyethylene (Utracki, 1989; Lee and Denn, 2000; Fang et al., 2005). However, due to structural differences between resins, many undesirable effects may occur such as immiscibility of the components and undesirable morphological changes (Arnal et al., 2001; Wignall et al., 2000) as well as premature onset of flow instabilities (Utracki, 1989; Perez et al., 2005). These effects obviously influence the economic feasibility of the processes as well as the mechanical properties of the final products (Utracki, 1989; Cho et al., 1998; Yamaguchi and Abe, 1999; Ho et al., 2002). In chapter 3 we studied the miscibility between a linear polyethylene (Ziegler-Natta hexane copolymer of LLDPE) and four branched polyethylenes (LDPEs) using differential scanning calorimetry (DSC) and several rheological methods (Delgadillo-Velazquez et al., 2007). It was found that these blends are immiscible at high low-density polyethylene (LDPE) concentrations (typically greater than 20 wt%) and miscible at smaller LDPE ones. The effects of LCB on the rheology were assessed by means of parallel-plate and extensional rheometry. It was found that shear is insensitive to additions of small amounts of LDPE into LLDPE (up to 20 wt% in many cases) particularly if the viscosity curve of LDPE is about the same or lower than that of the corresponding LLDPE. On the other hand, extensional rheometry was found sensitive to addition of only 1 wt% of LDPE into LLDPE at high Hencky strain rates (typically greater than 5 s -1 ) and for the blends that contained the LDPE with the highest molecular weight. Such rates are not easily accessible by commercial extensional rheometers. The SER Universal Testing Platform from Xpansion Instruments is the only known extensional rheometer that can perform reliable experiments at such high Hencky strain rates (Sentmanat, 2003, 2004).  A version of this chapter has been published. Delgadillo-Veldzquez, 0.; Hatzikiriakos, S.G. (2007), Processability of LLDPE/LDPE blends: Capillary extrusion studies, Polymer Engineering and Science, 47, 1317-1326. 4  121  In this work, we study systematically the processing behavior of a LLDPE with four LDPEs that have viscosity curves which lie above, about the same and below that of the LLDPE. The same blends used in Chapter 2 are tested in this work. The processability of all blends is studied in detail in capillary rheometry in order to determine the effects of long chain branching (LCB) on the onset of flow instabilities collectively known as melt fracture. We are interested to know how the addition of various amounts of LDPE (of varying molecular weight) can affect the onset of flow instabilities such as surface, oscillating and gross melt fracture. In addition, how the details of flow, particularly the magnitude and period of oscillations are influenced by the presence of small amounts of LDPE. Surprisingly, it is reported here that flow details in oscillating melt fracture flow details are extremely sensitive to subtle changes in the structure of polymers.  5.2. Experimental. 5.2.1. Polyethylene Resins and Blends The polyethylene resins used in this work are those used in Chapter 2, i.e. a LLDPE (LL3001) and four different LDPE's: LD200, EF606A, 6621 and 1321. Their respective labels as well as their melt indices and densities for all these polymers are listed in Table 2-1 (see Chapter 2). For the blending procedure, refer also to section 2.2.1.  5.2.2. Rheological techniques Parallel-plate rheometry was performed to determine the linear viscoelastic properties of the pure components. Details on the linear viscoselasticity of blends and experimental conditions can be found in Chapter 2 and in Delgadillo-Veldzquez et al. (2007). Capillary extrusion measurements were conducted at 150°C and 190 ° C using a capillary die having a diameter equal to 0.762 mm and a length-to-diameter ratio, L/D, equal to 16. The onset of melt flow instabilities (melt fracture) were determined for the pure resins and their blends. The surface of the extrudates was analyzed with an Olympus MIC-D microscope. Selective images of the extrudates are presented in this chapter.  122  5.3. Results and discussion. 5.3.1. Capillary Rh eom etry The flow curves of the pure components and those of their blends, were determined at 150 ° C and 190 ° C by means of the capillary rheometer as described earlier. For the first set of blends, LLDPE (LL3001.32)/ LDPE (LD200), the results are shown in Figure 5-1. First, a significant viscosity mismatch between the LLDPE (LL3001) and LDPE-I (LD200) can be observed (also seen in Figure 2-1 from their complex viscosities). Due to this, addition of up to 20% of LDPE-I into LLDPE does not seem to have a significant effect on its viscosity. The flow curves seem to overlap. Differences can clearly be seen only at concentrations as high as 50wt% in LDPE. Similar observations for this system were made by DelgadilloVelazquez et al. (2007).  1  LiD=1 6 . D=0.762 min T=150  °C •  0 A  A  •  0  •  V  •  •  •  •  •  •  0  ■  • 0.01  LLDPE (LL3001) 1% LDPE I (LD200) 5% LDPE I (LD200) 10% LDPE I (LD200) 20% LDPE I (LD200) 50% LDPE I (LD200) 75% LDPE I (LD200) LDPE I (LD200)  ^ 10 1^102^103 10 4 1 Apparent shear rate, 1A (s" ).  Figure 5-1. The apparent flow curves of blends in Blend System I (LL3001/LD200) at 150 °C. The processability in capillary extrusion of the individual components and their blends are determined in terms of the onset of melt fracture phenomena, i.e. the critical shear rates and stresses at which extrudate distortions appear. In general, there are three types of 123  instabilities which might occur in the capillary extrusion of polyolefins (Hatzikiriakos and Migler, 2005). First, there is a critical shear stress at which small amplitude periodic distortions appear on the extrudate surface and these phenomena are known as surface melt fracture or sharkskin (Migler, 2005). At higher apparent shear rate values and in spite of the fact a fixed volumetric flow is used, the pressure and thus the shear stress oscillates between two extreme values due to a combination of wall slip and melt compressibility. This phenomenon is known as stick-slip and/or oscillating melt fracture (Georgiou, 2005). At higher shear stress values the flow becomes again steady, although gross distortions appear on the surface of the extrudate. The latter phenomena associated with gross extrudate distortions are collectively known as gross melt fracture (Dealy and Kim, 2005). As discussed above the results for the first set of blends are plotted in Figure 5-1. For pure LLDPE, the onset of sharkskin was observed to occur at a critical wall shear stress value of 0.19 MPa, a value consistent with other reported values in the literature (Ramamurthy, 1986; Hatzikiriakos and Dealy, 1992). Table 5-1 lists all critical shear rate and stress values for the onset of all three types of instabilities at 150 ° C. It is noted that sharkskin and stickslip phenomena does not occur in the case of pure LDPE-I, again consistent with previous reports (Ramamurthy, 1986). Addition of up to 20wt% of LDPE into LLDPE does not seem to influence the critical values for the onset of surface melt fracture, which completely disappears at amounts of LDPE higher than 50vvt%. The onset of stick-slip phenomena was found to gradually disappear with increasing amount of LDPE and this is discussed below into more detail. Finally, the onset of gross melt fracture of blends seems to shift to smaller critical shear stress values with increase of LDPE amount, an observation consistent with the critical shear stress values of the pure components. Similar results were obtained at 190 ° C as can be seen from the second part of Table 5-1. Figure 5-2 plots the flow curves of the pure components and their blends in system II, LL3001/EF606. Again, due to significant viscosity mismatch, no effect on the flow curve can be seen up to addition of 20wt% of LDPE-II (EF606). Table 5-2 lists the critical shear rate and stresses for the onset of gross melt fracture phenomena. The results are similar to those reported for blend system I discussed earlier. First, sharkskin is not eliminated with the addition of small amounts of LDPE (i.e. no effect up to 20%). The effect on stick-slip is evident even at small amounts of LLDPE i.e. the amplitude of the oscillations gradually  124  decrease even at amounts as low as 1 wt% LDPE. Finally, the onset of gross melt fracture of blends seems to shift to smaller critical shear stress values with increase of LDPE amounts.  Table 5-1. Critical shear rates and stresses for Blend I (LL3001/LD200) at 150 ° C and 190 ° C 150 ° C Polymer  Sharkskin MF crw (MPa;  i  )  A (s - 1  Stick-slip )  aw (MPa;  Gross MF  2 1 A (s 1 )  a w (MPa;  Y, 4 (s -1)  )  LLDPE (LL3001)  0.19  50  0.40-0.31  230  0.42  700  1% LDPE  0.19  50  0.37-0.28  250  0.42  800  5% LDPE  0.19  50  0.34-0.26  300  0.41  700  10% LDPE  0.18  50  0.33-0.27  350  0.40  550  20% LDPE  0.17  50  -  -  0.46  700  50% LDPE  0.16  80  -  -  0.23  180  75% LDPE  -  -  -  -  0.14  100  0.13  400  LDPE-I (LD200)  190 °C  Stick-slip  Sharkskin MF  Gross MF  ow (MPa)  j124 (s -1 )  ov (MPa)  21 A (s 1 )  avv (MPa)  fi A 0 1 )  (LL3001)  0.17  90  0.42-0.39  850  0.41  1100  1% LDPE  0.17  100  0.41-0.39  950  0.42  1100  5% LDPE  0.17  100  0.42-0.41  950  0.41  1100  10% LDPE  0.17  100  -  -  0.42  950  20% LDPE  0.16  100  -  -  0.41  950  Polymer  -  LLDPE  125  LiD=16 D=0. 762 mm. T= 150° C  2  ^ck  co  • • • •  2 a  ; 1a ^  a  W^ cé ^a 4 •^• •  A  A  • ••  ,  0.1  • •  6ci cp  • •  A •^•  Co  co  0.01  o  LLDPE (LL3001) 1% LDPE II (EF606) • 5% LDPE II (EF606) o 10% LDPE (EF606) A 20% LDPE II (EF606) A 50% LDPE II (EF606) • 75% LDPE II (EF606) • LDPE II (EF606)  10 1^102^103 Apparent shear rate,  A  ')'  ^  104  (S -1 ).  Figure 5-2. The apparent flow curves of blends in Blend System II (LL3001/EF606) at 150 °C.  Figures 5-3 and 5-4 depict the flow curves of blends of system III (LL3001/6621) and system IV (LL3001/1321) respectively. Viscosities of the two pure components in both these blend systems are closer. However, the effect of LDPE addition into LLDPE on their processability is similar to those reported above for the other two blend systems. The critical shear rate and shear stress values for the onset of melt fracture phenomena are listed in Tables 5-3 and 5-4 respectively. It is noted that the onset of gross melt fracture for the LDPE III (6621) and LDPE-IV (1321) occur at very low rates, less than 15 s  -1  for both resins.  Figures 5-5 to 5-8 show images of the typical extrudate appearances for the four blend systems at selected apparent shear rates (15, 100, 350 and 1000 s -1 ). In all blend systems similarities can be observed. Smooth extrudates are obtained at 15 s -1 in most cases, sharkskinned extrudates at 100 s-1, stick-slip or oscillating melt fractured extrudates at 350 s and finally gross melt fractured extrudates at 1000 s -1 .  126  Table 5 2. Critical shear rates and stresses for Blend System II (LL3001/EF606) at 150 ° C a -  190 ° C  150 ° C Polymer  Sharkskin MF ow (MPa,  )%A  (S 1 )  Stick-slip ow (MPa,  Gross MF  I1 A (S -1 )  ow (MPa;  2 A (s - 1 )  LLDPE (LL3001)  0.19  50  0.40-0.31  230  0.42  700  1% LDPE  0.19  50  0.39-0.35  350  0.44  900  5% LDPE  0.17  50  0.40-0.37  350  0.42  700  10% LDPE  0.18  50  0.41-0.4  450  0.44  600  20% LDPE  0.17  50  -  -  0.48  600  50% LDPE  0.17  80  -  -  0.19  100  -  -  0.15  80  0.104  90  75% LDPE  -  LDPE ll -  (EF606) 190 °C  Sharkskin MF  Stick-slip  Gross MF  Polymer  ow (MPa)  f1 A (S -1 )  ow (MPa)  2 1. A 0 1 )  aw (MPa)  2 A (S -1 )  LLDPE (LL3001)  0.16  90  0.42-0.39  850  0.41  1100  1% LDPE  0.16  90  0.41-0.39  900  0.41  1100  5% LDPE  0.16  90  0.40-0.39  900  0.41  1100  LDPE  0.15  90  -  0.4  950  20% LDPE  0.15  90  -  -  -  10%  _  127  L/D=16 D=0.762 mm^  A  A A  17 * AiAA^ AA ,e, A T=150 0 0^, i 0 fig ..I '. 1  ,,  g 41 *4 ; • *** yu• y • •  , ^ • o LLDPE (LL3001) el V !^ •^x 1% LDPE III (6621) • • 5% LDPE III (6621) ^ 10% LOPE III (6621) • ► 20% LDPE III (6621) •^ • 50% LOPE III (6621) i^ • 75% LDPE III (6621) • LDPE III (D0W6621)  10'  ^  10 2  ^  103  ^  104  Apparent shear rate, "'A (s ). Figure 5-3. The apparent flow curves of blends in Blend System III (LL3001/662I) at 150 °C. 1  L/D=16 D=0.762 mm a_  6, 40  T=150 ° C  A A^1.21  1 0  *  #^•  •  U) U)  CU as  .c an  co  0.1  I  • • ■ • A  • •  LLDPE (LL3001) 1% LDPE IV (1321) 5% LDPE IV (1321) 10% LDPE IV (1321) 20% LDPE IV (1321) 50% LDPE IV (1321) 75% LDPE IV (1321) LDPE IV (1321)  10 1^102^103  ^  104  Apparent shear rate, J A (S -1 ). Figure 5 - 4. The apparent flow curves of blends in Blend System IV (LL3001/1321) at 150 °C  128  Table 5 3. Critical shear rates and stresses for Blend System III (LL3001/6621) at 150 °C. -  Sharkskin MF Polymer  ow (MPa)  Stick-slip  fi A (s-1)  6w  (MP a)  Gross MF  f1 A (S-1)  6w  (VEN)  2f 1 (s 1) i  LLDPE (LL3001)  0.19  50  0.40-0.31  230  0.42  700  1% LDPE  0.19  50  0.37-0.30  300  0.42  700  5% LDPE  0.19  50  0.36-0.32  300  0.39  700  10% LDPE  0.19  50  0.37-0.34  300  0.43  700  20% LDPE  0.19  50  -  -  0.40  300  50% LDPE  0.19  50  -  -  0.17  40  75% LDPE  0.17  50  -  -  0.13  25  0.09  15  LDPE-III (6621)  Table 5 4. Critical shear rates and stresses for Blend System IV (LL3001/1321) at 150 ° C -  Sharkskin MF Polymer  crw (1VIPa)  2 i A (s  Stick-slip 1)  Gross MF  f1i w (MPa)  IA (s 1)  ow OVIPa)  2i A (s 1)  LLDPE (LL3001)  0.19  50  0.40-0.31  230  0.42  700  1% LDPE  0.18  50  0.39-0.35  350  0.43  700  5% LDPE  0.18  50  0.45-0.41  350  0.42  700  10% LDPE  0.19  50  0.40-0.36  300  0.40  500  20% LDPE  0.19  50  -  -  0.41  300  50% LDPE  0.2  50  -  -  0.23  70  75% LDPE  0.17  50  0.16  30  0.10  15  -  -  LDPE-IV (1321)  129  Figure 5-5. Images of extrudates for Blend system I (LL3001/LD200) extruded at 150 °C. 15^100^I^350^1000  MOPE (LL3001),  PA) LDPE I  IOW* LDPE I  130  Figure 5-6. Images of extrudates for Blend system II (LL3001/EF606) extruded at 150 °C.  r^),^15^100  350  131  Figure 5-7. Images of extrudates for Blend system III (LL3001/6621) extruded at 150 °C. 04 );^15^100^350^1000  I LLDPE (LL3001)  5% UWE MI  1 10 Yo LDPE M (  r 260A  LDPE M  I 50% LDPE Mi  1 75%  LDPE  LIPPE (6624  M  132  Figure 5-8. Images of extrudates for Blend system IV (LL3001/1321) extruded at 150  AO 4 Y  °C.  1000  LLDPE LL3001)  I 5% LIME PI  ;  UWE nr:  2o1/4 LDPE  50% LDPE  Lan IVi  LIM IV; 0324  133  5.3.2. Stick-slip Flow Regime As discussed above pressure oscillations were obtained in the capillary extrusion of LLDPE and LLDPE with the addition of LDPE up to about 1 Owt%. In all blends systems (IIV) these stick-slip or oscillating instabilities were eliminated with the incorporation of 20wt% of LDPE. It is noted that pure LDPE does not exhibit such a flow regime. It was also noted that the addition of even large amounts of LDPE have little effect on the sharkskin and gross melt fracture behavior of LLDPE. Strikingly, the addition of only 1 wt% of LDPE into LLDPE has a significant effect on the oscillating melt facture of LLDPE as can be seen in Figures 5-9 to 5-12. The amplitude of the oscillations gradually decreases with increasing amounts of LDPE starting from even lwt%. Figure 5-13 plots the amplitude of the oscillations as a function of the LDPE wt% addition. In all blend systems the amplitude decreases with increasing amount of LDPE (wt%). At 20wt% of LDPE no pressure oscillations exist as these have been eliminated due to the presence of sufficient amount of long branches. Such effects at small LDPE concentrations could not be detected up in shear rheology cf. Chapter 2. For instance, the blends with 1 wt% LDPE essentially shows the exact same shear behavior with the pure LLDPE in both capillary and parallel-plate rheometrical tests. Small differences could only be seen in extensional rheology only at high extensional rates i.e. greater than 5s -1 and only for the blends that include the LDPEs with the highest molecular weights. This is clearly illustrated in Chapter 2 (see Figure 2-9). Therefore, the oscillating flow regime is sensitive to the presence of long chain branching. Since stick-slip is a phenomenon due to the combined effects of wall slip and compressibility (Georgiou, 2005). It seems that long branches suppress slip effects to certain extend. Finally, the consistency of the above observations, even at 1% and 5% of wt% of LDPE also supports that the individual components were thoroughly mixed.  134  27  LLDPE (LL3001)  25 F2 23 or)  24  1% LDPE I (L^0) /I  2 22 20 X18  Cr_  16 24  5% LDPE I (LD200)  16 23 CL 21 ri) 19 or)  20% LOPE I (LD200)  28 EL 26 2 c1) 24 5  0) 22 0_ 20 0  ^  50^100^150 Time (s)  ^  200  Figure 5-9. Pressure oscillations in capillary extrusion of LL3001/EF606A blends at yA350.sH and 150 ° C.  135  27 "Fe a- 25  LLD PE (LL300 1)  23  O13) 21  a  19 27  a2  1% LDPE II (EF606)  23  vs !di 21  a. 19 29  ca 0-  27  2 25 0)  as 23  a 21 29  10% LDPE II (EF606)  2277 25 cvpi23 ) .  .  a 21 29  20% LOPE II (EF606)  0- 27 2  a.-) 25 co ai 23  a  21 0^5 010 0^150  Time (s)  200  Figure 5 10. Pressure oscillations in capillary extrusion of LL3001.32/EF606 blends at ff, = and 150 °C. -  400s -1  136  LLDPE (LL3001)  23 rn  19 -17 2 15 co  co co a) 1 3  a  11 25  a_ 23 cu, 21 co 19  a)  O: 17 ca  27  a 25 2 223 T, Q.  19  20% LDPE III (6621)  29 0  -  2  27  0) 25  co 01 23  L. 21 0  50  s) 150  200  Figure 5-11. Pressure oscillations in capillary extrusion of LL3001/662I blends at y A = 350s ' and 150 °C. -  137  iki l 1\I  LLD PE (LL3001)  3j  ill'  l  1  tiii  1% LDPE IV (1321)  27 225 223 0)  T,21  a 19  5% LDPE IV (1321)  31 a2  2  a  •  • 2  10% LDPE IV (1321)  29 13-  27  2 E 25  I  Cl) 23 a 21 30  •  20% LDPE IV (1321)  28 26 0)  24  a 22 50^.100^150  Time (s)  200  Figure 5-12. Pressure oscillations in capillary extrusion of LL3001/132I blends at 2;,, = °C.  350s ' and 150 -  138  EL 6  • o •  0  -• -  2 c 5 0  A  •  LLDPE-LDPE I (LD200) LLDPE-LDPE II (EF606) LLDPE-LDPE III (6621) LLDPE-LDPE IV (1321)  •  m —4 (/)  3  • A  2  0  n. E  0  0 ^ ^ ^ ^ 0.00 0.05 0.10 0.15 0.20  w% LDPE Figure 5-13. The amplitude of pressure oscillations as a function of w% of LDPE for blends in the four systems extruded at 150 ° C  5.4. Conclusions. The processing behavior of a number of LLDPE/LDPE blends with emphasis on the effects of long chain branches was studied extensively in this chapter. A Ziegler-Natta, linear low-density polyethylene was blended with four low-density polyethylene LDPE's having distinctly different molecular weights. Capillary extrusion experiments revealed that the onset of sharkskin and gross melt fracture are slightly influenced with the addition of LDPE into LLDPE. However, it was found that the amplitude of the oscillations in the stick-slip flow regime, decreases consistently with the weight fraction of LDPE. Amounts as low as 1% wt of LDPE have a significant effect on the amplitude of pressure oscillations. These effects are clearly due to the presence of LCB. Since stick-slip is a phenomenon due to the combined effects of wall slip and compressibility, the presence of LCB certainly suppresses wall slip effects. Furthermore, it was observed that the onset of this flow regime was shifted to higher shear rates with increase of LDPE content.  139  On the other hand, it was observed that shear rheology is not sensitive enough to detect the addition of small levels of LDPE. Extensional rheology (uniaxial extension) can detect levels of LDPE as small as 1 wt% only at high Hencky strain rates (typically greater than 5 s -1 ) and only for certain blends, particularly those with LDPE of high molecular weight (blend systems III and IV) It is suggested that the magnitude of oscillations is a sensitive method capable of detecting low levels of LCB and therefore can possibly be used for this purpose.  140  5.5. References. Arnal, ML, Sanchez, Muller AJ (2001) Miscibility of Linear and Branched Polyethylene by Thermal Fractionation: Use of the Successive Self-nucleation and Annealing (SSA) Technique, Polymer, 42: 6877-6890. ,  Cho K, Lee BH Hwang K, Lee H, Choe S (1998) theological and mechanical properties in polyethylene blends. Polym Eng Sci 38: 1969-1975 Dealy JM; Kim, S (2005) Gross melt fracture in extrusion, in Polymer Processing Instabilities: Control and Understanding, S.G. Hatzikiriakos and Migler K.B. (Eds), 207-236, Marcel Dekker, NY. Dealy, JM and Wissbrun KF' (1990) in Melt Rheology and its Role in Plastics Processing Theory and Applications. Van Nostrand Reinhold, New York Delgadillo-Velazquez, 0; Hatzikiriakos, SG; Sentmanat, M (2007) Thermorheological Properties of LLDPE/LDPE Blends Rheol. Acta, 47: 19-31 Fang, Y, Carreau, PJ, Lafleur, PG (2005) Thermal and Rheological Properties of mLLDPE/LDPE Blends Polym. Eng. Sci. 45: 1254-1269. Gabriel C, Miinstedt H (2003) Strain hardening of various polyoleftns in uniaxial elongational flow J Rheol 47: 619-630 Georgiou, G (2005) Stick-slip Instability, in Polymer Processing Instabilities: Control and Understanding, S.G. Hatzikiriakos and Migler K.B. (Eds), 161-206, Marcel Dekker, NY. Hatzikiriakos SG, Migler KB (ed) (2005) Polymer processing instabilities. Control and understanding Marcel Dekker, New York Hatzikiriakos, SG; Dealy,JM (1992) Wall slip of molten high density polyethylene. II. Cappillary rheometer studies, J. Rheol. 36: 703-741 . Hatzikirikos, S.G (2000), Long chain branching and polydispersity Effects on the Rheological Properties of Polyethylenes. Polym Eng Sci 40: 2279-2287 Ho K, Kale L, Montgomery S (2002) Melt strength of linear-low density polyethylene/low density polyethylene blends. J Appl Polym. Sci 85: 1408-1418 Lee, HS and Denn, MM (2000), Blends of Linear and Branched Polyethylenes, Polym. Eng. Sci., 40: 1132-1142. Migler, KB (2005) Sharkskin Instability in extrusion, in Polymer Processing Instabilities: Control and Understanding, S.G. Hatzikiriakos and Migler K.B. (Eds), 121-160, Marcel Dekker, NY. Miinstedt H, Steffl T, Malmberg A (2005) Correlation between rheological behavior in uniaxial elongation and film blowing properties of various polyethylenes. Rheol Acta 45: 14-22 Perez R, Rojo E, Fernandez M, Leal V, Lafuente P, Santamaria A (2005) Basic and applied Theology of m-LLDPE/LDPE blends: miscibility and processing features, Polymer 46: 8045-8053 Ramamurthy AV (1986) Wall slip in viscous fluids and influence of materials of construction, J.  141  Rheol. 30: 337-357. Sentmanat ML (2003) Dual windup extensional rheometer. US Patent No. 6,578,413 Sentmanat, M (2004) Miniature universal testing platform: from extensional melt rheology to solid state deformation behavior. Rheol Acta 43: 657-699 Utracki, L.A. (1989) in Polymer Alloys and Blends. Thermodynamics and Rheology, Hanser, Munich, Vienna, New York. Wagner MH, Kheirandish S, Yamaguchi M (2004) Quantitative analysis of melt elongational behavior of LLDPE/LDPE blends. Rheol Acta 44: 198-218 Wignall, GD, Alamo, RG, London, JD, Mandelkern, L, Kim, MH Lin, JS, Brown, GM (2000) Morphology of Blends of Linear and Short-Chain Branched Polyethylenes in the Solid State by Small-Angle Neutron and X-ray Scattering, Differential Scanning Calorimetry, and Transmission Electron Microscopy, Macromolecules, 33: 551-561. Yamaguchi M, Abe S (1999) LLDPE/LDPE blends I. Rheological, thermal and mechanical properties. J Appl Polym Sci 74: 3153-3159  142  6. CAPILLARY EXTRUSION STUDIES OF LLDPE/LDPE BLENDS: EFFECT OF MANUFACTURING TECHNOLOGY OF LLDPE AND LONG CHAIN BRANCHING. 5 6.1. Introduction. The processability of linear low-density polyethylenes (LLDPEs) can be improved by blending with a small amount of a low-density polyethylene (Utracki, 1989; Lee and Denn, 2000; Fang et al., 2005). However, due to structural differences between resins, many undesirable effects may occur such as immiscibility of the components and undesirable morphological changes (Arnal et al., 2001; Wignall et al., 2000) as well as premature onset of flow instabilities (Utracki, 1989; Perez et al., 2005). These effects obviously influence the economic feasibility of the processes as well as the mechanical properties of the final products (Utracki, 1989; Cho et al., 1998; Yamaguchi and Abe, 1999; Ho et al., 2007). In Chapter 2 we studied the miscibility between a Ziegler-Natta hexane copolymer of LLDPE (ZN-LLDPE) and four branched polyethylenes (LDPEs). It was found that these blends are immiscible at high LDPE concentrations (typically grater than 20 wt%) and miscible at smaller LDPE weight concentrations; besides, extensional rheometry was found sensitive to the addition of LDPE. The processing behavior of the same blends was also studied in Chapter 5. It was found that in capillary extrusion, the onset of sharkskin and gross melt fracture are slightly influenced with the addition of LDPE into ZN-LLDPE. However, the amplitude of the oscillations in the stick-slip flow regime was found to scale well with the weight fraction of LDPE. In particular, amounts as low as 1 wt% of LDPE were observed to have a significant effect on the amplitude of pressure oscillations. These effects are clearly due to the presence of LCB. Furthermore, it was observed that the onset of this flow regime was shifted to higher shear rates with increase of LDPE content. For metallocene LLDPE's the controlled MWD and branching content given by metallocene catalysts makes feasible to study the effect of M,„ MWD and LCB on the linear 5  A version of this chapter has been accepted for publication. Delgadillo-Velkquez, 0.; Hatzikiriakos, S.G. (2008), Capillary extrusion studies of LLDPE/LDPE blends: Effects of manufacturing technology of LLDPE and long chain branching, International Polymer Processing, in press.  143  viscoelastic behavior separately (Wood-Adams and Dealy, 2000; Wood-Adams et al., 2000; Wood-Adams, 2001; Malmberg et al., 2002; Wei et al., 2007). Thus, the thermorheological behavior of a metallocene polyethylene is quite different than a Ziegler-Natta one. In fact, in Chapter 3 we studied the thermorheology and miscibility of four different blends systems, consisting of two metallocene-LLDPE's (one butene and one octene) blended with a LDPE, and two Ziegler-Natta LLDPE's (one hexene and one octene copolymer) blended with the same LDPE. It was observed that blends of both m-LLDPE's with LDPE shown better miscibility than the respective blends with ZN-LLDPE. Hence, mLLDPE/LDPE blends should possess different processing behavior than ZN-LLDPE/LDPE blends. In this chapter, we study systematically the processing behavior of four LLDPE's blended with a single LDPE studied rheologically in Chapter 3. Two Zielger-Natta LLDPE's were used in this study (one hexene and one octene copolymer) and two metallocene-LLDPE's (one butene and one octene). The processability of all blends is studied in detail in capillary rheometry in order to determine the effects molecular structure of LLDPE on the onset of flow instabilities known as melt fracture. We are interested to know how the addition of various amounts of LDPE (of varying molecular weight) can affect the onset of flow instabilities such as surface, oscillating and gross melt fracture of the particular LLDPE. In addition, how the details of flow, particularly the magnitude and period of oscillations are influenced by the presence of small amounts of LDPE. It was found oscillating melt fracture flow details are extremely sensitive to subtle changes in the structure of polymers.  6.2. Experimental. 6.2.1. Polyethylene resins and blends. The metallocene LLDPE resins used in this study were an octene copolymer (AffinityPL1840G), supplied by Dow Chemicals, a butene copolymer produced by ExxonMobil (Exact3128). In addition, two Ziegler-Natta LLDPE were used, an hexene copolymer, produced by ExxonMobil (LL3001) and an octene copolymer (Dowlex2045G), supplied by Dow Chemicals. The LDPE resin used in this work is 6621 provided by Dow Chemicals. All of the above LLDPE's have a similar Melt Index value  144  (MI); of around 1, whereas the LDPE resin has a much lower value of MI. The metallocene LLDPE resins have been labeled as m-LLDPE I and m-LLDPE II for the butene and octene copolymers, respectively; likewise the Ziegler Natta LLDPE has been labeled as ZN-LLDPE I and ZN-LLDPE II for the hexene and octene copolymers. Table 3-1 lists all the polymers used along with their melt indices and densities. The LDPE resin was melt blended respectively with each LLDPE resin in order to create LDPE/LLDPE blends having weight compositions of 99/1, 95/5, 90/10, 80/20, 50/50 and 25/75. The blending was performed as follows: the original components were mixed and grinded in a Brabrender mixer in order to reduce their pellet size to ensure their thoroughly mixing. Then, the mixture in the form of flakes was blended into a single screw extruder, at low processing speed (20 rpm), using a screw having mixing elements near to the end of the metering zone. The temperature of the die was kept at 160 °C. The extrudates were then pelletized for easy handling. The blend 99/1 was produced in two dilution steps, the first being the 95/5. The final blends between the different LLDPE's with the LDPE (6621) are labeled as follows: the two Zigler-Natta blend systems as, ZNLLDPE I/LDPE and ZN-LLDPE II/LDPE respectively, and the two metallocene blend systems as m-LLDPE ULDPE and m-LLDPE II/LDPE respectively.  6.2.2. Rheological techniques. Parallel-plate rheometry was performed to determine the linear viscoelastic properties of the pure components and their blends. Experiments performed at different temperatures, namely, 130°C, 150°C, 170°C, 190°C, and 210°C. Mastercurves were obtained at the reference temperature of 150°C. The pure components and their blends were rheologically characterized in simple extension using the SER Universal Testing Platform. The results and details on the linear viscoelasticity and extensional rheology of all blends can be found in chapter 3. Capillary extrusion measurements were conducted at 150 ° C using a capillary die having a diameter equal to 0.762 mm and a length-to-diameter ratio, L/D, equal to 16. The onset of melt flow instabilities (melt fracture) was determined for the pure resins and their blends. The surface of the extrudates was analyzed with an Olympus MIC-D microscope, similarly as in chapter 5. Selective images of the extrudates are presented here.  145  6.3. Results and discussion 6.3.1. Capillary rheometry. The flow curves of the pure components and those of their blends, were determined at 150 °C by means of the capillary rheometer as described above. For the first set of blends, ZN-LLDPE I (LL3001)/ LDPE (6621), the results were presented already in Chapter 5 (see Figure 5-3). Viscosities of the two pure components in both these blend systems are close to each other; however, addition of LDPE up to 20% composition, does not seem to have a significant effect on its viscosity and the processability of the blends and the flow curves seem to overlap. Differences can clearly be seen only at concentrations as high as SOwt% in LDPE. As discussed above, the onset of gross melt fracture for the LDPE occur at very low shear stress, less than 0.08 MPa. For pure ZN-LLDPE I, the onset of sharkskin was observed to occur at a critical wall shear stress value of 0.19 MPa, a value consistent with reported values in the literature (Ramamurthy, 1986; Hatzikiriakos and Dealy, 1992). The critical shear rate and stress values for the onset of all three types of instabilities at 150 ° C were listed in the Chapter 6 (Table 6-3). It is noted that sharkskin and stick-slip phenomena does not occur in the case of pure LDPE, again consistent with previous reports (Ramamtzthy, 1986). Addition of up to 20wt% of LDPE into LLDPE does not seem to change the critical values for the onset of surface melt fracture behavior, which completely disappears at amounts of LDPE higher than 50wt%. The onset of stick-slip phenomena was found to gradually disappear with increasing amount of LDPE and this is discussed below into more detail. Finally, the onset of gross melt fracture of blends seems to shift to smaller critical shear stress values with increase of LDPE amount, an observation consistent with the critical shear stress values of the pure components. Figure 6-1 plots the flow curves of the pure components and their blends in system II, ZN-LLDPE II (Dowlex)/LDPE (6621). Again, due to significant viscosity mismatch, no effect on the flow curve can be seen up to addition of 20wt% of LDPE. Table 6-1 lists the critical shear rate and stresses for the onset of gross melt fracture phenomena. The results are similar to those reported for blend system I; as discussed above, sharkskin is not eliminated with the addition of small amounts of LDPE (i.e. no effect up to 20%). The effect on stickslip is evident even at small amounts of LLDPE i.e. the oscillations disappear at amounts as  146  low as 5 wt% of LDPE. Finally the onset of gross melt fracture of blends seems to shift to smaller critical shear stress values with increase of LDPE amount. 1.0  L/D= 16 D= 0.762 T= 150 °C  0o a  a0  •  4.4,01 4 ^— ••  V  8  ,  Yv • „ , • ••  4 • ••-  n  4  ••  o • • • •  • • •  10 1  ^  102  ZN-LLDPE 11 (Dowlex) 20% LDPE (6621) 50% LDPE (6621) 75% LDPE (6621) LDPE (6621)  ^  Apparent shear rate,;5.A (s "1  10 3 )  Figure 6-1. The apparent flow curves of blends in Blend System II (Dowlex/662D at 150 °C.  Table 6-1.^Critical^shear rates^and stresses^for Blend^System II, ZN-LLDPE (DOWLEX)/LDPE(6621) at 150 ° C.  Sharkskin MF Polymer  Stick-slip  Gross MF 2,1^(s -1  crw (MPa)  ):,4 (s 4 )  aw (MPa)  2:A (s 4 )  aw (MPa)  0.23  70  0.43-0.40  700  -  1% LDPE  0.22  70  0.43-0.4  700  -  5% LDPE  0.23  70  -  -  -  -  10% LDPE  0.23  70  -  -  0.56  1500  20% LDPE  0.23  70  -  -  0.425  400  50% LDPE  0.11  15  -  -  0.18  40  75% LDPE  0.09  10  -  -  0.13  20  -  -  -  -  0.08  15  LLDPE  )  -  (DOWLEX)  LDPE  -  (6621)  147  Figures 6-2 and 6-3 depict the flow curves of blends with metallocene-LLDPE's, system III (m-LLDPE I/6621) and system IV (m-LLDPE II/6621). The effect of the addition of LDPE into LLDPE on their processability is similar to those reported above for the first two blend systems. Only at 75 wt% LDPE composition a difference in the flowcurve is observed. The critical shear rate and shear stress values for the onset of melt fracture phenomena are listed in Tables 6-2 and 6-3 respectively. In contrast to the other LLDPE resins, the metallocene octene copolymer (m-LLDPE II-Affinity) exhibits no stick-slip regime. As observed in chapter 6, LCB suppress such flow oscillations. Although m-LLDPE II is a metallocene-LLDPE and exhibits no strain hardening, and in view of its significant shear thinning, it is reasonable to assume that processes a small degree of LCB in its molecular structure. Furthermore, as discussed in chapter 4, a high value of activation energy (58.7 kJ/mol), and complex thermorheological behavior were found for this resin. Both are fingerprints of LCB presence.  LID =16 D = 0.762 mm T=150 ° C  6.0. 4 4* #1 „ v^ • *• Tr •  ••  •  y'Vvir • * • - ^ O..  m-LLDPE I (Exact) 20% LDPE (6621) 50% LDPE (6621) 75% LDPE (6621) LDPE (6621)  • • • •  0.01  10 1^102^lo' Apparent shear rate,  "A (  (s 1 ).  Figure 6-2. The apparent flow curves of blends in Blend System III (Exact/662I) at 150 °C.  148  •  Table 6-2. Critical shear rates and stresses for Blend System III, m-LLDPE(Exact  3128)/LDPE(6621) at 150 ° C. Sharkskin MF  Stick-slip  Gross MF  ffil (s -1 )  crvv (MPa)  )2 ,4 (s 4 )  ow (MPa)  fi,^(S-1)  0.18  30  0.45-0.41  200  0.45  700  1% LDPE  0.18  30  0.46-0.43  200  0.45  600  5% LDPE  0.18  30  0.45 0.44 -  400  0.46  500  10% LDPE  0.19  30  -  -  0.45  200  20% LDPE  0.18  30  -  -  0.43  125  50% LDPE  0.14  20  -  -  0.25  600  75% LDPE  0.08  10  -  -  0.63  30  -  -  -  -  0.08  15  Polymer  ow (MPa)  LLDPE  (Exact 3128)  LDPE  (6621)  1  LID = 16 D= 0.762 mm T= 150 °C  •  a • •  •  •A •• • •  ts a A iAgg : 411i • • * A^ • •• • o •  A ▪ •  m-LLDPE H (Affinity) 209/0 LDPE (6621) 50% LDPE (6621) 25% LDPE (6621) LDPE (6621)  10 1^102^  1o3  Apparent Shear Rate, IA (s 1 )  Figure 6-3. The apparent flow curves of blends in Blend System IV(Affinity/662I) at 150 °C.  149  Table^6-3.^Critical^shear^rates^and^stresses^for^Blend^System^IV,^mLLDPE(Affinity)/LDPE(662I) at 150 ° C.  Sharkskin MF Polymer  Stick-slip  Gross MF  ow (MPa)  ,i,4^(s-1)  ow (MPa)  ),,,^(s-1)  crw (MPa)  ;?,4^(s -i )  0.14  30  -  -  0.43  300  1% LDPE  0.13  30  -  -  0.43  300  5% LDPE  0.15  30  -  -  0.44  300  10% LDPE  0.15  30  -  -  0.45  300  20% LDPE  0.15  30  -  -  0.36  175  50% LDPE  0.09  10  -  -  0.18  40  75% LDPE  0.09  10  -  -  0.12  20  -  -  -  -  0.08  15  LLDPE (DOWLEX)  LDPE (6621)  Figures 5-7 (for blend system I) and 6-4 to 6-6 (for bend systems II to III) show images of typical extrudate appearances at selected apparent shear rates (15, 100, 350 and 1000 s -1 ). In all blend systems similarities can be observed. Smooth extrudates are obtained at 15 s -1 in most cases, sharkskinned extrudates at 100 s -1 , stick-slip or oscillating melt fractured extrudates at 350 s -1 and finally gross melt fractured extrudates at 1000 s -1 .  150  Figure 6-4. Images of extrudates for Blend system II (Dowlex/6621) extruded at 150 .C.  151  Zg I  11 i , I^I'^1111 II 11111 1-  if  ^  I  000T^0i£^OOT Do OSI 3E PP 11-14 x 3 (IZ99/ 4 DEx) III tillsAs PwIa 103 sawpralxa Jo sa&urf -s-9 ani2u  Figure 6-6. Images of extrudates for Blend system III (Exact/6621) extruded at 150 °C.  1000  Affinity (LL3001)  1 1 111 I 1  1  1094 LDPE  2096 LDPE  1•1111=11111M S^M111111=11111■1111^IM111111=111111!^11111=111111=^11111=1111111=11■MMIV^MIMI=^11111=1111=11•1  509 6 LDPE ,  ^I 1^. ,^. :1 I  iI 1: I II 1 i  r  ^1 :k^ ^... ^1  1  i  i  !^':{utinifi^  1  1 III  I.^  153  6.3.2. Stick-slip flow regime As discussed above pressure oscillations were obtained in the capillary extrusion of LLDPE and its blends with the addition of LDPE. The amount of LDPE needed to eliminate oscillations completely depends on the structure of LLDPE. In blend system I, with the hexane ZN-LLDPE component (ZN-LLDPE I) these stick-slip or oscillating instabilities were eliminated with the incorporation of 20 wt% of LDPE (see Figure 5-11). For blend system II, with octane ZN-LLDPE (ZN-LLDPE II) the oscillations disappear at 5 wt% of LDPE. In the case of the butane metallocene-LLDPE (m-LLDPE I), stick slip is eliminated with 10 wt% of LDPE. Finally, for the octane metallocene-LLDPE (m-LLDPE II) this regime was not observed due to the presence of small amount of LCB in its structure. As already discussed LDPE does not exhibit oscillating flow regime. It was also noted that the addition of even large amounts of LDPE have little effect on the sharkskin and gross melt fracture behavior of LLDPE. Strikingly, the addition of only 1 wt% of LDPE into LLDPE has a significant effect on the oscillating melt facture of LLDPE as can be seen in Figures 5-11 in chapter 5 and Figures 6-7 and 6-8. The amplitude of the oscillations gradually decreases with increasing amounts of LDPE starting from even 1 wt%. Figure 6-9 plots the amplitude of the oscillations as a function of the LDPE wt% addition. In all blend systems the amplitude decreases with increasing amount of LDPE (wt%). At 20wt% of LDPE no pressure oscillations exist as these have been eliminated due to the presence of long branches. Such effects at small LDPE concentrations could not be detected in shear rheology as observed in chapters 3 and 4. For example, the blends with 1 wt% LDPE essentially show the exact same shear behavior as pure LLDPE in both capillary and parallel-plate rheometrical tests. Small differences could only be seen in extensional rheology only at high extensional rates i.e. greater than 5 s -1 and only for the blends that include the LDPEs with the highest molecular weights. This is clearly illustrated in Figure 3-8 for all blend systems. Therefore, the oscillating flow regime is very sensitive to the presence of long chain branching. Since stick-slip is a phenomenon due to the combined effects of wall slip and compressibility (Georgiou, 2005), it seems that long branches suppress slip effects to a certain extend. The consistency of the rheological measurements, especially those of 1% and 5% wt LDPE clearly supports that all the blends were thoroughly mixed.  154  = 700 sA  ZN-LLDP E H (Dowlex)  Nti 81117\1 1 '1 W1 1  LID= 16 D= 0.762 mm T = 150 ° C  = 700 ,s"  1  1% LDPE (6621)  28 a.  a  LID = 16 = 0.762 mm T= 150 ° C  .  25  A =  700 .3 -1  ^  5° LDPE 6621)  28 es 0a U,  U)  cr.  26  LID =16 D^mm T =150 ° C ^ ^ 120 100 20^40^60^80 Time (s)  Figure 6-7. Pressure oscillations in capillary extrusion of Dowlex/662I blends at y A = 700s - ' and 150 °C  155  30  = 40Cs-' m-LL OPE I (E xaci 3128)  2 29  y 28  LD = 16 D = 0.782 mm T = 150 ° C  27  = 400 s ^1% LDPE (6621)  30  -  E 29  co 28  LD = 16 D= 0• 762 mm 27 T = 150 °C  L.D = 16 D = 0.762 1 27 T = 150 ° C .  30  0_ 2 29 0  LSD = 16 D = 0.762 mm 27 T 150 a C ^ ^ ^ 40^60^60 100 120 0^23 Time (s)  Figure 6-8. Pressure oscillations in capillary extrusion of Exact/662I blends at f/ A = 400s ' and 150 -  156  6 0 5  • ■  ZN-LLDPE I (LL300)/LDPE ZN-LLDPE II (Dowlex)/LDPE A m-LLDPE I (Exact)/LDPE  •■••  ^-  T =150 ° C  ▪ 4 • a ^• 0• 3  • 2 ^A^• ■ A  E 0 ^ 0  ■  A  10  15  20  wt % LDPE Figure 6-9. The amplitude of pressure oscillations as a function of w% of LDPE for blends in the four systems extruded at 150 °C.  6.4 Conclusions. The processing behavior of a number of LLDPE/LDPE blends was studied extensively with emphasis on the effects of type of LLDPE and long chain branching on the processability. Two Ziegler-Natta, and two metallocene linear low-density polyethylenes, having distinctly different molecular architectures, were blended with one low-density polyethylene (LDPE). Capillary extrusion experiments revealed that the onset of sharkskin and gross melt fracture are slightly influenced with the addition of small LDPE amounts into LLDPE. However, it was found that the amplitude of the oscillations in the stick-slip flow regime scales well with the weight fraction of LDPE. Amounts as low as 1 wt% LDPE have a significant effect on the amplitude of pressure oscillations, indicating good mixing conditions. These effects are clearly due to the presence of LCB. Since stick-slip is a phenomenon due to the combined effects of wall slip and compressibility, the presence of LCB certainly suppresses wall slip effects. It is suggested that the magnitude of oscillations is a sensitive methods capable of detecting low levels of LCB at least for resins having similar structure i.e. comonomer type and MWD. 157  6.5. References. Arnal, ML, Sanchez,ller, AJ (2001) Miscibility of Linear and Branched Polyethylene by Thermal Fractionation: Use of the Successive Self-nucleation and Annealing (SSA) Technique, Polymer, 42: 6877-6890. Cho K, Lee BH Hwang K, Lee H, Choe S (1998) rheological and mechanical properties in polyethylene blends. Polym Eng Sci 38: 1969-1975 Dealy JM; Kim, S (2005) Gross melt fracture in extrusion, in Polymer Processing Instabilities: Control and Understanding, S.G. Hatzikiriakos and Migler K.B. (Eds), 207-236, Marcel Dekker, NY. Fang, Y, Carreau, PJ, Lafleur, PG (2005) Thermal and Rheological Properties of mLLDPE/LDPE Blends Polym. Eng. Sci. 45: 1254-1269. Georgiou, G (2005) Stick-slip Instability, in Polymer Processing Instabilities: Control and Understanding, S.G. Hatzikiriakos and Migler K.B. (Eds), 161-206, Marcel Dekker, NY. Hatzikiriakos, SG; Dealy,JM (1992) Wall slip of molten high density polyethylene. II. Cappillary rheometer studies, J. Rheol. 36: 703-741 . Ho K, Kale L, Montgomery S (2002) Melt strength of linear-low density polyethylene/low density polyethylene blends. J Appl Polym Sci 85: 1408-1418 Lee, HS and Denn, MM (2000), Blends of Linear and Branched Polyethylenes, Polym. Eng. Sci., 40: 1132-1142. Malmberg A, Gabriel C, Steffl T, Miinstedt H, Li5fgren B (2002) Long-chain branching in metallocene-catalyzed polyethylenes investigated by low oscillatory shear and uniaxial extensional rheometry. Macromolecules 35: 1038-1048 Perez R, Rojo E, Fernandez M, Leal V, Lafuente P, Santamarfa A (2005) Basic and applied rheology of m-LLDPE/LDPE blends: miscibility and processing features, Polymer 46: 8045-8053 Ramamurthy AV (1986) Wall slip in viscous fluids and influence of materials of construction, J. Rheol. 30: 337-357. Utracki, LA (1989) in Polymer Alloys and Blends. Thermodynamics and Rheology, Hanser, Munich, Vienna, New York. Wei X, Collier JR, Petrovan S (2007) Shear and elongational theology of polyethylenes with different molecular characteristics I. Shear rheology. J App Polym Sci 105: 309-316 Wignall, GD, Alamo, RG, Londono, JD, Mandelkern, L, Kim, MH. Lin, JS, Brown, GM (2000) Morphology of Blends of Linear and Short-Chain Branched Polyethylenes in the Solid State by Small-Angle Neutron and X-ray Scattering, Differential Scanning Calorimetry, and Transmission Electron Microscopy, Macromolecules, 33: 551-561. Wood Adamsand Dealy, JM (2000) Using theological data to determine the branching level in metallocene polyethylenes. Macromolecules 33: 7481-7488 Wood-Adams P (2001) The effect of long chain branching on the shear flow behavior of  158  polyethylene. J Rheol 45: 203-210 Wood-Adams P, Dealy JM, de Groot AW, Redwine David 0 (2000) Effect of molecular structure on the linear viscoelastic behavior of polyethylene. Macromolecules 33: 74897499 Yamaguchi M, Abe S (1999) I ,TDPE/LDPE blends I. Rheological, thermal and mechanical properties. J Appl Polym Sci 74: 3153-3159  159  7. CONCLUSIONS, CONTRIBUTION TO KNOWLEDGE AND RECOMMENDATIONS.  7.1. Conclusions. The thermorheological and processing behavior of several LLDPE/LDPE blend systems were studied. It was found that the presence of long chain branching and the manufacturing technology of LLDPE have a strong influence on the thermorheology of the blends. The thermodynamic behavior of all blends was studied using different rheological techniques and differential scanning calorimetry (DSC). The rheological criteria applied to assess polymer miscibility included time temperature superposition principle (TTS), Van Gurp-Palmen plots, zero-shear viscosity vs. composition plots in semi-log scale, Cole-Cole plots and analysis of the weighted relaxation spectra. Good agreement was found among most of the rheological criteria for immiscibility. Ziegler-Natta LLDPE resins are in general miscible with LDPE at small compositions, usually below 20 wt% in LDPE. Transition to immiscible blends was observed at higher LDPE compositions. On the other hand, metallocene-LLDPE resins were observed to be more miscible with LDPE than their Z-N counterparts. Shear and extensional rheological properties of pure resins and their blends were studied in detail to examine the effects of long chain branching. All LLDPE's studied have shown no deviation from the viscoelastic envelope of 3ri + . On the other hand all LDPE resins observed to exhibit strain hardening, indicating the presence of large amounts of LCB. In the case of the blends, strain hardening was found to be a function of LCB. This was observed to be more evident at Hencky strain rates greater than 5 s -1 . It was also found that strain hardening was also evident even at small LDPE blend compositions such as 1 wt% and 5 wt%. It can be concluded that extensional rheology is a sensitive tool to detect even small amounts of LCB. However, it was found that this is not the case for shear rheology (linear viscoelasticity). An increase of the energy of activation (E a ) with LDPE composition was also established. This is also an indication of the LCB presence in the blends. Additionally the presence of LCB was also observed by the shape of the Van Gurp-Palmen plots. At high  160  LDPE compositions, the blends exhibit high sensitivity to temperature, leading to thermorheologically complex behavior, i.e. good superposition can not be achieved. Hence, the presence of LCB induces thermorheologically complex behavior. The processing behavior of all blend systems as well as those of the pure resins was studied in capillary extrusion. The onset of sharkskin, and gross melt fracture instabilities were slightly influenced by the addition of small LDPE amounts. This was observed for all blend systems. However, the amplitude of oscillations in stick-slip was found to scale well (to decrease) with LDPE addition, an effect clearly caused by the presence of LCB in the blends. Regarding the mixing conditions, the consistency of the effect of LCB in the blends among all rheological methods (especially at very low content of LDPE, i.e. 1% and 5%) together with the trends observed in DSC analysis is a strong indication of good mixing conditions. A final finding of this thesis includes the analysis of the onset of sharkskin and stick-slip melt fracture in the processing of an LLDPE resin using three different die geometries; namely, cylindrical, rectangular slit and annular. The critical apparent shear rate and wall shear stress for the onset of sharkskin was observed to be the highest in the case of annular flow, compared to those in slit and capillary dies. This is because in annular flow, the higher surface area-to-volume aspect ratio of the extrudate's surface provides another degree of freedom for a lower stress state configuration for the material in the area of the exit of the die which is the site of initiation of sharkskin. Stick-slip regime was found to be absent in annular extrusion. In capillary and slit die, the onset of this instability is shifted to higher apparent shear rates when the temperature is increased form 150 ° C to 190 ° C.  7.2. Contribution to the knowledge. Several contributions to knowledge have resulted from this research work. These are identified as follows. 1. The thermorheologically complex behavior of several LLDPE/LDPE blends was studied illustrating the effects of LCB and manufacturing technology of LLDPE's.  161  2. Uniaxial extensional rheology was found to be a sensitive tool to detect small levels of microstructure changes in the blends. Strain hardening was observed in blends of LDPE compositions as low as 1 wt%, when the Hencky strains are greater than 5 s -1 . 3. The sharkskin and oscillatory melt fracture behavior of a LLDPE was studied at two different temperatures simultaneously in capillary, slit and annular flows. Oscillatory melt fracture was observed only in capillary and slit flows. In addition, it was observed that the critical shear rate and stress for the onset of sharkskin in annular flow is considerably higher than those detected in slit extrusion and those higher than the ones determined in capillary flow. This finding has shown that to study melt fracture phenomena in the lab and in to relate them to real polymer processing operations, a capillary extrusion is not enough. 4. Based on observations on point 3, it is proposed that a critical surface stress condition per unit surface area must be achieved for sharkskin to occur. It was also argued that the annular flow allows for a three dimensional spiraling flow that provides additional degrees of freedom for the stress concentration at the exit to be relieved. 5. In capillary extrusion, the amplitude of oscillations in stick-slip decrease with LDPE addition in the blend. This was observed even at small LDPE weight fractions, regardless the molecular weight of the LDPE resin. Hence, the effect of long chain branching can also be inferred in capillary extrusion.  7.3. Recommendations for future work. Several important aspects for the study of LLDPE/LDPE blend miscibility and processing are yet to be studied. These are recommended below for possible future research work. 1. In this study, the information about the macromolecular structure for all polyethylenes was given in terms of the melt index, density and zero-shear viscosity. To have more quantitative information about long chain branching (LCB), molecular weight (MW) and its distribution (MWD), analytical techniques are needed, such as nuclear magnetic resonance ( 13 C NMR), gel permeation chromatography (GPC) (Wood-Adams et al., 2000; Wood-Adams and Costeaux, 2001) and size exclusion chromatography (SEC)coupled with laser light scattering (LALLS) (Gabriel and Miinstedt, 2002) . 162  2. The structure of the co-crystals present in LLDPE/LDPE blends should be studied using microscopy techniques. This will indicate the molecular characteristics of LLDPE and LDPE that make them compatible or incompatible. 3. Given the complex macromolecular structure of LLDPE, in particular ZN-LLDPE, a model is needed to predict the linear viscoelastic behaviour of their blends that takes into account the different phases present in immiscible polyethylenes. Park and Larson (2006) have developed a model that predicts the linear viscoelasticity of binary blends of monodisperse linear polymers. This model can be the basis to include the dynamics of long chain branching and polydispersity. 4. A constitutive equation capable to predict the dependence of strain hardening on LDPE blend composition was developed recently (Wagner et al., 2004). This model could be further validated with the extensional rheology experiments done in this study. 5. The effect of long chain branching on strain induced crystallization needs to be studied in shear and extensional flows. It would be desirable to know if the co-crystals formed under shear or extensional flows, have any effect on the mechanical properties of the blends. 6. The study of melt fracture phenomena in slit die and annular die extrusions, should be extended to metallocene-LLDPE' s and the rest of the blends studied in this work. Such a study can reveal effects of small amounts of long chain branching on stick-slip and sharkskin melt fracture phenomena.  163  7.4. References. Gabriel C, Miinstedt H (2002) Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear. Rheol Acta 41: 232-244 Park, SJ; Larson RG (2006) Long-chain dynamics in binary blends of monodisperse linear polymers. J. Rheol. 50: 21-39. Wagner MH, Kheirandish S, Yamaguchi M (2004) Quantitative analysis of melt elongational behavior of LLDPE/LDPE blends. Rheol Acta 44: 198-218 Wood-Adams P, Dealy JM, de Groot AW, Redwine David 0 (2000) Effect of molecular structure on the linear viscoelastic behavior of polyethylene. Macromolecules 33: 7489-7499 Wood-Adams P, Costeux, S (2001) Thermorheological behavior of polyethylene: Effects of microstructure and long chain branching. Macromolecules 34; 6281-6290  164  APPENDIX A SHIFT FACTORS FOR POLYETHYLENE RESINS AND THEIR BLENDS. The values for the horizontal shift factors calculated in applying the TTS method from the Arrenius equation to produce the mastercurves, at the reference temperature of 150 ° C for all virgin resins and their blends are listed in Tables A-1 to A-7. Table A-1. Horizontal shift factors for LL3001/LD200 blends at T„ T (° C) 130 150 170 190 210  LLDPE LL3001 1.60 1.00 0.65 0.44 0.31  1% LDPE 1.59 1.00 0.66 0.45 0.32  50/0 LDPE 1.62 1.00 0.65 0.43 0.30  10% LDPE 1.63 1.00 0.64 0.43 0.29  20% LDPE 1.64 1.00 0.64 0.42 0.29  Table A-2. Horizontal shift factors for LL3001/EF606A blends at Tr T (°C) 130 150 170 190 210  LLDPE LL3001 1.60 1.00 0.65 0.44 0.31  1°A LDPE 1.60 1.00 0.65 0.44 0.31  5% LDPE 1.60 1.00 0.65 0.44 0.31  10% LDPE 1.60 1.00 0.65 0.44 0.31  f  20% LDPE 1.67 1.00 0.63 0.41 0.28  = 150 ° C  50% LDPE 1.80 1.00 0.59 0.36 0.23  ef  75% LDPE 2.12 1.00 0.50 0.27 0.15  LDPE LD200 1.88 1.00 0.56 0.33 0.21  = 150 °C  50% LDPE 1.87 1.00 0.57 0.34 0.21  Table A-3. Horizontal shift factors for LL3001/6621 blends at Tre f = 150 ° C 50/0 LLDPE 1% 10% 20% T (° C) 50% LL3001 LDPE LDPE LDPE LDPE LDPE 130 1.60 1.04 1.60 1.65 1.70 2.00 150 1.00 1.00 1.00 1.00 1.00 1.00 170 0.65 0.96 0.65 0.64 0.62 0.53 190 0.44 0.93 0.44 0.42 0.40 0.30 210 0.31 0.90 0.31 0.29 0.26 0.18  75% LDPE 2.14 1.00 0.50 0.27 0.15  75% LDPE 2.26 1.00 0.48 0.24 0.13  LDPE EF606 2.40 1.00 0.45 0.22 0.11  LDPE 6621 2.47 1.00 0.44 0.21 0.10  165  Table A-4. Horizontal shift factors for LL3001/132I blends at Tref = 150 C ° 5% LLDPE 1% 10% 20% 50% T CC LL3001 LDPE LDPE LDPE LDPE LDPE 130 1.60 1.64 1.66 1.70 1.80 2.20 150 1.00 1.00 1.00 1.00 1.00 1.00 170 0.65 0.64 0.63 0.62 0.59 0.49 190 0.44 0.42 0.42 0.40 0.36 0.25 210 0.31 0.29 0.28 0.26 0.23 0.14 )  Table A-5. Horizontal shift factors for Dowlex/662I blends at T CC )  130 150 170 190 210  LLDPE Dowlex 1.49 1.00 0.69 0.50 0.37  1% LDPE 1.49 1.00 0.70 0.50 0.37  5% LDPE 1.58 1.00 0.66 0.45 0.32  10% LDPE 1.57 1.00 0.66 0.46 0.32  Tre f =  20% LDPE 1.67 1.00 0.63 0.41 0.27  50% LDPE 1.83 1.00 0.58 0.35 0.22  )  T CC )  130 150 170 190 210  LLDPE Affinity 2.29 1.00 0.47 0.24 0.13  1% LDPE 2.34 1.00 0.46 0.23 0.12  5% LDPE 2.32 1.00 0.46 0.23 0.12  10% LDPE 2.36 1.00 0.46 0.23 0.12  Tre f =  20% LDPE 2.41 1.00 0.45 0.22 0.11  LDPE 1321 2.22 1.00 0.48 0.25 0.14  150 °C  Table A-6. Horizontal shift factors for Exact/662I blends at Tref = 150 °C 5% LLDPE 1% 10% 20% 50% T CC Exact LDPE LDPE LDPE LDPE LDPE 130 1.53 1.53 1.70 1.70 1.70 2.03 150 1.00 1.00 1.00 1.00 1.00 1.00 170 0.68 0.68 0.62 0.62 0.62 0.53 190 0.48 0.47 0.40 0.40 0.40 0.29 210 0.35 0.34 0.27 0.27 0.26 0.17  Table A-7. Horizontal shift factors for Exact/662I blends at  75% LDPE 2.34 1.00 0.46 0.23 0.12  75% LDPE 2.08 1.00 0.51 0.28 0.16  75% LDPE 2.28 1.00 0.47 0.24 0.13  LDPE 6621 2.47 1.00 0.44 0.21 0.10  LDPE 6621 2.47 1.00 0.44 0.21 0.10  150 ° C 50% LDPE 2.58 1.00 0.42 0.19 0.09  75% LDPE 2.62 1.00 0.42 0.19 0.09  LDPE 6621 2.47 1.00 0.44 0.21 0.10  166  LDPE I (LD200) —c— LDPE II (EF606A) LDPE III (6621) ^ LDPE IV (1321) A^ LLDPE (LL3001)  -4  ^  -3  -2^-1^0  ^^  1  2  (1/T —1/Tref x 10 4 , IC' Figure A-1. Horizontal shift factor, (LL3001) and all LDPE resins.  0  co^1  UT,  as a function of (1/T — 1/Tref ), in K 1 for LLDPE -  ZN-LLDPE I (LL3001) —9— ZN-LLDPE II (Dowlex) --N— m-LLDPE I (Exact) - -o-- m-LLDPE II (Affinity) —A-- LDPE (6621)  4.11  4m•  ca  H  0 N IV  0 0.1 -4^-3^-2^-1^0  ^^  1  2  WT —1/Tref ) x10 4 , IC 1 Figure A-2. Horizontal shift factor, U T , as a function of (1/T —1/T ref ), in K -I for LDPE (6621) and all LLDPE resins.  167  APPENDIX B DSC MELTING PEAKS BY DIFFERENT CALORIMETERS. In this appendix, the comparison of melting peaks using 2 different calorimeters are shown for selected resins and blends; namely, the Shimadzu DSC 60 and TA Q1000. The melting thermograms performed with the Shimadzu (DSC 60) calorimeter, were obtained using only the first heating cycle. On the other hand the melting endotherms corresponding to the TA Q1000, were obtained from the second heating cycle. Details for the cooling rates are given in section 4.2.2. In all cases, the agreement of the melting peaks measured with both pieces of equipment is excellent.  LL3001/6621(90/10) -,7"----  0 ti.• 4.1  CU CD  I  I  90  100  110  T  ^DSC 60 Q1000  c c) 120^130  140  Figure B 1. DSC melting thermograms of 90:10 LL3001/662I blend obtained with a Shimadzu DSC 60 and TA Q1000 calorimeters. -  168  LL3001/6621(25/75)  1  0 4.. 4-.  CO  a)  i yr  90  100  110  1,  AL  (°C)^  120  Q1000 ^DSC 60  130^140  Figure B 2. DSC melting thermograms of 25:75 LL3001/662I blend obtained with a Shimadzu DSC 60 and TA Q1000 calorimeters. -  Exact/6621(25/75)  7  ------  0 m4-,  cs a) X  TA ^ DSC 60  70  80  90  T (°C)  100  —  110^120  Figure B 3. DSC melting thermograms of 25:75 Exact/662I blend obtained with a Shimadzu DSC 60 and TA Q1000 calorimeters. -  169  

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