Melt flow singularity in linear polyethylene: influence of molar mass, molar mass distribution and carbon-based fillers

Transcription

1 Loughborough University Institutional Repository Melt flo singularity in linear polyethylene: influene of molar mass, molar mass distribution and arbon-based fillers This item as submitted to Loughborough University's Institutional Repository by the/an author. Additional Information: A Dotoral Thesis. Submitted in partial fulfillment of the requirements for the aard of Dotor of Philosophy of Loughborough University. Metadata Reord: Publisher: Han Xu Please ite the published version.

2 This item as submitted to Loughborough s Institutional Repository ( by the author and is made available under the folloing Creative Commons Liene onditions. For the full text of this liene, please go to:

3 Melt flo singularity in linear polyethylene; Influene of molar mass, molar mass distribution and arbon-based fillers By Han Xu A DOCTORAL THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIRMENTS FOR THE AWARD OF DOCTOR OF PHILOSOPHY OF LOUGHBOROUGH UNIVERSITY Supervisors: Prof. Sanjay Rastogi Prof. Mo Song Department of Materials Loughborough University

4 ABSTRACT In the reent past it has been found that a onsiderable pressure drop ourred during the extrusion of linear polyethylene in the ourse of apillary flo. The pressure drop resides ithin a narro temperature indo of one to to degrees Celsius. In this researh the hydrodynami ondition and moleular origin of the extrusion indo of linear polymer ere investigated further. The advantage of the extrusion indo, viz. smooth extrudate ith less die sell ratio attained at lo extrusion pressure and temperature, has potential in industrial appliations. Hoever, the extrusion indo, orresponding to linear polyethylene (PE) ith relatively lo polydispersity (<7), has a narro indo temperature interval, ira 1~2 C, thus it ould not be applied to industrial sale proessing at the industrial sale. To have a fundamental insight and make the proess industrially viable, researh in this thesis as devoted to broaden the extrusion indo to tolerate the thermal flutuations in onventional proessing. To ahieve this goal moleular eight dependene of indo temperature and flo ritialities is revealed. The hydrodynami onditions of the extrusion indo observed in a rate-ontrolled rheometer and stik-slip flo studied in a stressontrolled rheometer ould be traed bak to the same origin, viz. slip flo arises due to the disentanglement of adsorbed hains on apillary all from free hains in the bulk. Seondly, a dual indo effet as unovered in the ourse of apillary flo of a bimodal PE, hih is onsistent ith the indo temperature dependene on moleular eight. Moreover, it as found that flo indued orientation ithin the indo effet is even less than that observed in steady state flo at a relatively lo shear rate. This implies that in the indo region only relaxed free hains are extruded through the apillary die and most of the adsorbed hains, hih ould be disengaged from the entangled melt, remain stiking to the inner apillary all. This observation is onsistent ith the hydrodynami origin of high-surfae-energy-die slip flo. Finally, a unimodal linear PE ith extremely broad moleular eight distribution, i.e. polydispersity (PDI) is 27, shoed a broad indo effet, ira 8 C, at an appropriate apparent shear rate. The moleular origin of suh a broad indo effet is due to its broad moleular eight distribution. These results have further impliations for energy effiient proessing. Keyords: Polyethylene, extrusion, pressure-drop, moleular eight dependene, indo effet, slip flo, helial distortion slip flo, broad extrusion indo. I

5 ACKNOWLEDGEMENTS I ould like to thank Professor Sanjay Rastogi and Professor Mo Song for their guidane and support. I ould also like to thank Dr Lada Corbeij-Kurele of SABIC - Europe for kindly providing the ommerial polyethylenes. I ant to take this opportunity to thank all the staff in Department of Materials for their help, espeially for Dr Jie Jin, Mr Andy Woolley, Mr Ray Oen, Mr John Bates and Dr David Ross. I also ish to thank the folloing people, Nilesh Patil, Kamal Yusoh, Anurag Pandey, Sara Rona, Giuseppe Forte, Carmine Invigorito, Yohan Champouret and Maurizio Villani,. I ould also like to express my gratitude to EPSRC, ORSAS and ESRF for their finanial support. Finally, a personal thank is given to my family and friends for their love and enouragement. II

6 LIST OF SYMBOLS A Surfae area a T b * D D e D D e /D d E E a e F s γ& Resaled ritial apparent shear rate Slip flo fator Entanglement distane Extrudate diameter Capillary die diameter Die sell ratio Spaing beteen the planes in the lattie Elasti modulus Ativation energy for hain relaxation Extensional L/R Shear fore F T f Tensile fore Hermans Orientation fator G G(t) G ο N HBC HSE h Shear modulus Relaxation shear modulus normalized by the plateau modulus Plateau shear modulus Hydrodynami boundary ondition High surfae energy Thikness I (β ) The diffrated intensity from the planes normal to the -axis. k B Boltzmann onstant L Capillary length Δ L Elongational displaement LSE L 0 Lo surfae energy Original length L 1 dl l Final length Inremental inrease in length Current length III

7 M M L Critial moleular eight Lo moleular eight omponent M H High moleular eight omponent M Weight average moleular eight MWD M Z M n * Moleular eight distribution End tail moleular eight Loer limit moleular eight for indo effet Poer la index/ Rabinoitsh orretion fator Δ P Pressure differene P L P 0 PDI Q Q a Q C Q S R R g r SL T T min T onset T s T ter t V s (M) 2α Total pressure drop for apillary flo Total pressure drop for pure onvergent flo, zero die length die Polydispersity Volumetri output rate Applied flo rate Volumetri output rate orresponding to stik flo omponent in slip flo Volumetri output rate orresponding to slip flo omponent in slip flo Die radius Gas onstant Distane to the entre of apillary Slip flo Temperature Temperature orresponding to the pressure minimum in indo effet. Onset temperature of indo effet Onset temperature of flo indued solidifiation Termination temperature of indo effet Time Slip veloity Weight fration of a given moleular eight omponent Die entry angle IV

8 β γ& γ& a The angle beteen the fibre or rod diretion and the -axis of orthorhombi PE rystal orresponding to the hain diretion Shear rate Apparent all shear rate γ& a Applied apparent shear rate γ& a,slip Slip flo apparent all shear rate γ& a,stik Stik flo apparent all shear rate γ& Critial apparent shear rate h γ& Critial apparent shear rate orresponding to onset appearane of gross shape distortion p γ& Critial apparent shear rate orresponding to onset appearane of periodi bulk distortion γ& Critial apparent shear rate orresponding to onset appearane of γ s γ& s γ& T γ& ε ε& η η a η 0 * η λ λ 0 indo effet Shear strain Critial apparent shear rate orresponding to onset appearane of flo indued solidifiation at a given temperature. True all shear rate Wall shear rate Tensile strain Strain rate Shear visosity Apparent shear visosity Zero shear visosity Complex visosity Reptation time at shift temperature/indo temperature Reptation time at referene temperature λ rep Reptation time/relaxation time μ Coeffiient of visosity V

9 σ σ Shear stress Critial shear stress for stik-slip transition h σ Critial all shear stress orresponding to the onset appearane of helial σ E Tensile stress σ min Wall shear stress at pressure minimum orreted by Cogsell orretion σ /T min min Resaled all shear stress orresponding to the pressure minimum in indo effet σ p Wall shear stress orresponding to the onset appearane of pressure osillation σ Wall shear stress u σ Upper limit all shear stress in pressure osillation l σ Loer limit all shear stress in pressure osillation distortion. σ, Correted all shear stress τ y ν v z x ω Yield shear stress Adsorbed hain density Linear flo veloity of a fluid at ertain distane to the entre of apillary Displaement under shear Rotational frequeny VI

10 TABLE OF CONTENTS ABSTRACT ACKNOWLEDGEMENTS LIST OF SYMBOLS TABLE OF CONTENTS I II III VII CHAPTER 1 INTRODUCTION AND OBJECTIVES OF PROJECT Introdution Objetive of the dissertation Sope of the dissertation 3 CHAPTER 2 LITERATURE REVIEW Brief overvie of polyethylene and proessing Basi revie of rheology The elasti solid (Hookean Solid) The ideal fluid (Netonian Fluid) Non-Netonian fluids Normal stress Revie of apillary rheology Shear stress at all Shear rate at all Corretions for apillary rheometer Bagley orretion Cogsell orretion Die sell Melt irregularities Extrusion indo of linear polyethylene Stik-slip transition Reptation time Moleular haraterisation of linear polyethylene via rheology route Summary 32 CHAPTER 3 EXPERIMENTAL Materials Methodology 34 VII

11 3.2.1 Differential Sanning Calorimetry (DSC) Gel Permeation Chromatography (GPC) Field Emission Gun Sanning Eletron Mirosopy (FEGSEM) Advaned Rheologial Expansion System plate-plate rheometer(ares) Capillary Rheometry Speimen preparation for apillary rheologial haraterisation Dynami temperature seep (DTS) Isothermal step rate test (ISR) Isothermal mono-rate time seep (IMTS) Die sell measurement MeF3 Mirosope Ex-situ Wide Angle X-ray Sattering (WAXS) 40 CHAPTER 4 MATERIAL CHARACTERISATION Polymer harateristis DSC GPC ARES plate to plate rheometry Nanoomposites haraterisations-fegsem 47 CHAPTER 5: MOLECULAR ORIGIN OF WINDOW EFFECT Introdution Results Melt flo singularity of PE-A The effet of shear rate on indo effet Disussion Moleular origin of narro extrusion indo (Region III) Flo indued solidifiation (Region IV) Conlusion 65 CHAPTER 6: MELT FLOW SINGULARITY OF BIMODAL POLYETHYLENE Introdution Results The basi effet of melt flo singularity of PE-B The effet of apparent shear rate on the melt flo singularity of PE-B Windo effet at isothermal onditions Isothermal mono-rate time seep haraterisation The effets of die geometry on extrusion indo Slip flo veloity Study flo indued orientation via ex-situ ide angle X-ray sattering (WAXS) Disussion Stik-slip flo Hydrodynami boundary onditions of indo effet Moleular origin of the double extrusion indos The influene of die geometry on flo ritialities Conlusions 104 VIII

12 CHAPTER 7 BROAD EXTRUSION WINDOW OF LINEAR POLYETHYLENE Introdution Results The broad extrusion indo of PE-C The effet of apparent shear rate on melt flo singularity of PE-C Isothermal step rate (ISR) rheologial haraterisation The impat of extrusion indo on die sell The effet of die geometry on extrusion indo Slip flo veloity Disussion The moleular origin of broad extrusion indo The effet of extrusion indo on die sell The influene of die geometry on flo ritialities Conlusion 128 CHAPTER 8: THE INFLUENCE OF NANOFILLERS ON THE MELT FLOW SINGULARITY OF LINEAR POLYETHYLENE Introdution Results Disussion The impat of the CB/MWCNTs on the extrusion indo of PE-A The effet of the CB/MWCNTs on flo indued solidifiation of PE-A Conlusions 136 CHAPTER 9 CONCLUSIONS AND FUTURE WORK 138 REFERENCES 145 IX

13 Chapter 1 Introdution and objetives of projet 1.1 Introdution In the last five deades after the development of Ziegler-Natta heterogeneous atalysts polymer siene and tehnology have gron hand in hand. The ease in proessing of polymers and tailoring of the moleular arhiteture for the desired mehanial properties has been one of the main auses for this fast development. Impat of the revolution in this materials siene is experiened in our daily life, for instane in pakaging, building and onstrution, automotive, eletrial and eletronis, medial devies and others. Polymer appliations an be divided into ommodity plastis, engineering polymers and funtional polymers. Among the ommodity plastis, polyethylene (PE) is one of the highly dominating plastis in the market on aount of its advantageous properties, suh as its lighteight, high speifi modulus, hemial resistane, reylability et. Considering the variation in available moleular arhitetures and thus the desired mehanial properties, polyethylene is a generi name for the polymer. For example, polymers suh as polyethylene, having the same moleular onfiguration an be used for ommodity purposes and also for the highly demanding appliations suh as prostheses, body implants, body armour et. The vastly different final properties, from beverage ontainers to bulletproof armour, arises from the hemial struture ontrolled by polymer synthesis and moleular morphology ahieved during proessing. Polymers are usually proessed in the melt state, for semi-rystallised polymers, or in the rubbery state, for fully amorphous polymers. Among the onventional proessing tehniques, extrusion is one of the popular proesses applied to manufature polymer produts sine it is a ontinuous proess apable of making produts of any length. During extrusion polymer pellets are fed into the barrel from the hopper manually or vauum fed automatially. The hopper often has a dryer on the top to remove moisture from the polymer pellets. When the resins enter the extrusion barrel, it is transported by the rotating sre hih is poered by an eletri motor. Sine the rotating sre drags the resins and additives toards the die, the polymer moleules slide over eah other, reating fritional heat hih melts the material during drag flo. External heating devies provide additional heating. One the polymer is melted, 1

14 it flos through a tailored die, hih shapes it to a ertain form. Then the plasti is ooled, and either ut into desired setions or rolled up. With inreasing aareness of redution in the energy osts and greenhouse gas emissions it is getting essential to find energy effiient proessing routes, hih math the onsensual request in most of the developed and developing ountries. Conventional proessing of polyethylene (PE) is usually performed at muh higher temperatures, i.e. 160 C, above its melting point. These high temperatures are prerequisite to avoid any interferene of melt flo instabilities. Hoever, there is a narro extrusion indo situated in beteen the flo instability and flo indued solidifiation regions. The extrusion indo is a speifi melt flo singularity in extrusion, here polymer melts an be extruded smoothly ithout any distortion and the orresponding extrusion pressure shos a signifiant redution. It implies that the extrusion indo does offer potentially distint advantages for energy-effiient proessing. Therefore, numerous studies have been devoted to investigate the mehanism responsible for this indo effet and flo ritialities of the extrusion indo. Hoever, the moleular origin of this indo effet is still unrevealed. On the other hand, there is an apparent drabak of this indo effet onsidering industrial appliations sine it is too narro to be adopted in polymer proessing. In industrial appliations, the indo effet should be at least several degrees in order to tolerate thermal flutuations during proessing. Considering the above unknon issues, this researh is devoted to study the moleular origin of the indo effet and to broaden the extrusion indo ith respet to the extrusion proessing of polyethylene. 1.2 Objetive of the dissertation The prime objetive of this researh is to explore ho to broaden the extrusion indo of linear PE. To ahieve the desired objetive the reported study ill onsider: 1) The hydrodynami ondition of the indo effet. 2) The moleular origin of the extrusion indo. 3) The effet of nanofillers ith distint morphologies on the indo effet of linear PE ith a narro moleular eight distribution. 4) The influene of moleular eight distribution on the extrusion indo. 2

15 5) The hydrodynami origin of stik-slip flo in the ourse of the rate-ontrolled apillary flo. 6) The influene of varying die geometries on flo ritialities. 1.3 Sope of the dissertation Chapter 2 of the thesis gives brief overvie of PE, from polymerisation to proessing. The revies in this hapter fous on flo behaviour and melt irregularities during apillary flo. Furthermore, researh performed on the melt flo singularity of PE and the stik-slip transition is revieed. In Chapter 3, three different samples of high density polyethylene (HDPE) used in this study are haraterised via Differential Sanning Calorimetry (DSC), Gel Permeation Chromatography (GPC) and Advaned Rheologial Expansion System (ARES) to identify the moleular eight, polydispersity, melting point and rystallinity. The adopted methodology for the haraterisation of the polymers is also introdued. The moleular origin of the indo effet is a matter of debate and is not ell understood. Therefore a moleular eight dependene of flo ritialities ill be introdued to eluidate the melt flo singularity of linear PE in hapter 4. In this ork, the hydrodynami origin of the indo effet is eluidated and linked ith stik-slip transition theory observed in a stress ontrolled rheometer. The moleular eight dependene of flo ritialities is quantitatively studied. In Chapter 5, a bimodal PE having to distint molar mass distributions is used to study the influene of molar mass and molar mass distribution on the indo effet. The bimodal polymer shos an unexpeted dual indo effet. The nature of dual indo effet is revealed and the influene of die geometries on the flo ritialities is investigated. A slip flo veloity test is performed to verify the appearane of slip flo in the extrusion indo regime. Finally, the disentanglement mehanism of slip flo is verified ith the help of ex-situ ide angle x-ray sattering (WAXS) experiments. 3

16 In Chapter 6, unimodal linear PE having broad molar mass distribution shos an intriguing broad extrusion indo. The same rheologial haraterisations as mentioned in hapter 5 are performed to study the moleular origin and hydrodynami onditions of the broad indo effet. From the reported studies it is apparent that the relaxation dynamis of a strethed hain has impliations on the indo effet. Thus, in Chapter 7, to arbon based nanopartiles ith different partile morphologies are used to modify the relaxation dynamis of polymer hains. To have insight on the influene of the nano-fillers, different onentrations of the nano-partiles are added to the polymer matrix. The linear PE hosen for the studies is the polymer having relatively narro moleular eight distribution, used in hapter 4. Finally, in Chapter 8 onlusions have been summarised and future ork has been proposed. 4

17 Chapter 2 Literature revie 2.1. Brief overvie of polyethylene and proessing Polyethylene (PE) inludes linear lo density polyethylene (LLDPE), lo density polyethylene (LDPE) and high density polyethylene (HDPE). It is the major member of the polymer family ith 28 perent of total plasti demand in Europe in 2006, hih is for the most idely used plasti, ompared ith the other four high-volume plastis inluding PP 19%, polyvinylhloride (PVC) 13%, polystyrene (PS) 7% and polyethylene terephthalate (PET) 7% 1. With respet to the hemial struture of PE, suh as the bakbone length and branh density/length, the hemist an design the final polymer arhiteture by seleting distint atalysts that inlude Ziegler Natta and metalloene/ post-metalloene atalysts et. and hoosing various polymerisation onditions inluding temperature, pressure and time. PE as first synthesised by Faet and Gibson in laboratories of ICI in 1933 and ICI obtained the patent for its ommerial prodution in A axy solid substane as formed in the reation tube after polymerisation of ethylene and benzaldehyde in a high-pressure autolave. The axy solid as termed as lo density polyethylene (LDPE). The lo density arises from the lo rystallinity, resulting from high ontent of branhes. During the free radial polymerisation, short and long branhes are formed in transfer reations. Therefore, polymer hains ere diffiult to pak into rystal. Although LDPE has poor mehanial properties due to the lo rystallinity, it is still extensively used for pakaging on aount of its ease in proessing. The seond breakthrough in polymerisation of ethylene ourred 20 years later. In 1950s 3 Ziegler synthesised high density polyethylene (HDPE) at lo pressure and temperature using a heterogeneous titanium atalyst. Folloing that, Natta in 1954 applied this tehnology to synthesize polypropylene 4. The heterogeneous atalyst system, today named after Ziegler-Natta, an yield linear PEs. The near absene of side branhes enhanes the rystallinity. 5

18 It is ell knon that the performane of a polymer produt relies on moleular eight. Generally speaking, ith inreasing moleular eight, the final produt properties suh as modulus, abrasion and fatigue resistane are enhaned. Therefore, ultra high moleular eight polyethylene (UHMWPE) is seleted as a material in prostheses appliations, artifiial knee and hip joints 5 and is also used for the development of high performane fibres 6. Hoever, the resulting problem ith the higher molar mass polymer is diffiulty in proessing. PE is onventionally proessed in the melt state by injetion moulding, extrusion and film bloing or blo moulding 7, in hih the proessability is strongly dependent on melt visosity. It is ell knon that the melt visosity inreases steeply ith inreasing moleular eight ( M dependene of 3.4, hen ), obeying a poer M is above a ritial molar mass M 8, here the ritial molar mass is dependent on the molar mass beteen entanglements. Oing to the high melt visosity, UHMWPE is intratable in onventional proessing route. In order to proess UHMWPE, a more ompliated route: solution-spinning 9, for instane, is adopted. Hoever the final produt profile is limited to fibre and tapes. Hene, there is a ompromise beteen the ease of proessing and the performane of produt. 6

19 Figure 2.1: A plot of logarithmi zero shear visosity vs. logarithmi eight average moleular eight 8. On the other hand, the final produt properties are also dependent on hain morphology developed during proessing. One example is melt flo rystallisation behaviour, hih an govern the final produt properties and performane. Under flo onditions rystallisation behaviour exhibits signifiant differenes ompared ith that under quiesent onditions. Firstly, flo indued rystallisation/ solidifiation auses a shift the melting point of the polymer to higher temperature ompared to that at a quiesent state 10. This means that under flo onditions nulei and resulting rystalline phases an form above the thermodynami melting point at the quiesent ondition. Seondly, the rystallisation rate of the polymer melt an be enhaned during melt flo by promoting the formation of rystal nulei 11. Last but most important, it is observed and studied in detail that an interloking rystal struture referred to as shish-kebab ould develop under highly oriented melt flo onditions 12. Partiularly, in the early stages of rystallisation, preursors ith a ertain degree of order form under the melt flo ondition. One the size of a 7

20 groing preursor is beyond a ritial dimension, it beomes a rystalline nuleus, induing the formation of anisotropi rystallites. The relatively high moleular eight polymer hains possessing long relaxation time form a fibril ore referred to as a shish and then short polymer hains rystallizes on it forming numerous staks of lamellae named as a kebab. In summary, the final produt properties suh as mehanial and optial properties an be modified via various proessing onditions Basi revie of rheology Rheologial haraterisation of thermoplasti materials an be performed in both solid state and molten state. Generally speaking, the final produt performane is governed by solid rheology properties. On the other hand, the proessability an be related to polymer melt properties. The rheologial properties depend on material intrinsi nature and proessing onditions. Visoelasti polymer melt behaves neither as an elasti solid nor a Netonian fluid The elasti solid (Hookean Solid) An ideal elasti deformation obeys Hooke s la (i.e. the stress is linear ith the strain) 13. In simple tensile or ompression deformation the imposed fore is perpendiular to the surfae of ation. σ E = F T / A (2.1) L1 dl L1 ε = = ln (2.2) l L L0 0 σ E = E ε (2.3) As a linear elasti material, the tensile stress σ E is proportional to the strainε The ideal fluid (Netonian Fluid) In shear deformation the imposed shear fore is parallel to the surfae. σ = F / A (2.4) s γ S = x / h (2.5) σ =G γ S (2.6) dx v γ& = 1 = (2.7) h dt h σ =η γ& (2.8) 8

21 The definition of variables is given in the list of symbols. An imposed shear stress auses deformation hih inreases steadily ith time until the stress is released and the deformation is reversible and onstant. σ is proportional to γ& and the linear gradient is termed the oeffiient of visosity 13. The oeffiient of visosity remains unaffeted ith imposed shear stress, and is independent of time Non-Netonian fluids Many materials in real life are non-netonian fluids, suh as polymer melts, PVC pastes, kethup, starh suspensions, paint, blood, shampoo et. The σ -γ& relationship of Netonian fluids an be desribed by a single onstant value, oeffiient of visosity. In non-netonian fluids, hoever, the relation beteen the shear stress and the strain rate is nonlinear, and an even be time-dependent. On the other hand, non- Netonian fluids have viso-elasti properties, in hih it behaves like a visous liquid under ertain onditions but it also shos partial elasti reovery after deformation 13. There are three lasses of non-netonian fluids: 1) Bingham body: this kind of material annot be deformed until an internal struture ollapses above a yield stress, folloing hih γ& inreases linearly as the τ rises. 2) Pseudoplasti: Most polymer melt behave like a pseudoplasti. For this lass of fluids, visosity dereases as shear rate inreases, referred to as a shear thinning effet. 3) Dilatany: For this lass of materials, μ (dynami melt visosity) inreases ithγ&, termed as shear thikening. A typial example is PVC plastisols over a limited range of shear rates 14. In vie of flo urve of pseudoplasti, it is apparent that the proportionality beteen shear stress and shear rate is not onstant. Therefore the ratio of shear stress to shear rate is referred to as apparent visosity μ a rather than oeffiient of visosity used for Netonian liquids. It is to be pointed out that η a at a given shear rate is the slope of seant dran from the origin to the point of shear rather than the slope (tangent dran) of the σ -γ& urve. This is one of the reasons hy it is termed as apparent visosity. One of the possible reasons to eluidate pseudoplasti behaviour is attributed to the redution in entanglement points under orientation during the shear. For example, pseudoplasti, polymer melts, onsists of extensively entangled and 9

22 randomly oriented moleular hains at quiesent onditions. Under shear the moleule hains tend to be aligned in the flo diretion and beome oriented. As a onsequene, the redued points of entanglements under shear give rise to the delining μ a ith inreasingγ& 13. Figure 2.2: Shear stress vs. shear rate for Bingham bodies, Dilatant fluids and Pseudoplasti fluid ompared ith a Netonian fluid. τ is the yield shear stress 13. y Figure 2.3: Visosities as a funtion of shear rate for a dilatant fluid, a Netonian fluid and a pseudoplasti fluid hih possess the same zero shear visosity at the interept

23 Many equations have been established to desribe pseudoplasti behaviour 15. Hoever, only one of them hih has been found to be used is Ostald- de Waele equation: σ (γ& n = K ) (2.9) Non-Netonian fluids have time-dependent flo behaviour, in hih μ a varies ith time of shearing. Time-dependent flo behaviour arises from the disentanglement of moleules during the timesale of the applied shear. There are to basi timedependent non-netonian pseudoplasti fluids: 1) Thixotropy: The longer the fluid undergoes shear stress, the loer the visosity. 2) Rheopexy: The longer the fluid undergoes shear stress, the higher the visosity. Both thixotropy and rheopexy take a long time to reover to their initial state after essation of shear. The visosity of thixotropi or rheopeti material is dependent on the time of stirring ompared to a pseudoplasti material hih relies on the shear rate. Polymer melts exhibit a visoelasti response to stress or stain. The rheology of visoelasti materials an be desribed by to omponents: one is dashpot representing the visosity; the other is spring depiting the elasti modulus. There are to ell-knon models to simulate visoelasti behaviour. 1) Maxell model: a Netonian visous dashpot is plaed in series ith a Hookean elasti spring 16. It an desribe the stress relaxation at a onstant strain. Hoever, it fails to represent the reep behaviour at a given stress. 2) Kelvin-Voigt model: a Netonian visous dashpot is plaed in parallel ith a Hookean elasti spring. It an desribe reep behaviour at a given stress. Hoever, it fails to represent the stress relaxation at a onstant strain Figure 2.4: Shemati representations for Maxell model and Kelvin-Voigt model. 11

24 2.2.4 Normal stress The stress generated in flo onditions onsists of to omponents: one is the shear stress, and the other is the normal stress. With respet to visoelasti liquids suh as polymer melts, the normal stress is apparent hen a flo system undergoes a hange in ross-setion area. In the ourse of apillary flo polymer melt is fored to flo through a apillary or slit die to form a ertain shape, here the hange of rosssetion area of polymer melt is signifiant. As a onsequene, normal stress influenes the flo behaviour during the entry of polymer melt into the die and dominates some features of polymer melt suh as die sell Revie of apillary rheology Capillary rheometer is a idely used instrument to determine the rheologial properties of polymer melts quantitatively. It overs the strain rate range of interest in pratie proessing from 1s -1 to 10,000s -1 and it an measure useful rheology properties hih are essential for engineering purposes 20. During apillary flo it is realised that the volumetri flo rate inreases as the head pressure applied to a liquid at the other end of a pipe is inreased. Based on a ell-knon Poiseuille la 17, the output rate-pressure differene relationship is postulated: 4 Q = πδpr / 8η L (2.10) Where R is the radius of the apillary, L is the apillary length and η is the shear visosity. Here η is assumed to be independent ofγ&. Hoever, in the real ase of polymer melts, the melt visosity is apparent shear visosity rather than the oeffiient of visosity; hene it is referred to using the Greek symbol η rather than μ. For pseudoplasti η dereases as γ& inreases. There are several assumptions required to be onsidered to derive the quantitative relationship of rheologial properties 13 : 1) The all flo veloity of fluids is zero and there is no-slip at the apillary all. 2) The fluid is time-independent. 3) The flo pattern is onstant all along the apillary, i.e. laminar flo. 4) The flo is in the isothermal ondition. 5) The volume of the polymer melt is inompressible. 12

25 2.3.1 Shear stress at all The shear stress at the apillary all for a fully developed steady-state flo an be derived from the balane fores on a ylindrial element of fluid ith length of dz and radius r, in hih the hydrostati fore in the flo diretion F 1 should ompensate the sum of hydrostati fore in the opposite of flo diretion F 2 and drag fore on the surfae of the element F 13 3 : F = 0 = F + F + F (2.11) 2 F 1 = P π r (2.12) 2 F = [ P + ( P / Z) dz] πr (2.13) F 3 = On substituting equations (2.12)-(2.14) into equation (2.11): P π r 2 π 2 [ P + ( P / Z) dz] r + πrdzτ 2 =0 For a uniform pressured distributed apillary, Therefore, the shear stress is obtained as: 2 πrdzτ (2.14) ΔP 2L / r P / Z remains unaffeted by Z. σ = (2.15) The equation above applies to all time-dependent fluids and Netonian or poer la fluids. The shear stress an be determined if the pressure differene beteen the to ends of a apillary and the apillary geometries are knon Shear rate at all The shear rate at all an be alulated by the folloing assumptions. Considering the profile of flo veloity in a apillary, the linear veloity of the fluid at distane r from the entre is defined as v z (hen r = R, v z =0). Therefore, Q an be alulated by integrating the linear flo rate ith respet to r beteen the limits 0 and R 20 : R R Q = 2π rvzdr = 2π rvzdr (2.16) Considering the shear stress profile along the radius of apillary: 0 0 R r = τ (2.17) τ Substituting equation (2.15) and (2.17) into equation (2.16) and rearranging the yield all shear rate, γ& : 13

26 1 dq γ& = (3Q + ΔP ) (2.18) 3 πr dδp Simplify the equation by assuming Q is linear ith Δ P an give a onvenient equation to determine the apparent shear rate, γ& a : 4Q γ a = 3 πr & (2.19) The above equation fails to represent the rheologial properties of time-dependent polymer melt during shear flo. Hene the all shear rate alulated from this equation is referred as apparent all shear rate. In order to determine the true all shear rate, γ& T, the Rabinoitsh orretion is used to justify the simple equation (2.19): 3n + 1 4Q γ T = ( ) 3 4n πr Where n is the poer la index in equation (2.9). & (2.20) Corretions for apillary rheometer Bagley orretion When measuring rheologial properties during apillary flo of a high visous polymer melt in apillary flo, there are three main soures of errors inluding reservoir and frition losses, ends pressure drop (Bagley orretion) and nonparaboli veloity profile (Rabinoitsh orretion) 18. Regarding the end pressure drop, a total pressure drop measured by pressure transduer ill involve some pressure ontribution from extensional properties, suh as entry pressure drop and exit pressure drop. The former is attributed to the onvergent flo, referred to as elongational flo, ourring at the entrane of die, and the latter arises from elasti relaxation/ elasti reovery hen the deformed pseudoplasti melt leaves the die. Hene, in order to attain the true apillary pressure drop, the effet of extensional properties should be extrapolated and deduted from the total pressure drop. An end orretion is reommended to derive the true all shear stressτ T. Historial method, Bagley orretion 19, is used to dedut the end pressure drop, oing to extensional properties, from the total pressure drop. A plot of pressure drop versus die L/R ratio at varying fixed γ& a gives a series of straight lines and an extrapolated bak to zero pressure. The interept of straight line on zero pressure gives a orretion on 14

27 apillary die length, referred to as effetive die length. If the material only undergoes shear flo, the graph ould have an interept at the origin. If there is a degree of extensional flo inluding any elasti response and vortex flo, the interept at Δ P =0 is at a negative L/R value, e. This value an then be used to alulate the true shear stress, τ T, at the all by the formula shon belo 13 : T ΔP = 2( L / R + e) τ (2.21) Hoever the Bagley orretion requires extensive experimentation using at least three or preferably more apillary dies ith large L/D ratio in order to ahieve aurate results; on the other hand, if the data is non-linear due to melt ompressibility or some all slip, omplex extrapolated method suh as ubi or quadrati fit must be required to analyse the results. Therefore, it may not be aurate beause of the non-linearity problems Cogsell orretion The Cogsell method as adopted to resolve the aforementioned problems in hih the end pressure drop an be deduted from total pressure drop using an orifie die onsidered as zero length die. The advantage of this method is its independene on extrapolation, resulting in the most aurate determination of extensional properties under various proessing onditions. In ase of the tin-bore rheometer, the extensional data suh as extensional pressure drop are obtainable. On the other hand, the same onditions are used for both parts of the test (apillary and orifie die). Therefore, the experimental errors (due to operator, temperature et) an be eliminated. 15

28 Figure 2.5(a): A shemati diagram of pressure drop distribution of apillary flo, shoing the end orretion inluding the entry and exit pressure drops. Figure 2.5(b): An enlarged shemati diagram of pressure drop distribution of apillary free flo (L 0 =0.25mm). In the Cogsell method, the orreted shear pressure orresponding to the apillary flo, P C, an be attained by deduting the end pressure drop of orifie flo from the 16

29 total pressure drop of apillary flo, P C = P L - P 0. Therefore, the orreted all shear stress resulting from Cogsell method is as folloing: ( PL Po ) = 2L / R Where: P L is total pressure drop for apillary flo, inluding entry pressure drop, apillary pressure drop and exit pressure drop, τ (2.22) P 0 is total pressure drop for orifie die, zero die length die, inluding entry pressure drop and exit pressure drop. In pratie, great auray is attained by ombining a long die ith an orifie die 20 as the differene beteen the L and the L t, true apillary length, is negligible hen L/R Die sell Die sell is a ommon effet ourring in polymer extrusion. It is desribed that the extrudate ross-setion area is greater than the ross-setion area of die. Numerous studies have been devoted to study die sell and the moleular origin of it 21.The onsensus is that die sell arises from elasti reovery 22. In quiesent onditions polymer hains are oiled up in an almost random status. During the onvergent flo at the die entry, the moleular hains are orientated and tend to align in the flo diretion. The strethed hain onformation resulting from hain orientation an be maintained during apillary flo under a ertain shear. Hoever, one the polymer melt is extruded out of the die, the orientated hains begin to oil bak due to the elasti reovery, resulting in longitudinal shrinkage and lateral expansion. It is also found that the leading ends of the extrudate have a onvex shape after shrinkage 13. It supports the fat that higher shear rate ours lose to the die all leading to higher shrinkage on the outside surfae of the extrudate. The folloing effets of various flo onditions on die sell are reported in literature: 1) Die sell inreases ith apparent shear rate up to a limit rate hih is near to but belo the ritial shear rate of melt frature. Beyond this point, die sell delines until the melt frature ours 21(d). 2) Die sell dereases ith inreasing temperature at a fixed shear rate 21(d). 17

30 3) Die sell dereases ith the length of the die at a fixed shear rate 21(a)(). This effet is onsistent ith the fat that greater residene time in the apillary redues the die sell 21(g). 4) Die sell enhanes ith reservoir-to-apillary diameter ratio belo a ertain value 21(e). Regarding the influene of moleular harateristis on die sell, there are many ontraditory results. Beynon et al. 21(d) studied the effet of moleular eight on die sell using LDPE. They found that the die sell inreases ith M. Hoever, Metzger and Matlak reported the opposite results using HDPE 21(g). With respet to the impat of moleular eight distribution, it is found that die sell inreases ith the ratio of M / M n 21(j). The reported ontraditions in the results an be attributed to distint moleular harateristis of the synthesised polymer suh as M, M / M and branh density. n Melt irregularities Aording to the pioneering studies performed by Nason 23, Tordella 24, Bagley 25 and others 26, it has been observed that melt irregularities, also termed as melt frature, emerge hen γ& a reahes or goes beyond the ritial value. The melt irregularities are lassified into to lasses: one is melt instabilities and the other is extrudate distortions. Based on numerous experimental observations of melt frature, it is found that melt instabilities and extrudate distortion often take plae simultaneously. Hoever, the extrudate distortion an our ithout any sign of melt instabilities, on the other hand, the melt instabilities alays give rise to the extrudate distortion. The melt irregularities of PE have been idely studied inluding lo density polyethylene (LDPE) and high density polyethylene (HDPE). HDPE is the polymer studied in this thesis. At the loest shear rate, both lasses of materials sho a smooth and glossy extrudate. With inreasingγ& a, distint melt irregularities emerge at varying flo ritialities. The first emergene of extrudate distortions, surfae irregularity, is situated at the upstream flo pattern. The surfae irregularity, also referred to as surfae melt frature, loss of gloss, surfae roughness or sharkskin, is haraterised by a series of 18

31 ridges perpendiular to the flo diretion. The effet of moleular harateristis on sharkskin has been studied by Hoells and Benbo 26(). It as found that moleular eight has little effet on sharkskin hereas moleular eight distribution appears to play an important role in surfae irregularity. It has been knon that: (i) Broad moleular eight distribution loers the suseptibility to sharkskin. (ii) Lo selling ratio and higher the value of poer la index n (in equation 2.9) enhane the degree of sharkskin. The mehanism involved in the development of sharkskin is based on experimental observations. Sharkskin is dependent on the extrudate veloity (shear rate) and temperature. One of the possible reasons for sharkskin is attributed to the elasti energy released at the exit of the die. One the polymer melt is extruded out of the die, the huge pressure differenes give rise to a drop in the flo veloity. As a onsequene, the tensile fores build up at or near the extrudate surfae exeeding the tensile strength of the melt, this results into tearing of the surfae folloed by stress release. With further extrusion the sharkskin repeats hen tensile fore goes beyond the surfae tensile strength. There is a unique flo behaviour, knon as flo disontinuity, ourring hen or σ p, the ritial shear rate/shear stress orresponding to the onset of pressure osillation, is attained. This anomalous pulsing flo, notably ith HDPE, as first studied using a stress-ontrolled rheometer by Bagley 25. In Figure 2.7 it as found that there as a sudden jump in Q hen p γ& Δ P attains a ritial value at steadily inreasing pressure. In reverse the onset appearane of disontinuity is at a loer pressure C. A onsistent result is obtained ith a rate-ontrolled rheometer. When the ritial apparent shear rate is attained, a stik-slip flo is observed during the melt flo. It is haraterised by periodi bulk distortion aompanied ith pressure osillation, here the relationship beteen shear rate and shear stress breaks don. It is observed that the extrudate shos a spiral thread and a straight rod-like thread alternatively. The mehanism responsible of periodi bulk distortion is idely aepted to arise from apillary flo sine this effet is not observed in apillary free flo ith a zero-length die 21(i). The periodi bulk distortion appears to be related to slip flo effet and melt ompressibility. Regarding the role of moleular eight and 19

32 moleular eight distribution on flo ritialities, it is found that the onset of osillatory flo dereases ith inreasing eight average moleular eight and the broader the moleular eight distribution the higherγ&. p Sine flo instabilities set up the boundary ondition of polymer proessing, numerous studies have been devoted to investigate the nature of flo instabilities by adjustment of either proessing onditions or polymer parameters in order to minimise flo instabilities and broaden the onventional proessing indo. To moleular origins are suggested to eluidate the appearane of flo disontinuities. The first possible reason is stik-slip flo oing to the polymer desorption from the melt all interfae 27. The polymer hains losest to the apillary all fail to adsorb on the apillary all and, as a onsequene, a slip flo ours. Another approah is suggested that the stik-slip transition arises from the disentanglement of the adsorbed hains from the bulk at the melt-all interfae 28. It has been idely aepted that the first mehanism responsible is related to a lo surfae energy die, viz. a die oated by proessing aid to redue surfae energy of apillary all. By ontrast the disentanglement of the adsorbed hains from the bulk free hains is likely to our ithin the apillary flo of a high surfae energy die, viz. no-oating metal die. 20

33 Figure 2.6: Various extrudate distortions under melt frature (a-b) shark-skin of LLDPE and HDPE extrudates,() the extrudate of HDPE shos periodi distortions (d) smooth extrudate of PS in slip flo (e-f) Helial distortion observed in extrusion of PS and PP at high shear rate (From Agassant et al., ). 21

34 Figure 2.7: A shemati diagram of dual output flo urve during pulsing flo of HDPE at varying imposed pressure using a stress-ontrolled rheometer (after Bagley et al., (a) ) There is no periodi bulk distortion ourring in the melt flo behaviour of LDPE. Nevertheless, both LDPE and HDPE display gross shape distortions, knon as melt frature, hen the shear rate reahes a ritial value. The gross shape distortion starts from helial distortion initially and beomes haoti and uneven ith a further inrease in the apparent shear rate. It is to be noted that the ritial shear rate is usually related to the apparent all shear rate orresponding to the onset appearane of distortion, rather than the stritly orreted true shear rate at the all. It seems to reah an agreement in literature that the gross shape distortion arises from the entry orifie. The ritial apparent shear rate for the onset of helial distortion, γ& h, inreases ith temperature signifiantly. Hoever, there is less impat of temperature on the ritial shear stress 26(j). 2.4 Extrusion indo of linear polyethylene There is an unusual melt flo effet observed in the ourse of apillary extrusion of linear polyethylene (PE) as depited in Figure 2.8. It as found that a signifiant 22

35 pressure drop ours in a narro temperature indo, referred to as an extrusion indo at or around 150 C 30. Within this extrusion indo, a redued flo resistane as aompanied ith smooth extrudate and omparatively little die sell. The observed speifi melt flo singularity during extrusion of linear polyethylene is not preditable and explainable from onventional rheology. Besides the intrinsi sientifi interest, this extrusion indo is also a subjet for the development of energy-effiient proessing, sine it has an indisputable advantage in pratial proessing on aount of the lo temperature and pressure proessing ondition, ombined ith the absene of extrudate distortions. Figure 2.8: A plot of pressure vs. temperature shoing the indo effet. The vertial lines symbolize osillations in pressure 31. Sine the first disovery of melt flo singularity of linear polyethylene, numerous studies have been devoted to explore the hydrodynami origin of the extrusion indo 31. Hoever, the moleular origin of the melt flo singularity is still not learly eluidated 31. Keller et al. 30 suggested that suh a sudden pressure drop in extrusion indo ould not arise from rheologial onsiderations alone and must result to the formation of a high entropy symmetri phase, suh as the possible hexagonal paking of hains. It is also knon that high hain mobility along the - axis exists in the hexagonal phase of linear polyethylene due to eak Van der Waals 23

36 interation beteen the intermoleular hains. If it is possible to attain this kind of mobile mesophase in a flexible polymer, typially polyethylene during extrusion indo, the moleular origin of extrusion indo ould arise from elongation-floindued orientation induing the liquid to mesophase transition 30. Figure 2.9 shos the shemati plot of free energy versus temperature in hih the G h represents the mobile hexagonal phase lying beteen G L (liquid) and G o (orthorhombi) having a negative slope. Aording to thermodynamis, the hexagonal phase annot appear in quiesent ondition sine G h is alays situated above G o or G L. Hoever, under flo ondition all the Gibbs free energies shift to high value. Hoever the effets of flo rate on G h.and G L are more pronouned ompared ith G o, ausing the greater shift in the free energy urves of G L and G h ompared to G o. Suh a shift auses appearane of the thermodynamially stable hexagonal phase. Figure 2.9: Shemati plot of Gibbs free energy, G, versus temperature, T. At quiesent ondition the free energy for liquid phase, G L, orthorhombi phase G o and hexagonal phase G h are shon by solid lines. Under flo ondition the onstrained liquid phase G L, orthorhombi phase G o and hexagonal phase G h shift to high value as shon by dash lines. In flo onditions the melting temperature inreases from T m to T m. And a narro temperature interval in beteen T h-o and T m orresponds to a thermal dynami stable hexagonal phase 30. Folloing this line of researh, Kolnaar together ith Keller 31 dediated a part of his researh to study the possibility to attain suh a mobile hexagonal phase in the ourse 24

37 of apillary flo. Hoever, his results ere in disagreement ith the Keller s earlier hypothesis. In apillary flo, the elongational flo indued orientation strongly relies on the onvergent flo at the die entrane. Smit and Van der Vegt 32 studied the quantitative relationship beteen die entrane angle (2α) and the ritial apparent elongational flo rate, defined as the onset of sharp pressure upsing during extrusion, leading to blokage of the flo. Where K ε& γ& 2α & ε = K & γ tan 2α (2.23) is a onstant; is ritial elongational flo rate orresponding to the onset appearane of flo indued solidifiation. is ritial apparent shear rate assoiated ith the first appearane of the flo indued solidifiation. is the die entrane angle. Aording to the equation (2.23) proposed by Smit and van der Vegt, it an be onluded that the strength of the elongational flo inreases ith the die entrane angle (2α). If Keller s hypothesis is orret, ritial apparent shear rate, γ&, orresponding to the onset appearane of extrusion indo should derease ith die entrane angle. Hoever, Kolnaar found that γ& remains unaffeted by varying die entrane angles. Moreover, it as also observed that the extrusion indo also emerges in the onstrition-free pure tube flo (polymer extruded through a rheometer barrel). These systemati studies lead Kolnaar and Keller to onlude that the indo effet does not rely on onvergent flo. Therefore elongation-floindued orientation fails to explain the mehanism of melt flo singularity of linear polyethylene. Folloing this observation, Kolnaar onduted his further researh to study the effet of die length and die diameter on flo ritialities of the extrusion indo. The observations ere that hange in die geometry had less or no effet on the existene and appearane of the extrusion indo. On the other hand, apillary flo is a prerequisite for the existene of the indo effet sine the melt flo singularity vanishes on apillary free flo using an orifie die (orifie alone ithout a apillary). 25

38 The next question is hether or not shear flo an indue the phase transition from orthorhombi to hexagonal phase/mesophase. Therefore, Kolnaar et al 33 performed real-time ide angle X-ray sattering (WAXS) experiments using a high intensity X- ray beam to explore the moleular origin of the extrusion indo of linear polyethylene. Aording to the plot of intensity versus double Bragg refletion angle (2q) at an extrusion indo temperature, viz. 149 C, a single eak refletion (interspaing d = 0.220±0.003) arises from rystalline phase loated at the shoulder of broad peak orresponding to the melt amorphous phase. On subtration of the observed diffration pattern ith the X-ray diffration pattern obtained in the quiesent ondition, a lear peak as observed. The emergene of the single refletion leads to the onlusion that the presene of high-temperature rystalline phase arises under the applied flo onditions. The inoming question as to address the nature of this rystalline phase. The authors attributed the single refletion to the high symmetry hexagonal phase, emerging during the apillary flo. Meanhile van Bilsen 34 also studied the phase transition ourring in the indo effet via the same tehnique (i.e. in-situ X-ray sattering (WAXS) experiments). He also found that there as only one eak refletion besides the amorphous sattering at 150±1 C. Moreover, aording to his results, all the harateristi refletions from the orthorhombi phase vanished instantaneously at 150±1 C. The reasons hy the unique single refletion observed at 150±1 C annot arise from the orthorhombi phase, are not only beause the single refletion is loated at 2θ hkl =20.9 hih is 0.8 belo the Bragg refletion angle of (110) Orth at 149±1 C, but also beause the intensity of the single refletion at 150 C as stronger than the (110) Orth refletion at 149 C. In aordane ith the preliminary experiments, a single refletion as also observed from onstrained melting experiments of ultra-oriented ultra-high moleular eight PE fibres 35 (e.g. 2θ hkl =20.42 / d=0.221nm at 152 C) and slightly rosslinked polyethylene fibre 36 (e.g. 2θ hkl =20.3±0.3 / d=0.222±0.003nm at 150 C 36(b) ). The observed single refletions from the above studies reveal the existene of hexagonal phase. With respet to the Bragg refletion angle (2θq hkl =20.9 /d=0.216) at 150±1 C observed in Bilsen s experiments, it is in beteen the 2θ Orth 110 and 2θ hex 100. Considering that the shear flo in apillary is not strong enough to onstrain the 26

39 polymer hains, the single refletion at 2θ hkl =20.9 /d=0.216 as attributed to the shear indued mesophase ith symmetrial hexagonal paking rather than a hexagonal phase. After numerous experiments, inluding rate-ontrolled rheology and stress-ontrolled rheology, a onsensus has been reahed that the extrusion indo of linear polyethylene arises from slip flo. Kolnaar 37 illustrated the indo effet arising from the slip flo and attributed it to either pure all slip or slip film flo. In the pure all slip, the polymer hains lose to the apillary all are fully desorbed from the apillary all and they simply flo along the all. Whereas in the slip film flo a thin layer of interfae is formed lose to the all favouring a muh redued visosity ompared to the bulk. Hoever, Kolnaar did not give a lear eluidation regarding the moleular origin and hydrodynami origin of the indo effet. In addition, Kolnaar pointed out that the hydrodynami boundary onditions of the indo effet ere governed by to ritial shear rates orresponding to the onset of indo effet and helial distortion, γ& and h γ& respetively. In detail, γ& gives the loer limit hydrodynami boundary ondition and the upper limit is dependent onγ& h. Within the extrusion indo regime of HDPE (148~152 C) it as found that both surfae distortions and periodi bulk distortions ere absent. Whereas, gross shape distortions an emerge in the extrusion indo regime. Regarding the moleular eight dependene on flo ritialities, Kolnaar pointed out that as a -4.0 poer of the moleular eight. On the other hand, γ& saled h γ& also shoed a poer la dependene on the moleular eight hih saled as To harateristi boundary onditions had an intersetion in the plot of upper limit γ& against M. The h γ& and loer limit M orresponding to this intersetion point as referred to the loer limit moleular eight (M * ). Kolnaar estimated the ritial moleular eight to be 10 5 g mol -1, i.e. Kolnaar argued that no indo effet ill be antiipated if the seleted HDPE has moleular eight belo M *. 27

40 2.5 Stik-slip transition It is observed that linear PE might undergo a superfluid-like stik-slip transition in the ourse of stress-ontrolled apillary flo. The transition as desribed by a onsiderable disontinuity in the flo rate, ourring hen the shear stress reahes a ritial value 38 It as found that the ritial all shear stress σ C orresponding to the onset of superfluid like stik-slip transition as linear ith temperature. In addition, the resaled stress σ C / T remained onstant, suggesting that the stik-slip transition ourred at a ritial hain deformation. The ritial all shear stress σ C as found to sale ith the -0.5 poer of the moleular eight and saled linearly ith temperature ranging from 200 to 260 C. Wang 39 first quantitatively haraterised the superfluid like stik-slip transition. These studies ere in ontrast ith a spurt flo phenomenon observed in rate-ontrolled rheometer. An extrapolation length b as first addressed by Wang to quantify the magnitude of a large disontinuity of flo rate ourring during the slip-stik transition at a ritial stress. b as defined as: b= V s / γ (2.24) T Where V s is slip veloity; γ T is the true all shear rate. Figure 2.10: a shemati diagram of slip flo ourring in a apillary die. Where D is the die diameter and the extrapolation length b is related to the true shear rate at the all and apparent slip veloity, Vs 39. The volumetri output rate during slip flo onsists of slip flo omponent and stik flo omponent: 28

41 Where S Q S 2 = Q + πr V (2.25) C Q is the entire slip flo volumetri output rate; Q is volumetri output rate orresponding to stik flo omponent in slip flo; R is die diameter. s C 4Q Substituting equation (2.19), here s 4Q & γ a = and & γ 3 T =, and equation (2.24) into 3 πr πr equation (2.25) yield: R b = ( & γ a/ & γ T 1) (2.26) 4 Aording to extensive study of stik-slip transition at varying temperature, it as found that b saled as a 3.4 poer of the moleular eight and as linear ith apparent shear visosity, η a, but as independent of temperature. It implies that b is an intrinsi material property. The moleular eight dependene of ritial all shear stressσ and extrapolation length b implies the moleular origin of stik-slip transition and slip flo may be due to the disentanglement mehanism. When the ritial all shear stressσ is attained, a sudden slip flo emerges as the adsorbed hains disentangle from the surrounding free hains. As a onsequene, the materials of die onstrution may not have any impat to the appearane of stik-slip transitions, as long as the melt/all interfaial interations an be sustained during the disentanglement of adsorbed hains from free hains. Aording to disentanglement mehanism, the adsorbed hains at melt/all interfaes after disentanglement from bulk free hains should remain attahing on the metal surfaes of inner apillary all rather than being extruded out through the die. It oinides ith a spetrosopi study of polyethylene-metal interfae after peeling 40. C C An anomalous stik-slip transition ourred hen the temperature as belo 200 C, in hih the resaled ritial shear stress σ / T dereased ith loering temperature and the extrapolation length b inreased as the temperature delined. This anomalous effet at loer temperature as attributed to the effet of flo-indued mesophase on disentanglement mehanism. Aording to Brohard and de Gennes theory 41, Wang derived an expression to quantify the ritial shear stress ( σ ) for the stik-slip transition. 29

42 Where It as found that νk B T σ = * (1.26) D σ is the ritial shear stress for the stik-slip transition, ν is the adsorbed hain density, kb is Boltzmann onstant, T is temperature, * D is the entanglement distane. σ / T remains unaffeted at high temperature, from 200 C to 260 C. Hoever, σ / T dereases ith loering the temperature (<200 C) based on experimental results. Considering the inrease in adsorbed hain density as the temperature dereases, it appears that entanglement distane should inrease further ith loering temperature. Suh a possibility leads Wang to suggest that floindued mesophase should appear at loer temperatures. Moreover, suh an oriented struture at the melt-all interfae eases the disentanglement of tethered hains from the free hains at or beyond the ritial shear stress. 2.6 Reptation time A ell-established reptation model 42 has been used to represent onstrained hain dynamis. In this model, a polymer hain is surrounded by or entangled ith neighbouring hains. On aount of this topologial onstraint, long range displaements are only possible by snake-like motion along the imaginary tube axis. The relaxation time λ rep for a onstrained hain to vaate the original tube, viz. reptation time, is proportional to the square of the ontour length L divided by the reptation veloity ν ( λ rep =L/ν ), in hih the ontour length is linear ith the moleular eight and the reptation veloity is proportional to the reiproal of moleular eight. Hene, the reptation time an be quantified in terms of moleular eight: M λ (2.27) 2 rep ~ 3 ~ M 1 M 2.7 Moleular haraterisation of linear polyethylene via rheology route Mehanial and physial properties of polymer depend on moleular eight, M, and moleular eight distribution, MWD. In priniple it is possible to invert this relationship so the moleular harateristis from rheology data ould be determined. 30

43 In the reent to deades numerous methods ere developed to determine M and MWD from the melt rheology data of polymer. To lassify, there are to types of model, viz. Visosity Model and Modulus Model. The visosity model is based on the relationship of M and MWD ith the visosity of polymer melt at a ertain shear rate. It has been reported that M of a given polymer an be estimated from zero shear visosity, η 0. For a linear polymer, η 0 is linear ith M 43. With inreasing the moleular eight beyond a ritial value, M, there is a poer la relationship beteen η 0 and M, viz η = M 44. On the other hand, many analytial visosity models have been developed to predit the MWD from a rheologial flo urve of melt visosity,η, vs. shear rate, γ& 45. The modulus model presents visoelasti properties of a polymer. In the modulus model the relaxation spetrum an be onverted from the time domain to the moleular eight domain, folloed by a regularized integral inversion to reover the MWD urve 48. Gt () 1/ β = F (, t M) ( M) d(ln M) ο G N ln( M e ) (2.28) Where G(t) is relaxation modulus normalized by the plateau modulus, β G ο N, F(t,M) is a kernel funtion desribing the relaxation behaviour of a monodisperse omponent of moleular eight M. The eight fration of the MWD funtion is represented by (M). The exponent, β, is a parameter assoiated ith the mixing behaviour of the hains. For instane, β is 1 for simple reptation and 2 for double reptation theory. M e is the average moleular eight beteen entanglements. In this thesis double reptation theory as applied in modulus model 46. Compared ith the single reptation model proposed by de Gennes 42, double reptation theory takes aount of the ontribution of higher-order entanglements and the effet of the tube dilation. The β imposed from the double reptation theory is a value of ira 2, in fat slightly higher than One of the suessful algorithms is developed by Mead 48. It is 31

44 ommerialised by TA instruments in their Orhestrator softare and is adopted to predit the M and MWD as desribed in hapter 3 of this thesis. 2.8 Summary In this hapter a brief overvie of polyethylene and the fundamental theory of rheology ere revieed. Regarding the extrusion indo, the speifi singularity in extrusion behaviour of linear polyethylene does have potential to enhane energy effiient proessing on aount of the signifiant redution in extrusion pressure and loer extrusion temperature. Whereas the extrusion indo reported in the early publiations is too narro to be adopted in ommerial polymer proessing, it has been revealed that the moleular origin of stik-slip transition emerging at a ritial shear stress is attributed to the disentanglement of the adsorbed hains on the apillary all from the free hains in the bulk. If the stik-slip transition and the extrusion indo an be linked together by a quantitative moleular eight dependene of flo ritialities, the nature of to effets an be attributed to the same mehanism. If the extrusion indo arises from the disentanglement mehanism, it is a key to broaden the extrusion indo, hih ill be addressed in the researh study. 32

45 Chapter 3 Experimental The materials used in this study and the methodology applied to study the extrusion indo ill be stated in this hapter. Three linear polyethylenes ith distint moleular harateristis ere seleted to study the effet of molar mass distribution on the indo effet. Folloing that to nano-sized fillers, viz. arbon nanotubes and arbon blak, ere added into one of the linear polyethylenes to investigate the influene of nanofillers on the indo effet. Regarding the experimental methodology, three neat polymers ere haraterised via gel permeation hromatography (GPC) and advaned rheologial expansion system. With regard to the nanoomposites, sanning eletron mirosopy (SEM) as applied to observe the filler morphologies and filler distribution/dispersion in the polyethylene matrix. The main experimental ork as arried out via a tin-bore apillary rheometer. Here the indo effet, flo behaviour and extrudate profiles ere studied and reorded. Finally the extrudate surfae orientation orresponding to the indo ondition as studied via miro-beam ide angle X-ray sattering in ESRF. 3.1 Materials The polymers under investigation ere grades of high density polyethylene (HDPE) supplied by Borealis and SABIC Europe respetively and referred to as PE-A, PE-B and PE-C. Table 3.1: Polymer harateristis results from GPC a M Sample Supplier Modality (g mol -1 ) M n (g mol -1 ) M /M n M z (g mol -1 ) PE-A SABIC unimodal 89,750 24, ,00 PE-B Borealis bimodal 170,500 12, ,000 PE-C SABIC unimodal 303,000 17, ,785,000 Multi-alled arbon nanotubes (MWCNTs), haraterised ith 50μm length and 20nm diameter, ere supplied by Chendu Institute of Organi Chemistry, Chinese Aademy of Sienes. Nano-sized Carbon blak (CB) ith 28nm diameter as supplied by CABOT. To arbon-based nanofillers, MWCNTs and CB, ere homogeneously distributed into PE-A using a physial route. The loading of MWCNTs and CB in PE-A are 0.2t% and 0.6t% respetively. PE-A a Refer to the molar eight distribution urves, figure 4.1 and 4.2, in hapter 4, and the material data sheets are inluded in Appendix A. 33

46 nanoomposites ere kindly prepared by Dr Jie Jin via a onfidential physial router in the Department of Materials, Loughborough University. 3.2 Methodology Differential Sanning Calorimetry (DSC) A standard TA DSC Q200 as adopted to perform thermal analysis. Eah sample as eighed by a preise balane and enapsulated in a standard aluminium pans and lids. An idential empty pan ith lid as used as a referene. Nitrogen flo rate into the thermal ell as set-up at 50m 3 min -1. DSC as alibrated using indium and tin. Thermal analysis as performed to determine the melting temperature and fusion enthalpy of nasent and melt rystallised polymer. The method is used to investigate the rystallization temperature and rystallization enthalpy. An idential thermal programme adopted for eah sample is as follos: 1. Isothermal at 25 C for 5mins 2. Ramp to 160 C at 10 C min -1 (The first heating run) 3. Isothermal at 160 C for 5 min (To remove the entire thermal history) 4. Ramp to 25 C at 10 C min Isothermal at 25 C for 5min 6. Ramp to 160 C at 10 C min Gel Permeation Chromatography (GPC) GPC as used for moleular haraterisation of the investigated polymers. High temperature GPC as performed in Polymer Laboratories of Rapra, using GPC220 under the supervision of Dr Steve Holding. A single solution of eah polyethylene speimen as prepared by dissolving 15.0 mg of sample into 15m 3 solvent, 1,2,4- trihlorobenzene ith anti-oxidant and heating at 190 C for 20 minutes on shaker. Eah sample solution as filtered through a glass fibre filter and a part of solution as moved into a glass sample vial. In order to attain thermal equilibrium ondition of eah sample, there as a thirty minutes delay in a heated sample ompartment. After that, part of the ontents as injeted in eah vial automatially. The Chromatographi onditions ere: (1) Columns: PLgel guard plus 2 x mixed bed-b, 30 m, 10 μm; (2) Solvent: 1,2,4-trihlorobenzene ith anti-oxidant; 34

47 (3) Flo-rate: 1.0 m 3 min -1 (nominal), (4) Temperature: 160 C (nominal), (5) Detetor: refrative index (& Visotek differential pressure). Finally, the data as olleted and analysed using Polymer Laboratories Cirrus 3.0 softare Field Emission Gun Sanning Eletron Mirosopy (FEGSEM) A high resolution FEGSEM ith 5kV aeleration voltage as used to observe morphology of the nanofillers, and the dispersion and distribution of nanofillers, MWCNTs and CB, in PE-A matrix. The signal as olleted by InLens detetor. As MWCNTs and CB are eletrially ondutive, FEGSEM experiment of eah nanoomposite as arried out ithout gold oating Advaned Rheologial Expansion System plate-plate rheometer(ares) Dynami frequeny seep (DFS) measurements ere performed on an ARES strain ontrolled rheometer ith osillatory shear in the linear visoelasti regime at temperature of 160 C ith angular frequenies (ω ) ranging from to 500 rad s -1 and a onstant strain of 5%. Prior to the DFS measurements, dynami strain seep (DSS) measurements ere performed to investigate the linear visoelasti regime of eah polymer ithin broad strain region from 0.01% to 100% at a frequeny of 500rad s -1 or 100rad s -1. Eah sample as first hot-ompressed at 160 C in a steel mould 1mm thik and 25mm inner diameter. The ompressed sample as used for the plate-plate rheology measurements. Finally the rossover point of storage modulus (G ) and loss modulus (G ) and moleular eight harateristis (M, M n, M /M n and M z ) ere determined and alulated via the Orhestrator softare provided by TA Instruments Capillary Rheometry A Rosand tin-bore rheometer as used to study the melt flo behaviour of three polymers, in hih the extrusion pressure as measured via a built-in pressure transduer situated at upstream of the die, as shon shematially in Figure 3.1. Three thermoouples ere fitted ithin the reservoir all at three different loations: top barrel, middle barrel and die. Flomaster softare as used to ontrol the rheometer, then ollet and analyse the rheologial data. The rheometer barrel diameter is 15mm and a series of dies ith varying die geometry shon in Figure 3.2 ere used. 35

48 Figure 3.1: Shemati representation of the tin bore rheometer used in extrusion experiments. 36

49 Figure 3.2: Shemati diagrams of axial ross setions of orifie die and apillary dies shoing the differenes in die geometries inluding apillary length (L/mm),apillary diameter (D/mm) and die entrane angle (2α/rad). L-D- 2α values orresponding to eah die are shon at the bottom of eah Figure. The die entry angle is represented by a radian number(radian= (degree π)/180 ). 37

50 Speimen preparation for apillary rheologial haraterisation Prior to rheologial haraterisation, polymer pellets or poders ere ompated at ambient temperature and then heated up to a pre-heating temperature, far above the melting point. This step as required to erase the grain boundary and remove the air traps, and eventually to gain a homogenous melt hih is prerequisite for apillary rheology measurements. The pre-heating temperature and time are dependent on moleular harateristis ( M ) and melt flo behaviour. For example high moleular eight PE required more time to attain the homogenous melt ompared to the lo moleular eight PE. On the other hand, different moleular eight PEs possess various indo temperatures and distint melt instability regime; hene, varying preheating temperatures ere seleted in pre-test setting. Table 3.2: Pre-heating setting for sample preparation prior to the rheologial haraterisation. Sample Pre-heating temperature ( C) Pre-heating time(min) PE-A PE-B PE-C Dynami temperature seep (DTS) A DTS as performed to probe the indo loation hile ooling melt at a onstant rate, ira 1.5 C min -1 and at a onstant shear rate. At a given piston veloity at fixed barrel and apillary dimensions the shear rate remained onstant. DTS only onsists of ooling run to avoid any interferene of residual solid phase on melt flo behaviour. Aims of DTS experiments ere as follos: 1. To determine the ritial apparent shear rate, γ&, orresponding to the onset of the indo effet. 2. To determine the indo loation and temperature interval. Sine DTS is nonisothermal rheologial haraterisation, it an merely give general information on indo loation. In order to loate the real indo temperature, isothermal step rate tests ere performed. 3. To investigate the impat of the shear rate on the indo effet Isothermal step rate test (ISR) In ontrast to the DTS a stati experiment as onduted to study the melt flo behaviour at the isothermal onditions in hih the extrusion pressures ere reorded at different shear rates ith time. After pre-heating as ompleted, the barrel and 38

51 apillary die ere ooled to pre-seleted temperature for 15mins to attain equilibrium thermal ondition prior to the ISR. The objetives of ISR ere as follos: 1. To investigate the melt flo behaviour at isothermal onditions ith varying step hanges in shear rate. 2. To justify the existene and appearane of indo effets under isothermal onditions. 3. To study the hydrodynami origin of the indo effet Isothermal mono-rate time seep (IMTS) Melt flo instabilities ere studied in IMTS in hih the extrusion pressures ere reorded as a funtion of time, at a fixed apparent shear rate, hile the barrel temperature as kept onstant. IMTS as also adopted to determine the flo ritialities inluding the onset apparent shear rates orresponding to periodial bulk distortion, indo effet and helial distortion/ gross shape distortion, referred to as p γ&, γ& andγ& h. On the other hand, the slip flo veloities ere also determined in IMTS. The apparent shear rates orresponding to a given shear stress ere reorded in the apillary flo using different dies ith onstant L/R ratio. (Die geometries L(mm)-D(mm)-2 α (rad) of apillary dies used in slip flo veloity measurement ere as follos: π, π, π and π ). The thermal history in IMTS as idential ith ISR. The objetives of IMTS ere to: 1. To determine the ritial apparent shear rates assoiated ith the onset of pressure osillation, indo effet and helial distortion. 2. To study the melt irregularities at varying shear rates and distint temperatures. 3. To determine the slip flo veloity Die sell measurement The die sell as measured by an in-situ laser detetor situated at 2m under the apillary die. During the measurement, the extrudates ere ontinuously ut off manually to maintain the measuring length no more than 15m in order to avoid the sagging effet MeF3 Mirosope Photographs of PE extrudate ere taken via Reihert-Jung MeF3 mirosope ith a maro unit using a refletive light. The exposure time as fixed at 3.11ms. 39

52 3.2.7 Ex-situ Wide Angle X-ray Sattering (WAXS) Flo indued orientation as studied by ex-situ WAXS experiments performed on the beam line ID11 of the European Synhrotron Radiation Faility (ESRF) in Grenoble. Eah sample, PE-B, as extruded through a apillary die(16-1-π) folloed by quenhing in ie ater to 0 C in order to minimise the influene of hain relaxation on flo indued orientation. Consequently, more flo indued orientation as maintained on the surfae layer of extrudate ompared ith self-ooling in the atmosphere. After extrudate melts ere fully solidified, eah extrudate as slied along the longitudinal diretion from both sides to ahieve a proximate orthorhombi setion ith thikness of 250 μm depited in Figure 3.3. An elliptial miro beam ith 15 μm major axis and 5 μm minor axis sanned the pre-setioned extrudate mounted perpendiularly on a 3.17mm ide slot on a opper plate. The monohromati X-ray ith a avelength =0.417nm probed the pre-setioned extrudate along the transverse diretion of extrudate. To-dimensional X-ray diffration patterns ere reorded on ESPIA Frelon detetor and orreted for spatial distortion. Prior to the data analysis the sattering of air and sample free holder as subtrated from the sattering of eah sample. Finally the data ere analysed via FIT2D softare provided by ESRF. Figure 3.3: Shemati diagram of a pre-setioned extrudate on left. The enlarged diagram ith gradual disolouring effet on right represents for surfae edge of pre-setioned extrudate. 40

53 Chapter 4 Material haraterisation 4.1 Polymer harateristis DSC Table 4.1 summarizes DSC data of eah sample. The melting temperature is broadly onsistent ith expetations from thermal analysis of PE. Table 4.1: Thermal analysis of three different polyethylenes (Appendix E) T Sample m onset T m peak H m ( C) ( C) (J g -1 ) X (%) PE-A PE-B PE-C GPC PE-A and PE-C are unimodal linear polyethylenes supplied by SABIC Europe. The moleular harateristis of eah sample ere determined by GPC as shon in Table 3.1 and Figure 4.1. One symmetri distribution peak for the to samples onfirms unimodal nature of PE-A and PE-C respetively. Aording to GPC data depited in Figure 4.1, it is apparent that PE-A and PE-C have different M and MWD. Compared to PE-C, PE-A is lo molar mass linear polyethylene ith omparatively narro molar mass distribution. The polydispersity of PE-A is analogous to Kolnaar s samples 31. Hoever, M of PE-A is loer than all the Kolnaar s linear PEs. The sample, PE-B, as supplied by Borealis. Aording to the moleular eight distribution urve shon in Figure 4.2, it an be observed that PE-B shos bimodal molar mass distribution. 41

54 Figure 4.1: Moleular eight distributions of PE-A and PE-C. GPC measurements of eah sample have been done tie. 42

55 Figure 4.2: Moleular eight distribution of bimodal polyethylene PE-B ARES plate to plate rheometry Moleular harateristis an also be determined via rheology route. First step is to determine a linear visoelasti regime for a given polymer via the dynami strain seep (DSS) experiment, in hih storage modulus, G, and loss modulus, G, are reorded and plotted against strain rate as shon in Figure 4.3. It an be seen that G and G remain unaffeted ithin a strain region from 0.1% to 10%. Therefore, this region is referred to as linear visoelasti regime. Folloing DSS a dynami frequeny seep (DFS) as performed to measure the rheologial properties at different frequenies ith a fixed strain seleted in the linear visoelasti regime. As shon in Figure 4.4, there is a rossover point of G and G for PE-A and PE-C respetively. It is ell-knon that a lo moleular eight linear polymer ith narro molar mass distribution shos a rossover point (G /G ) loated at higher angular frequeny and higher modulus ompared ith a high moleular eight linear polyethylene haraterised ith a broader moleular eight distribution. Therefore, it is possible to ahieve qualitative information about M and M / M in omparison of the rossover points obtained in DFS. Aording to Figure 4.5, the G /G rossover point of PE-C situated at lo frequeny and the lo modulus ompared ith PE-A, suggests that the polymer PE-C is a high moleular eight polymer ith broad molar mass distribution. These results are in agreement ith the quantitative results obtained in GPC. n 43

56 Figure 4.3: Dynami strain seep results of logarithmi storage modulus G, loss modulus G (Pa) vs. shear strain γ s (%) shoing the linear visoelastiity regime under osillatory shear, hile holding a fixed frequeny at 500rad s -1 for PE-A and 100rad s -1 for PE-C at a onstant temperature of 160 C. 44

57 Figure 4.4: A logarithmi plot of storage modulus G (Pa), loss modulus G (Pa), loss angle/phase shift δ and omplex visosity η *(Pas) against frequeny ω (rad s -1 ). The dynami frequeny seep performed at 5% strain. 45

58 Figure 4.5: To unimodal linear polyethylenes possessing distint moleular eight and polydispersity sho different rossover point of storage modulus and loss modulus in the logarithmi plot of storage modulus and loss modulus against frequeny. The positions of respetive rossover points indiate the relative moleular eight and molar mass distribution. To quantitatively study the moleular harateristis through the use of rheologial measurements, numerous studies have been devoted to establish the relationship of measured rheology properties ith the knon values for M and M / M based on the preditions of linear visoelasti models 46. Aording to double-reptation model 48, the polymer harateristis ere alulated by TA Orhestrator softare and the results are shon in Table 4.2 and synthesised MWD traes are exhibited in Figure 4.6. As a benhmark, results from GPC are ompared ith the modelling results in order to predit the apability of the double-reptation model for determination of polymer harateristis. It is found that M and M n M / alulated based on double reptation model are in good agreement ith the GPC results exept an apparent differene of M / M beteen them for PE-C. One of the possible reasons n is that the rheology route is more sensitive to small amounts of high moleular eight polymer. In other ords, GPC is not a reliable tehnique to determine the moleular n 46

59 eight beyond ira 10 6 g mol -1 or a broad moleular eight distributed polymer ith a high moleular eight fration above approx g mol -1. Table 4.2: Polymer harateristis results of PE-A and PE-C from ARES plate-plate rheometer ompared ith GPC results Tehnique Sample M (g mol -1 ) M n (g mol -1 ) M /M n ARES PE-A 74,200 28, GPC PE-A 89,750 24, Tehnique Sample M (g mol -1 ) M n (g mol -1 ) M /M n ARES PE-C 349,100 12, GPC PE-C 303,000 17, Figure 4.6: Synthesised moleular eight distribution traes for PE-A and PE-C based on the double reptation model, resulting from the dynami frequeny seep in the linear visoelastiity regime of eah polymer. The entanglement moleular eight 1900g mol -1 and minimum reptation moleular eight 4000g mol -1 ere the input parameters for alulation. 4.2 Nanoomposites haraterisations-fegsem Figures 4.7 and 4.8 sho partile morphologies of CB and MWCNTs. It an be seen that CB are spherial nano-partiles ith aspet ratio of one. In ontrary to CB, rodlike MWCNTs possess high aspet ratio. From figures 4.9 and 4.10 it may be stated that both CB and MWCNTs are finely distributed on the surfae of PE-A poder. 47

60 Figure 4.7: FEGSEM image shoing the morphology and partile size of CB Figure 4.8: FEGSEM image shoing the morphology and partile size of MWCNTs 48

61 Figure 4.9: FEGSEM image of 0.2t%CB-PE-A Figure 4.10: FEGSEM image of 0.2t%MWCNTs-PE-A. 49

62 Chapter 5: Moleular origin of indo effet 5.1 Introdution The extrusion indo of linear polyethylene (PE) as first addressed by Keller et al. 30. The eight average molar mass of those PEs under Keller s study are in beteen 10 5 g mol -1 and 10 6 g mol -1 The indo effet as desribed by a pressure drop ourring at and around 150 C for a onstant material throughput rate ithout any distortion. The advantages of the indo effet are less proessing energy for ontinuous flo ithout flo instabilities and uniform smooth extrudate ith less die sell. Therefore the extrusion indo an offer an energy effiient proessing route to proess linear PE ithout extrudate distortion at a given volumetri flo rate. Hoever, the narro temperature indo annot be adopted for industrial appliations. Therefore, to make the proess appliable, broadening of the indo effet is a requisite. To ahieve the goal it is also essential to understand hydrodynami origin of the indo effet. As stated in the earlier hapter, one of the possible reasons for the appearane of the indo is slip flo. Hoever, there is no lear eluidation regarding the hydrodynami origin of the effet of slip flo on the indo. One of the possible slip flo mehanisms is related to the disentanglement of adsorbed hains from free hains. In detail, the oriented tethered hains are likely to at as a lubriant and provide smooth flo. Suh a general possibility of disentanglement of tethered hains from free hain in bulk melt at or above a ritial flo rate has been addressed by Brohard and de Gennes 41. These onepts have been further strengthened by the systemati studies performed by Wang 39. Hoever, there is a lak of quantitative study on the flo ritialities of extrusion indo in order to link that ith stik-slip theory. 5.2 Results Melt flo singularity of PE-A The polymer used for studies in this hapter is PE-A, moleular harateristis of hih are shon in Chapter 3 (Table 3.1) of this thesis. To reall, molar mass and molar mass distribution of PE-A are 89,750g mol -1 and 3.7 respetively as determined by GPC. Kolnaar et al. estimated that linear PE ith M <10 5 g mol -1 has no indo effet. Hoever no experimental data for the molar masses loer than the ritial molar mass is provided in the literature. In this respet the present study is likely to 50

63 be the first on the melt flo singularity of the linear PE ith M loer than the * Keller s ritial moleular eight ( M ~10 5 g mol -1 ). Figure 5.1 depits the basi melt flo behaviour of PE-A. During the dynami temperature seep experiments (DTS) at shear rate of 225s -1 starting from 160 C, three types of harateristi flo behaviour, viz. stik flo, indo effet and flo indued solidifiation, are observed in four temperature regions: (a) At higher temperature (>144 C) orresponding to the stik flo region, no melt frature or extrudate distortion appears and the extrusion pressure steadily inreases ith dereasing temperature. (b) Within the extrusion indo (144 C~142 C), a onsiderable pressure drop emerges and a smooth extrudate ith no melt irregularities are observed. () In beteen 142 C~139 C, the flo behaviour is situated in the stik flo region again after the termination of indo effet terminates at 142 C. (d) At loer temperature (<139 C), extrusion pressure inreases signifiantly and eventually sings up toards the upper limit pressure of rheometer. These flo behaviours ere first addressed by Odell et al 50 and are referred to as flo indued solidifiation, at the end no flo through the die is observed. To investigate the moleular origin of the indo effet the polymer PE-A has been seleted as a referene sample. The influene of arbon-based nanofillers on extrusion indo is addressed in hapter 7. Figure 5.1 shos distint flo behaviour orresponding to apillary flo and apillary free flo. During DTS experiment at a shear rate of 225s -1, a apillary die (L-D-2α:16-1-π) b and an orifie die (L-D-2α:0-1-π) ere attahed at the bottom of barrels on left and right side of the apillary rheometer. Hene, both the apillary flo and the apillary free flo an be ompared in the same flo ondition simultaneously. It is found that there is no existene of extrusion indo hen the polymer melt is extruded through the orifie die. Hoever, in apillary flo, an apparent pressure drop omplemented ith uniform flo of the extrudate ithout any melt frature and extrudate distortion, ours in a narro temperature indo, b L-D-2α: L is apillary length, D is apillary inner diameter and 2α radian of apillary die entry angle. 51

64 residing beteen 144 C~142 C. The harateristis of the indo effet observed in this lo molar mass PE are similar to the earlier findings, here high molar mass as used. Figure 5.1: A plot of extrusion pressure against temperature for orifie die(l-d-2: 0-1-π) and apillary die (L-D-2α: 16-1-π). D225s -1 is an abbreviation for dynami temperature seep ith a fixed apparent shear rate at 225s The effet of shear rate on indo effet The effet of apparent shear rate on the extrusion indo is studied further in the dynami ooling experiments, as depited in Figure

65 Figure 5.2: Extrusion pressure against temperature traes for different shear rates indiating the ritial shear rate orresponding to the onset of extrusion indo (L-D-2α: 16-1-π) The ritial apparent shear rate, γ&, orresponding to the onset of the indo effet, is 225s -1. Belo this shear rate no extrusion indo is observed. With inreasing apparent shear rate (>225s -1 ), the extrusion indo and pressure osillation region shifts to high temperature, Figure 5.2, suggesting shear rate dependene of the onset of the indo temperature. Finally, it is orth noting that the pressure minima observed in the indo region is loer than the extrusion pressure observed belo the ritial shear rate, suh as (200s -1 ). This suggests that distintion in the hydrodynami ondition exists in the indo and non-indo regions. 5.3 Disussion One of the requirements of the performed rheologial studies is the isothermal ondition. It is desired that the system attains the thermal equilibrium state. Though in dynami temperature seep (DTS) the set ooling rate of 1.5 C min -1 annot ompletely fulfil the stati isothermal requirement, it had been shon in Kolnaar s 53

66 study that the indo temperature only shifts by less than 1 C on varying the ooling rate inluding isothermal experiments 31(a). Before disovering the moleular origin of indo effet here e reonile the existing onepts on flo behaviour as depited shematially in the Figure 5.3. The shemati plot of pressure trae reorded in DTS test of PE-A an be lassified into four regions: Region I (as shon in Figure 5.3): stik flo region observed at high temperatures here the extrudate flos smoothly through the apillary die ithout distortion. In suh a stable melt flo extrusion pressure ontinuously inreases as the temperature diminishes, thus the apparent shear visosity is proportional to the reiproal temperature, obeying an Arrhenius type relationship: Where η a is the apparent shear visosity, E a is the melt/ solid state flo ativation energy, Ea RT η a = Ae / (5.1) R is the universal gas onstant. It is to be noted that during onventional proessing PE falls in this region. Region II: stik-slip flo region shos pressure osillation and it is also referred to as periodi distortion. 54

67 Figure 5.3: To shemati plots of extrusion pressure vs. temperature, shoing four distint flo regions: (I) stable flo, (II) stik-slip flo, (III) extrusion indo and (IV) flo indued solidifiation. (a) Flo behaviour of PE-A ith eight average moleular eight belo 10 5 g mol -1 ; (b) Flo behaviour of PE ith eight average moleular eight above 10 5 g mol -1 (Kolnaar and Keller, 1994, 1995, ) 55

68 Region III: A melt flo singularity in a narro temperature interval ours in this region. Compared ith the flo onditions in Region I, melt flos ontinuously through the apillary die, but at loer pressures and temperatures. Region IV: A sudden upsing in the extrusion pressure is observed hen the temperature dereases belo a ertain ritial value during the DTS test. The reason ould be attributed to the rystallisation of polymer melt under the flo onditions. Therefore, it is termed as flo indued solidifiation. It is orth highlighting that PE-A ith moleular eight belo the suggested ritial value ( M < M * ) shos an isolated indo effet ithout inferene of flo indued solidifiation. Hoever, in ontrast, other linear PEs ith relatively high moleular eight ( M > solidifiation. * M ) exhibit extrusion indos aompanied by flo indued Moleular origin of narro extrusion indo (Region III) In Region III, the neat polymer, PE-A, shoed a onsiderable pressure drop over a narro temperature interval, referred to as the extrusion indo. Although many researhes 30,31 have been devoted to study the extrusion indo, the moleular origin of the indo effet is still unrevealed. Regarding the mehanism responsible, it is found that apillary flo gives rise to the extrusion indo, rather than elongational flo 31. On the other hand, it has been reported that the ritial apparent shear rate follos a poer la dependene on moleular eight hih sales ith - 4.0±0.1 31().These findings reveal that the indo effet arises hen a ertain strethed hain onformation an be maintained at or near the flo ritialities during apillary flo. Moreover, it as also observed that indo temperatures ere dependent on moleular eight 31(a). Therefore, it is impossible to ompare the ritial apparent shear rates for different molar mass PE at different temperatures. In order to ompare flo ritialities at the same temperature, it is essential to introdue a shift fator a T (in Table 5.1) to reflet the temperature dependene of the hain relaxation time, λ rep. Figure 5.4 shos the superposition of ritial apparent shear rate, γ&, for different molar masses of linear PEs. It is found that the resaled ritial apparent shear rate, a T γ&, sales ith -3.7±0.2 poer of the moleular eight. here a T is 56

69 obtained from an Arrhenius equation, Eq 4.6, here the ativation energy is KJ mol This poer la relationship offers the internal link beteen moleular origin of the extrusion indo and stik-slip flo theory. In detail, Wang studied a superfluid-like stik-slip transition 5 using a stress-ontrolled rheometer. He pointed out that the ritial shear stress, σ, sales ith -0.5 poer of the M at different temperatures, 160 C and 200 C. It is apparent that to flo ritialities, γ& and σ an be onneted by a universal poer la relationship beteen M and shear 3.75± visosity, η. (i.e. γ& M, σ M and η M σ = ηγ ). Therefore, the slip flo emerging ithin the extrusion indo at the ritial shear rate may arise from an idential hydrodynami origin of slip flo observed in stress-ontrolled rheometer, based on moleular eight dependene of flo ritialities. Even though the to experiments ere performed using different apillary dies, it has been reported by Keller and Kolnaar 31(b) that the flo ritialities remain less affeted ith different apillary die geometries. Table 5.1: The resaled ritial shear rates of PE-A and the other three samples used in Kolnaar s researh 31 (referene temperature is 160 C). Sample M (g mol -1 ) PDI γ& (s -1 ) T min ( C) PE-A 89, PE-KA 262, PE-KB 381, PE-KC 708, a T a γ& T (s -1 ) Another internal link beteen the stik-slip theory and the extrusion indo effet needs to be highlighted. Wang reported a lo-temperature anomaly, viz. the resaled ritial shear stress σ / T dereases ith dereasing temperature T (<200 C). Wang suggested that a flo-indued ordered phase may our and ease the disentanglement of adsorbed hains from free hains at lo temperature. In fat, suh a flo-indued ordering has been deteted by in-situ WAXS experiments in rate-ontrolled apillary flo ithin the extrusion indo. A single refletion orresponding to d=0.216nm at 2θ hkl =20.9 (for CuKα radiation ith avelength of 0.154nm) as observed during extrusion of HDPE at the indo temperature. Suh a flo indued mesophase emerging at the PE/all interfae an assist the disentanglement of tethered hains adhered to the apillary all from the hains in the bulk (free hains). 57

70 Therefore, the moleular mehanism of both the extrusion indo and superfluid-like stik-slip transition, at lo temperature <160 C, may be attributed to the same origin. In detail polymer hains are adsorbed on the inner apillary all and then those adsorbed hains are oriented along the flo diretion. At an appropriate flo onditions, viz. shear rate and temperature, the strethed hain onformation of adsorbed hains an be maintained and disentangled from the free hains. Figure 5.4: Resaled ritial apparent shear rate as a funtion of eight average moleular eight. The unfilled symbol represents the resaled ritial shear rate of PE-A, the M of hih is * belo the suggested ritial moleular eight ( M =10 5 g mol -1 ) and the rest of filled symbols are taken from literature (PE-KA: PDI=3.1, PE-KB: PDI=5.1, and PE-KC: PDI=6.5 31(a) ). Aording to the moleular origin of the indo effet, the appearane of the extrusion indo is orrelated ith a ertain strethed hain onformation. Suh a strethed hain onformation is dependent on relaxation time of polymer hains and the imposed shear rate. Polymers exhibit time-dependent visoelasti behaviour 49. In order to attain and maintain the strethed hain onformation for slip flo, the applied strain rate, viz. shear rate, should be greater than the inverse of the harateristi relaxation time. As a onsequene the internal relaxation, viz. oiling bak, annot our prior to the disentanglement of the adsorbed hains from the free hains. The 58

71 Weissenberg number indiates the boundary ondition for the oil-streth transition andis defined by 51 : W λ t rep i = (5.2) Where λ rep is the harateristi relaxation time of a polymer hain and t is the harateristi time of the fluid deformation rate. On substitution of the all shear rateγ for1 / t, the Weissenberg number an be expressed as: When & Wi = λ repγ (5.3) W i <1, polymer hains an reah internal equilibrium (i.e. oil state) faster than hanges arising from the externally imposed strain. Therefore in suh a situation, slip flo annot our. A oil-streth transition ours hen W i =1. In order to attain hydrodynami boundary ondition of ontinuous slip flo orresponding to high surfae energy die, W i should be above 1. Aording to reptation model 42, the relaxation time λ rep is proportional to the square of the ontour length divided by the tube diffusion oeffiient. The ontour length is linear ith moleular eight, and the tube diffusion oeffiient is inversely proportional to the moleular eight. Hene, the reptation time is λ (5.4) 3 rep ~ M Therefore, if the to PEs ith distint M have respetive indo effets at a given temperature, the higher moleular eight PE ith a longer relaxation time should exhibit the indo effet at a loer shear rate ompared to the lo moleular eight PE. It oinides ith the steep inverse poer la relationship beteen the a T γ& and M. 59

72 Figure 5.5: Temperature at pressure minimum (in the indo region) as a funtion of logarithmi M. Filled data points are from the experiments reported in Kolnaar s paper (PE- KM: PDI=7.5, PE-KB: PDI=5.1, PE-KC: PDI=6.5 and PE-KD: PDI=4.2 31(a) ). The unfilled symbol is from the polymer used in this thesis (PE-A). The extrapolated dash line refers to the possibility of the indo temperature antiipated in the high moleular eight PE (>10 6 ) having molar mass distribution belo 7.0. On the other hand, the harateristi relaxation time is also dependent on T. It an be estimated by the Arrhenius type equation: 1 1 = e λ λ 0 Ea R T g (5.5) E a 1 1 a T = exp (5.6) Rg T T0 Where λ is relaxation time at shift temperature/indo temperature, λ 0 is the relaxation time at referene temperature. E a is the ativation energy for hain relaxation, R g is gas onstant, and T is indo temperature. Aording to equation 4.5, the relaxation time dereases dramatially ith inreasing temperature. For a given linear PE ith a ertain M, there is a ritial temperature onset T orresponding to the onset of the stationary strethed hain onformation at a given apparent shear rate γ& γ& ( a ). Above this temperature, the strethed hain onformation of the adsorbed 60

73 hain annot be maintained ithin the time sale for the entire disentanglement of the adsorbed hains from free hains. For the narro extrusion indo the onset T is ira 1 C above T min (a temperature orresponding to the pressure minimum ithin the extrusion indo). Aording to the temperature dependene of the indo effet on the molar mass, if to PEs ith distint M sho indo effets at a given apparent shear rate, the higher moleular eight PE is expeted to exhibit indo effet at the higher temperature and the loer moleular eight PE is likely to have the indo effet at the loer temperature. Hoever, the ritial apparent shear rates for the onset of indo effets, different beteen high γ&, are M and lo M PEs. It is to be realised that the extrusion indo in the high M PE arises at the lo γ& indo effet is observed at highγ& of different ; hereas in the lo M PE the. In order to ompare the indo temperatures M PEs at the same apparent shear rate, the influene of shear rate on indo temperature need to be taken into aount. It is found that the extrusion indo an shift to higher temperature ith inreasing apparent shear rate. For an example, as shon in Figure 5.6, a high effet, b, atγ&, here referred to be as M PE referred as 2 shos an onset indo 2 γ&, hih is loer than that, 1 γ&, of lo PE. To have a proper omparison for the indo temperature in the to molar masses the applied shear rate in the high molar mass PE should be set at an apparent shear rate required for the lo molar mass (i.e. γ& = ( γ& +γ& )). On inreasing the shear 1 2 M rate from γ& to ( γ& +γ& ) the extrusion indo b ill shift to a higher temperature, b, 2 2 from 2 T min to 2 T min +T. Consequently, to extrusion indos for to different molar masses (high and lo) an be ompared at the same apparent shear rate as shon in Figure 5.6. At the idential apparent shear rate, 1 γ&, the indo temperature, apparently higher than that, T 1 min, of the lo M shon in Figure T min +T, of high M PE, sine T 1 min is loer than PE is 2 T min as 61

74 Figure 5.6: A shemati diagram of indo effet orresponding to to distint moleular eight PEs. The blak urve represents the extrusion indo of lo moleular eight PE. On the other hand, the grey urves represent extrusion indo of high moleular eight PE ourring at T 2 min and T 2 min+t at different shear rates. With inreasing apparent shear rate from γ& 2 to 2 1 ( γ& +γ& =) γ&, the extrusion indo orresponding to the high moleular eight PE shifts from T 2 min to the high temperature T 2 min+t. The onset temperature of the indo effet, T onset, is dependent on the relaxation time and the imposed shear rate, hereas the moleular origin of the termination temperature of the indo effet is still unrevealed. Keller suggested that the indo effet eases hen flo indued solidifiation ours 30. Hoever, it is found that the indo effet of PE-A terminates prior to the appearane of flo indued solidifiation, see Figure 5.1. Therefore, it implies that indo termination annot be simply explained by the solidifiation of the melt. One of possible reasons for the indo termination of PE-A an be related to the slip flo-hydrodynami boundary ondition ( SL - HBC ). With dereasing temperature the frequeny of adsorption and desorption proess of hains on the apillary all is likely to derease. This ould result into the inrease in density of the adsorbed hain segments on the apillary all, ν. Belo the indo temperature, ith dereasing temperature as the free volume also dereases, see Figure 5.7 at 142 C, it is less likely 62

75 for hains in the bulk to disengage from the adsorbed hain segments on the apillary all. Thus one the disengagement proess of hains in the bulk from the adsorbed hains is suppressed, the ease in floability ill be hindered ausing the inrease in pressure ultimately leading to indo termination. The overall moleular effet ill ause re-appearane of stik flo region at lo temperatures in the intermediate prior to the sudden derease in the free volume due to rystallisation and after the termination of the indo effet. Suh a possibility is further strengthened by onsidering that the ritial shear rate for disentanglement of adsorbed hains inreases ith inrease in surfae overage. Thus at a given shear rate as the density of adsorbed segments inreases the tendeny to slip ill derease. This ould be the origin for derease in distane beteen entanglements. On dereasing temperature further, the inreased bulk density and the arising onstraints due to flo ill indue solid state solidifiation due to rystallisation. Figure 5.7: Shemati vie of hydrodynami onditions arising from stik flo and slip flo orresponding to the flo behaviours observed in DTS at shear rate, 250s-1. At high temperature, 63

76 e.g. 150 C, stik flo is likely to our, as shon on top, here adsorbed hains annot maintain the strethed hain onformation. As the temperature redues to the extrusion indo temperature, 144 C, slip flo mainly ours due to the disentanglement of the adsorbed hains from free hains sine the strethed hain onformation of the adsorbed hain an be retained at the indo temperature in the time sale of the entire disengagement. With further dereasing temperature to 142 C, more hains or hain segments from the same hain an adsorb on the inner apillary all, thus dereasing the entanglement distane and suppressing the disengagement of free hains from the adsorbed hains Flo indued solidifiation (Region IV) Belo a ertain temperature the apparent visosity inreases dramatially and eventually the apillary is bloked. The reason for that has been interpreted by floindued rystallisation/solidifiation 50. The onset temperature of flo indued solidifiation, T s, is defined as a temperature orresponding to the sudden upsing in apparent shear visosity as shon in Figure 5.8. From Table 5.2, it is found that the T s inreases ith apparent shear rate. Regarding moleular origin of the flo indued solidifiation, randomly oiled polymer hains are first oriented during onvergent flo. If suh strethed hain onformation an be maintained in apillary flo, the oriented hains an at as preursor for further rystallisation. Hoever, the flo indued ordered phase is unstable under Bronian motion at elevated temperature. In order to maintain suh a strethed hain onformation, the Weissenberg number must reah or go beyond a ritial value. Aording to oil-streth theory, the strethed hain onformation an be maintained hen ε& λ rep >>1 here ε& is strain rate, here is related to apparent shear rate, and λ rep is relaxation time of agile polymer hain. It is ell knon that the λ rep dereases ith temperature. Therefore, a higher shear rate is required to maintain suh a strethed hain onformation at higher temperature, resulting in a higher T s. It is important to note that flo indued solidifiation and indo effet are both time dependent effets and are related to the strethed hain onformation. Hoever, the appearane of flo indued solidifiation requires a high Weissenberg number ompared to the indo effet. In other ords, moleular hains need to be more highly oriented and aligned in flo diretion to form a preursor for further rystallisation/solidifiation. On the other hand, in order to indue rystallisation, the size of the preursor must reah a ritial value. Therefore, onsidering flo indued rystallisation suh a strethed hain onformation needs to be maintained at high 64

77 temperature longer than that for the indo effet, so that the preursor an gro and reah the ritial partile size for further rystallisation. Therefore, the indo effet an our at high temperature, due to the loer Weissenberg number, ompared to flo indued solidifiation. Figure 5.8: Logarithmi plot of apparent shear visosity as a funtion of reiproal temperature indiating the flo indued solidifiation effets emerging at C, i.e / (T onset )= Results from dynami temperature seep of PE-A at shear rate of 200s -1 in Figure 5.2. Table 5.2 The onset temperature of flo indued solidifiation of PE-A at different apparent shear rate. Apparent shear rate (s -1 ) T s ( C) Conlusion The appearane of extrusion indo of PE-A implies that the ritial moleular * eight, M, for the indo effet is belo 10 5 g mol -1, an observation in ontradition to the suggested value given by Keller and Kolnaar. 65

78 With regards to the effet of shear rate on extrusion indo, it as found that the indo effet shifted to high temperature ith inreasing apparent shear rate. On the other hand, T s inreased ith the apparent shear rate sine flo indued ordered phase an only be maintained at higher strain rate ith inreasing the temperature. The moleular eight dependene is an exquisite feature of the indo effet and reveals the moleular origin of extrusion indo. The resaled ritial apparent shear rate, at γ&, shoed a poer la dependene on M that sales ith -3.7±0.2. This M dependene gives a quantitative relationship beteen stik-slip theory and extrusion indo. Therefore, moleular origin of melt flo singularity of linear PE is onluded to arise from slip flo due to the disengagement of tethered hains on apillary all surfae from the free hains, here the aligned tethered hains may give rise to the formation of olumnar like mesophase and finally ease the disengagement proess. 66

79 Chapter 6: Melt flo singularity of bimodal polyethylene 6.1 Introdution In the previous hapters it is onlusively shon that moleular origin of the extrusion indo arises from the disengagement of tethered hains adhered to the apillary all from the free hains (hains residing in the bulk), ith assistane of a possible appearane of the olumnar mesophase. Aording to the disentanglement mehanism 39, high moleular eight linear PE has the potential to possess a higher temperature indo due to the relatively longer relaxation time 51. In this hapter, a bimodal PE, referred to as PE-B, is seleted to investigate the effet of bimodal moleular eight distribution on the melt flo singularity. The material used in this hapter, oded as PE-B, is synthesised by to different Ziegler Natta atalysts, here one atalyst synthesises the high molar mass and the other atalyst is for the lo molar mass. Hene, PE-B an be onsidered as a moleular blend of to different moleular eight omponents mixed. For these fundamental studies, the synthesised sample PE-B is kindly provided by Borealis. 6.2 Results The basi effet of melt flo singularity of PE-B The bimodal PE, PE-B, shos an analogous melt flo singularity, depited in Figure 6.1, in DTS as unimodal linear PE. The pressure drop ours ithin a temperature interval, 144~147 C, in hih polymer melts are extruded smoothly ithout any distortion. In vie of flo behaviour, stik flo starts from a high temperature, here the extrusion pressure gradually inreases ith dereasing temperature. Belo 156 C, the flo behaviour of PE-B is situated in the pressure osillation regime, in hih the extrudate shos periodi bulk distortion. One the temperature redues to 147 C, a smooth extrudate ith minimum die sell is observed. With a further derease in the temperature, folloing the extrusion indo regime (<144 C), the extrusion pressure jumps up dramatially and a onsiderable inrease in die sell ours. Figure 6.2 shos four typial extrudate profiles at 140 C, 146 C, 152 C and 160 C, orresponding to four distint flo regimes: flo indued solidifiation, extrusion indo, melt instabilities and stable melt flo respetively. The die sell ratios sho a minimum value in the extrusion indo temperature as shon in Figure

80 It is orth noting that the observed extrudate profiles in Figure 6.2 at 152 C onsist of three lasses. Starting from right hand side a helial distortion ours in slip flo, just after the extrusion pressure reahes the maximum value. Folloing that, fairly smooth extrudate is observed in the slip flo regime at relatively lo apparent shear rate ompared to the helial distortion slip flo. Finally, very smooth extrudate shon on the left hand side emerges in the stik flo regime. It is apparent that the die sell ratio of smooth extrudate yielded in the slip flo is higher than that in the stik flo. The effet of apillary flo on extrusion indo is studied using a tin-bore rheometer, and ompared ith apillary free flo. Besides the end pressure orretion, tin bore rheometer an offer a route to perform tin rheologial haraterisation simultaneously in the same ondition. Prior to rheologial measurements, the sample PE-B as filled into eah barrel and as subjeted to idential thermal history. Folloing the pre-heating the same piston veloity as applied in DTS (Dynami Temperature Seep), resulting in an idential apparent shear rate. Capillary die attahed on the left barrel led to apillary flo, hereas orifie die on the right side resulted in a apillary free flo. It is apparent that a onsiderable pressure drop emerges at the indo temperature in the apillary flo as shon in Figure 6.1, hereas no indo effet is observed ithin pure onvergent flo. These findings are in agreement ith the earlier studies 31 and onfirm that the onvergent flo is not the origin of the indo effet, hile apillary flo failitates the appearane of the indo effet. 68

81 Figure 6.1: A plot of extrusion pressure vs. temperature reorded during dynami ooling run at a given apparent shear rate of 150s -1, shoing the pressure minimum at 146 C (Cooling rate 1.50 C min -1, M = , apillary die geometry L-D-A: 16-1-π, Orifie die geometry: 0-1-π). PLeft orresponds to extrusion pressure drop in apillary flo and PRight is assoiated ith extrusion pressure drop in apillary free flo. Figure 6.2: Photographs of extrudates obtained in DTS at different temperature at a fixed shear rate of 150s -1 69

82 Figure 6.3: Die sell ratio as a funtion of temperature reorded in ISR at a fixed shear rate, 150s The effet of apparent shear rate on the melt flo singularity of PE-B The influene of apparent shear rate on the melt flo behaviour of PE-B is shon in Figure 6.4. The ritial shear rate orresponding to the onset of the indo effet is determined in DTS. The extrusion indo appears at a minimum shear rate of 108s -1, referred to as a ritial shear rate γ& for PE-B. Belo this ritial value, no indo effet is observed in the extrusion of PE-B, here the extrusion pressure gradually inreases ith the dereasing temperature throughout the entire experimental temperature sale. The gradual inrease in pressure is attributed to the inrease in melt visosity (η ), hih obeys a familiar Arrhenius type of relationship beteen η and T. Above the ritial shear rate γ& for PE-B, a single pressure drop ours in the indo temperature interval. In addition, it is observed that there is an inverted saddle shaped pressure osillation pattern ourring at a shear rate of 150s -1. With a further inrease in the apparent shear rate, at 300s -1, three pressure drops emerge instead of one. One pressure drop loated at the lo temperature regime 146~148 C is named as lo temperature indo, here the smooth extrudate ithout any distortion is observed. If this lo temperature indo has the same moleular origin 70

83 as single extrusion indo observed at lo shear rate, suh as at a shear rate of 108s -1, it is apparent that ith the inrease in the shear rate the indo effet shifts to high temperature and pressure minimum shifts to high value. Regarding the middle temperature pressure drop, hereafter referred to as the middle temperature indo, it possesses loest pressure minimum loated at C in omparison ith the other pressure drops. On the other hand, the middle temperature indo is loated at a broad temperature regime from 148 C to 154 C. The extrudate obtained in this regime is smooth and glossy ith no distortions. Besides the to pressure drops, the third pressure drop is observed at the highest temperature, beteen 154 C to 158 C. Although there is no pressure osillation ourring in the high temperature pressure drop, the extrudate in this regime exhibits fine sale surfae distortion as shon in Figure 6.5 at 155 C. From these observations it is apparent that the extrusion indo of the bimodal PEs is relatively ompliated at high shear rates and opens a possibility to iden the narro pressure drop in linear PEs. Figure 6.4: A plot of extrusion pressure vs. temperature reorded during DTS of PE-B at different apparent shear rate, 50s -1, 108s -1, 150s -1 and 300s -1 ith a onstant ooling rate 1.50 C min -1 (apillary die geometry: L-D-A: 16-1-π). Figure 6.5 shos different extrudate profiles obtained at various temperatures in DTS at the shear rate of 300s -1. It is to be realised that the periodi bulk distortion ours 71

84 above 158 C. This temperature is muh higher than that observed at the loer shear rate of 150s -1. The die sell ratios reorded in ISR experiments are plotted against temperature in Figure 6.6. From this Figure it is apparent that die sell ratio has to minima, at C and 152 C, hih oinide ith indo loation, viz. indo temperatures ourring in DTS at a shear rate of 300s -1, depited in Figure 6.4. In addition the die sell ratio at 152 C is loer than at C. Figure 6.5: Photographs of extrudate obtained in DTS at different temperatures at a fixed shear rate, 300s

85 Figure 6.6: The die sell ratio as a funtion of temperature reorded in ISR at a fixed shear rate, 300s Windo effet at isothermal onditions In dynami experiments, extrusion pressures are reorded ith dereasing temperature at a ooling rate of 1.50 Cmin -1. In spite of the slo ooling rate, thermal equilibrium annot be attained on aount of thermal lag in beteen the apillary all and polymer melt. To verify the existene and appearane of the indo effet in isothermal flo onditions a series of isothermal step rate (ISR) rheologial haraterisations ere performed at various temperatures. Figure 6.7 depits a series of plots of extrusion pressure vs. time at different shear rates reorded at isothermal onditions. In these set of experiments hile the temperature is kept onstant, shear rate is varied ith time. The resultant hanges in pressure orresponding to apillary flo (Pleft) and apillary free flo (Pright) are reorded. From Figures 5.7(a-), it is apparent that extrusion pressure at 150s -1 is less than that at 50s -1. These high shear rate anomalies an only be interpreted by distint hydrodynami onditions beteen stik flo and slip flo. Further evidene to verify the appearane of slip flo in extrusion indo flo onditions ill be shon in slip flo veloity measurements. A omparison of pressure at a speifi shear rate an be made by ompiling the experimental data at different temperatures. For instane, 73

86 shaded regions in Figure 6.7 orrespond to extrusion pressures reorded during the isothermal apillary flos at a speifi shear rate of 150s -1. Compiling all the isothermal results together, a panorama plot of extrusion pressure vs. temperature at a shear rate of 150s -1 is shon in Figure 6.8(a). It depits hange in extrusion pressure ith temperature at a fixed shear rate of 150s -1 in hih a pressure minimum observed at 146 C is onsistent ith indo temperature loation found in DTS shear rate of 150s -1. Figure 6.8(b) depits extrusion pressures reorded in ISR at a shear rate of 300s -1, in hih triple pressure drops oinide ith the high shear rate indo effet observed in DTS at 300s -1 as ell. These isothermal studies omplement the existene of extrusion indo and indo temperature loation determined by DTS experiments. Hoever, the pressure minima reorded in ISR is higher than those measured in DTS, hih may arise from thermal lag in DTS. Figure 6.7(a): ISR results at 144 C sho the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. 74

87 Figure 6.7(b): ISR results at 145 C sho the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. Figure 6.7(): ISR results at 146 C sho the extrusion pressure vs. time at different shear rate. Pressure profile at 150s -1 are highlighted and ompared ith others at different isothermal onditions. 75

88 Figure 6.7(d): ISR results at 147 C sho the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. Figure 6.7(e): ISR results at 148 C sho the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. 76

89 Figure 6.7(f): ISR results at 150 C shos the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. Figure 6.7(g): ISR results at 152 C shos the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. 77

90 Figure 6.7(h): ISR results at 154 C sho the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. Figure 6.7 (i): ISR results at 155 C sho the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. 78

91 Figure 6.7 (j): ISR results at 158 C sho the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. Figure 6.7(k): ISR results at 160 C sho the extrusion pressure vs. time at different shear rate. Pressure profiles at 150s -1 are highlighted and ompared ith others at different isothermal onditions. In addition, at all temperatures periodi bulk distortion and pressure osillation are not observed in apillary free flo. These findings further onfirm that periodi bulk distortion arises from apillary flo. Seondly, it is found that the extrusion pressure 79

92 inreases ith the imposed shear rate in the stik flo regime. Finally, it is orth pointing out that there is no slip flo ourring in the ourse of apillary free flo (flo of the extrudate through the orifie alone), hih is in the agreement of that the apillary flo gives rise to the indo effet. The ISR results fully omplement the existene of indo effet observed in DTS. From the omparison it ould be stated that the indo loation and pressures minimum from DTS oinides ith the results obtained from the isothermal experiments, even though the thermal equilibrium annot be attained in DTS. Therefore, DTS ould be suggested to investigate the indo effet sine ISR experiments are more time-onsuming tehnique. Parameters that ould be determined in DTS at the ooling rate of 1.50 C min -1 are the ritial apparent shear rate for the onset of the indo, γ& temperature loation., indo temperature intervals, and indo Figure 6.8(a): A plot of extrusion pressures vs. temperature at a shear rate of 150s -1 reorded in ISR for the bimodal sample PE-B. The vertial lines represent osillations in the pressure (Die geometry: L-D-2α: 16-1-π). 80

93 Figure 6.8(b): A plot of extrusion pressure vs. temperature at a shear rate of 300s -1 reorded in the ISR experiment. The Figure shos three pressure drops loated at 146 C, 152 C and 158 C. These observations are in aordane ith DTS results for the sample PE-B, see Figure 6.4. The vertial line at 160 C represents osillations in the pressure (Die geometry: L-D-2α: 16-1-π) Isothermal mono-rate time seep haraterisation Melt frature is a ommon problem enountered in plasti extrusion. The onset of melt irregularities indiates boundary onditions for polymer proessing. Considering the indo effet, to flo ritialities indiate the boundary ondition of the extrusion indo. Therefore, an isothermal mono-rate time seep (IMTS) haraterisation as adopted to determine the flo ritialities, in hih the ritial p apparent shear rates inluding γ&, γ& and γ& h, orresponding to onset of periodi bulk distortion, indo effet slip flo and helial distortion respetively, are determined at a given temperature. In addition, melt instabilities and extrudate distortions are also studied in IMTS at different temperatures and apparent shear rates. Sine polymer melts have memory effet, the flo history does influene the rheologial behaviour. Therefore, IMTS is adopted to determine the extrusion pressure at a single shear rate (mono-rate) ithout any interferene of pre-flo history. In this respet ompared to ISR experiments, IMTS is more aurate. The melt frature observed in the ourse of apillary flo of PE-B falls into to ategories, namely periodi bulk distortion, assoiated ith pressure osillations, and helial distortion. Hoever, surfae melt frature, referred to as shark-skin, does not emerge during the apillary flo of PE-B at varying flo onditions. Figure 6.9 shos extrusion pressure at different shear rates reorded in IMTS test at 170 C. The 81

94 extrudate profiles and flo behaviour are desribed as follos ith the inreasing shear rate: (1) The extrudate is smooth and glossy hen the shear rate is beloγ& p. In addition, surfae distortion is not observed in the high-shear-rate stik flo of the bimodal polymer, PE-B; before the appearane of the pressure osillation. Hoever, suh a shark-skin effet usually ours at high-shear-rate stik flo of unimodal polyethylene ith relatively lo polydispersity, (2) At and above the γ& p (346s -1 ), pressure osillations are observed and are aompanied ith periodi bulk distortion. The pressure osillation possesses a regular pattern of inreasing and dereasing pressures as a funtion of time, shon in Figure Combining the reorded pressure osillations in Figure 6.13 and the orresponding extrudate profile shon in Figure 6.9(b), it is found that eah yle of pressure osillation observed at 170 C onsists of to steps. In the first step, the extrusion pressure inreases gradually during stik flo, yielding a smooth and glossy extrudate. With inreasing extrusion pressure, before attaining the maximum value, the efflux rate drops to the minimum. One the pressure reahes the maximum value, extrusion pressure dereases dramatially in a short time and the resultant extrudate shos helial distortion. (3) With inreasing the apparent shear rate further, at or above h γ& (510 s -1 ), helial distortion ours during slip flo ithout any trae of pressure osillation. The extrusion pressure orresponding to the onset ourrene of helial distortion sueeds the minimum pressure of pressure osillation at the highest apparent shear rate. In addition, the extrusion pressure in this regime inreases ith the imposed apparent shear rate. With respet to the flo behaviour and extrudate profiles observed at relatively lo temperature at 158 C and 152 C, it is found that the slip flo falls into to ategories in both the stik-slip flo and the stationary slip flo. One is helial distortion slip flo as aforementioned at 170 C, the other is termed as indo effet slip flo sine the flo onditions and extrudate profile are idential to the indo effet. Regarding the stik-slip flo observed at 158 C and 152 C, pressure osillation ours hen the γ& γ& a p and the resultant extrudate profiles are shon in Figure 6.10(b) at 220s -1 and Figure 6.11(b) at 110s -1. It an be observed that there are three types of extrudate 82

95 profiles emerging in the pressure osillation regime rather than to at 170 C ith the shear rate of 370s -1. The only differene is the emergene of disrete indo effet slip flo. It ours after extrusion pressure reahes a ritial value during the pressure osillation. The resultant extrudate is smooth but ith higher die sell ratio ompared ith smooth extrudate yielded in the disrete stik flo at the same shear rate. With regards to stationary slip flo, indo effet slip flos our first hen the γ& reahes or exeeds the orrespondingγ& a 6.11(b) at 240s -1. When γ& a γ& h, as shon in Figure 6.10(b) at 260s -1 and, helial distortion slip flo ours. As the temperature delines further, at 146 C as depited in Figure 6.12, the helial distortion slip flo does not appear in the periodi distortion regime as shon in Figure 6.12(b). Figure 6.9(a): Flo urve for PE-B reorded at 170 C. The vertial lines represent the pressure osillations. The arros indiate the γ& at 346s -1 and γ& at 510 s -1. p h 83

96 Figure 6.9(b): Typial extrudate profiles at 170 C, shoing smooth extrudate in the stik flo regime at 200s -1, periodi bulk distortion at 370s -1 in the stik-slip flo regime and helial distortion at 550s -1. Figure 6.10(a): Flo urve for PE-B reorded at 158 C. The vertial lines represent the pressure osillations. The arros indiate the γ& at 170s -1, γ& at 259s -1 and γ& at 405s -1. p h 84

97 Figure 6.10(b): Typial extrudate profiles at 158 C, shoing smooth extrudate at 160 s -1 in the stik flo regime, periodi bulk distortion at 220s -1 in the stik-slip flo regime, and smooth extrudate again at 260 s -1 in the indo effet slip flo regime and helial distortion at 450 s -1. Figure 6.11(a): Flo urve for PE-B reorded at 152 C. The vertial lines represent the pressure osillations. The arros indiate the γ& at 103s -1, γ& at 240 s -1 and γ& at 375 s -1. p h 85

98 Figure 6.11(b): Typial extrudate profiles at 152 C, shoing smooth extrudate at 100s -1 in the stik flo regime, periodi bulk distortion at 110s -1 in the stik-slip flo regime, smooth extrudate again at 240s -1 in the indo effet slip flo regime and helial distortion at 425s -1. Figure 6.12(a): Flo urve for PE-B reorded at 146 C. The vertial lines represent the pressure p osillations. The arros indiate the γ& at 60s -1, γ& at 103s -1. The insert shos there is no helial distortion ourring at 620s

99 Figure 6.12 (b): Typial extrudate profiles at 146 C, shoing smooth extrudate at 50s -1 in the stik flo regime, periodi bulk distortion at 100s -1 in the stik-slip flo, smooth extrudate again at 150 s -1 in the indo effet slip flo regime and helial distortion at 650s -1. In omparison ith the hydrodynami boundary onditions at varying temperatures, it is found that the flo ritialities of p γ& and γ& shift to higher values ith inreasing temperature. In addition, the pressure minima and maxima of pressure osillation inrease ith temperature. With respet to the helial distortion, at high temperatures ( 158 C), it is found that the distortion ours hen the resultant all shear stress attains a ritial value, σ h, at and around 0.194~0.195MPa, hih remains h independent of temperature. Hoever, there is lo-temperature anomalies of σ. As h shon in Figure 6.11(a), the σ redues to 0.145MPa at 152 C hih temperature is situated in the temperature interval of the middle temperature extrusion indo observed in DTS and ISR experiments. Whereas, the σ h inreases to 0.235MPa at 146 C orresponding to the lo temperature indo loation. These findings suggest that the existene of extrusion indo at 152 C or flo indued solidifiation at 146 C is likely to have impats on theσ. h It is orth highlighting the σ h dependene of the extrudate profile in periodi distortion. In pressure osillation, the upper limit all shear stress, here referred to 87

100 asσ ; orresponds to the pressure maximum in the spurt flo; on the other hand, u loer limit all shear stress, σ, is assoiated ith the minimum pressure. l a) As shon in Figure 6.13, at high temperature 170 C, σ is equal to Therefore, only helial distortion slip flo ours in the disrete slip flo. b) At middle indo temperature, 152 C, σ h lies beteen h u σ and l σ. l σ as h shon in Figure It is found that σ indiates boundary ondition beteen the disrete helial distortion slip flo and the disrete indo effet slip flo. In eah pressure osillation yle, one the extrusion pressure reahes the upper limit, polymer melt aumulated in the disrete stik flo spurts out and shos helial distortion until σ reahesσ. Folloing that the flo behaviour is loated in the disrete indo effet slip flo regime hen σ < σ. h h u ) At lo temperature, 146 C, σ is greater than σ, only the disrete indo effet slip flo ours in the periodi distortion regime. h Figure 6.13: Pressure osillation reorded in IMTS test at 170 C at an apparent shear rate of 370s -1, shoing eah yle of pressure osillation onsists of to steps: 1 is the disrete stik flo; 2 is the disrete helial distortion slip flo. 88

101 Figure 6.14: Pressure osillation reorded in IMTS test at 152 C at an imposed apparent shear rate of 150s -1, shoing eah yle of pressure osillation onsists of three steps: 1 is the disrete stik flo; 2 is the disrete helial distortion slip flo and 3 is the disrete indo effet slip flo. Figure 6.15: Pressure osillation reorded in IMTS test at 146 C at an imposed apparent shear rate of 60s -1, shoing eah yle of pressure osillation onsists of to steps: 1 is the disrete stik flo; 2 is the disrete indo effet slip flo. 89

102 6.2.5 The effets of die geometry on extrusion indo Variation of apillary length: The role of apillary flo in the melt flo singularity of PE-B as investigated and ompared ith apillary free flo using an orifie die. It as found that the extrusion indo vanished in apillary free flo as shon in Figure 6.16 and 6.17, sine no pressure drop ours hen the polymer melt flos through an orifie die. From here it is apparent that the existene and appearane of the indo effet is strongly dependent on apillary flo. In other ords, elongational flo is not mehanism responsible for the melt flo singularity of polyethylene sine no indo effet is observed from the onvergent flo alone. On the other hand, it is found that the appearane of the indo effet is independent of apillary length. Finally it is also found that γ& remains unaffeted ith varying apillary length, viz.108±5s -1. Figure 6.16: Lo shear rate, 150s -1, indo effets of PE-B ith varying the die length (16-1-π, 12-1-π, 8-1-π, 4-1-π and 0-1-π viz. orifie die). 90

103 Figure 6.17: High shear rate, 300s -1, indo effets of PE-B ith varying die length (16-1-π, π, 8-1-π and 0-1-π viz. orifie die) Variation of die entry angle: Elongational flo is not the origin of melt flo singularity. Hoever, it may have an influene on flo ritialities. Varying the die entry angle an adjust the elongational strength during the onvergent flo for fixed barrel and apillary diameters. The elongational strength is expeted to inrease as the entry angle rises on aount of ensuing larger onvergene at die entry. The γ&, orresponding to the onset appearane of the indo effet at 146 C is plotted against the die entry angle as shon in Figure 6.18(a). It is found that γ& orresponding to the lo temperature indo inreases as the die entry angle dereases. On the other hand, for the middle temperature extrusion indo, Figure 6.18(b). γ& is independent of the die entry angle, depited in 91

104 Figure 6.18(a): γ& for lo temperature indo at 146 ith varying entry angle (16-1-π, /6π, /3π, /2π, and /3π) Figure 6.18(b): γ& for middle temperature indo at 152 C ith varying entry angle ith onstant apillary length and bore diameter (16-1-π, /6π, /3π, /2π, and /3π) 92

105 6.2.6 Slip flo veloity The slip veloity as determined ith a series of dies having different bore diameters, but the L/R ratio of eah die is kept onstant at 32; hene, the end pressure orretion is not required. Slip flo veloities ere performed at to harateristi indo temperatures, 146 C and 152 C as shon in Figure 6.19(a-b). It is found that slip flo ours hen the imposed γ& a is above the orrespondingγ&. Therefore, it gives mutual support to the hydrodynami ondition of extrusion indo, viz. slip flo. In addition, the slip flo veloity inreases ith imposed γ& a as shon in Table 6.1(a-b). Figure 6.19(a): The volumetri output rate at different all shear stress plotted as a funtion of the inverse of die radius at 146 C. Slip veloity is determined from the gradient of eah line. 93

106 Figure 6.19(b): The volumetri output rate at different all shear stress plotted as a funtion of the inverse of die radius at 152 C. Slip veloity is determined from the gradient of eah line. Table 6.1(a): Slip veloity as a funtion of all shear stress at 146 C. Shear stress (MPa) Slip flo veloity (mm s -1 ) σ 1 = σ 2 = σ = σ 4 = σ = Table 6.1(b): Slip veloity as a funtion of all shear stress at 152 C. Shear stress (MPa) Slip flo veloity (mm s -1 ) σ 1 = σ 2 = σ = σ 4 = σ = Study flo indued orientation via ex-situ ide angle X-ray sattering (WAXS) The effet of temperature on flo indued orientation as studied at a shear rate of 50s -1 in hih there is no appearane of the indo effet. As shon in Figure 6.20, 94

107 the orientation effet during apillary flo inreases as the extrusion temperature dereases. At 150 C there is no ar observed in X-ray diffration patterns. It indiates that there is no orientation remaining on the surfae layer of extrudates. Whereas, ith dereasing the extrusion temperature to 148 C, tin saddle shaped X- ray diffration pattern orresponding to (110) are observed on the equator. It indiates that an oriented struture formed during apillary flo and an be retained after extrusion. This orientation struture is orrelated to tisted kebabs 52. As the extrusion temperature dereases further, to 146 C and 144 C, saddle shaped X-ray diffration patterns on eah side move toards the equator and merge into eah other to form to single peaks on the equator. This X-ray diffration pattern is assoiated ith no tisted kebabs, viz. more highly oriented struture ompared to that at 148 C. On the other hand, the alulated Hermans orientation fators of -axis (Figure 6.21) also indiate that the orientation effet on surfae layer of extrudate tends to be more pronouned ith dereasing temperature. 95

108 Figure 6.20: X-ray diffration patterns of extrudate surfae at different extrusion temperatures, but at the same apparent shear rate, 50s -1. White arros sho the flo diretion of extrudate. 96

109 Figure 6.21: Hermans orientation fators as a funtion of extrusion temperature at the same apparent shear rate, 50s -1. Here the orientation degree of PE is quantified via the Hermans orientation fator, f hih an be alulated from an equation as (6.1) shon belo: f 2 (3 < os β > 1) 2 = Where β is the angle beteen the flo diretion and the hain diretion, viz. the - axis of orthorhombi PE rystal. Generally speaking the orientation fators are alulated based on (200) and (020) refletions. Sine the (020) refletion for PE does 2 not exist, the os β > is alulated via Wilhinsky s method 53 using the (110) and (200). < 2 < os The os β > is alulated as follos: < hlk (6.1) 2 2 β >= < os β > < os β > (6.2) os 2 β hkl = π 2 0 I ( β ) os π I ( β ) sin β sin β dβ β dβ < Where I(β ) is the diffrated intensity and β is azimuthal angle. os β > and 2 < 200 os β > are alulated by Eq 6.3 aording to the diffration intensity at (6.3) 97

110 different azimuthal angles of inner diffration ring and outer diffration ring respetively (Appendix D). Aording to the slip flo theory orresponding to a high surfae energy die, e.g. metal die ithout oating, slip flo arises from disentanglement of adsorbed hains from free hains. Therefore, the adsorbed hains are likely to keep attahing on the inner apillary all; on the other hand, the free hains are extruded out of the die after disentanglement from tethered hains, resulting in a less oriented surfae layer of extrudate. In order to give support to this theory in pratie, an ex-situ WAXS as performed to study the flo indued orientation on the extrudate surfae after extrusion. It is apparent that in-situ WAXS annot be ompetent to this aim sine it is impossible to identify the disengagement interfae beteen adsorbed hains and free hains. Moreover, this interfae might not exist for an inompletely developed slip flo, espeially for a broad moleular eight distributed polymer or bimodal polymer. [All samples used in ex-situ WAXS experiments are from ISR tests]. To explore the indo effet on flo indued orientation, X-ray diffration patterns of extrudate surfae layer are ompared at different apparent shear rates, but extruded at an isothermal ondition, i.e. indo temperature, 146 C, orresponding to the pressure minimum of extrusion indo ourring at 150s -1. It is depited in Figures 6.22 that there is a highly orientated struture, orresponding to no tisted kebab, observed at lo apparent shear rate, 50s -1. Hoever, an unexpeted less orientation is observed at high shear rate of 150s -1,and the folloing X-ray diffration patterns orresponding to higher apparent shear rates also possess less orientation ompared ith stik flo, at 50s -1. One of possible reasons for the high shear rate anomaly is due to slip flo. Combining ith the results from ISR at 146 C as depited in Figure 6.7(), it is found that slip flo is the hydrodynami origin of indo effet, hih oinides ith the existene of indo effet slip flo. In addition, ith further inreasing the apparent shear rate in the indo effet slip flo region, the orientation fators inrease slightly; hoever they are still muh less than that obtained in stik flo at a lo shear rate of 50s -1. Moreover, hain relaxation should be taken into aount sine the orientations are not determined in in-situ experiments 98

111 Figure 6.22: X-ray diffration patterns as a funtion of apparent shear rate at the same extrusion temperature, 146 C. White arros sho the flo diretion of extrudate 99

112 Figure 6.23: Hermans orientation fators as a funtion of apparent shear rate at the same extrusion temperature, 146 C. 6.3 Disussion Stik-slip flo Numerous studies have been devoted to investigate the origin of spurt flo, here referred to as stik-slip flo 26,54. The general effet of stik-slip flo is pressure osillation as a funtion of time, observed in the ourse of rate-ontrolled apillary flo. Aording to Kolnaar s studies 31(), the extrudate profiles observed in pressure osillation onsist of three repeating units: (a)surfae distortion, also referred to as sharkskin effet, ourring in the disrete stik flo, (b)helial distorted extrudate emerging in the high-shear-rate disrete slip flo after the pressure reahes the maximum value and ()smooth extrudate obtained in lo-shear-rate disrete slip flo. Hoever, in the apillary flo of PE-B sharkskin does not our under any flo onditions prior to the appearane of pressure osillation. This oinides ith previous studies by Hoells and Benbo 26(). It as found that a broad moleular eight distribution loers the suseptibility to sharkskin. The disappeared sharkskin effet in stik flo of PE-B is a symptom of distint extrudate profiles ourring in stik-slip flo of bimodal moleular eight distributed linear polyethylene. It as found that in stik-slip flo of PE-B a smooth extrudate ith lo die sell ratio yielded in the disrete stik flo. 99

113 The hydrodynami origin of the stik-slip flo in rate ontrolled rheometer an be eluidated by stik-slip flo theory 39. Prior to stik-slip flo, a steady state stik flo an be fully developed at lo shear rate here no slip flo ours, and a smooth and glossy extrudate is yielded. With inreasing the imposed piston veloity, the apparent shear rate inreases. One the imposed γ& a reahes theγ& p, spurt flo ours. At the beginning of the stik-slip flo, the extrusion pressure builds up gradually in the disrete stik flo due to the differene beteen the applied flo rate Q 2 a VπR b = (V is piston veloity, Rb is radius of barrel) and the real volumetri output rateq. When the extrusion pressure/ the all shear stress reahes the ritial value ( σ = σ ), slip flo ours and extrusion pressure drops suddenly. u Extrudate profiles in either disrete slip flo or stationary slip flo are dependent onσ. When σ σ, helial distortion slip flo ours. On the other hand, hen h σ > σ h σ, indo effet slip flo emerges. The stik-slip flo observed in the stress ontrolled apillary flo is signified by a jump in the flo rate at a ritial shear stress σ. Therefore σ indiates the hydrodynami boundary ondition for stik-slip flo. Hoever, neither σ nor γ& a are under ontrol in the rate ontrolled apillary flo. σ periodially inreases and dereases ith the pressure osillation. Meanhile, the real apparent shear rate γ& a hanges as a funtion of time. It is orth highlighting that the real apparent shear rate, γ&, is not equal to the applied apparent shear rate, γ&, during stik slip flo sine a Q is not idential ithq a. The γ& a falls into to atalogues: one is assoiated ith the disrete stik flo, named as stik flo apparent all shear rate γ& a a, stik, the other orresponds to disrete slip flo, termed as slip flo apparent all shear rateγ&. During disrete stik flo it is apparent that γ& a, stik starting from 4 / R a, slip 3 Q a π and then u gradually dereases until σ reahes σ. On the other hand, γ& a, slip starts from a 3 maximum value and redues to 4Q a / π R. 100

114 Figure 6.21: A shemati plot of real apparent shear rate as a funtion of time during stik-slip flo in the rate-ontrolled apillary rheometer. The blak urve denotes the extrusion pressure in melt instability; the dash line shos the applied apparent shear rate, and the gray urves represent the real apparent shear rate, viz. γ& a, slip in region one and γ& a, stik in region to Hydrodynami boundary onditions of indo effet Conventional polymer proessing is performed in the steady state stik flo regime. The hydrodynami boundary ondition is governed by a ritial shear rate, orresponding to the onset of periodi bulk distortion, or referred to as bamboo effet. Here this ritial shear rate is signified by p γ&. Whereas, it as found that the steady state stik flo is not the only polymer proessing ondition sine the smooth extrudate ith uniform throughput rate an also be determined in the indo effet. The orresponding hydrodynami ondition is indo effet slip flo. Compared ith stik flo, the indo effet slip flo ours at relatively higher shear rate and lo temperature, and the orresponding hydrodynami boundary onditions are dominated by to ritial shear rates, rate of the indo effet slip flo and the γ& and h γ&. The γ& is the loer limit shear h γ& is the upper limit shear rate Moleular origin of the double extrusion indos Bimodal PE an be onsidered as a PE-PE blend via hemial route. It onsists of to moleular eight omponents, one is the lo moleular eight omponent M, and the other is the high moleular eight omponent M H. Prior to exploring the moleular origin of the dual indo effet, the nature of single extrusion indo of L 101

115 PE-B at lo temperature, ourring at the ritial apparent shear rate of PE-B, 108s -1, need to be revealed. Aording to the moleular eight dependene of the ritial apparent shear rate, M H is likely to give rise to the onset single extrusion indo. Hoever, suh a lo indo temperature does not obey the theoretial predition regarding the moleular eight dependene of indo temperature, Figure 6.5. In order to give a theoretial explanation for this ontradition, the hain dynamis of entangled fluids need to be realled. The marosopi shear stress applied in the omplex fluids is transferred to eah moleular via entanglement onstraints. In the moleular sale, aording to the reptation model, the entanglement onstraints on eah polymer hain arise from its neighbouring hains ating as a onfining tube along its ontour. Regarding the indo effet the adsorbed hains need to be strethed by neighbouring hains via entanglement onstraints under flo ondition. For a broad/bimodal molar mass distributed linear polyethylene, the polymer hains have a ide range of lengths. Some of the entanglement onstraints beteen the short hains and long tethered hains ill disappear and unreoverable under flo ondition sine short hains, initially entangled ith an adsorbed long hain, are likely to oil bak on another previously entangled long hain at high-temperature flo ondition. Therefore, the short free hain is likely to release the entanglement onstraint ith the long adsorbed hain resulting in easing onstraint release. Consequently, the onset indo effet of M H shifts to lo temperature and ours at high ritial shear rate in order to maintain the strethed onformation of long hains via limited entanglement onstraints. With inrease in the shear rate the single extrusion indo arising from the slip flo of M H shifts to higher temperature and also broadens, see figure 6.4. Above the ritial shear rate the broadened extrusion indo of M H may be attributed to M L sine random oiled short hains an hinder the long hain adsorption on the apillary all, resulting to a lo indo termination temperature. When the applied shear rate rises further to 300s -1, a duel indo effet ours. The lo temperature indo is likely to arise from indo effet slip flo of M L. In omparison of pressure minima in the dual extrusion indo, the high temperature indo has the lo pressure minimum. It is oinided ith the moleular eight 102

116 dependene of ritial shear stress, i.e. the higher the moleular eight, the lo the ritial shear stress. Even though the ritial shear stress for the onset of indo effet is also dependent on temperature, onsidering the lo temperature anomaly, the lo ritial shear stress for the high temperature indo should be still attributed to M H. In summary, M H and M L give rise to high temperature indo and lo temperature indo respetively. The moleular origin of high-surfae-energy-die slip flo is attributed to the disentanglement of tethered hains on apillary all from free hains in bulk. Hoever, there is no evidene to support this. In this hapter, ex-situ WAXS results give some support to this theory. At the indo temperature, 146 C, orientation fators of C-axis are ompared at different apparent shear rate as depited in Figure It as found that the orientation fator of C-axis at 50s -1 is higher than those at 150s -1, 200s -1 and 300s -1. It an only be eluidated by indo effet slip flo, in hih the adsorbed hains are strethed during apillary flo and are retained in a strethed hain onformation. Suh strethed adsorbed hains form a self lubriation layer on the inner apillary all and redue the surfae energy of the apillary all to ease the slip flo. Consequently only free hains ith less orientation are extruded through the apillary die The influene of die geometry on flo ritialities Change length ith diameter and entry angle onstant. Capillary flo gives rise to the melt flo singularity of PE sine there as no indo effet ourring during melt flo through an orifie alone, viz. apillary free flo. It implies that the appearane of indo effet does not rely on onvergent flo. Regarding the effet of apillary length on flo ritialities of extrusion, it is found that the indo effet is independent of the apillary length Change entry angle ith diameter and length onstant. The influene of onvergent flo on the indo effet as studied using different entry-angle dies ith a fixed apillary diameter and apillary length. Thus the elongational strength an be altered by varying the die entry angle. Though the onvergent flo does not give rise to the melt flo singularity, it influenes the flo 103

117 ritialities regarding the lo temperature indo. It as found that the γ& inreases as the die entry angle dereases. Hoever, the γ& for the middle temperature indo is independent of the die entry angle. It implies that the prestrethed hain onformation formed in onvergent flo is likely to assist the development of the strethed hain onformation at lo temperature. Hoever, the pre-strethed hain onformation is unstable at high temperature due to the Bronian flutuation. Hene, the of the die entry angle. γ& of middle temperature indo, at 152 C, is independent 6.4 Conlusions This is the first study to reveal melt flo singularity of bimodal PE in the ourse of apillary flo. Bimodal PE-B shoed a dual indo effet in both isothermal and non-isothermal onditions hen the T andγ& a reah ritial values. Based on moleular eight dependene of flo ritialities, the lo temperature indo is attributed to the slip flo of M L and the high temperature indo arises from the slip flo of M H. The ex-situ WAXS results strengthen the slip flo theory orresponding to high surfae energy die. In the indo effet slip flo, less orientation as observed from X-ray diffration pattern of extrudate surfae. This result an be eluidated by slip flo mehanism that only free hains are extruded out of the apillary die after disentanglement from adsorbed hains; hoever, the adsorbed hains left in the inner apillary all onstitute a self-lubriation layer to ease the slip flo. The hydrodynami origin of the extrusion indo is attributed to the indo effet slip flo, hih is set in beteen the pressure osillation regime and helial distortion regime. It as found that the hydrodynami boundary onditions of indo effet slip flo are governed by to flo ritialities, viz. γ& and h γ&. The extrudate profiles in the disrete slip flo and the stationary slip flo are dependent onσ. Helial distortion ours hen σ σ h ; hereas if σ h > σ σ, indo effet slip flo emerges. 104

118 Regarding the influene of various die geometries on flo ritialities of the extrusion indo, first of all, it as found that the melt flo singularity of PE-B is attributed to apillary flo. Seondly, the indo effet is independent of apillary length. Finally, it as proven that the dereasing die entry angle. Hoever, γ& orresponding to lo temperature indo inreases ith γ& for the middle temperature indo remains unaffeted. It suggests that the pre-strethed hain onformation formed during onvergent flo may ease the appearane of indo effet slip flo at lo temperature, but it has no apparent effet at high temperature. 105

119 Chapter 7 Broad extrusion indo of linear polyethylene 7.1 Introdution A bimodal polyethylene, PE-B, shoed a dual indo effet. Aording to the moleular eight dependene of flo ritialities and indo temperature, the lo temperature indo arises from lo moleular eight omponent and the high temperature indo is attributed to high moleular eight omponent. It implies that a polyethylene (PE) ith extremely broad moleular eight distribution may have a broad extrusion indo. Therefore in this hapter a PE, ith broad moleular eight distribution (MWD=27) is seleted to study the indo effet. 7.2 Results The broad extrusion indo of PE-C A linear PE, PE-C, having harateristis of broad moleular eight distribution, shos a broad pressure drop situated in a lo temperature regime, from 150 C to 160 C, in DTS at the shear rate of 50s -1. Within this broad temperature interval, polymer melt is extruded through the apillary die at a uniform throughput rate. Suh a broad extrusion indo has remarkable potential in energy-effiient proessing for PE. Compared ith melt flo behaviour of relatively narro moleular eight distributed PE, there is an irregular pressure osillation pattern observed in melt flo instability regime, from 170 C to 165 C during ooling, viz. the extrusion pressure tends to be stabilised and gives a sign of indo effet slip flo. Hoever, it finally returns to pressure osillation. Suh an irregular pressure osillation pattern indiates ourrene of a meta-stable indo effet slip flo prior to the broad extrusion indo regime. Regarding the indo effet during ooling, till 155 C, the extrusion pressure remains at minimum. Belo 155 C the pressure inreases gradually as the temperature dereases. One the temperature reahes 150 C, the flo indued solidifiation ours aompanied by a signifiant upsing in pressure. 106

120 Figure 7.1: A plot of extrusion pressure against temperature shoing a broad extrusion indo of PE-C at the shear rate of 50s -1 (Die geometry: L-D-2α: 16-1-π) Figure 7.2: Photographs of extrudate obtained in DTS at a fixed shear rate, 50s

121 7.2.2 The effet of apparent shear rate on melt flo singularity of PE-C Figure 7.3 gives an overvie of indo development ith inreasing the imposedγ& a. At loγ& a, 8s -1, the extrusion pressure inreases steadily as the temperature diminishes and no melt flo singularity ours during the DTS. The extrudate is smooth and glossy throughout the entire temperature regime (from 180 C to 142 C) at lo shear rate (<10s -1 ). With inreasing γ& a to 10s -1, a pressure drop is observed in a narro temperature interval loated at 150 C. Sine it is the onset ourrene of the extrusion indo, the ritial apparent shear rate, γ&, for the indo effet of PE-C is determined as 10s -1 for the die geometry of 16-1-π. Surprisingly, it is also found that the flo behaviour at a ritial shear rate of 10s -1 is also free of the melt instability and extrudate distortion. The unexpeted extrudate profile at the ritial shear rate may arise from the broad moleular eight distribution of the polymer studied. As the shear rate inreases to 40s -1, the single pressure drop turns to multi-pressure drops. In addition, a higher indo temperature leads to a loer pressure minimum. The temperature regime from 150 C to 155 C, orresponding to the appearane of multiindos one by one ith inreasing the shear rate, is named the indo development regime. On further inreasing the shear rate to 50s -1, the multi-indos merge together and eventually form a broad extrusion indo. Moreover the broad extrusion indo extends from 155 C to 160 C. As γ& a inreases further, to 75s -1, suh a broad indo broadens further, to 164 C, as shon in Figure 7.4. The enlargement of broad extrusion indo ith the further inrease in shear rate is referred to as the indo broadening effet hen the γ& a 40s -1. The orresponding temperature regime, from 155 C to 164 C is named the indo broadening regime. 108

122 Figure 7.3: A plot of extrusion pressure versus temperature shoing the melt flo behaviour at various shear rates, in hih the onset appearane of the indo effet indiates the ritial apparent shear rate, 10s -1 ( Die geometry: L-D-2α: 16-1-π) Figure 7.4: The indo broadening effet on inreasing γ& a from 50s -1 to 70s -1 (Die geometry: L- D-2α: 16-1-π) 109

123 7.2.3 Isothermal step rate (ISR) rheologial haraterisation A harateristi pressure trae reorded in ISR is shon in Figure 7.5(d) at 165 C. There are three representative melt flo regimes: (a) steady state flo orresponding to the fully developed stik flo, (b) melt instability assoiated ith pressure osillation and () slip flo onsisting of indo effet slip flo and helial distortion slip flo. Distintions beteen the indo effet and helial distortion slip flos ere desribed in Chapter 5 of this thesis. The existene of a broad extrusion indo is verified via ISR. Extrusion pressures reorded in ISR at a shear rate, 50s -1 are plotted as a funtion of temperature in Figure 7.7. The Figure shos a broad pressure drop situated in beteen 160 C and 150 C, hih oinides ith the indo temperature interval orresponding to the broad pressure drop observed in DTS at the apparent shear rate of 50s -1. It is to be noted that the loer-limit temperature for the isothermal experiment is 150 C, at or belo this temperature flo indued solidifiation emerges, resulting in a signifiant upsing in extrusion pressure. Finally apillary flo eases. As shon in Figure 7.5(a), flo indued solidifiation ours hen γ& a is at or above 50s -1. Therefore, the ritial apparent shear rate, γ& s, orresponding to the onset of the flo indued solidifiation, at 150 C is 50s -1. To reall it as determined that the onset temperature of flo indued solidifiation, T s, is 150 C in DTS at a shear rate of 50s -1. Therefore both DTS and ISR results give mutual support to eah other regarding the flo ritialities of flo indued solidifiation. To reveal the hydrodynami origin of the broad indo effet, melt flo behaviour of PE-C and orresponding extrudate profiles ere studied via ISR. The stable pressure traes after the osillations in Figure 7.5 an only be attributed to the slip flo mehanism. Therefore, it is onluded that slip flo ours at the broad extrusion indo flo onditions. For instane, in ISR tests at a given apparent shear rate of 50s -1, slip flos our at 150 C, 155 C and 160 C. With further inreasing the ISR temperature, pressure osillations emerge. Thus slip flo is the hydrodynami ondition of the broad extrusion indo. Additional evidene to prove the appearane of slip flo in the broad extrusion indo flo onditions ill be shon later in the slip flo veloity measurements, Figures 7.14 and

124 Figure 7.5(a): A plot of pressure vs. time at different shear rate, 20s -1, 35s -1, 50s -1, 75s -1 and 100s -1, reorded in a stati experiment at 150 C ( Die geometry: L-D-2α: 16-1-π) Figure 7.5(b): A plot of pressure vs. time at different shear rate, 20s -1, 35s -1, 50s -1, 75s -1 and 100s -1, reorded in a stati experiment at 155 C ( Die geometry: L-D-2α: 16-1-π) 111

125 Figure 7.5(): A plot of pressure vs. time at different shear rate, 20s -1, 35s -1, 50s -1, 75s -1 and 100s -1, reorded in a stati experiment at 160 C ( Die geometry: L-D-2α: 16-1-π) Figure 7.5(d): A plot of pressure vs. time at different shear rate, 20s -1, 35s -1, 50s -1, 75s -1 and 100s -1, reorded in a stati experiment at 165 C ( Die geometry: L-D-2α: 16-1-π) 112

126 Figure 7.5(e) A plot of pressure vs. time at different shear rate, 20s -1, 35s -1, 50s -1, 75s -1 and 100s -1 reorded in a stati experiment at 170 C (Die geometry: L-D-2α: 16-1-π) Figure 7.5(f): A plot of pressure vs. time at different shear rate, 20s -1, 35s -1, 50s -1, 75 s -1 and 100s -1 reorded in a stati experiment at 180 C (Die geometry: L-D-2α: 16-1-π) 113

127 Figure 7.5(g): A plot of pressure vs. time at different shear rate, 20s -1, 35s -1, 50s -1, 75 s -1 and 100s -1 reorded in a stati experiment at 190 C (Die geometry: L-D-2α: 16-1-π) Figure 7.5(h) A plot of pressure vs. time at different shear rate, 20s -1, 35s -1, 50s -1, 75s -1, 100s -1 and 150s -1 reorded in a stati experiment at 200 C (Die geometry: L-D-2α: 16-1-π) 114

128 Figure 7.6: Mirosope observations of three extrudates obtained in ISR ith shear rate, 50s -1, at 150 C, 155 C and 160 C from top to bottom. It an be observed from Figure 7.6 that extrudate profiles orresponding to the broad extrusion indo, at the shear rate of 50s -1, sho different surfae morphologies at different temperatures. Starting from high temperature at 160 C, the orresponding flo ondition is situated in indo broadening regime. The resultant extrudate shos an expeted fine-sale surfae distortion. This kind of rough extrudate ith fine sale surfae distortion as reported in the literature 25(a). Regarding the effet of indo temperature on the extrudate profile, it is observed that the fine-sale surfae 115

129 distortion emerging in the indo broadening regime gradually eakens as the temperature diminishes; finally it disappears hen the extrusion temperature is belo 155 C. Belo 155 C, a glossy and smooth extrudate is observed in indo development regime as shon in Figure 7.6 at temperature 150 C. This implies that the indo effet an minimise and final eliminate surfae distortion on dereasing the temperature. Figure 7.7: A plot of extrusion pressure against temperature at shear rate 50s -1, in hih eah data point is reorded from isothermal onditions in the stati experiment. The vertial bars denote osillations in the pressure (Die geometry: L-D-2α: 16-1-π) The impat of extrusion indo on die sell The die sell ratios reorded in ISR are plotted against temperature as shon in Figure 7.8. It is found that the selling ratio at shear rate, 8s -1, inreases gradually as temperature dereases and eventually inreases rapidly hen flo indued solidifiation ours at 150 C. When the imposed γ& a reahes the ritial value, 10s -1, it is observed that a minimum selling ratio emerges at 150 C, hih is onsistent ith the indo temperature observed in DTS and ISR at 10s -1. At the shear rate of 50s -1, a onsiderable drop of die sell ratio is also observed ithin the temperature interval of the broad extrusion indo, see Figure 7.9. Moreover at 50s -1, the diesell ratio of the extrudate obtained at the indo temperature, 158 C, is idential to 116

130 the die-sell ratio at 200 C. The similarity in die-sell ratio at the to distint extrusion temperatures annot be explained simply by the ontinuum rheology of polymer melts and requires the onsideration of moleular origin of the indo effet. In addition, the minimum die sell ratio emerging at indo temperature offers a speial advantage in polymer proessing, viz. an aurate produt dimension ontrol. Figure 7.8: Selling ratio as a funtion of temperature reorded in ISR at fixed shear rates of 8s -1 and 10s -1 (Die geometry: L-D-2α: π) 117

131 Figure 7.9: Selling ratio as a funtion of temperature in ISR at a fixed shear rate of 50s -1 (Die geometry: L-D-2α: π) The effet of die geometry on extrusion indo Variation of apillary length Theγ& values for various apillary lengths ith the fixed bore diameter (1mm) and entrane angle( π ) are determined in the DTS experiments, here the onset appearane of the indo effet for a 16mm length apillary die ours hen the γ& a reahes 10s -1 as shon in Figure 7.3. From Figure 7.10 it is found that the γ& almost remains unaffeted by varying the apillary lengths. The unhanged ritial shear rate suggests that the γ& is independent of apillary length. Figures 7.11 and 7.12 sho the extrusion pressure vs. temperature traes reorded in both apillary flo and apillary free flo (0-1-π ). In the ourse of apillary free flo the extrusion pressure inreases gradually ith dereasing temperature. The sudden inrease in pressure arises from the flo indued solidifiation. Hoever, the absene of indo effet in the apillary free flo onfirms that the origin of the extrusion indo of broad molar mass distributed polyethylene does not arise from onvergent flo. 118

132 Figure 7.10: Critial shear rate, γ as a funtion of L (apillary die geometry: D=1mm, 2α =π ) Figure 7.11: Extrusion pressure vs. temperature traes reorded in dynami experiment, 12s -1, using a series apillary die ith various die length. 119

133 Figure 7.12: Extrusion pressure vs. temperature traes reorded in dynami experiment, 50s -1, using a series apillary die ith various die lengths Variation of die entry angle It is ell knon that the strength of elongational flo an be altered by varying die entry angle sine onvergent flo promotes elongational flo. Regarding the broad extrusion indo, the effet of varying entry angles on γ& is studied in a flo system ith various die entry angles ith the fixed barrel and apillary diameters. It is revealed that the γ& remains independent of the die entry angle (Figure 7.13). These experimental findings strongly suggest that the onvergent flo has non-effet on the extrusion indo of PE-C. 120

134 Figure 7.13: Critial apparent shear rate of PE-C vs. die entry angle (die length, L=16mm; apillary diameter D=1mm) Slip flo veloity A slip flo haraterisation as performed to verify the appearane of slip flo in the extrusion indo of PE-C. Aording to the plots of γ& a vs. 1/R, here R is the apillary radius, from Figure 7.14 and 7.15, it an be observed that γ& a remains unaffeted ithin the stik flo regime at lo shear rate, hereas slip flo ours hen the orresponding γ& a is above the γ& for the apillary die ith a bore radius of 0.5mm. It suggests that the slip flo ours at the flo onditions orresponding to the indo effet. These results onfirm that the indo effet slip flo is the hydrodynami ondition of the broad extrusion indo. Moreover, it is also found from Table 7.1 that slip veloity inreases ith the σ, ithin the slip flo regime. 121

135 Figure 7.14:The volumetri output rate at different all shear stress plotted as a funtion of the inverse of die radius at 150 C. Slip veloity is determined from the gradient of eah line. Figure 7.15:The volumetri output rate at different all shear stress plotted as a funtion of the inverse of die radius at 155 C. Slip veloity is determined from the gradient of eah line. Table 7.1(a): The slip veloity determined at 150 C aording to the gradient of volumetri output rate vs. the inverse of apillary diameter. Shear stress Slip flo veloity (MPa) (mm s -1 ) σ 1 = σ 2 = σ = σ =

136 Table 7.1(b): The slip veloity determined at 155 C aording to the gradient of volumetri output rate vs. the inverse of apillary diameter. Shear stress Slip flo veloity (MPa) (mm s -1 ) σ 1 = σ 2 = σ = σ = Disussion The moleular origin of broad extrusion indo This is the first study of melt flo singularity of linear PE ith a broad moleular eight distribution. From Figure 7.4, it as observed that the broad extrusion indo ours at an appropriate shear rate, 50s -1, hih should be higher than the ritial shear rate for the loest moleular eight omponent. In ontrast to the narro extrusion indo of linear PEs haraterised by a relatively narro moleular eight distribution (PDI<7), the broad extrusion indo an offer an energy-effiient proessing route sine it an be tolerant thermal flutuations during polymer proessing. Figure 7.16 Synthesised moleular eight distribution traes of PE-C and PE-KM. 123

137 Samples Table 7.2 the melt flo ritialities for PE-KM 31 and PE-C. Critial onset apparent shear rate (s -1 ) Temperature minimum at the ritial shear rate ( C) PE-KM PE-C In order to study the effet of moleular eight distribution on the narro extrusion indo of PE-C ourring at the ritial onset apparent shear rate, γ& =10s -1, one of Kolnaar s samples, PE-KM, is seleted to ompare ith PE-C. Regarding the moleular harateristis, PE-C and PE-KM have distint eight average moleular eight, M, and moleular eight distribution, MWD, (i.e. PE-C: M =349,100 g mol -1 MWD=27.8 ; PE-KM: M =280,000 g mol -1 MWD=7.5 see Table 7.2). Aording to the moleular eight dependene on flo ritialities, the high moleular eight linear PE should exhibit onset of the indo effet at loer shear rate ompared to the lo moleular eight linear PE. Hoever γ& of PE-C is greater than that of PE-KM. One of the possible reasons may be attributed to the lo moleular eight PE omponents in PE-C. The synthesised moleular eight distribution urves of PE-KM and PE-C are shon in Figure It an be seen that PE-C onsists of high perentage of lo molar mass PEs, here the lo end molar mass is even loer than that of PE-KM. These lo molar mass agile hains, ith short relaxation time, have a signifiant impat on the indo effet arising from the ating moleular eight omponent in PE-C. First of all, the short hains an redue the effetive adsorbed hain density hih is defined as a number of adsorbed hains per unit area on apillary all. Seondly, the presene of short hains an interrupt the adsorption of long hains on the apillary all and perturb the strethed hain onformation of long hains at indo temperature due to Bronian flutuation. Consequently, the onset of the indo effet of PE-C ours above the predited ritial shear rate (~4s -1 ) based on the moleular eight dependene of flo ritiality. In summary, the presene of lo molar mass omponent shifts the ritial shear rate haraterised via rheology route 124

138 for indo effet to the higher values. This negative effet is likely to be even orse at the higher temperature. Figure 7.17: A shemati diagram shoing the effet of hindered disentanglement proess of long hains, ourring at lo temperature, resulting in the termination of the entire disentanglement of adsorbed hains from free hains, even though adsorbed short hains are fully disentangled from free hains in bulk. PE-C an be onsidered as a blend of linear PEs ith different moleular eight omponents. Eah moleular eight omponent has a harateristi indo temperature. Aompanied ith eah indo effet arising from different moleular eight omponents, a broad temperature indo ours at an appropriate shear rate (50s -1 ). The appropriate shear rate is higher than the ritial shear rates of different molar mass omponents presenting in the PE-C. The loest indo temperature of PE-C is 150 C as shon in Figure 7.3. It implies that there is no trae of any loer temperature extrusion indos, orresponding to the loer molar mass linear polyethylenes (<100,000 g mol -1 ), even if the apparent shear rate inreases. The disappearane of all the lo temperature indos (<150 C) is attributed to the terminated slip flo hydrodynami ondition of short hains ith presene of long hains. Considering to key fators in the indo effet slip flo, one is the maintained strethed hain onformation, and the other is the disentanglement of adsorbed hains from free hains. At high temperature, long hains possessing longer relaxation time an enhane the strethed hain onformation of shorter hains under flo ondition. At loer temperature, hoever, it an also ease the disentanglement of adsorbed hains from the free hains due to the inrease in the entanglement density ith bulk hains resulting from dual/multi adsorption points of eah long 125

139 hain as shon in Figure Therefore, the indo effet assoiated ith lo molar mass omponent fails to exist in the broad extrusion indo. There are to distint types of flo behaviour found in the broad extrusion indo of PE-C. One is named as the indo development regime, and the other is termed as the indo broadening regime. Within the indo development regime, extrusion indos emerge at different temperatures one by one, up to 155 C, as the applied apparent shear rate inreases (from 10s -1 to 40s -1 ). It is found that the subsequent indos our at higher temperatures ith even loer pressure minima. Aording to the indo temperature dependene on moleular eight and flo ritialities, those high temperature indos are attributed to the higher moleular eight omponents. If the indo temperature still obeys the moleular eight dependene at 155 C, the indo effet at 155 C should arise from a linear polyethylene ith M above but near 1,000,000 g mol -1 aording to the extrapolation plot of the indo temperature vs. moleular eight depited in Figure 5.5. Generally speaking, PE ith M above 1,000,000 g mol -1 is an intratable material by onventional polymer proessing routes like extrusion and injetion moulding. Kolnaar also pointed out that the upper limit moleular eight for the narro indo effet 31(a) as around 1,000,000g mol -1. Hoever the existene of high temperature indo at 155 C suggests a possible route to proess the intratable PE ith assistane of agile short hains ithin extrusion indo flo onditions. With regards to the indo broadening regime, it as found that the pressure minimum remains unaffeted during ooling until the temperature reahes 155 C. It is apparent that the moleular origin of indo broadening annot be attributed to slip flo of M Z sine the onstant pressure minimum ontradits moleular eight dependene of flo ritialities. One of possible reasons for indo broadening is attributed to the slip flo of ating moleular eight omponents (~1,000,000 g mol -1 ) ith assistane of the UHMWPE omponent (~3,000,000 g mol -1 ) in PE-C. From rheologial haraterisation, PE-C ontains UHMWPE omponent hih is situated at the far end of moleular eight distribution urve (> M Z ). Suh extremely long hains have no indo effet themselves. Whereas they an failitate the orientation of long hains and maintain the strethed hain onformation at even high 126

140 temperatures. In addition, it as also found that the indo broadening effet extends to high temperature on inreasing apparent shear rate further from 50s -1 to 70s -1. Aording to oil-streth transition theory, the higher the apparent shear rate, the higher the onset temperature of the indo effet. As γ& a inreases, the strethed hain onformation of long hains an be maintained at even higher temperature ith aid of extremely long polymer hains, M Z, to ounterat the negative effet of Bronian flutuation of short hains and maintain the unstable strethed hain onformation of long hains as the temperature inreases. Consequently, the extrusion indo at 70s -1 is broader than that at 50s -1, even though the T s at 70s -1 is higher than that at 50s -1. Looking bak to the melt flo singularity of a bimodal polyethylene, PE-B, there are three pressure drops observed in the ourse of apillary flo of PE-B at an apparent shear rate of 300s -1. In fat the high temperature pressure drop arises from indo broadening effet The effet of extrusion indo on die sell It is ell knon that the die sell arises from the elasti reovery of strethed hains. Aording to slip flo theory orresponding to high surfae energy die, most of the adsorbed hains remain tethered on the apillary all and free hains are extruded out of the apillary die. The disentanglement degree of the free hains during the indo effet slip flo governs the die sell ratio of extrudate. Windo effet slip flo ours at ertain flo ritialities. When the extrusion temperature is lose to the indo temperature, ±1 C, slip flo ours at an appropriate apparent shear rate. Hoever, the slip flo hydrodynami ondition is not fully developed until the temperature reahes the ritial indo temperature. Therefore, the minimum die sell ratio ours at the very extrusion temperature orresponding to the pressure minimum ithin the extrusion indo, here the indo effet slip flo is fully developed. It as also found that the die sell ratios reorded at 158 C and 200 C for PE-C are idential at a shear rate of 50s -1. One of the possible reasons is due to the distint hydrodynami onditions. At 158 C it is slip flo, hoever, at 200 C it is stik flo. High temperature stik flo, at 200 C, has lo die sell ratio, arising from short 127

141 relaxation time of polymer hains at high temperature. Hoever, lo temperature slip flo shos the lo die sell ratio that is attributed to disentangled free hains ourring ithin indo effet slip flo The influene of die geometry on flo ritialities Change length ith diameter and entry angle onstant. With regards to the broad extrusion indo, pure orifie flo does not give rise to the broad indo effet. Aording to slip flo theory assoiated ith high surfae energy die, polymer hains should attah and adsorb on the apillary all first, and then adsorbed hains are oriented to a ertain strethed hain onformation, finally suh tethered hains an disentangle from free hains and slip flo ours. Therefore, the apillary flo is a prerequisite for the appearane of slip flo sine ylindrial apillary all provides a high surfae energy substrate for hain attahment. Whereas the γ& is independent of the apillary length Change entry angle ith diameter and length onstant. It as knon that indo effet is not attributed to onvergent flo; hoever, it may have an effet onγ&. It as revealed that the γ& of PE-B inreases as the die entry angle redues for lo temperature extrusion indo. By ontrast, the γ& of PE-C and the middle temperature indo of PE-B are independent of the die entry angle. It implies that pre-strethed hains only have an effet on γ& at lo temperature, sine suh pre-aligned hains an only be maintained at lo temperature and redue the ritial strain rate for the onset of strethed hain onformation for slip flo. Hoever, pre-aligned hains are likely to be unstable at high temperature, e.g.150 C. Therefore, variation of die entry angle has no effet on γ& of PE-C. 7.4 Conlusion Linear PE ith broad moleular eight distribution exhibits a broad extrusion indo. Subsequent to a narro extrusion indo ourring at 10s -1, intriguing multi-indos emerged as the shear rate inreases to 40s -1. Eventually all the extrusion indos merged ith eah other forming a broad extrusion indo at a shear rate of 50s

142 It as found that the γ& of PE-C is higher than the predited value based on moleular eight dependene sine the presene of agile short hains redues the effetive adsorbed hain density and also perturbs the strethed hain onformation of the ating moleular eight omponents. The multi-indos observed in the indo development regime are attributed to indo effet slip flos orresponding to diverse moleular eight omponents in PE-C. Eah moleular eight omponent in PE-C has a indo effet at or around the harateristi indo temperature, obeying the moleular eight dependene. In the indo development regime, extrusion indos emerge at different temperatures, up to 155 C, ith inreasing applied apparent shear rate from 10s -1 to 40s -1. Higher temperature indos have an even loer pressure minimum, obeying the dependene of resaled all shear stress on moleular eight. Prior to the indo development regime, the indo broadening regime ours at a shear rate of 50s -1 or above. This effet is attributed to the UHMWPE omponent in PE-C. Aording to the oil-streth theory, UHMWPE ith longer relaxation time an maintain the strethed hain onformation of long hains at even higher temperatures. As a onsequene, the indo effet an extend to 160 C or even higher temperatures ith further inreasing of the shear rate. It is also implies that the intratable UHMWPE an be proessed, ith the assistane of ertain loading of inner lubriant, i.e. agile short hains. Regarding the effet of die geometry on flo ritialities, it as found that the apillary flo is a mehanism responsible for the broad extrusion indo. Hoever, flo ritialities of the extrusion indo are independent of apillary length. On the other hand, it is found that the variation of die entry angle has no effet on γ& of PE- C sine the pre-aligned hain onformation ourring in onvergent flo annot be maintained at higher temperature, 150 C. 129

143 Chapter 8: The influene of nanofillers on the melt flo singularity of linear polyethylene 8.1 Introdution The similar moleular omposition of arbon nanotubes and polyethylene (PE) gives rise to the favourable epitaxial mathing beteen the to. Moreover, it is ell knon that the presene of nanofillers an influene the hain dynamis 55 and thus is likely to influene the indo effet. Considering the relatively high relaxation times of the several-mirometer length nanotubes ompared to the lo molar mass flexible linear PE moleules, the nanotubes are likely to maintain the strethed state thus favouring the indo effet. Hoever, by hanging the aspet ratio of the filler from nanotubes to spherial partiles suh as arbon blak, the antiipated hain orientation near the apillary all an be influened negatively opposing the appearane of indo effet. Considering the above thoughts, in this hapter to arbon-based nanofillers, multialled arbon nanotubes (MWCNTs) and arbon blak (CB), ere used to modify the melt flo behaviour of linear PE. Prior to the study of flo behaviour of PE nanoomposites, the studies have been performed on the neat sample, as shon in hapter Results In this hapter PE-A, ith narro moleular eight distribution, as seleted as a referene material to study the effet of arbon based nanofillers on indo effet of linear PE. 130

144 Figure 8.1: A plot of extrusion pressures as a funtion of temperature reorded during dynami ooling experiments ith a onstant shear rate at 250s -1 (L-D-2α: 16-1-π) shoing the melt flo behaviour of neat PE-A and PE-A ith 0.2t%MWCNTs and PE-A 0.2t%CB. Figure 8.2: A plot of orreted pressures as a funtion of temperature reorded during dynami ooling experiments ith a onstant shear rate at 250s -1 (L-D-2α: 16-1-π) shoing the melt flo behaviour of neat PE-A and PE-A ith 0.2t%MWCNTs and PE-A ith 0.6t%MWCNTs. 131

145 Figure 8.3: A plot of orreted pressures as a funtion of temperature reorded during dynami ooling experiments ith a onstant shear rate at 250s -1 (L-D-2α: 16-1-π) shoing the melt flo behaviour of neat PE-A and 0.2t%CB-PE-A and 0.6t%CB-PE-A. Figure 8.1 shos that the indo effet remains unaffeted on the addition of 0.2t% of the to arbon-based nanofillers respetively. Hoever, apparent differenes are observed in the flo indued solidifiation region. Within this region, the extrusion pressure of 0.2t% MWCNTs-PE-A and 0.2t%CB-PE-A inreases steeply. A loser omparison beteen the to arbon nanofillers suggests that the building-up rate is more pronouned in PE-MWCNTs omposites. The effet of various loadings of MWCNTs on the melt flo behaviour of the linear PE is depited in Figure 8.2. On inreasing the loading of MWCNTs to 0.6t%, a distint derease in the pressure minimum is observed, though the idth of the temperature indo does not hange. The drop in pressure minimum of 0.6t%MWCNTs-PE-A is ira 2 MPa loer than that of the neat PE-A. This indiates a signifiant impat of MWCNTs on the flo ritialities of the indo effet of linear polyethylene. In addition, ithout any sign of indo broadening, the temperature indo of 0.6t%MWCNTs-PE-A shifts to a higher temperature (145 C). 132

146 In the ontrast to the nanotubes, the 0.6t% CB reinfored PE-A has the opposite effet on melt flo behaviour, see Figure 8.3. Compared to the neat polymer, PE-A, in the presene of the arbon blak (a) the onset temperature of the extrusion indo shifts to a loer temperature (b) and the drop in pressure is redued. The ontraditing observations beteen 0.6t%CB-PE-A and 0.6t%MWCNTs-PE-A, implies that the filler morphology has a signifiant impat on flo ritialities. 8.3 Disussion The impat of the CB/MWCNTs on the extrusion indo of PE-A The extrusion indo remains unaffeted on addition of 0.2t%CB or 0.2t%MWCNTs into PE-A matrix. Hoever, ith further inrease in the eight perentage of the nanofillers, from 0.2t% to 0.6t%, different aspet-ratio nanofillers have distint impats on the extrusion indo. Regarding the indo effet of the 0.6t%MWCNTs-PE-A, it is found that, in Figure 8.2, the pressure minimum is ira 2MPa loer than that of neat PE-A or 0.2t%MWCNTs-PE-A. The drop in pressure suggests a loer all shear stress for the slip flo. Aording to Brohard and de Gennes theory 41, the ritial all shear stress for stik-slip transition an be quantified as in the equation (1.26). The all shear stress for slip flo is dependent on the adsorbed hain density ν and entanglement distane * D at a given temperature. The adsorbed hain densities,ν, remain less unaffeted on addition of the MWCNTs sine there is a only small amount of MWCNTs present in the PE-A matrix. Therefore the loer all shear stress for slip flo is attributed to the inreasing entanglement distane ith addition of 0.6t%MWCNTs in the PE-A matrix. In fat, high-aspet-ratio MWCNTs ith longer relaxation time an ease the alignment of moleular hains in the flo diretion. Moreover, the presene of MWCNTs along the all-melt interfae an maintain the strethed hain onformation at higher temperature as shon in Figure 8.4. Hene, the aligned adsorbed hains attahed to the nanotubes ill possess less entanglement. Consequently, the effetive entanglement distane of 0.6t%MWCNTs-PE-A is greater than that in the neat PE-A, resulting in a deeper pressure drop observed in extrusion indo. 133

147 On the other hand, CB, hoever, have an opposite effet on pressure minimum of the extrusion indo, depited in Figure 8.3. Spherial shaped CB an inhibit hain alignments as shon in Figure 8.5. At the moleular length sale the spherial shaped CB an indue the strethed polymer hain to oil bak. As a onsequene, presene of the CB an hinder the hain disengagement and maintain the entanglement density beteen the adsorbed hains and free hains, resulting in a higher ritial shear stress for the onset of slip flo ompared ith the neat polymer, PE-A. The effet of CB on the extrusion indo is referred to as boling ball effet. Besides the distint impat on the pressure minima, the presenes of to different aspet-ratio nanofillers in PE-A matrix also has different effets on indo temperature interval. Aording to the slip flo-hydrodynami boundary onditions, SL - HBC, MWCNTs have potential to broaden the extrusion indo sine they an maintain the strethed hain onformation of agile PE hains at even higher temperature due to epitaxial groth of PE on MWCNTs 55,56. In pratie, it is found that the onset temperature, T onset, of indo effet inreases from 144 C to 145 C on addition of the 0.6t%MWCNTs in PE-A. Hoever, it is also observed that the presene of the MWCNTs rises the termination temperature, T ter, of the indo effet. It implies that the presene of the MWCNTs may also ease the disentanglement of adsorbed hains from the free hains due to the inreased melt visosity at higher temperature ompared to the neat polymer, PE-A. In summary, the MWCNTs an only shift the indo to a higher temperature rather than broadening the extrusion indo. In ontrast, CB shos an opposite impat on indo temperature interval. Due to the boling ball effet, the unstable strethed hain onformation annot be maintained in the presene of the spherial CB at high temperatures. Therefore, the addition of 0.6t% CB dereases the T onset of indo effet. Consequently, onsidering an almost unhanged T ter of 0.6t% CB-PE-A, it is onluded that the spherial CB annot broaden the extrusion indo either. 134

148 Figure 8.4: The effet of MWCNTs on the onset temperature of extrusion indo. Compared to the neat polymer the presene of MWCNTs in polymer matrix promotes the hain alignment along the flo diretion and maintains the strethed hain onformation at higher temperature, 145ºC, here the neat polymer does sho indo effet. Figure 8.5: The effet of CBs on the onset temperature of extrusion indo. In the presene of CBs the strethed hain onformation of some of the adsorbed hains, denoted by darker gray hains, annot be maintained at 144ºC, the onset temperature of indo effet for the neat polymer. Thus ompared to the neat polymer, the orientation and adsorption is perturbed in the presene of CBs. 135