Rheological and film blowing properties of various low density ......Rheological and film blowing...
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Rheological and film blowing properties of various low density polyethylenes and their blends Der Technische Fakultät der Universität Erlangen-Nürnberg Zur Erlangung des Grades D O K T O R – I N G E N I E U R vorgelegt von Thomas Steffl Erlangen, 2004
Transcript of Rheological and film blowing properties of various low density ......Rheological and film blowing...
Rheological and film blowing properties of various low density polyethylenes and
their blends
Der Technische Fakultät der
Universität Erlangen-Nürnberg
Zur Erlangung des Grades
D O K T O R – I N G E N I E U R
vorgelegt von
Thomas Steffl
Erlangen, 2004
Als Dissertation genehmigt von
der Technischen Fakultät der
Universität Erlangen-Nürnberg
Tag der Einreichung: 13.06.2003
Tag der Promotion: 28.11.2003
Dekan: Prof. Dr. A. Winnacker
Berichterstatter: Prof. Dr. H. Münstedt
Prof. Dr. M. H. Wagner
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Rheologische Eigenschaften verschiedener Polyethylene niedriger
Dichte und deren Verarbeitungsverhalten beim Folienblasen
Technische Fakultät der
Universität Erlangen-Nürnberg
Thomas Steffl
Erlangen, 2004
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Inhaltsverzeichnis 1 Einleitung und Motivation.......................................................................................4
2 Molekulare Struktur und rheologische Eigenschaften in
Scherung und Dehnung...........................................................................................8
2.1 Literaturübersicht......................................................................................................8
2.2.1 Experimentelle Methoden 12
2.2.2 Scherrheologische Untersuchungen......................................................................13
2.2.3 Dehnrheologische Untersuchungen.......................................................................14
2.3 Einfluss von Langkettenverzweigungen auf Rheologische Eigenschaften.............20
2.3.1 Materialien..............................................................................................................20
2.3.2 Scherrheologisches Verhalten von LLDPE / LDPE Blends................................23
2.3.3 Einfluss von Langkettenverzweigungen auf das uniaxiale Dehnverhalten.............32
2.3.4 Einfluss der LLDPE Matrix auf das Dehnverfestigungsverhalten von
LLDPE / LDPE Blends............................................................................................39
2.3.5 Dehnrheologisches Verhalten eines langkettenverzweigten Metallocen LLDPE...41
2.3.6 Zusammenfassung: Einfluss der Langkettenverzweigungen................................43
2.4 Einfluss der Molekulargewichtsverteiling auf das uniaxiale Dehnverhalten...........44
2.4.1 Einfluss einer hochmolekularen Komponente auf das Dehnverhalten...................44
2.4.2 Einfluss einer breiten Molekulargewichtsverteilung auf das Dehnverhalten...........47
2.4.3 Einfluss einer hochmolekularen Komponente auf das Dehnverhalten...................51
2.4.4 Zusammenfassung: Einfluss der Molekulargewichtsverteilung............................55
2.5 Einfluss von Kurzkettenverzweigungen auf das Dehnverhalten...........................56
2.5.1 Einfluss der Comonomerverteilung auf dehnrheologische Eigenschaften.........56
2.5.2 Dehnrhoelogisches Verhalten eines Metallocen-LLDPE mit
bimodaler Comonomerverteilung...........................................................................63
2.5.3 Zusammenfassung: Einfluß der Comonomerverteilung auf
dehnrheologische Eigenschaften..........................................................................65
2.6 Vergleich des Scherrheologischen Verhaltens ausgewählter
Polyethylene...........................................................................................................65
2.7 Zusammenfassung: Scher- und Dehnverhalten von Polyethylenen niedriger Dichte
und deren Blends
3 Rheotens Experimente...........................................................................................70
3.1 Literaturübersicht....................................................................................................70
3.2 Experimenteller Aufbau und Auswertung der Ergebnisse................................71
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3.2.1 Experimenteller Aufbau.........................................................................................71
3.2.2 Einfluß der Beschleunigung auf die experimentellen Ergebnisse.......................73
3.2.3 Auswertung von Schmelzfestigkeit und Draw Resonance................................74
3.3 Materialien für Rheotens und Folienblasexperimente.......................................78
3.4 Schmelzfestigkeit....................................................................................................79
3.5 Die relative Draw Resonance...............................................................................81
3.6 Zusammenfassung der Rheotensexperimente......................................................85
4 Charakterisierung des Verhaltens verschiedener Polyethlene
im Folienblasprozess..............................................................................................87
4.1 Einleitung................................................................................................................87
4.2 Literaturübersicht....................................................................................................88
4.2.1 Der Extrusionvorgang.............................................................................................88
4.2.2 Das Folienblasen....................................................................................................89
4.2.3 Verhalten verschiedener Polyethylene im Folienblasprozess................................93
4.3 Experimenteller Aufbau der Folienblasanlage.......................................................94
4.4 Folienblasen...........................................................................................................98
4.4.1 Druckverhältnisse im Extruder...............................................................................98
4.4.2 Stabilität der Folienblase im Folienblasprozess...................................................100
4.4.3 Abzugskräfte im Folienblasprozess....................................................................103
4.4.4 Homogenität der Folien.......................................................................................105
4.5 Zusammenfassung: Verhalten von Polyethylenen beim Folienblasen.................110
5 Korrelationen........................................................................................................112
5.1 Korrelation der Draw Resonance mit der Homogenität der Deformation
in uniaxialer Dehnung..........................................................................................112
5.2 Korrelation der Ergebnisse des Folienblasens, der rheologischen Experimente
und der Rheotens Tests.......................................................................................115
5.2.1 Korrelation des Schmelzedrucks im Extruder mit den Scherviskositäten..........115
5.2.2 Korrelation der Blasenstabilität und Abzugskraft im Folienblasversuch mit dem
Dehnverhalten in uniaxialer Dehnung und der Schmelzfestigkeit im
Rheotensversuch..................................................................................................118
5.2.3 Korrelation der Folienhomogenität mit Instabilitäten in uniaxialer Dehnung
und Rheotens Experimenten.............................................................................119
5.3 Zusammenfassung der Korrelationen..................................................................123
6 Zusammenfassung...............................................................................................124
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ANHANG A: Materialien im Folienblasversuch............................................................127
ANHANG B: Thermische Stabilität...............................................................................128
ANHANG C: Reproduzierbarkeit....................................................................................131
ANHANG D: Symbole und Abkürzungen.......................................................................138
Literaturverzeichnis..........................................................................................................140
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Einleitung Folienextrusion ist ein weitverbreitetes Verarbeitungsverfahren in der Kunststoff-
technologie. Die so hergestellten Filme werden im täglichen Leben auf vielfache Weise
benutzt, zum Beispiel als einfache Plastiktüten, als Säcke für schwere Güter in der
Landwirtschaft oder in der Bauindustrie oder als sehr dünne Filme für Kondensatoren
oder Speichermedien. Noch immer ist der Markt für Polymerfilme am Wachsen. Allein der
Sektor Lebensmittelverpackungen, welcher 1994 ein Volumen von 18 Mrd. Dollar hatte,
wurde für 2001 auf 23 Mrd. Dollar geschätzt (Müller 1998). Wenn man berücksichtigt,
dass 59% aller Verpackungsmaterialien aus Kunststofffolien hergestellt werden, so ist
offensichtlich, dass auf einem hart umkämpften Markt die ökonomische Herstellung von
Folienprodukten die wichtigste Vorraussetzung, ist um dem Preisdruck standhalten zu
können. Um trotz harter Konkurrenz auf dem Markt für Kunststofffolien zu überleben,
müssen die Produktionsabläufe und die hier verwendeten, maßgeschneiderten
Kunststoffe permanent weiterentwickelt werden. Die wachsende Nachfrage nach
komplexeren, mehrlagigen Filmen und höheren Durchsätzen verlangt nach Kunststoffen,
die schnell und mit hoher Produktqualität verarbeitet werden können.
Polyethylen niedriger Dichte (LDPE) ist bei der Verarbeitung im Folienblasverfahren weit
verbreitet. Die gutmütigen Verarbeitungseigenschaften erlauben es, LDPE auf relativ
einfachen und kostengünstigen Folienblasanlagen mit großen Durchsätzen zu fahren.
Jedoch ist der Einsatz von LDPE Filmen aufgrund der begrenzten mechanischen
Eigenschaften eingeschränkt. Der Einsatz von linearen Polyethylenen niedriger Dichte
(LLDPE) hingegen ermöglicht überlegene Folieneigenschaften, wie höhere Zugfestigkeit
und höhere Durchstoßfestigkeit. Jedoch zeigt LLDPE geringere Durchsatzraten auf dem
Extruder und eine unzureichende Prozessstabilität beim Folienblasvorgang. Um diese
Probleme zu umgehen, sind hochspezialisierte und teure Folienblasanlagen notwendig. In
der Praxis wird oft ein Kompromiss zwischen kosteneffektiver Herstellung und
gewünschten Folieneigenschaften geschlossen, indem man mit LDPE-LLDPE Blends
arbeitet.
In den letzten Jahren haben Metallocen-Katalysatoren in der Polymerisierungstechnologie
von Polyolefinen zu einer Reihe neuer Produkte geführt, bei denen gezielt molekulare
Eigenschaften, wie Molekulargewichtsverteilung, Comonomergehalt, –verteilung und
Langkettenverzweigungen beeinflusst werden können. Diese Technologie eröffnet die
große Möglichkeit, die Verarbeitungs- und Folieneigenschaften der Polymere durch einen
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maßgeschneiderten molekularen Aufbau den Vorgaben der Produktion und des
Endproduktes anzupassen. Dies ist jedoch nur möglich, wenn Korrelationen zwischen
dem molekularen Aufbaus der Polyethylenmoleküle und dem Verarbeitungsverhalten im
Folienblasprozess sowie den Endprodukteigenschaften bekannt sind.
Ein Vergleich verschiedener Polyethylene zeigt den Einfluss der molekularen Struktur auf
die rheologischen Eigenschaften und das Verarbeitungsverhalten. Drei Typen von
Polyethylenen sind kommerziell erhältlich. Polyethylen hoher Dichte (HDPE) besteht aus
linearen Molekülketten. Lineares Polyethylen niedriger Dichte (LLDPE) enthält eine
Struktur kurzer Seitenketten, die, abhängig vom verwendeten Monomer, eine Länge von
bis zu 6 Kohlenstoffatomen haben können. Diese nennt man Kurzkettenverzweigungen.
Polyethylen niedriger Dichte (LDPE) besitzt eine verzweigte Struktur der Molekülkette.
Man spricht in diesem Fall von einer langkettenverzweigten Struktur.
Die verschiedenen molekularen Strukturen spiegeln sich in charakteristischen
rheologischen Eigenschaften wider. So besitzt LDPE ein stark ausgeprägtes,
strukturviskoses Verhalten in einer Scherströmung. Das heißt, bei hohen Scherraten zeigt
es eine deutlich kleinere Scherviskosität als HDPE oder LLDPE mit einer vergleichbaren
Molekulargewichtsverteilung. Da Scherströmungen in allen Arten von
Extrusionsprozessen eine wichtige Rolle spielen, entstehen bei der Verarbeitung von
HDPE und LLDPE höhere Drücke im Extruder, weshalb eine höhere Motorleistung
benötigt wird.
In einer Dehnströmung zeigen langkettenverzweigte Produkte ein dehnverfestigendes
Verhalten. Die Dehnviskosität der Probe steigt dabei mit wachsender Dehnung
überproportional an. Dieser Effekt hat positive Auswirkungen auf das freie
Verformungsverhalten. Bei einer Probe mit einem ungleichen Querschnitt erfährt eine
Stelle mit einem kleineren Querschnitt eine höhere Spannung als die umliegenden Stellen
mit einem größeren Querschnitt. Deshalb wird sie sich hauptsächlich an dieser
Schwachstelle verformen, was dazu führt, dass die Probe dort immer dünner wird und
schließlich reißt. Im Falle eines dehnverfestigenden Verhaltens verhärtet sich die Stelle,
die eine größere Deformation erfährt. Aus diesem Grund wird dieser Effekt auch
Selbstheilungseffekt genannt. Dies ist der Grund, warum aus langkettenverzweigten
Produkten bei Prozessen, die hauptsächlich auf uniaxialen oder planaren Deformationen
beruhen, homogenere Endprodukte hergestellt werden können. Als relevante
Verarbeitungsmethoden sind Faserspinnen, Blasformen, Folienblasen oder Schäumen zu
nennen.
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Die neue Generation von Metallocen-Katalysatoren und neue Reaktortechnologien
erlauben nun die gezielte Einarbeitung von Langkettenverzweigungen in LLDPE Produkte
und eine gezielte Steuerung von Konzentration und Verteilung von
Kurzkettenverzweigungen. Dies eröffnet neue Möglichkeiten, für spezielle Anforderungen
der verarbeitenden Industrie maßgeschneiderte Polyethylene herzustellen. Andererseits
ist von Interesse, ob diese Eigenschaften auch mittels Herstellung von Blends aus
konventionellen Polyethylenen zu erreichen sind.
In der folgenden Arbeit wird nun der Einfluss der molekularen Parameter auf die
Rheologie und auf das Verarbeitungsverhalten beim Folienblasen von verschiedenen
Polyethylenen untersucht. Die molekularen Eigenschaften wie Langkettenverzweigungen,
Molekulargewicht, Molekulargewichtsverteilung, Comonomergehalt und -verteilung
können dabei variiert werden. Der erste Teil der Arbeit konzentriert sich auf die
Auswirkungen der molekularen Parameter auf die rheologischen Eigenschaften. Um die
einzelnen Faktoren voneinander zu separieren, werden von ausgesuchten Proben
Blendserien hergestellt, welche mit kommerziellen Produkten verglichen werden können.
Schließlich werden auch zwei neue Metallocen-Produkte untersucht, und deren
Eigenschaften werden denen konventioneller Polyethylene gegenübergestellt. Im zweiten
Teil der Arbeit werden ausgesuchte Proben mittels Rheotens-Experimenten
charakterisiert. Diese sollen eine Brücke schlagen zwischen den rheologischen
Untersuchungen und dem praktischen Verarbeitungsverhalten beim Folienblasen,
welches im dritten Teil der Arbeit untersucht wird.
Wenn es am Schluss gelingt, den molekularen Aufbau von Polyethylen und dessen
rheologische Eigenschaften mit den Verarbeitungseigenschaften zu korrelieren, ist dies
eine deutliche Erleichterung bei der Entwicklung neuer Polyethylenprodukte.
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Zusammenfassung Die Ergebnisse der Untersuchungen können unter zwei verschiedenen Gesichtspunkten
diskutiert werden. Zum einen sollen die rheologischen Eigenschaften und die
Verarbeitungseigenschaften verschiedener Polyethylene verglichen werden, wobei die
große Anzahl an Proben die Erstellung qualitativer Beziehungen erlaubt. Zum anderen
wurden Zusammenhänge herausgearbeitet, die den molekularen Aufbau der Polyethylene
mit den rheologischen Eigenschaften korrelieren. Somit ist eine Argumentationskette vom
molekularen Aufbau bis zu den Verarbeitungseigenschaften geschaffen .
Es wurde gezeigt, dass wichtige Verarbeitungseigenschaften, wie Extrusionsdrücke,
Blasenstabilität und Folienhomogenität mit den rheologischen Eigenschaften in Scherung
und uniaxialer Dehnung in Korrelation gebracht werden können. Diese wiederum sind
Folge der molekularen Struktur der verwendeten Proben.
Wie bereits aus der Literatur bekannt, zeigt langkettenverzweigtes LDPE ein
ausgeprägtes Dehnverfestigungsverhalten, welches man bei linearen LLDPE nicht
beobachten kann. Aufgrund von LLDPE/LDPE Blend Serien wurde gezeigt, dass bei
Langkettenverzweigungen das dehnverfestigende Verhalten mit Zunahme der
Verzweigungen (LDPE-Gehalt) deutlich ansteigt. Hierbei wird die Intensität der
Dehnverfestigung nicht durch die Viskosität der linearen Matrix beeinflusst. Es hat sich
jedoch gezeigt, dass die Abhängigkeit der Dehnverfestigung von der Dehnrate bei
höheren Matrixviskositäten zu niedrigeren Dehnraten verschoben wird. Dieser Effekt wird
besonders bei Kriechexperimenten in Dehnung offensichtlich. Das klar dehnverfestigende
Verhalten eines Metallocen-LLDPEs, welches eine verschwindend geringe Anzahl an
Langkettenverzweigungen enthält (<1 CH3 /10000 C), kann nicht mittels einer
LLDPE/LDPE-Blend Serie simuliert werden. Diese metallocen-katalysierten
Langkettenverzweigungen müssen eine rheologisch effektivere Verzweigungsstruktur
besitzen als Verzweigungen in herkömmlichem LDPE. Die langkettenverzweigten
Produkte zeigen eine sehr gute Verarbeitbarkeit im Folienblasprozess. Aufgrund der
Strukturviskosität zeigt das LDPE niedrige Extrusionsdrücke. Besonders im Vergleich zu
einem LLDPE und deren Blend kann nachgewiesen werden, dass die Blasenstabilität
während des Folienblasens durch die Langkettenverzweigungen eindeutig verbessert
wird. Die aus langkettenverzweigten Produkten hergestellten Folien zeigen die besten
Folienhomogenitäten aller untersuchten Materialien.
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Dehnverfestigendes Verhalten kann auch durch die Polymerisation von Produkten mit
einer hochmolekularen Komponente in der Molekulargewichtsverteilung erreicht werden.
Infolge ihrer höheren Molmasse und der weniger ausgeprägten Strukturviskosität zeigen
diese Produkte deutlich höhere Extrusionsdrücke als das Vergleichs-LDPE. In der
weiteren Verarbeitung zeigen sie eine ausgesprochen gute Blasenstabilität, obwohl in
Rheotensversuchen eine sehr starke „Draw Resonance“ auftrat. Die aus diesen LLDPEs
hergestellten Folien waren die inhomogensten der untersuchten Polyethylene. Trotz der
gemessenen Dehnverfestigung können bei diesen Produkten bei hohen, uniaxialen
Dehnungen sehr starke Inhomogenitäten beobachtet werden, die zu einem Reißen der
Proben führen. Es hat sich gezeigt, dass die untersuchten Proben, welche auch
hochmolekulare Fraktionen in ihrer Molekulargewichtsverteilung aufweisen, nur eine sehr
limitierte Ausziehfähigkeit besitzen, obwohl sie bei kleineren Dehnungen
dehnverfestigendes Verhalten aufweisen.
Die Variation der Kurzkettenverzweigungsstruktur hatte keine Auswirkungen auf die
Rheologie und die Verarbeitung der Polymere.
Einige Effekte der Metallocen-LLDPE können mit den bisherigen Erfahrungen nicht erklärt
werden. Zum einen zeigt das langkettenverzweigte mLLDPE eine deutlich höhere
Dehnverfestigung als man von Experimenten mit LDPE aufgrund der Anzahl der
Langkettenverzweigungen erwarten kann. Zum anderen wurden im Extruder, im
Widerspruch zu den scherrheologischen Untersuchen deutlich geringere
Extrusionsdrücke gemessen.
Beim Vergleich von Verarbeitungseigenschaften, Rheotens Experimenten und
dehnrheologischen Untersuchungen konnten folgende Zusammenhänge etabliert werden.
Die Scherviskositäten können qualitativ mit den im Extruder gemessenen Drücken
korreliert werden. Materialien mit einer hohen Scherviskosität erzeugen auch hohe Drücke
im Extruder und führen somit zu einem niedrigeren maximalen Durchsatz. Die Metallocen-
Produkte bilden hierbei eine Ausnahme, da deren Drücke im Extruder deutlich niedriger
waren als gemäß den scherrhelogischen Untersuchungen erwartet.
Materialien, bei denen während des Folienblasens hohe Abzugskräfte des
Folienschlauches ermittelt werden konnten, zeigten eine sehr große Blasenstabilität.
Qualitativ stimmten diese Kräfte mit den im Rheotens-Versuch ermittelten
Schmelzefestigkeiten und den Dehnviskositäten der Proben überein. Materialien mit
hohen Dehnviskositäten und hohen Schmelzefestigkeiten können mit einer guten
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Blasenstabilität verarbeitet werden. Dabei spielt es keine Rolle, ob die hohe
Dehnviskosität durch eine starke Dehnverfestigung, hervorgerufen durch
Langkettenverzweigungen, oder durch ein hohes Molekulargewicht erreicht wird.
Proben, die in Dehnversuchen bei höheren Dehnungen plötzlich versagen und reißen,
zeigen in Rheotensversuchen ein sehr instabiles Dehnverhalten. Die „Draw Resonance“
ist sehr stark ausgeprägt, und die Ausziehfähigkeit ist begrenzt. Diese Produkte weisen
beim Folienblasen eine sehr schlechte Folienhomogenität auf.
Somit kann das rheologische Verhalten von verschiedenen Polyethylenen in Scherung
und Dehnung mit dem Verhalten im Folienblasen korreliert werden. Es kann gezeigt
werden, dass Langkettenverzweigungen die Blasenstabilität und die Folienhomogenität
nachhaltig verbessern. Hierbei zeigen LLDPE/LDPE-Blends und langkettenverzweigte
Metallocen-Produkte gleichermaßen eine deutliche Verbesserung gegenüber linearen
Produkten. Hochmolekulare Komponenten hingegen weisen klare Nachteile beim
Extrusionsvorgang und bei hohen Dehnungen auf. Ein ideales Produkt zur Verarbeitung
im Folienblasprozeß enthält somit Langkettenverzweigungen und keine hochmolekularen
Komponenten. Da Blends von LLDPE mit LDPE gegenüber reinem LLDPE immer auch
einen Kompromiss bezüglich der mechanischen Eigenschaften darstellen, könnten neue
langkettenverzweigte Metallocen-LLDPE Produkte die hervorragenden
Verarbeitungseigenschaften von LDPE mit den guten Folieneigenschaften von LLDPE
vereinen.
CONTENTS
1 INTRODUCTION AND MOTIVATION ............................................................................... 4
2 CORRELATION OF MOLECULAR STRUCTURE AND RHEOLOGICAL
PROPERTIES IN SHEAR AND ELONGATIONAL FLOW....................................................... 8
2.1 Literature survey ......................................................................................................... 8
2.2 Experimental methods .............................................................................................. 12 2.2.1 Molecular analysis: Gel permeation chromatography (GPC) ............................. 12 2.2.2 Shear Rheology.................................................................................................. 13 2.2.3 Elongational Rheology ....................................................................................... 14
2.3 Influence of long-chain branching on rheological properties..................................... 20 2.3.1 Samples ............................................................................................................. 20 2.3.2 Shear rheology of LLDPE / LDPE blends........................................................... 23 2.3.3 Influence of long-chain branches on elongational flow....................................... 32 2.3.4 Influence of the LLDPE matrix on the strain-hardening behaviour of blends ..... 39 2.3.5 Elongational rheology of a long-chain branched metallocene LLDPE................ 41 2.3.6 Conclusions of the influence of long-chain branching on rheology .................... 43
2.4 Influence of molecular weight distribution on elongational rheology......................... 44 2.4.1 Influence of a higher molecular weight component on elongational rheology.... 44 2.4.2 Rheological behaviour of a sample with a broad molecular weight distribution . 47 2.4.3 Influence of a high molecular weight tail on rheological properties in
elongational flow.............................................................................................................. 51 2.4.4 Conclusions on the influence of high molecular weight components on the
elongational viscosity....................................................................................................... 55
2.5 Influence of comonomers on rheological properties ................................................. 56 2.5.1 Influence of comonomer distribution on elongational viscosity........................... 56 2.5.2 Elongational behaviour of a metallocene LLDPE with a bimodal comonomer
distribution ....................................................................................................................... 63 2.5.3 Conclusions on the influence of the comonomer distribution on the behaviour
in elongational flow.......................................................................................................... 65
2.6 Comparison of the rheological behaviour in shear of selected samples................... 65
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2.7 Conclusions: Shear and elongational Rheology of polyethylenes and polyethylene
blends ................................................................................................................................. 67
3 RHEOTENS EXPERIMENTS.......................................................................................... 70
3.1 Literature survey on Rheotens experiments ............................................................. 70
3.2 Experimental set-up of the melt-strength test and evaluation of the results ............. 71 3.2.1 Experimental set-up ........................................................................................... 71 3.2.2 Influence of the acceleration on experimental results ........................................ 73 3.2.3 Evaluation of melt strength and draw resonance ............................................... 74
3.3 Samples for Rheotens and film blowing experiments ............................................... 78
3.4 The melt strength test ............................................................................................... 79
3.5 The relative draw resonance of characteristic polyethylenes ................................... 81
3.6 Conclusion on the Rheotens experiments ................................................................ 85
4 FILM BLOWING OF POLYETHYLENES ........................................................................ 87
4.1 Introduction ............................................................................................................... 87
4.2 Literature survey: The film blowing process.............................................................. 88 4.2.1 Extrusion step..................................................................................................... 88 4.2.2 Film blowing step................................................................................................ 89 4.2.3 Performance of different polyethylenes in film blowing ...................................... 93
4.3 Experimental setup of the film blowing line............................................................... 94
4.4 Film blowing .............................................................................................................. 98 4.4.1 Melt pressures in the extruder............................................................................ 98 4.4.2 Stability of the bubble in the film blowing process............................................ 100 4.4.3 Take-up forces in the film blowing process ...................................................... 103 4.4.4 Homogeneity of the blown films ....................................................................... 105
4.5 Conclusion on the behaviour of polyethylenes in the film blowing process ............ 110
5 CORRELATIONS .......................................................................................................... 112
5.1 Correlation of draw resonance and inhomogeneous deformation in elongational
rheology ............................................................................................................................ 112
5.2 Correlation of results of film blowing experiments, rheological experiments and
Rheotens test.................................................................................................................... 115 5.2.1 Correlation of melt pressure in the extruder and shear viscosity...................... 115
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5.2.2 Correlation of bubble stability and take-up force in film blowing with
elongational behaviour and melt strength measured in Rheotens experiments............ 118 5.2.3 Correlation of film homogeneity with instability behaviour in uniaxial
elongation and Rheotens experiments .......................................................................... 119
5.3 Conclusions on correlations.................................................................................... 123
6 SUMMARY .................................................................................................................... 124
APPENDIX A: MATERIALS USED FOR FILM BLOWING EXPERIMENTS........................ 127
APPENDIX B: THERMAL STABILITY ................................................................................. 128
APPENDIX C REPRODUCIBILITY...................................................................................... 131
APPENDIX D: SYMBOLS AND ABBREVIATIONS ............................................................. 138
LITERATURE....................................................................................................................... 140
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1 Introduction and motivation
Film extrusion is one of the most widespread processing techniques for commercial
polymers. The resulting film products are widely used in our daily life, from simple plastic
bags up to heavy duty bags in the farming and building industry, very thin capacitor films
and dimensional stable video recording films. And the market for polymer films is still
growing. Just the sector of food packaging, which had a volume of 18 billion dollars in
1994, is aimed for 23 billion dollars in 2001 in Europe (Müller 1998). Taking into account
that 59 % of all packaging are made of polymer films, it is obvious that on this hard-fought
market the economic production of the films is the key to bear up against the pricing
pressure. To survive the tough competition in the polymeric film industry the production
process and the tailoring of the film blowing resins are constantly evolving. The growing
demand for more complex, multilayered films and higher outputs require resins that can
be run stable and with a high product quality under these circumstances.
Up to now low-density polyethylene (LDPE) is widely used in film processing by the
tubular film blowing process. Its easy processing properties make it possible to run LDPE
on relatively simple and inexpensive film blowing lines with high outputs and thus enable
the economic manufacture of polyethylene films. However, the performance of these films
is limited by their mechanical properties. As far as these features are concerned another
class of polyethylenes is the counterpart. Linear low-density polyethylene offers superior
film properties, like higher tensile strength and elongation at break, outstanding film
puncture resistance and greater stiffness. But the performance of LLDPEs on film blowing
lines exhibits some disadvantages like low extruder outputs and an insufficient process
stability. To overcome the arising problems highly specialized and expensive film blowing
lines are necessary. In practice the film blowing resins are often optimised by blending
LDPE and LLDPE accepting a compromise between the most economic processing and
desired film properties.
Recent developments in the metallocene catalyst polymerisation technology enable a
specific tuning of the molecular parameters of the polymer, like molecular weight
distribution, comonomer content and its distribution and long-chain branches. This ability
offers great possibilities to optimise the processing and film properties of the resins by
polymerising tailored polymers for the demands of the production and the application of
the product. To set the base for a specific tailoring it is necessary to establish relations
5
_______________________________________________________________________
between molecular parameters, the processing behaviour in the tubular film blowing and
the properties of the end product.
To exemplify the influence of the molecular structure on the rheological and processing
properties different types of polyethylene can be compared. The commercially available
three types of polyethylene are: linear high density polyethylene (HDPE) which has a
linear chain structure, the linear low-density polyethylene which has a short-chain
branched molecular structure and finally the long-chain branched low density polyethylene
(LDPE). Short-chain branches are defined as chains not longer than 6 ethylen monomer
units, i.e. 6 carbon atoms, whereas long-chain branches have no defined length. HDPE
and LLDPE resins, without containing fractions of high molecular weight molecules, show
different rheological properties in comparison with LDPE. LDPE shows a very pronounced
shear-thinning behaviour. This means, that at high shear rates the shear viscosity of the
LDPE is lower than the shear viscosity of a HDPE or LLDPE of the same average
molecular weight. As shear deformations dominate in all kinds of extrusion processes,
HDPE and LLDPE cause higher pressures in the extruder and higher motor loads. Thus
they have a worse processing/extrusion behaviour than LDPEs of comparable molecular
weights.
6
_______________________________________________________________________
total strain
elon
gatio
nal v
isco
sity strain hardening
1
2
21
ε = ε 0
. .
Figure 1: Schematic sketch illustrating the influence of the strain-hardening effect on the homogeneity behaviour of deformation in elongational flow.
In elongational deformation long-chain branching has the peculiarity of a so-called strain
hardening behaviour. The viscosity of a strain-hardening sample is growing
disproportionately with increasing applied strain. This effect has positive consequences on
the deformation behaviour as shown in Figure 1. An inhomogeneity, a spot with a minor
cross-section than the surrounding sample material suffers a higher strain. In case of a
non strain-hardening sample the deformation becomes more and more inhomogeneous
and finally leads to a failure at high strains. However, strain-hardening samples show a
rising viscosity at the higher strains which occur at the inhomogeneous spot. As a result
this spot shows a higher resistance against further deformation. This self-healing effect is
the reason for a more homogeneous deformation of samples showing strain-hardening
behaviour. As a consequence long-chain branched samples can be formed to more
homogeneous products in processes dominated by uniaxial or planar deformations like
fibre spinning, blow moulding, foaming or film blowing. Therefore LDPE outmatches
conventional LLDPEs with regard to the processing properties and homogeneity of the
end product.
7
_______________________________________________________________________
The new metallocene catalysts and new reactor technologies enable the incorporation of
long-chain branches in LLDPE’s and a specific tuning of the concentration and distribution
of short-chain branches. This lays the foundations to design tailored film blowing resins
which match the demands of processing and product properties. Otherwise it is of great
interest whether the properties of these new metallocene polyethylenes can be realized by
a tailored preparation of blends of conventional polyethylene resins.
To set the base for the development of tailor made metallocene catalysed LLDPEs
(mLLDPE) this study investigates the influence of molecular parameters on rheology and
processing behaviour. In case of polyethylene five molecular parameters can be varied:
the long-chain branching structure, the molecular weight and the molecular weight
distribution and finally the type and content of the comonomer. The first part of the work
concentrates on the influence of the first three molecular parameters on the rheology of
the polymer melt. To allow the separation of the effects of different molecular parameters
blends were prepared from selected samples. After that the results of the blend series
were compared to the properties of typical commercial polyethylenes. Finally, two recently
developed mLLDPEs were investigated and the consequences of their unique molecular
structure are discussed with respect to their rheological properties. The second part deals
with the technical Rheotens experiment which should bridge the rheological and
processing behaviour of the samples. In a third part the behaviour of the samples in the
film blowing process is studied and related to the results of the rheological experiments.
The aim is to bring together the molecular structure and the processing behaviour. This
should enable an aimed development of new tailored film blowing resins. In addition the
knowledge of the rheological behaviour of the blends and the metallocene LLDPEs
enables a economic decision whether the postulated goals in processing can be reached
by the development of a new polymer or by a targeted composition of a blend.
8
_______________________________________________________________________
2 Correlation of molecular structure and rheological properties in shear and elongational flow
In the first part of this research rheological properties of polyethylenes and blend systems
are investigated with respect to their molecular structure. Each of the blend systems is
targeted on one molecular parameter like long-chain branching, molecular weight
distribution or short-chain branching structure.
2.1 Literature survey
Polyethylenes are the most commonly used polymers. In the molten state their properties
are strongly dependent on the molecular structure, especially in elongational flow. In the
following a brief overview is given of the experimental results of the influence on long-
chain branching, the molecular weight distribution and the short-chain branching structure
on rheological properties.
Long-chain branching (LCB) has been found to have significant effects on the rheological
behaviour of the polymer melt. It is well established that long-chain branching leads to an
increase of the flow activation energy, to a distinct shear thinning behaviour and to strain
hardening behaviour in elongational flow.
The shear thinning behaviour of LCB-PE is so pronounced that the viscosity level can be
orders of magnitude lower than for a comparable LLDPE at high shear rates (Ghijsels,
Ente et al. 1992; Abraham, George et al. 1996). The behaviour in shear flow of
LDPE/LLDPE blends are discussed in literature controversely. The shear flow behaviour
investigated by Goyal changed gradually from the typical behaviour of the LDPE to the
behaviour of LLDPE (Goyal, Bohnet et al. 1995). Similar results of Abraham show a slight
positive deviation from the logarithmic rule of additivity (Abraham, George et al. 1992).
Contradicting to these results Müller presented two blend systems which show hardly any
change in their shear viscosity behaviour up to the addition of 25 % LLDPE to an LDPE
matrix (Müller, Balsamo et al. 1994). Two LLDPE/LDPE blend systems were investigated
by Utracki and Schlund. They revealed different compositional dependence of the zero-
shear viscosity. One blend system followed the logarithmic mixing rule whereas the other
blend system showed positive deviation compared to the mixing rule (Utracki and Schlund
1987). As the results in literature are somewhat confusing no universal mixing rule for this
9
_______________________________________________________________________
blend system can be found by comparing the rheological behaviour in shear of different
LPDE/LLDPE blend systems.
For pure LDPE Münstedt and Laun showed 1981 in an elaborate study that the strain
hardening behaviour depends on the number of long-chain branches (Münstedt and Laun
1981). They found no strain hardening for linear HDPE, whereas the amount of strain
hardening of branched LDPE is dependent on the number of long-chain branches. But not
only the number of long–chain branches determines the strain hardening behaviour.
Moreover, the topology of the long-chain branches is influencing the intensity of strain
hardening. Latest developments in metallocene polymerisation enable the purposeful
incorporation of long-chain branches in LLDPE. These long-chain branches turn out to act
highly effective in elongational flow (Malmberg 2000). However, their molecular
architecture (i.e. branching structure) is not fully understood yet. Summing up long-chain
branching has several effects on the shear properties which all have positive
consequences for the production process. The pronounced shear thinning effect leads to
low viscosities at shear rates relevant for extrusion processes and as a consequence of
the high activation energy, LDPE can be processed at lower temperatures than LLDPE.
Apart from the branching structure, the molecular weight distribution is another structural
parameter, which influences the rheological properties.
In general the zero shear viscosity is independent of the molecular weight distribution. It is
a function of the molecular weight and, as Gabriel showed in detail in his thesis,
influenced by the branching structure of the molecule (Gabriel 2001). However, the shear
rate dependence of the viscosity is influenced by the molecular weight distribution.
Comparing two polymers with an identical molecular weight Mw but a different molecular
weight distribution, the broader distributed product will deviate from the zero shear
viscosity at smaller shear rates than a product with a narrow molecular weight distribution.
At high shear rates the curves of the shear viscosity intersect and the broadly distributed
product has a higher viscosity than the narrow one. (Münstedt 1986)
10
_______________________________________________________________________
Figure 2: Time-dependent elongational viscosity of two polystyrene samples with a different molecular mass distribution. Influence of a broad molecular weight distribution on elongational rheology. (Münstedt 1980)
In elongational flow samples with a broad molecular weight distribution show strain
hardening behaviour, as illustrated in Figure 2 (Münstedt 1980). Münstedt showed this
effect for two different polystyrenes with a polydispersity Mw/Mn =2.3 (PS IV) and 1.9 (PS
III). The same effect was found by Minoshima et al. for polypropylenes. They observed
strain hardening behaviour for broadly distributed polypropylenes at all measured strain
rates (0.01 – 2 s-1), whereas for narrow molecular weight distributions no strain hardening
behaviour could be found (Minoshima, White et al. 1980). Sebastian compared the
elongational viscosity growth function of a broadly distributed LLDPE to a narrowly
distributed LLDPE. The broadly distributed LLDPE exhibited a distinct strain hardening
behaviour which showed increasing strain hardening for decreasing strain rates, whereas
the narrowly distributed LLDPE showed no strain hardening behaviour (Sebastian and
Dearborn 1983). However, no explicit molecular data was given. In a very elaborated
study Schlund and Utracki investigated 10 LLDPEs with different molecular weight
distributions in elongational flow (Schlund and Utracki 1987a; Schlund and Utracki 1987b).
The eight gas-phase polymerized samples did not show any strain-hardening behaviour
although three of the samples had a broad molecular weight distribution. A thermally
pretreated sample and an LLDPE prepared in a solution process showed strain hardening
behaviour, although their molecular weight distribution was not as broad. A careful
11
_______________________________________________________________________
interpretation of these results is necessary as latest investigations of Gabriel indicate that
very low amounts of long-chain branches can distinctly alter the rheological behaviour of
polymers (Gabriel 2001). It can be shown that the viscosity dependence of samples
showing a rising strain hardening behaviour for decreasing strain rates like the sample
described by Sebastian can be compared to samples which were aimed to contain very
few long-chain branches.
Figure 3: Time-dependent elongational viscosity of two polystyrenes. Influence of a separate high molecular component on elongational rheology. (Münstedt 1980)
Comparing the previously discussed results from literature it becomes obvious, that the
polydispersity Mw/Mn alone is an insufficient measure of the molecular weight distribution.
Small amounts of high molecular weight components have a minor effect on the width of
the molecular weight distribution, but have a distinct effect on the behaviour in
elongational flow. Figure 3 displays the experiments for the broadly distributed PS IV and
the bimodal PS II containing a high molecular weight component. The strain hardening
behaviour of the bimodal molecular weight distribution is much more distinct than that of
the broadly distributed sample.
Only few investigations of the influence on rheological properties of the short-chain
branching structure can be found in literature. Especially the investigation of
12
_______________________________________________________________________
HDPE/LLDPE blends is very rare. Blending HDPE with LLDPE does not offer the
advantages like blending LLDPE with LDPE. LLDPE as well as HDPE is difficult to
process. The most discussed point is the miscibility of the two chain structures. It can be
shown that in case of a similar molecular weight the linear and the short chain branched
samples are miscible. However no significant influence of the short chain branching on
shear properties can be found (Karbashewski, Kale et al. 1993). The extrudate swell was
increased by the addition of HDPE to an LLDPE matrix.
All in all the rheological behaviour is influenced by molecular parameters like long-chain
branching structure and their amount in the polymer resin, molecular weight distribution
and high molecular weight components. However, exact correlations of molecular
parameters and rheological behaviour in elongational flow are not established. In the
following work characteristic molecular parameters like long-chain branching, molecular
weight distribution and comonomer content are studied by preparing model-blend systems
and by investigating characteristic samples.
2.2 Experimental methods
2.2.1 Molecular analysis: Gel permeation chromatography (GPC)
The gel permeation chromatography characterises the molecular weight and the
molecular weight distribution. For the measurement a low concentrated polymer solution
is driven through columns filled with a gel of different pore size at a constant flow rate. The
method takes advantage of the dependence of the hydrodynamic volume Vh of the
molecule on the molecular weight. Smaller molecules can diffuse into the pores of the gel
and need a longer time to pass through the column. The bigger the molecules, the shorter
is the elution time of the molecule in the column. As a result the polymer leaves the
columns fractionated by their molecular size. Behind the columns the concentration c is
measured as a function of time. These can be converted to a function of molecular weight
by comparing them to a calibration standard. This calibration standard should be a well
characterized monodisperse sample. As no monodisperse polyethylene samples are
available, the samples are characterized with polystyrene standards, where the relation to
polyethylene is known. The results obtained are only valid for linear polyethylenes, as the
branching structure influences the radii of the molecules. For branched samples the
measured molecular weight tend to lower values. Thus, the molecular weight distribution
of branched samples can only be compared by their elution graph. The molecular weight
values of the long-chained branched LDPEs were obtained by light scattering.
13
_______________________________________________________________________
The measured weight average molecular mass Mw and the number average molecular
mass Mn are defined as follows:
∑∑
=
ii
iii
w c
McM
∑∑
=
iii
ii
n Mc
cM
/ (1)
ci: concentration of polymer of the molecular mass Mi
For the following characterisations a high temperature GPC Waters 150-C was used to
evaluate the molecular characteristics of the samples. The solvent was TCB, the
temperature of the measurements was chosen as 135°C and the flow rate was 1 ml/min.
2.2.2 Shear Rheology
For the processing behaviour, shear deformations play a major role, as they are the
dominant deformation in the extrusion process. The shear rheological behaviour was
evaluated by a cone-plate and a plate-plate shear rheometer. Melt rheological
measurements in shear were performed on an ARES strain controlled shear rheometer
(Rheometrics Scientific). For the given shear rates γ& the shear stress τ is measured. The
shear viscosity is defined as the proportionality factor relating the shear stress and the
shear rate in simple shear:
γτη&
= (2)
The thermal stability of the samples was checked by dynamic time sweep experiments at
a temperature of 150°C, a strain of 3% and a frequency of 0.01 s-1 or 0.1 s-1 using a plate-
plate geometry with a gap of 1.5 mm. For the evaluation of the activation energies,
thermal stability was tested up to 210°C. The results of the thermal stability are compiled
in the appendix. Dynamic data were obtained over a frequency range of 0.01 – 100 rad/s,
with a deformation which was adapted to the properties of the sample at varying
temperatures.
14
_______________________________________________________________________
2.2.3 Elongational Rheology
The elongational experiments were carried out using a Münstedt type elongational
rheometer which was first introduced in 1979 (Münstedt 1979). The aim is to measure the
uniaxial elongational viscosity µ(t) which is defined as:
H
ttε
σµ&
)()( = (3)
σ(t): tensile stress Hε& : strain rate, Hencky measure
According to the general definition of a viscosity the elongational viscosity is the ratio of
stress and deformation rate. In the rheometer a defined deformation can be applied to
molten polymer samples measuring the occurring forces.
electro-optical lengthmeasurement
force transducerheating liquid
toothed belt
pull rod
motor
sample
glass vessel
silicon oilρ ρ( ) ( )T Toil sample≈
guide slide
Figure 4: Münstedt type elongational rheometer
15
_______________________________________________________________________
Its details are principally shown in Figure 4. The sample of cylindrical shape is stretched
vertically in a silicon oil bath which density at 150°C matches the density of the molten
polymer. As a result no gravitational forces act on the sample. This enables the
investigations of samples of a broad viscosity range in a highly accurately temperated
state. Small deformation rates and long experimental times can be realized.
The samples are prepared by extruding the polymer at 150°C into a bath of an ethylene
water mixture. To rule out influences of pre-treatment of the sample the polymer rods are
subsequently relaxed in an oil bath at 130°C. Depending on the sample viscosity this
procedure can take up to 30 minutes. The extrusion parameters are chosen to gain a final
rod diameter of the relaxed sample of about 5 mm. Next the relaxed rods are sawn to
25 mm long cylinders.
PlatesAluminium
Prepared SampleRodPellets
Extrusion
Relaxing Oil Bath
5 mm
25 mm
Figure 5: Steps of the sample preparation for elongational experiments
Aluminium plates are glued to the abutting faces. These plates can be fixed to the force
transducer and the pulling rod. A detailed description of the sample preparation can be
found in the PhD thesis of S. Kurzbeck (Kurzbeck 1999).
After the prepared sample has been fixed in the elongational rheometer the setup is sunk
in a heated silicon oil bath. For polyethylenes the oil temperature is set to 150°C. To
eliminate a sagging of the samples the oil density is matched to the density of the
polyethylene melt at measuring temperature. The sample is elongated by a servo drive
which is coupled with an electro optical length measurement. As the deformation of the
sample is computer controlled, various deformation and stress histories can be performed.
The strain εH is calculated in Hencky measure:
16
_______________________________________________________________________
0
lnLL
H =ε (4)
εH: Hencky strain L: actual sample length; L0: initial sample length
The tensile force F(t) is measured by a force transducer which is situated in the oil bath. In
stressing experiments the Hencky strain rate was kept constant. It is defined as:
00
)()(
1)(ln)( εεε && =⋅===dt
tdLtLL
tLdtdt
dtd
HH (5)
Then the deformation of the sample is described by the following equation:
tL
tL⋅= 0
0
)(ln ε& (6)
teLtL ⋅⋅= 0
0)( ε& (7)
For the evaluation of the time-dependent elongational viscosity the stress as a function of
time must be calculated. As the stress is defined as the force per cross-section, the
sample cross-section as a function of time must be calculated. Assuming a constancy of
volume i.e.:
00)()( LAtLtA ⋅=⋅ (8)
A(t): actual sample cross-section A0: initial sample cross-section
it follows:
tHeAtA ⋅= ε&
0)( (9)
Using equation (7) it follows for the elongational viscosity:
t
HHH
HeA
tFtA
tFtt ⋅
⋅=
⋅== ε
εεεσµ &
&&& 0
)()(
)()()( (10)
17
_______________________________________________________________________
3η+(t)LLDPE
LDPE strain hardening
elon
gatio
nal v
isco
sity
µ(t)
[Pas
]
time t [s-1]
Figure 6: Schematic sketch of the results of elongational stressing experiments. The strain hardening LDPE shows a distinct rise of the elongational viscosity at high strains whereas the LLDPE follows the threefold of the linear viscoelastic start-up curve (Trouton-law).
In addition to the constant strain rate experiments, creep experiments were performed for
some samples. In creep experiments the tensile stress on the sample is kept constant
during the deformation and the deformation rate is measured as a function of time.
.)()()( const
tAtFt ==σ (11)
σ: tensile stress F: measured force A: cross section of the sample
For long times, the deformation rate reaches a steady state which is characteristic for the
applied stress.
18
_______________________________________________________________________
σ = σ0
steady state
Hen
cky
stra
in ε H
time t st
rain
rate
time t
Figure 7: Schematic sketch of the experimental results of elongational creep experiments. Left graph: Hencky strain as a function of time. Right graph: The strain rate which is the time derivative of the
Hencky strain is plotted as a function of time
Figure 7 shows the typical results of creep experiments. For a given stress σ0 the
deformation of the sample is recorded as a function of time (left graph). The time
derivative gives the strain rate Hε& as a function of experimental time. For long
experimental times the strain rate reaches the steady-state value sε& . The steady-state
elongational viscosity follows as:
Ss ε
σσµ
&0)( = (12)
µs: steady-state elongational viscosity σ0: applied stress sε& : steady-state strain rate
According to the given equation a steady state viscosity µs(σ) can be calculated. After
performing the experiment for a number of stresses a curve like the one shown in Figure 8
is expected, if the sample shows a strain hardening behaviour.
19
_______________________________________________________________________
σ0, 1
< σ0, 2
σ0, 1 σ0, 2
linear behaviour 3η0
LLDPE
LDPE strain hardening
stea
dy-s
tate
elo
ngat
iona
l vis
cosi
ty µ
s(t)
applied stress σ0
Figure 8: Schematic sketch of a typical chart of the elongational steady-state viscosity as a function of applied stress with a sample showing strain-hardening behaviour (LDPE) and a non strain-hardening
LLDPE.
For a small applied stress, which correlates with a low strain rate, the sample shows linear
deformation behaviour. The calculated elongational steady-state viscosities match with
the threefold of the zero-shear viscosity according to the Trouton law. For higher stress
the onset of strain hardening can be observed and the steady-state elongational viscosity
runs through a maximum. If the applied stress is increased even further on, the viscosity is
decreasing.
Compared to the stressing experiments the steady-state viscosity µs at the steady-state
rate sε& represents the maximum viscosity for an applied strain rate 0ε& at high strains. In
creep experiments the steady-state rate is reached at lower strains than the steady-state
viscosity in stressing experiments. As the maximum strains are limited by the
experimental set-up the creep experiments enable a more detailed investigation of the
elongational viscosity in uniaxial deformation.
In the following investigations the presented two types of elongational experiments enable
an accurate description of the influence of molecular parameters of the samples on the
rate and strain dependence of the elongational viscosity.
20
_______________________________________________________________________
2.3 Influence of long-chain branching on rheological properties
It is an established fact that the long-chain branching structure of polyethylenes is
influencing the behaviour in shear flow and especially in elongational flow. However, a
quantitative description of the influence of long-chain branching is not given in literature.
Especially for the development of new long-chain branched metallocene mLLDPEs the
influence of small amounts of long-chain branches on rheology of the polymer melts is of
interest. In addition it can be checked whether the rheological properties of mLLDPEs can
be realized by LLDPE-LDPE blends.
2.3.1 Samples
As the polymerisation of a defined amount of long-chain branches in polyethylene resins
is nearly impossible and in addition their characterisation is not satisfactory with regard to
their structure, a polymerisation of a polyethlylene series with a defined long-chain
branching content fails. In the following investigation blend systems of LDPE and LLDPE
were used for a quantitative evaluation of the rheological properties. To get an idea of the
influence of the molecular weight on the strain-hardening behaviour two blend systems
were prepared, one with a LLDPE component of higher molecular weight and another with
a LLDPE component of lower molecular weight than the LDPE which was the same for
both series.
The chosen LDPE is an autoclave product. With 3.4 CH3-end groups per 1000 C atoms,
quantified by NMR, its number of long-chain branches is relatively low for an LDPE1. Two
LLDPE blend partners have been chosen which have a molecular weight distribution
without high molecular weight components and a moderate difference in molecular weight
compared to the LDPE.
1 13C-NMR gives exact quantitative number of C-Atoms with regard to the chemical bonds of their neighbor atoms. In case of polyethylene this method can differentiate between side branches of up to 6 carbons in length. Side branches with more than 6 carbons are filed as end groups of long chains. NMR results do not give absolute numbers of rheologically active long-chain branches, but are a supporting evidence for a quantitative assessment of long-chain branches.
21
_______________________________________________________________________
LDPE LLDPE 1 LLDPE2
Mw [g/mole] 130,000 92,000 150,000
Mw / Mn 11 5.1 7
LCB CH3/1000C 3.4 - -
Table 1: Molecular data of the blend partners of the LDPE/LLDPE blends. The molecular data of the LDPE was evaluated by light scattering.
The LLDPE 1 has a lower molecular weight than the LDPE blend partner, whereas the
LLDPE 2 has a slightly higher molecular weight than the LDPE. The molecular weights of
the LLDPEs are measured with the conventional GPC method. But due to the long-chain
branches of the LDPE molecules, the radii of the molecules decrease and the GPC based
on size exclusion measures too low molecular weights. Thus for the LDPE the Mw values
are measured by light scattering.
LLDPE 2
LLDPE 1
LDPE
c i
elution volume
Figure 9: GPC traces of the blend partners measured with a conventional GPC, elution graphs.
Comparing the elution plots of the LPDE and the LLDPEs, the shape of the curves of the
samples are very similar although the molecular data indicates a broader distribution of
the LDPE. In general the molecular weight distribution measured in a conventional GPC
22
_______________________________________________________________________
will be narrower for long-chain branched samples than the real distribution which is
measured with a light scattering equipment (Scholte 1983).
103 104 105 106
Mw = 150,000 g/moleMw/ Mn = 7
Mw = 92,000 g/moleMw/ Mn = 5.1
LLDPE 2LLDPE 1
blend partnerLLDPEs
w (M
)
molecular weight [g/mol]
Figure 10: GPC curves of the LLDPE blend components as a function of the molecular weight. As long-chain branches falsify the radii of the molecules, LDPE is not included in this graph.
Great store was set on the absence of high molecular weight fractions as it is known that
they might have a strong influence on the rheological properties. Their influence on the
elongational behaviour will be discussed in a later chapter. As can be seen in Figure 9,
the shapes of the three samples show no elaborated high molecular weight shoulders and
thus an influence of an altered shape of the molecular weight distribution on the
rheological properties of the blend series can be excluded. In Figure 10 the selected
LLDPE samples are plotted as a function of molecular weight. The curves indicate no
bimodality or high molecular weight tails for both products.
Two blend series were prepared. Each blend series comprised samples with 2%, 5%,
10%, 15% and 20% weight of the LDPE in an LLDPE matrix. One was prepared from the
LLDPE 1 and the LDPE. In this case the LLDPE linear product has the lower viscosity of
the blend partners. The second blend series was prepared with LLDPE 2 which has a
23
_______________________________________________________________________
higher molecular weight than the long-chain branched LDPE. Especially with respect to
the new long-chain branched metallocene LLDPEs which have only very few long-chain
branches, the influence of a low amount of long-chain branches is of interest. The blends
were prepared by a twin screw extruder at 190°C. To avoid a degradation of the
molecules during the blend composition 2000 ppm of Irganox B561 was added.
2.3.2 Shear rheology of LLDPE / LDPE blends
The rheological properties of the blend series of the LLDPE 1 and the LDPE have been
intensively studied in shear. For the reliability of the experimental results, the thermal
stability is of crucial interest. To evaluate the thermal stability, the storage modulus G’ was
measured at a constant frequency as a function of time under air atmosphere. A sample is
regarded to be stable, as long as the value of G’ does not change more than 5 % of its
starting value. In Figure 11 – 12 the results of the two blend components and one blend
(10 % content of LDPE) are displayed for temperatures of 170°C, 190°C and 210°C. As
the samples are stable for at least 5000 s at a temperature of 170°C, the thermal stability
for lower temperatures is guaranteed. At 190°C the samples are stable for at least 1500 s,
in case of the blend even for more than 4000 s. At 210°C the samples are not stable. The
blend has proven to be more stable than its components which is a result of the additional
amount of stabilizer added during blending.
0 1000 2000 3000 4000 5000
10
100
1000
10
100
1000
170°C
190°C
210°C5% tolerance
LDPE
γ=20%ω=0.1 rad/s
G' [
Pa]
time [s]
Figure 11: Thermal stability of LDPE at 170°C, 190°C and 210°C in air.
24
_______________________________________________________________________
0 1000 2000 3000 4000 5000 60001
10
100
1000
1
10
100
1000
170°C
190°C210°C 5% tolerance
LLDPE 1
γ=20%ω=0.1 rad/s
G' [
Pa]
time [s]
Figure 12: Thermal stability of LLDPE 1 at 170°C, 190°C and 210°C in air.
0 1000 2000 3000 4000 5000 60001
10
100
1000
1
10
100
1000
210 °C190°C
170°C5% tolerance
Blend90% LLDPE 110% LDPE
γ=20%ω=0.1 rad/s
G' [
Pa]
time [s]
Figure 13: Thermal stability of LLDPE 1/LDPE blend 90/10 at 170°C, 190°C and 210°C in air.
The dynamic viscosity functions of the blend components and the blends are displayed in
Figure 14. Dynamic viscosities were measured at 150°C with a strain of 20 %. Owing to its
25
_______________________________________________________________________
high molecular weight the LDPE has a higher shear viscosity at low shear rates than the
LLDPE 1. This situation is reversed at high shear rates. Due to a pronounced shear
thinning behaviour the viscosity of the LDPE is even lower than the shear viscosity of the
LLDPE 1 and the blends. This pronounced shear thinning behaviour is typical of long-
chain branched LDPEs and makes them more favourable for extrusion processes with
respect to their flow behaviour. Comparing the blend components to the blends of the
LLDPE 1 with 2 to 20 % LDPE content it can be seen, that the viscosity functions of the
blends are close to the viscosity function of the LLDPE 1. The blends with a content of
2 % and 5 % LDPE have an even lower shear viscosity function than the LLDPE 1 for all
measured shear rates. The behaviour of the 10 % blend is comparable to the LLDPE 1.
Whereas the blends with 25 and 20 % LDPE content exhibit a higher shear viscosity than
the LLDPE. Furthermore, these two blends show a more pronounced shear thinning
behaviour than the LLDPE 1 itself.
10-2 10-1 100 101 102
103
104
10-2 10-1 100 101 102
103
104
Blends ofLLDPE 1 with LDPE
T=150°C
LLDPE 1 2% LDPE 5% LDPE 10% LDPE 15% LDPE 20% LDPE LDPE
Iη*I
[Pas
]
ω [rad/s]
Figure 14: Dynamic shear viscosities of the LDPE – LLDPE 1 blend series at 150°C as a function of the angular frequency.
To get a deeper insight into the shear behaviour of this blend system the zero shear
viscosities were measured at different temperatures to see whether this unusual effect of
the viscosity as a function of LDPE content is temperature dependent. To point out the
26
_______________________________________________________________________
characteristic behaviour of this blend system the results are compared to the relation of
the zero shear viscosity as a function of weight content of the blend partners.
( ) ( ) ( )2,021,10 lglglg ηηη ww o += (12)
w1,w2: weight fractions η0,1, η0,2: zero shear viscosities of the blend components
This equation is obeyed by “ideal” mixtures, devoid of large thermodynamic interactions.
In Figure 15 the zero shear viscosities of the blend series are plotted as a function of the
weight content of LDPE for the temperatures of 150°C, 170°C and 190°C. At 150°C the
zero shear viscosity of the LDPE (12000 Pas) is much higher than that of the LLDPE 1
(4600 Pas), but blends with a low content of LDPE (2 % and 5 %) have an even lower
viscosity than the LLDPE.
0.0 0.2 0.4 0.6 0.8 1.0
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
150°C 170°C 190°C
log
Iη*I 0
wLDPE
2000
3000
4000
5000
600070008000900010000
zer
o sh
ear v
isco
sity
|η*| 0
[Pas
]
Figure 15: Zero shear viscosity from dynamic-mechanical experiments as a function of weight content LDPE at three different temperatures
The previously introduced simple logarithmic rule of additivity cannot be applied to the
blend system. Negative deviations from the mixing rule have been shown in literature
before by Utracki. According to Utracki it can be explained by an immiscibility of the blend
components (Utracki 1983). As a result of drop formation of the minor component the
27
_______________________________________________________________________
tangle volume2 is decreased, i.e. the number of entanglements of the LLDPE decreases.
and thus the viscosity decreases. A blend system of PA-6,6 and PET investigated by
Utracki et. al. shows a comparable behaviour of the zero shear viscosities. According to
the argumentation of Utracki this LLDPE / LDPE blend system is not miscible and the
blend components separate in the melt. As the miscibility of the blend components is
improved at higher temperatures the negative deviation decreases at rising temperatures.
The temperature dependence of the deviation of the zero shear viscosities should also
been seen in the flow activation energies of this blend series. The flow activation energies
are obtained by a horizontal shift if the G’ and G” curve at various temperatures as shown
in Figure 16 exemplified for the LDPE.
10-3 10-2 10-1 100 101 10210-1
100
101
102
103
104
105
LDPET0 = 150°C
Temperature [°C] 130 150 170 190 210
G'
G''
G' ,
G''
[Pa]
aTω [rad/s]
10-2 10-1 100 101 102
102
103
104
Figure 16: Mastercurves of G’ and G” the LDPE. The curves are shifted to the reference temperature 150°C.
2 Volume that could be used by the major component to form entanglements is taken by the minor component, which does not interact with the major component in case of an immiscible blend. Thus the number of entanglements per volume is decreased.
28
_______________________________________________________________________
2,0 2,1 2,2 2,3 2,4-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,22,0 2,1 2,2 2,3 2,4
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,2
.
EA = 31.6 kJ / mole
LLDPE 1 LDPE
EA = 56.0 kJ / mole
log(
a T(T,
T 0))
reciprocal temperature T -1 103 [K-1]
Figure 17:Arrhenius plot of the shift factors of the LDPE and the LLDPE 1. (Reference temperature 150°C)
The LDPE shows a simple thermo-rheological behaviour. Mastercurves can be
constructed in the temperature range of 130°C to 210°C. Figure 17 shows the Arrhenius
plots of the shift factors used for the mastercurves. The resultant flow activation energy of
the LLDPE 1 of 31.6 kJ/mole can be compared to values from literature (Gabriel 2001).
The flow activation energy of the LDPE of 56.0 kJ/mole is low for an LDPE which can be
related to the relatively low amount of long-chain branches compared to the majority of
LDPEs.
29
_______________________________________________________________________
0.0 0.2 0.4 0.6 0.8 1.0
30
35
40
45
50
55
600.0 0.2 0.4 0.6 0.8 1.0
30
35
40
45
50
55
60
LLDPE 1
LDPE
E A [kJ
/ m
ole]
wLDPE
Figure 18: Activation energies as a function of the weight content of LDPE
For the blend series the flow activation energies rises with increasing content of LDPE.
But the activation energies of the 2 % (EA = 30.1 kJ/mole) and the 5 % (EA = 30.6 kJ/mole)
blend are even lower than the activation energy of the pure LLDPE. In literature lower flow
activation energies of blends compared to the blend components are reported. Ghijsels et
al. show that LLDPE/LDPE blends had a distinctly lower flow activation energy than a
linear dependence of the blend components (Ghijsels, Ente et al. 1992). They account
“synergetic effects” for the low activation energy of blends with a low fraction of LDPE. But
no further explanation is given by the authors.
To judge, whether the shear thinning behaviour shows also an anomalous dependence on
the LDPE content for small weight contents, the mastercurves of the shear viscosities are
displayed in a so-called Vinogradov-plot. In this temperature-invariant description the
reduced viscosity η/η0 is plotted as a function of a reduced frequency η0 ω. With help of
this presentation of the experimental data it is possible to compare the shear thinning
behaviour of samples of different zero shear viscosity over a broad range of shear rates.
30
_______________________________________________________________________
101 102 103 104 105 1060.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
101 102 103 104 105 106
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
Blend system LLDPE 1 / LDPE
η/η
0
LLDPE 1 2% LDPE 5% LDPE 10% LDPE 15% LDPE 20% LDPE LDPE
η0 ω
Figure 19: Vinogradov plot of dynamic viscosity mastercurves of the LLDPE 1/LDPE blends and their blend partners.
The Vinogradov-plot of the viscosity mastercurves in Figure 19 shows clearly the distinct
shear thinning behaviour of the LDPE. Moreover, it supports the finding, that the blends
with 2 % and 5 % weight content LDPE exhibit not only no typical effect of long-chain
branching on their shear properties, they even show a slightly less distinct shear-thinning
behaviour than the LLDPE 1. A clearly stronger shear-thinning behaviour can only be
observed for LDPE contents of 15 and 20 %. If according to Utracki a drop formation of
the minor blend component is responsible for the observed effects, a phase separation
might be provable by thermoanalytical methods. Therefore the samples were run on a
Differential Scanning Calorimeter (DSC) heated from 70 to 140°C with a heating rate of
10°C per minute. After a defined cooling with 10 °C/min another heating was performed.
31
_______________________________________________________________________
80 100 120 140
80 100 120 140
80 100 120 140
80 100 120 140
first heating
LDPELLDPE1
LLDPE 1LDPE
heating rate: 10 K/min Tm= 124.7 °C
Tm= 114.8 °C
1st heating
End
o
hea
t flo
w
E
xo
T [°C]
second heating
T=116°C
temperature profile: 70 - 140 - 70 - 140heating rate: 10 K/min Tm= 135.7 °C
Tm= 113.6 °C
2nd heating
T [°C]
Figure 20: DSC thermograms of the blend components
70 80 90 100 110 120 130 140
70 80 90 100 110 120 130 140
60 70 80 90 100 110 120 130 140 150
60 70 80 90 100 110 120 130 140 150
Tm = 113.3°C
20% LDPE
15% LDPE
10% LDPE
5% LDPE
2% LDPE
Tm = 126.0°C
heating / cooling rate: 10K / mintemperature profile: 70 - 140 - 70 -140
T [°C]
second heatingfirst heating
0.5 W/g 0.5 W/g
5% LDPE
10% LDPE
15% LDPE
20% LDPE
2% LDPE
Tm = 125.4°Cheating rate: 10K/mIN
EN
DO
h
eat F
low
EXO
T [°C]
Figure 21: DSC thermograms of LLDPE - LDPE blends
The thermogram of the LLDPE 1 shows a shoulder at 116°C and a peak at 135.7°C after
being cooled and reheated, indicating that two types of crystals species are present
(Figure 20). The thermograms of the blends for the first heating show only one melt peak,
whereas for the second heating two distinct melt peaks occur (Figure 21). The lower peak
32
_______________________________________________________________________
can be attributed to the melting of the LDPE component, and the higher peak is
associated with melting of the LLDPE 1.
These observations indicate that for a reasonable slow cooling, the blend segregates
during crystallisation, whereas in the melt the LLDPE 1 and the LDPE are compatible
within the time window of extrusion processes, i.e. right after the extrusion step the blend
components are well mixed in the melt. Although on the base of the DSC investigations no
conclusions can be drawn with respect to the behaviour of the samples in the preceding
experiments in shear, as the blends reside some minutes molten in the rheometer without
shear deformation, it becomes obvious that the question of miscibility does not influence
the latter investigations regarding the flow behaviour in the extrusion process. For
extruded samples a phase separation cannot be seen in the thermo-analytical analysis. A
similar observation was made by S. Haghighat and A.W. Birley. They concluded that the
blend is miscible in the melt (Haghighat and Birley 1990).
Summing up the results obtained in shear rheology, the LLDPE – LDPE blends do not
show simple correlations as a function of the LDPE content. Especially for low
concentrations of long-chain branched polyethylene synergy effects can be observed, that
make a prediction of viscosity functions impossible. The blends of 2 and 5 % LDPE
content show a lower viscosity, a lower activation energy and a less distinct shear thinning
behaviour than the LLDPE. Only for the blends with more than 10 % weight content LDPE
a distinct influence of the LDPE on the shear behaviour of the blend can be observed.
2.3.3 Influence of long-chain branches on elongational flow
As it is well known from literature, linear and long-chain branched polyethylenes behave
distinctly different in an extensional flow field (Münstedt and Laun 1981). Long-chain
branched LDPEs exhibit a clear strain hardening behaviour, whereas for many linear
LLDPE no strain hardening is reported. In the latter case, the time dependent elongational
viscosity corresponds to three times the linear viscoelastic start up curve in shear. This
relation is called Trouton law.
Figure 22 shows the time-dependent elongational viscosity at 150°C of the LDPE and the
LLDPE 1 for a broad range of deformation rates. The results are typical of LDPE and
LLDPE resins. The behaviour in elongational flow of the long-chain branched LDPE is
measured for elongational rates from 3 s-1 to 0.01 s-1 up to a Hencky strain of εH= 3. For
this range of elongational rates the strain hardening behaviour of the LDPE is more
33
_______________________________________________________________________
pronounced for higher strain rates and decreases for slow deformation rates. At a rate of
0.01 s-1 no strain hardening can be observed.
10-1 100 101 102
104
105
.3η+(t, γ0=0.01s-1)
.ε0 [s
-1] 1 0.3 0.1 0.03 0.01
1 0.5 0.30.1
0.030.01
3.ε0 [s
-1]
LLDPE 1
LDPE
T = 150 °C
elon
gatio
nal v
isco
sity
µ(t)
[Pas
]
time t [s]
Figure 22: Elongational behaviour of the LDPE and LLDPE 1 at 150°C
In contrast to the LDPE, the LLDPE 1 shows no strain hardening behaviour for all de-
formation rates in the experimental window from elongational rates from 1 s-1 to 0.01 s-1.
Due to the low viscosity of the LLDPE 1 and the absence of strain hardening and its self
healing effects (see Figure 1), the samples deformed inhomogeneously at long
experimental times. This problem occurs for all samples of a relatively low viscosity at low
deformation rates. Due to a slight density mismatch between the samples and the
supporting oil in the vessel gravitational forces deform the sample and lead to an
apparently decreasing elongational viscosity. However, this decrease is a measurement
artefact. Due to the low viscosity the homogeneity of the samples could not be measured
after the experiment as the buoyancy deformed the sample right after the experiment
before the samples could be frozen in. However, a close look at the run of the viscosity
curve gives further information of the deformation homogeneity. As shown in Figure 23 the
samples of the LDPE could be drawn up to the maximum Hencky strain of 3, except the
34
_______________________________________________________________________
sample of the elongational rate at 0.01 s-1. At this rate the elongational viscosity drops at a
Hencky strain of 2.4. Here the samples starts to deform inhomogeneously. The smaller
the cross section, the lower is the force and the calculated viscosity3. This can be
correlated to the absence of strain hardening and consequentially the missing positive
effect of the self-healing effect. In addition experimental effects like the previously
mentioned density mismatch of sample and the oil come into play.
0,1 1104
105
εH max= 3
3
.ε0 [s
-1]
1
0.3
0.1
0.03
0.01
LDPE
T = 150 °C
elon
gatio
nal v
isco
sity
µ(t)
[Pas
]
Hecky strain εH
Figure 23: Elongational viscosity of the LDPE as a function of Hencky strain.
What impact has the addition of a small weight fraction of LDPE to the LLDPE 1 on the
elongational properties? Figure 24 shows the time-dependent elongational viscosities of
the LLDPE 1/ LDPE blends. In order to enable a better clarity of the graphs the results of
the different samples are shifted by factors. The previously described density effect pre-
vents an elongation up to a Hencky strain of 3 for the lowest deformation rate of 0.01 s-1.
Like the LDPE, the lowest rate shows no strain hardening for all blends. At high rates, 0.5
and 1 s-1 strain hardening is introduced with rising LDPE content. It is evident that already
an addition of 5 % LDPE is enough to change the elongational characteristics of the
3 The correct calculation of the viscosity relies on a homogeneous deformation of the sample.
35
_______________________________________________________________________
blend. At the strain rate of 1 s-1 a significant rise of the elongational viscosity can be
observed.
10-1 100 101 102102
103
104
105
3η0
/8
/4
/2
/16
20% LDPE
15% LDPE
10% LDPE
5% LDPE
2% LDPE
.
T = 150 °Cεmax= 3
strain rate ε0 [s-1]
1 0.5 0.1 0.01
elon
gatio
nal v
isco
sity
µ(t)
[Pa
s]
time t [s]
Figure 24: Time-dependent elongational viscosity of the LLDPE 1/LDPE blends at 150°C, the curves are shifted according to the given factors.
More information about the amount of strain hardening can be obtained by comparing the
steady-state elongational viscosities. The steady-state elongational viscosity represents
the maximum elongational viscosity at a prescribed stress. In Figure 25 the applied stress
and the resulting deformation of the samples are plotted as a function of time. The results
of the blend containing 20% LDPE for the applied stress of 10,000 and 20,000 Pas show
that the given stress is sufficiently constant after 0.3 seconds. This is the precondition for
reproducible and reliable results of creep experiments. The resultant deformation is
displayed in the right graph. The maximum Hencky strain of 3.75 is made possible by
using samples with a length of 10 mm. These short samples are necessary as high strains
are needed to reach a steady state of deformation. The deformation rate slows down with
rising time. The occurring strain rates are shown in Figure 26, where the strain rates are
plotted as a function of time. For high strains the deformation rate reaches a plateau
value. This steady-state of deformation is characteristic for the sample and the applied
stress at the given temperature. Combining the given stress and the resulting steady-state
deformation rate the steady-state elongational viscosity can be calculated.
36
_______________________________________________________________________
0 2 4 6 8 100
5000
10000
15000
20000
0 2 4 6 8 100,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
st
ress
σ
[Pa]
time t [s]
T = 150°C
applied stress 10,000 Pa 20,000 Pa
Hen
cky-
stra
in
ε Η
time t [s]
Figure 25: Applied stress and resulting deformation of a blend (20% LDPE) as a function of time.
Figure 26: Strain rate as a function of time
0 2 4 6 80,0
0,5
1,0
1,5
2,0
2,5
.
Blend:80% LLDPE20% LDPE
T = 150°C
applied stress 10,000 Pa 20,000 Pa
stra
in ra
te ε
[s-1]
time t [s]
37
_______________________________________________________________________
Figure 27 quantifies the stress dependence of the steady-state elongational viscosity. In
addition to the data from elongational experiments, the threefold of the zero shear
viscosity η0 is plotted to enable the quantification of the strain hardening behaviour. Due to
the low viscosity of the blends the experimental stress window was smaller than for the
LDPE. In case of the LLDPE 1 no steady state could be determined as inhomogeneities
occur. For low stresses the steady-state elongational viscosity is in the range of the linear
region. For increasing stress the elongational viscosities are rising, if the sample shows
strain hardening. The LDPE itself shows strain hardening for all rates within the
experimental window of the creep experiments.
103 104 105104
105
LDPE
20% LDPE15% LDPE10% LDPE 5% LDPE 2% LDPE
dotted curves: 3ηeo
2% LDPE 5% LDPE 10% LDPE 15% LDPE 20% LDPE LDPE
stea
dy-s
tate
elo
ngat
iona
l vis
cosi
ty µ
s [Pa
s]
stress σ0 [Pa]
Figure 27: Steady-state elongational viscosities as a function of applied stress at 150°C
The 2 % LDPE blend exhibits no strain hardening behaviour. The 5 % LDPE blend clearly
shows strain hardening for the higher strain rates. It can be concluded that the threshold
content of LDPE for strain hardening is between 2 and 5 % LDPE content. In addition
these experiments show a pronounced strain-hardening behaviour for LDPE contents of
10 to 20 % LDPE. For low applied stress the steady-state elongational viscosities match
the linear behaviour shown by the threefold of the zero shear viscosity.The linear
behaviour at low applied stress corresponds to the linear behaviour seen in stressing
38
_______________________________________________________________________
experiments, i.e. no strain hardening at low deformation rates. Compared to the LDPE the
onset of strain hardening is shifted to lower strain rates with rising amount of LLDPE.
To enable a better comparison with the results of the stressing experiments at a constant
strain rate these results can be displayed as a function of the steady-state rate (Figure
28). Now it can clearly be seen, that the hardening behaviour seen in the creep
experiments go along with the results of the experiments at a constant strain rate. At low
strain rates similar elongational viscosities are measured for the creep and stressing
experiments. In both experiments no strain hardening can be observed. The values match
the Trouton relation indicated by the threefold of the zero shear viscosity. For increasing
rate and stress the rising viscosity indicates the occurring strain-hardening. The measured
steady-state elongational viscosities are higher than the results obtained in stressing
experiments. They represent the maximum viscosity at the given strain rate for high
strains which cannot be realized in the stressing experiments.
0,01 0,1 1104
105
0,01 0,1 1
104
105
.
3η0 blend
3η0 LDPE
Blend 20% LDPE (creep experiment) Blend 20% LDPE (stressing experiment)
.
Blend (20% LDPE)
LDPE
dotted curves: 3ηeo
elongational rate ε0 [s-1]
elon
gatio
nal v
isco
sity
at H
enck
y st
rain
3 µ
[Pas
]
LDPE (creep experiment) LDPE (stressing experiment)
stea
dy-s
tate
elo
ngat
iona
l vis
cosi
ty µ
s [Pa
s]
steady-state elongational rate εs [s-1]
Figure 28: Steady-state elongational viscosities as a function of the steady state elongational rate at 150°C
All in all it can be shown that already a small amount of LDPE changes the characteristic
behaviour from linear to strain hardening. The onset on the rate scale and the maximum
quantity of this effect can be observed in creep experiments. With regard to processing it
39
_______________________________________________________________________
is possible to introduce an effective strain hardening with a low amount of LDPE addition
to an LLDPE resin.
2.3.4 Influence of the LLDPE matrix on the strain-hardening behaviour of blends
The influence of the amount of long-chain branched LDPE in a linear LLDPE matrix on the
elongational viscosity was investigated in the last chapter. In addition the influence of the
viscosities of the blend partners on the elongational behaviour can be checked. Therefore
a second blend series was prepared with the same LDPE component, but with an LLDPE
matrix which has a higher molecular weight (Compare Figure 9, Table 1) and thus a
higher shear viscosity than the LDPE.
10-1 100 101 102
104
105
.strain rate ε0 [s-1]
0.01 0.1 0.5
.3η+(t, γ0=0.01s-1)
1 0.50.3 0.1
0.03
0.01
3.ε0 [s
-1]LLDPE 2
LDPE
T = 150 °Cεmax= 3
elon
gatio
nal v
isco
sity
µ(t)
[Pas
]
time t [s]
Figure 29: Elongational behaviour of LLDPE 2 at elongational rates of 0.01, 0.1 and 0.5 s-1 at 150°C. For comparison the elongational behaviour of the LDPE is plotted.
As shown in Figure 29 in elongational deformation no strain hardening behaviour can be
observed for the LLDPE 2. For a direct comparison the elongational viscosity curves of
the blend partner, the LDPE are plotted. In the linear viscoelastic region the LLDPE 2 has
an approximately twice as high viscosity as the LDPE. Likewise the blend series of
LLDPE 1 and the LDPE, blends were prepared with 2, 5, 10, 15 and 20 % LDPE content.
40
_______________________________________________________________________
Like for the previous blend series creep experiments displayed in Figure 30 show, that it is
possible to introduce a strain-hardening effect by adding LDPE to the LLDPE 2 matrix.
The more LDPE is added to LLDPE 2 the more pronounced is the strain hardening
behaviour of the blend. In contrast to the first blend series the maximum of strain
hardening is shifted to lower rates for a matrix with a higher viscosity (Figure 30). Likewise
is the onset of strain hardening at lower strain rates. This can be related to longer
relaxation times and therefore to a non-linear behaviour for lower rates. The blend with a
concentration of 2% LDPE shows no strain hardening behaviour.
0,01 0,1 1
105
3η0 of the LDPE
3η0 of the blends
.
LCB Blend Series LLDPE 2 / LDPET=150°C
LDPE 20% LDPE 15% LDPE 10% LDPE 5% LDPE 2% LDPE
stea
dy-s
tate
elo
ngat
iona
l vis
cosi
ty µ
s [Pa
s]
steady-state rate εs [s-1]
Figure 30: Steady-state elongational viscosities of the blend series LLDPE 2 with LDPE. The zero shear viscosities of the blends are so similar, that they are not separately shown.
Summing up the creep experiments performed with the two blend series give an insight
into the dominating parameters of the elongational behaviour of long-chain branched
samples. In addition to the strain hardening properties of the LDPE component, the matrix
has a distinct influence on the elongational behaviour. By varying the viscosity of the
matrix, the longest relaxation times can be shifted and thus the onset of strain hardening
can be controlled. A matrix of a high viscosity shifts the onset and the maximum of strain
hardening to lower deformation rates.
41
_______________________________________________________________________
2.3.5 Elongational rheology of a long-chain branched metallocene LLDPE
Besides the LDPE a long-chain branched metallocene LLDPE, mLLDPE 11 is
investigated. Figure 31 displays the GPC trace of mLLDPE 11. It has a molecular weight
of 104,000 g/mole and the curve shows no evidence of high molecular weight components
over 1250,000 g/mole.
103 104 105 106
Mw = 104,000 g/mol
Mn = 22,000 g/mol
Mw/M
n= 4.6
LCB - mLLDPE 11
w (M
)
molecular weight [g/mol]
Figure 31: GPC curve of the long-chain branched mLLDPE 11
This single site material is polymerised with a catalyst that enables the formation of long-
chain branches.
mLLDPE 11
density [g/cm3] 0.921
Mw [g/mol] 104,000
Mn [g/mol] 22,400
Mw /Mn 4.6
Table 2: Molecular data of the long-chain branched mLLDPE 11
42
_______________________________________________________________________
However the amount of long-chain branches is so low, that they can be detected neither
by GPC-OLV4 nor 13C-NMR. A rough estimation should clarify the maximum number of
long-chain branches, which cannot be evaluated by 13C-NMR. Considering the resolution
associated with the NMR method of 0.1 CH3 groups per 1000 C atoms, this mLLDPE has
at the most 0.1 CH3/1000C. For the LDPE a number of 3.4 CH3/1000C was measured.
Downscaling the value for LDPE to the 2% LDPE blend, it has statistically 0.07 CH3 -
groups per 1000C. Figure 32 shows the results of elongational experiments performed at
a temperature of 150°C.
10-1 100 101 102
104
105
.
strain rate ε0 [s-1]
0.01 0.03 0.1 0.3 0.5 1 3η+(t, γ0=0.01s-1)
.
mLLDPE 11εmax= 3
T = 150 °C
elon
gatio
nal v
isco
sity
µ(t)
[Pas
]
time t [s]
Figure 32: Elongational behaviour of LCB - mLLDPE 11 at 150°C
Within the experimental window of elongational rates from 0.01 s-1 to 1 s-1 the sample
shows a distinct strain hardening behaviour. The maximum of the strain hardening is
measured at the rate of 0.3 s-1 (Figure 32). Compared to the previous blend series, the
strain hardening of the mLLDPE 11 is more elaborated and extends to lower strain rates.
Thus these long-chain branches must be very effective for the strain hardening in
elongational deformation. As the molecular weight distribution of the mLLDPE 11 contains
no high molecular weight fractions and as the molecular weight is in between the LLDPE 1
4 GPC-OLV: Gel Permeation Chromatography combined with an OnLine Viscosimetry
43
_______________________________________________________________________
and 2 the intensity of the strain hardening cannot be originated by the linear matrix. To
cause such a strong impact on the elongational properties with a very low content of long-
chain branches, the long-chain branched molecules themselves must have a branching
structure different from that of a conventional LDPE. According to the NMR results it can
be assumed that this sample contains only very few long-chain branched molecules. For
the given molecular weight Mw of the mLLDPE 11 of 104,000 g/mol, the average chain
length of the molecules is 7400 carbon atoms. For the given resolution of the NMR of 1
branch point for 10000 carbon atoms, on average every molecule has at the most 0.74
branches, i.e. not even one branch per molecule. If one molecule had only one branch it
could be regarded as a three arm star. On the basis of experiments with polybutadiene
Lohse et. al. report that a blend of three arm stars in a linear matrix does not cause strain
hardening in uniaxial extension (Lohse, Xenidou et al. 2000). But blends of comb
structured molecules in a linear matrix showed strain hardening behaviour. From this point
of view the mLLDPE 11 could be considered as a blend of linear molecules and a fraction
of highly branched molecules. These must have a very complex branching structure.
2.3.6 Conclusions of the influence of long-chain branching on rheology
Summing up the results obtained in shear rheology, the LLDPE – LDPE blends do not
show simple correlations as a function of the LDPE content. Especially for low
concentrations of long-chain branched polyethylene synergy effects can be observed, that
make a prediction of viscosity functions impossible. The long-chain branched LDPE has a
very pronounced shear thinning behaviour, whereas the addition of up to 10% LDPE to a
LLDPE matrix seems to have no impact on the shear thinning behaviour. But in
elongational flow the blend series show noticeably that already a small amount of 5%
LDPE is enough to introduce strain-hardening behaviour in elongational flow.
Furthermore, the matrix plays an important role in the rate dependence of the strain
hardening behaviour. A higher matrix viscosity leads to strain hardening at lower strain
rates. The strong strain-hardening behaviour of the mLLDPE11 shows that rheological
properties are not only dependent on the amount of long-chain branches. In addition, the
molecular parameters of the branching structure, like the branching distribution and
branch length, have a dominating importance. These molecular parameters cannot
directly be measured by the currently available analyzing methods. Elongational rheology
proves to be highly sensitive with respect to the branching structure of polymer melts. But
up to now an exact description of the molecular topology on the basis of the experiments
is not possible and only hypothesis can be discussed. Polymerizing defined branching
structures i.e. defined length of the branches and their functionality will be helpful. With
44
_______________________________________________________________________
the help of metallocene polymerized long-chain branched LLDPEs the molecular structure
of which can be controlled in the process, progress can be expected.
2.4 Influence of molecular weight distribution on elongational rheology
2.4.1 Influence of a higher molecular weight component on elongational rheology
As already seen in the comparison of the two LDPE–LLDPE blend series not only long-
chain branches have a strong influence on the drawing behaviour, but also the molecular
weight and subsequently the viscosity contribute to the elongational properties. Moreover
the molecular weight distribution can be varied. Especially, the high molecular weight
region has been shown to be of great importance for the rheological behaviour in
elongational flow.
LLDPE 1 LLDPE 3 (HMW) Blend 50% HMW
density [g/cm3] 0.924 0.921 n.m.
Mw [g/mol] 92,000 194,000 145,000
Mw / Mn 5.1 2.8 4.7
Table 3: Molecular data of the blend components LLDPE 1, LLDPE 3 and the LLDPE 1 / LLDPE 3 50/50% blend
To investigate the influence of the high molecular part of the molecular weight distribution
on the rheological properties the high molecular weight component LLDPE 3 was blended
to the unimodal LLDPE 1 (Table 3) to investigate, whether the strain hardening behaviour
changes by adding a fraction of distinct higher molecular weight (HMW – fraction). As the
blend was a candidate for film blowing experiments, the mixing of small amounts by
solution was not realistic. Blends were prepared with a content of 10 and 50 % by weight
of the high molecular weight LLDPE. To exclude a possible influence of short-chain
branches a HMW component with a similar density and therefore similar branching
structure was chosen. The HMW component had a narrow molecular weight distribution to
ensure a defined support of the high molecular weight region (Figure 33). The
homogeneity of the blends which were prepared on a twin screw extruder, was checked
by tape tests5. The cast tapes of the blends and the matrix component LLDPE 1 had a
5 tape test: An extruded tape is drawn to a thin layer. Inhomogeneous spots can be observed as gel particles. It is an easy to perform test of the homogeneity of polymer melts which components have a different viscosity.
45
_______________________________________________________________________
very similar gel level. Hence a sufficient dispersion of the HMW component in the
LLDPE 1 matrix can be assumed.
103 104 105 106
Mw = 145,000 g/mol
Mw/ M
n = 4.7
Mw = 194,000 g/molM
w/ M
n = 2.8
Mw = 92,000 g/mol
Mw/ Mn = 5.1
Blend 50% / 50%
LLDPE 1
HMW componentLLDPE 3
w (M
)
molecular weight [g/mol]
Figure 33: GPC curve of the blend components LLDPE 1, LLDPE 3 and the 50/50% blend
The GPC measurements confirm the addition of a higher molecular weight component to
the LLDPE 1. But the difference of the GPC curves of the blend components is not distinct
enough to obtain a bimodal molecular weight distribution of the blend. By the addition of
LLDPE 3 the GPC curve is shifted to higher molecular weights and as a result of the
narrow distribution of the LLDPE 3 the Mw/Mn value is decreased.
46
_______________________________________________________________________
10-1 100 101 102
104
105 εmax= 3
LLDPE 1 + 50% LLDPE 3
LLDPE 1 + 10 % LLDPE 3
LLDPE 1
.
T=150°C
elongational rate ε0 [s
-1] 0.01 0.03 0.1 0.3 0.5 1el
onga
tiona
l vis
cosi
ty µ
[Pas
]
time t [s]
Figure 34: Elongational behaviour of the LLDPE 1 and the blends with 10 % and 50 % LLDPE 3 at 150°C.
Due to problems with the high viscosity and unsolvable problems in the relaxation bath no
straight homogeneous samples of LLDPE 3 could be prepared to perform elongational
experiments. Figure 34 shows the results of the experiments of the 10 % and 50 % blend
and the LLDPE 1. Neither the blend with 10 weight percent, nor the blend with 50 weight
percent of the component with higher molecular weight showed a distinct influence of the
molecular weight distribution on the strain-hardening characteristics. The decrease of the
elongational viscosities of the 10 % blend and the LLDPE 1 can be traced back to the low
viscosity level of the samples. The samples of the 50% blend deform more
homogeneously. This can be related to the distinctly higher viscosity of the 50/50 blend.
For the analyzed blend no significant strain hardening could be produced by adding a
HMW component. A variation of the concentration of the HMW component only changes
the viscosity level of the blends. This finding can be understood by comparing the
molecular weight distributions and the average molecular weight Mw of the components.
The difference in Mw for the higher molecular weight component and the unimodal matrix
of a factor of 2.1 does not seem to be sufficient to have an effect on the elongational
behaviour.
47
_______________________________________________________________________
2.4.2 Rheological behaviour of a sample with a broad molecular weight
distribution
As shown in the last section the addition of the chosen HMW component did not change
the strain-hardening behaviour. However, adding blend partners with a higher molecular
weight than the LLDPE 3 leads to serious problems of the sample homogeneity. The only
practical way of preparing a considerable amount of blends of polyethylene is the mixing
in the extruder. This is limited to samples whose difference in molecular weight is not too
elaborated. To investigate the influence of high molecular weight fractions on the
rheological behaviour polymerized products must be found which already have the
desired molecular weight distribution. Therefore, the commercial Ziegler-Natta LLDPE 22
is being investigated which has a broad molecular weight distribution with high molecular
weight fractions, distinctly higher than the LLDPE 3.
LLDPE 22
density [g/cm3] 0.923
Mw [g/mol] 193,000
Mw / Mn 26
Table 4: Molecular data of LLDPE 22.
48
_______________________________________________________________________
103 104 105 106
Mw = 193,000 g/molMw/ Mn = 26
LLDPE 22
w
(M)
molecular weight [g/mol]
Figure 35: GPC curve of LLDPE 22.
As shown by the GPC analysis (see Figure 35) the sample has a broad molecular weight
distribution with a considerable amount of molecules in the high molecular region above
1,000,000 g/mol. It has a broader molecular weight distribution and higher molecular
weight fractions than the prepared blends of the LLDPE 1 and the higher molecular weight
LLDPE 3 component.
Figure 36 shows the result of elongational rheology experiments. The broad molecular
weight distribution and the high molecular weight fractions have a distinct influence on the
elongational properties. The elongational viscosity shows strain hardening for all strain
rates in the experimental rate window. The high molecular weight of Mw = 193,000 g/mol
is responsible for the high viscosity level of the sample. The distinct strain hardening
behaviour can be related either to the broad molecular weight distribution or to the high
molecular weight fractions.
49
_______________________________________________________________________
10-1 100 101 102
105
106
.
.
LLDPE 22T=150 °C
3η+(t, γ0=0.01s-1)
strain rate ε0 [s-1]
0.01 s-1
0.1 s-1
0.5 s-1elon
gatio
nal v
isco
sity
µ [P
as]
time t [s]
Figure 36: Elongational viscosity of LLDPE 22
The strain-hardening factor, which is the ratio of the measured elongational viscosity and
the linear viscoelastic start-up curve in elongational flow, at a Hencky strain of 2 is in the
same range of about 1.3 for all rates. In contrast to the long-chain branched samples the
amount of strain hardening is hardly dependent on the applied strain rate within the
experimental rate window. For small strains these samples deform very homogeneous
which is in accordance with the self healing effect of strain hardening samples. But at high
strains (~ εH= 2-3), the samples start to deform inhomogeneously and break a short time
after the first inhomogeneity was observed. This process develops so quickly that it is
hardly displayed in the graph of the elongational viscosity. Compared to the deformation
which was observed for the LLDPE 1 the LLDPE 22 shows a different development of the
sample homogeneity (Figure 37).
50
_______________________________________________________________________
Inhomogeneity of LLDPE 22
Inhomogeneity of LLDPE 1
Figure 37: Different development of inhomogeneities of LLDPE 1, caused by experimental effects (density mismatch), and LLDPE 22, caused by an inherent inhomogeneity in the drawing process.
As the viscosity is high and thus the influence of the small density mismatch of the
suspending oil and the melt is small, the inhomogeneous deformation at high strains can
be regarded as an inherent property of the sample and cannot be related to experimental
problems. Another support of this hypothesis is the independence of the sample
homogeneity on the waiting time between melting and the start of the experiment.
Whereas low viscous samples are deformed slowly during the waiting time by the small
density mismatch of the melt and the hot oil and thus their drawing homogeneity
decreases with increasing waiting time, for high viscous samples like the LLDPE 22 such
a behaviour cannot be observed. Within the usual waiting time a deformation of the
sample cannot be observed. Moreover the breakage of the samples is very reproducible.
As clarified in Figure 38 the samples deform inhomogeneously and tear before they were
drawn to the final length of Hencky strain 3.
51
_______________________________________________________________________
0,1 1
105
106εH = 3
.
LLDPE 22T = 150 °C
strain rate εo [s-1]
0.01 s-1
0.1 s-1
0.5 s-1elon
gatio
nal v
isco
sity
µ [P
as]
Hecky strain εH
Figure 38: Elongational viscosity as a function of strain of LLDPE 22
The onset of the inhomogeneous deformation can be seen in the dropping of the
elongational viscosity. Shortly after the first indication of a inhomogeneous deformation
the sample breaks and the curve is cut. Similar behaviour is reported by W. Minoshima et
al. They reported ductile failure for HDPEs with a broad molecular weight distribution at
low strains (Minoshima and White 1986).
In creep experiments no steady-state rate could be evaluated as the samples tore before
a steady-state was reached. Thus it can only be assumed that the sample can only be
drawn homogeneously up to a critical strain which seems to be slightly dependent on the
strain rate.
2.4.3 Influence of a high molecular weight tail on rheological properties in
elongational flow
As shown in the previous section, broad molecular weight distributions with fractions in the
high molecular weight region show a characteristic strain hardening and a
inhomogeneous deformation at high strains. In a next step a sample with a narrow
molecular weight distribution, however, a high molecular weight tailing of the molecular
weight distribution is investigated. The preparation of a well defined model blend is not
52
_______________________________________________________________________
possible, as the high molecular weight fractions cannot be mixed well enough in the low
molecular weight matrix. Thus the Ziegler Natta LLDPE 21 was chosen, whose GPC
curve shows a tailing in the high molecular weight region (see Figure 40).
LLDPE 21
density [g/cm3] 0.921
Mw [g/mol] 139,000
Mw / Mn 5.6
Figure 39: Molecular data of the LLDPE 21
However, this tail is difficult to detect by the GPC, as the construction of the base line
when evaluating the experimental results has a major influence on the detection of the low
concentrated high molecular weight fractions. The GPC traces from two independent GPC
measurements, performed on different equipment6 are displayed in Figure 40. Both
measurements detect fractions of up to 3,5·106 g/mol. As only 0.9 % of the molecules are
of molecular weights of 1.5·106 g/mol or higher this tail has a minor influence on the Mw/Mn
value. This high molecular weight tail contains molecules of twice as high molecular
weights than the HMW component in the blend series.
6 Both measurement and evaluation of the results was performed independently. The different noise level of the experiments is caused by a different setup of the software used.
53
_______________________________________________________________________
103 104 105 106
8x1059x105106 2x106 3x106 4x106 5x106
GPC 1 GPC 2
106
w (M
)
molecular weight [g/mol]
Mw = 139,000 g/molMw/ Mn = 5.6
LLDPE 21
GPC 1 GPC 2
w
(M)
molecular weight [g/mol]
Figure 40: GPC traces of LDPE 21 measured with two different GPC
For the blend samples the highest detected molecular weight fractions were at
1,3·106 g/mol.
The elongational viscosity curves of the LLDPE 21 are displayed in Figure 41. It shows a
distinct strain hardening behaviour at all strain rates. The strain hardening factor is
between 1.2 and 1.3 for all strain rates. Although the effect is faint, the strain hardening is
slightly more intense at lower strain rates. The occurring strain hardening cannot be
explained by the narrow molecular weight distribution of Mw/Mn of 5.6. In this case the high
molecular weight tail with its high relaxation times might be responsible for the non-linear
effects in elongational flow.
54
_______________________________________________________________________
10-1 100 101 102
104
105
.
.
T = 150 °CLLDPE 21
3η+(t, γ0=0,01s-1)
strain rate ε0 [s-1]
0.01 0.03 0.1 0.3 1 el
onga
tiona
l vis
cosi
ty µ
(t) [P
as]
time t [s]
Figure 41: Elongational behaviour in uniaxial flow of LLDPE21 which contains high molecular weight fractions
Like the deformation of the LLDPE 22, the samples of LLDPE 21 deform homogeneously
at low strains. But at high deformation they become rapidly inhomogeneous and finally
break. Samples drawn with a high deformation rate of 0.3 and 1 s-1 do not break within the
time of the experiment. However fully elongated they become rapidly more
imhomogeneous and tear although the sample length is constant after the experiment.
The sample cannot stand the internal stress. In Figure 42 the elongational viscosity is
plotted as a function of Hencky strain. It can be seen that samples drawn with high
elongational rates deform more homogeneous during the deformation than samples
drawn with low elongational rates. Thereby the inhomogeneous deformation of the sample
goes along with a decay of the measured elongational viscosity at high strains. All the
samples broke rapidly after the first inhomogeneous spot occurred either at the end of the
experiment or shortly after. Due to the relatively high viscosity of the sample, the
homogeneity behaviour cannot be explained by the earlier mentioned density mismatch.
The inhomogeneous drawing behaviour must be an inherent property of the sample.
Additional creep experiments failed as seen before for the LLDPE 22 with its broad
molecular weight distribution. A steady state could not be reached as the samples broke.
55
_______________________________________________________________________
0,1 1104
105
εH = 3
.
T = 150 °CLLDPE 21
strain rate ε0 [s-1]
0.01 0.03 0.1 0.3 1el
onga
tiona
l vis
cosi
ty µ
(t) [P
as]
Hecky strain εH
Figure 42: Elongational viscosity as a function of Hencky strain
All in all the LLDPE 21 and 22 have similar deformation characteristics. Both show strain-
hardening behaviour for all elongational rates and deform inhomogeneous at high strains.
Thus it can be assumed that the presence of high molecular weight fractions is the origin
of the inhomogeneous deformation behaviour.
2.4.4 Conclusions on the influence of high molecular weight components on the
elongational viscosity
It was not possible to influence the strain-hardening behaviour by adding a high molecular
weight component with a Mw of 193,000 g/mol to a matrix with a molecular weight of
92,000 g/mol. The preparation of blends with a higher difference of the molecular weight
of the blend partners can result in problems of miscibility and homogeneity of the blend. In
contrast to the blends, the samples LLDPE 21 with a high molecular weight tail and
LLDPE 22 with a broad molecular weight distribution show a distinct strain-hardening
behaviour. By comparing the GPC traces of the two samples it is obvious, that not the
polydispersity of the samples, but the presence of very high molecular weight components
is responsible for the strain-hardening behaviour. In both cases components of up to
3.5⋅106 g/mol were detected in the GPC analysis. Compared to the results on long-chain
56
_______________________________________________________________________
branched samples the strain hardening behaviour does not increase with rising strain rate
within the experimental window. Even more the LLDPE 21 shows a slight increase of the
strain hardening behaviour for lower strain rates. Both resins containing high molecular
weight fractions deform very homogeneously at small strains. But at high strains the
homogeneity deceases rapidly. As up to now the inherent failure characteristics of
polyethylene melts is not discussed in literature only vague explanations can be offered.
On a molecular basis the following hypothesis can be set up. In contrast to the high
molecular weight samples the long-chain branched molecules are more mobile in an
elongational flow field. At low elongational rates, the molecules can relax in the flow field
and no strain hardening effect occurs. For high rates these molecules are still mobile but
contribute remarkably to the elongational viscosity. Because of the mobility the strain
hardening effect lasts to higher strains. In case of the samples containing high molecular
weight fractions, these long molecules are not so mobile. Their entanglements contribute
to the elongational viscosity already at small deformation rates. In case of high strains
they are fully stretched and cannot resist a higher stress. The sample fails. According to
this argumentation comparing the LLDPEs 21 and 22 the mobility of the high molecular
weight molecules must be worse for the broadly distributed LLDPE 22 which also has a
higher molecular weight Mw. And in fact the LLDPE 22 breaks at lower strains than the
LLDPE 21.
It can be concluded that linear samples containing high molecular weight molecules can
show strain-hardening behaviour in elongational flow. The intensity is hardly dependent on
the deformation rate. The homogeneity of deformation is limited to low strains. The two
investigated samples could not be elongated to higher Hencky strains than 3. Finally all
samples break, in contrast to the samples without high molecular weight molecules. In
case of an inhomogeneous deformation the previously investigated LLDPE 1 tends to be
drawn to thin filaments.
2.5 Influence of comonomers on rheological properties
2.5.1 Influence of comonomer distribution on elongational viscosity
After investigating the effects of long-chain branching and molecular weight distribution on
the behaviour in elongational flow the short-chain branching structure is the last parameter
to be discussed. Linear HDPE and the short-chain branched LLDPE behave similar in
elongational flow in case of a comparable molecular weight distribution. According to the
classical doctrine both show no strain-hardening behaviour. However, no investigations
57
_______________________________________________________________________
are published that deal with the effect of a bimodal distribution of the short-chain
branches, i.e. a blend of HDPE and LLDPE. This becomes even more important as new
polymerisation reactor technologies enable the aimed production of polyethylenes bimodal
in their short-chain branching distribution. These new resins prove to have better
mechanical properties than conventional resins.
The aim was to show whether the mixing of polymers with different degrees of short-chain
branching (SCB) has an effect on the rheological behaviour. Therefore, the short-chain
branched LLDPE 4 was blended with a linear HDPE. To exclude effects of the molecular
weight distribution the blend components were aimed to have comparable melt flow rates,
and GPC traces.
LLDPE 4 HDPE
Mw [g/mol] 117,000 126,000
Mw / Mn 5.6 4.3
Table 5: Molecular data of the blend components LLDPE 4 and HDPE
103 104 105 106
Mw = 117,000 g/molMw/ Mn = 5.6
Mw = 126,000 g/molMw/ Mn = 4.3
LLDPE 4
HDPE
w (M
)
molecular weight [g/mol]
Figure 43: GPC curves of the blend components LLDPE 4 and the HDPE
58
_______________________________________________________________________
The results of the molecular characterisation of the blend components are displayed in
Figure 43. The blend contained 50% LLDPE and 50% HDPE. Figure 44 shows the time-
dependent elongational viscosities of the two blend components. The short-chain
branching structure of the polyethylenes has no influence on the behaviour in elongational
flow. Both blend components do not show strain hardening and the shape of the
elongational viscosity curve is similar. Due to slightly different molecular weights the
viscosity of the HDPE is slightly higher than of the LLDPE 4.
10-1 100 101 102
104
105
LLDPE 4
HDPE
.
T = 150 °Cεmax= 3
strain rate ε0 [s-1]
0.01 0.03 0.1 0.3 1el
onga
tiona
l vis
cosi
ty µ
(t) [P
as]
time t [s]
Figure 44: Elongational behaviour of the blend components HDPE and LLDPE 4 at 150°C
If the blend components are immiscible, the preparation of the LLDPE – HDPE is
expected to have a significant influence on the rheological properties. Therefore, the blend
was prepared in three different ways. This ensures that the effects of the degree of
dispersion can be seen in the following experiments. Two batches were prepared by
extruding a pellet – pellet combination. One of these batches is prepared with one
extruder run (Blend EX1) and the other with two extruder runs (Blend EX2). A third blend
was prepared by mixing LLDPE powder with HDPE powder (BLEND POW) and
subsequent extrusion.
59
_______________________________________________________________________
103 104 105 106
pellet-pellet Blend EX1 pellet-pellet Blend EX2 powder-powder Blend POW
w
(M)
molecular weight [g/mol]
Figure 45: GPC curves of the Blend EX1, Blend EX2 und Blend POW
To ensure that the molecular structure was not changed by the different blend
preparations, all blends were investigated by GPC. Figure 45 reconfirms, that all blends
are sufficiently stabilised. The differences in the measured molecular weights are within
the uncertainty of the experiment and the curves nearly overlap.
Blend EX 1 EX 2 POW
1 extruder run 2 extruder runs 1 extruder run
pellet - pellet pellet - pellet powder - powder
Mw [g/mol] 118,000 116,000 119,000
Mw / Mn 4.3 4.4 4.2
Table 6: Molecular data of the blends
60
_______________________________________________________________________
10-1 100 101 102
104
105
.
Blend Ex2
2 extruder runs
Blend EX1
1 extruder run
T = 150 °Cεmax= 3
elongational rate ε0 [s
-1] 0.01 0.03 0.1 0.3 1
elon
gatio
nal v
isco
sity
µ(t)
[Pas
]
time t [s]
Figure 46: Elongational behaviour of the 50/50 blend after one and two extrusion runs at 150°C
After one extrusion run blending pellets with pellets, the elongational flow characteristic is
not changed. As shown in Figure 46 the blend of 50% LLDPE and 50% HDPE does not
show strain hardening. A second extrusion run has no effect on the rheological behaviour
of the blend. Neither an effect on the strain hardening behaviour nor an effect on the
viscosity level can be observed in Figure 46.
Besides the number of extrusion runs, the influence of the blending procedure was
investigated by comparing pellet-pellet extrusion to a powder-powder mixing before the
extrusion step. In Figure 47 the elongational behaviour of the pellet-pellet blend EX1 and
the powder-powder blend POW is compared. Both have nearly identical curves of the
elongational viscosity. The slight deviations are within the inaccuracy of the experiment.
61
_______________________________________________________________________
10-1 100 101 102
104
105
.
BlendPOW
powder blend
BlendEX1
pelletblend
elongational rate ε0 [s
-1] 0.01 0.03 0.1 0.3 1
T = 150 °Cεmax= 3
elon
gatio
nal v
isco
sity
µ(t)
[Pas
]
time t [s]
Figure 47: Elongational behaviour of the 50/50 blend. Blends prepared from pellet-pellet and powder-powder mixing
More information about the melt morphology of the samples which are bimodal with
respect to the short-chain branching content, can be gained by applying thermo-analytical
methods. By the thermograms of the two blend components the samples can be well
distinguished by their melting temperature. On the one hand, the LLDPE has a melting
temperature of 123.7°C and shows a different melting behaviour in the first and second
heating. On the other hand the HDPE has a melting temperature of 133.6 to 135.7°C and
clearly has just one single melting temperature.
62
_______________________________________________________________________
80 100 120 140 160-3,0
-2,5
-2,0
-1,5
-1,0
-0,5
80 100 120 140 160
80 100 120 140 160
80 100 120 140 160
-3,0
-2,5
-2,0
-1,5
-1,0
-0,5HDPE
LLDPE 4LLDPE 4
HDPE
heating rate: 10 K/min Tm= 133.6 °C
Tm= 123.7 °C
1st heating
heat
flow
[ W
/g ]
T [°C]
heating rate: 10 K/min Tm= 135.7 °C
Tm= 123.6 °C
2nd heating
T [°C]
Figure 48: Thermograms of the blend components LLDPE 4 and HDPE after first and second heating
80 100 120 140 160
80 100 120 140 160
80 100 120 140 160
80 100 120 140 160
0.5 W/g0.5 W/g
Blend Ex2
Tm= 129.0 °C
heating rate: 10 K/min Tm= 128.9 °C
Tm= 129.1 °C
1st heating
END
O
Hea
t Flo
w
EXO
T [°C]
Blend Ex2
Blend EX1
Blend POW
Blend EX1
Blend POW
Tm= 131.0 °C
heating rate: 10 K/min Tm= 132.4 °C
Tm= 130.1 °C
2nd heating
T [°C]
Figure 49: Thermograms of the Blend EX1, Blend EX2 and Blend POW after first and second heating
The thermograms of the prepared blends show only a single melting point. The measured
melting temperatures are within the range of 130 to 132.4°C and thus in between the
LLDPE with 123.7 C and the HDPE with 135.7°C. The single melting peak gives no
indication of a possible two phase structure of the blend. In contrast to the melting peaks
of the LLDPE/LDPE blends, the LLDPE/HDPE blends show the same shape of the
melting peak for the first and the second heating.
63
_______________________________________________________________________
The thermograms of the prepared blend series did not indicate a two phase structure of
the HDPE/LLDPE blends. This allows the conclusion the linear and short-chain branched
molecules are miscible. As seen before the rheological behaviour is not altered by short-
chain branching. Thus short-chain branched and linear molecules can rheologically be
regarded as “linear” molecules.
2.5.2 Elongational behaviour of a metallocene LLDPE with a bimodal comonomer
distribution
Besides the previously discussed blend series of LLDPE 4 and an HDPE a metallocene
product is being investigated which has a bimodal comonomer distribution, too. This
mLLDPE, mLLDPE 12, is a reactor blend. The comonomer distribution was incorporated
in the polymerisation process7. Its GPC curve shows a slight shoulder at the higher
molecular weight edge (Figure 50).
mLLDPE 12
density [g/cm3] 0.935
Mw [g/mol] 101,000
Mn [g/mol] 6,600
Mw /Mn 15
Table 7: Molecular data of mLLDPE 12
In elongational experiments, the sample does not show strain hardening behaviour
(Figure 51). This is in accordance with the findings for the blend system prepared. The
comonomer structure of the samples does not influence the rheological behaviour in
elongational flow compared to the LLDPEs with an unimodal comonomer distribution like
LLDPE 1,2 and 4 (Figure 22, Figure 29 and Figure 44).
7 According to the manufacturer
64
_______________________________________________________________________
103 104 105 106
Mw = 101,000 g/molMw/ Mn = 15
mLLDPE 12
w
(M)
molecular weight [g/mol]
Figure 50: GPC curve of mLLDPE 12
10-1 100 101 102
104
105
.
elongational rate ε0 [s-1]
0.01 0.03 0.1 0.3 0.5 1 3η+(t, γ0=0.01s-1)
.
T = 150 °CmLLDPE 12εmax= 3
elon
gatio
nal v
isco
sity
µ(t)
[Pas
]
time t [s]
Figure 51: Elongational behaviour of mLLDPE 12
65
_______________________________________________________________________
2.5.3 Conclusions on the influence of the comonomer distribution on the
behaviour in elongational flow
An influence of comonomers and their distribution in the samples on the properties in
elongational flow cannot be found. The samples show no different behaviour in
elongational flow compared to the blend components. The results of the reactor blend
mLLDPE 12 goes along with the findings on the blend system investigated.
2.6 Comparison of the rheological behaviour in shear of selected samples
Although the behaviour in shear flow should not be a focus of this investigation, for later
argumentations the samples which are blown to films are discussed with respect to their
shear properties. The experiments were run at 190°C. This is the relevant temperature for
the extrusion step of the film blowing experiments in Chapter 4. The dynamic shear
viscosity is shown as a function of the angular frequency in Figure 52. The shear-thinning
behaviour of the LDPE and the similar curves of the LLDPE 1 and the blend (90%
LLDPE 1/ 10% LDPE) are already discussed in Chapter 2.3.2.
0.01 0.1 1 10 100
1000
10000
100000
0.01 0.1 1 10 100
1000
10000
100000T = 190°C
LLDPE 22
LLDPE 21
LLDPE 1
Blend
LDPE
mLLDPE 11
mLLDPE 12
shea
r vis
cosi
ty η
[Pas
]
frequency ω [1/s]
Figure 52: Dynamic shear viscosities of selected samples at 190°C as a function of the angular frequency.
66
_______________________________________________________________________
LLDPE 21 and LLDPE 22 do not reach the zero shear viscosity with in the experimental
window of shear rates. Both have zero shear viscosities, which are by factors higher than
the other five samples. With 139,000 g/mole (LLDPE 21) and 193,000 g/mole (LLDPE 22)
their molecular weights are the highest of the intoduced samples
.
mLLDPE 11 and mLLDPE 12 have slightly different molecular weights and they have
similar dynamic shear viscosities. The small amount of long-chain branches of the
LLDPE 11 seems to have no distinct effect on the shear viscosities.
With respect to the molecular weight the LDPE has very low shear viscosities. As shown
in Chapter 2.3.2 it has a higher flow activation energy than the LLDPEs. Hence at a
temperature of 190°C the more distinct dependence of the shear viscosity on the
temperature results in low shear viscosities compared to the LLDPEs and their molecular
weights.
A very elaborated discussion of the dependence of shear viscosity on the molecular
structure of polyethylene melts is presented in the thesis of C. Gabriels. (Gabriel 2001)
67
_______________________________________________________________________
2.7 Conclusions: Shear and elongational rheology of polyethylenes and
polyethylene blends
The blend series and polyethylene samples described in the preceding chapters have
emphasised both the influence of the branching structure and the molecular weight
distribution of polyethylene melts on the shear and elongational rheology. On the basis of
the experiments the following conclusions with respect to the influence of the
concentration of long-chain branches in a linear matrix can be drawn:
- Comparing the dynamic shear viscosities of LLDPE and LDPE it is obvious that the
LDPE has a very pronounced shear thinning behaviour, i.e. low shear viscosities at
high deformation rates. (Figure 14)
- When gradually increasing the long-chain branching content by adding LDPE to a
LLDPE 1 matrix, the viscosity and the activation energies do not follow a mixing rule.
The lowest values can be measured for the 2% LDPE blend. The 10% LDPE blend
shows a similar flow behaviour as the pure LLDPE. The anomalies for LDPE contents
up to 10% could be explained by an immiscibility of the blend component. However,
DSC measurements did not support this hypothesis. (Figure 14, 15, 18, 19)
- In elongational flow the LLDPE shows a linear behaviour, i.e. the elongational viscosity
follows the Trouton law. The long-chain branched LLDPE shows a distinct strain-
hardening behaviour. Its elongational viscostity rises disproportionally at high strains.
This increase is more decreasing with decreasing strain rates. (Figure 22)
- In order to obtain strain hardening behaviour the concentration of long-chain branched
molecules has to be higher than a certain (unknown) threshold level. For the
LLDPE/LDPE blends investigated this level is reached between 2 and 5% LDPE
content. (Figure 23)
- An increase in the long-chain branching concentration leads to a more pronounced
strain hardening behaviour. (Figure 23)
- The characteristics of the strain-hardening behaviour is not influenced by the viscosity
of the linear LLDPE matrix. Still, an increase of the strain hardening can be found for
rising strain rates, but the rate dependency is shifted to lower strain rates for a matrix
of higher viscosity. (Figure 30)
- The distinct strain hardening of mLLDPE 11 which contains a very low number of long-
chain branches (< 0.1 CH3/1000C) cannot be explained by the blend series (Figure
32). Thus these long chain branches must be very effective in influencing the
behaviour in elongational flow. Not only the number of long-chain branches, but also
68
_______________________________________________________________________
the topography of the molecules plays an important role for the strain-hardening
behaviour. However the topography cannot be evaluated by available experimental
methods.
- Homogeneity of deformation of the samples investigated with respect to long-chain
branching can be summarized as follows: Samples containing long-chain branches
and showing strain hardening in elongation can homogeneously be elongated up to
high strains. The linear samples tend to deform inhomogeneously with increasing
strain. The inhomogeneity is the more distinct the lower the viscosity of the sample is.
As low viscous samples can be deformed more easily by small acting forces, the
inhomogeneous deformation can be attributed to slight external influences which are
not compensated by a self-healing effect. Thus the observed inhomogeneities of the
LLDPEs and some blends are of experimental origin.
The influence of a short-chain branched high molecular weight component (Mw,matrix :
Mw,HMW < 0.5) on the elongational flow behaviour of LLDPE can be summarized as follows:
- Due to the higher viscosity of the HMW component, the shear viscosity increases as
expected with increasing concentration of the HMW component.
- The characteristic elongational behaviour of the linear LLDPE matrix (no strain
hardening) is not changed by adding the HMW component. There is some hint that
due to the HMW component a weak strain hardening occurs for the high strain rate of
1 s-1.
- The linear products LLDPE 21 (narrow MWD) and LLDPE 22 (broad MWD) show
strain hardening for all strain rates of the experimental window. Both products contain
high molecular weight components up to higher molecular weights than the high
molecular weight component of the blend series.
- In elongation the homogeneity of samples of LLDPEs 21 and 22 show a unique
dependence on the applied strain. At low strains the samples deform very
homogeneous. At a critical strain, which was between a Hencky strain εH of 2.4 and 3
the homogeneity of the samples decreases rapidly and the sample finally breaks. Due
to the high viscosities and the strain-hardening behaviour of the samples an external
perturbation as origin of the inhomogeneous deformation can be excluded. The
inhomogeneous deformation at high strains must be an inherent property of these two
samples, which both contain high molecular weight molecules.
69
_______________________________________________________________________
From the blends of linear HDPE with short-chain branched LLDPE it can be stated that
changing the short-chain branching concentration does not influence the behaviour in
elongational flow. This agrees with the metallocene reactor blend mLLDPE 12, which has
a bimodal comonomer distribution and shows no strain hardening, too.
70
_______________________________________________________________________
3 Rheotens Experiments
The Rheotens experiment is a technical laboratory experiment to evaluate the
elongational behaviour of polymer melts. In contrast to the fundamental elongational
rheology the strain rate is not constant during the experiment. Instead of an elongational
viscosity, the occurring forces or in many cases the calculated stresses are taken to
characterize the sample. Instabilities, called draw resonance, that occur in production
processes like melt spinning can be simulated and quantified. Therefore, the Rheotens
experiment can be a link between elongational rheology and processing properties.
3.1 Literature survey on Rheotens experiments
In literature the melt strength behaviour of polyethylene is mainly discussed with the
background of the application as a laboratory test method for the melt spinning and film
blowing process. In case of film blowing the results of the Rheotens test are correlated to
the bubble stability. A favourable bubble stability is obtained for polyethlylenes with a high
melt strength in the Rheotens experiment. Ghijsels investigated 21 different polyethylene
samples and evaluated the melt strengths of the samples (Ghijsels, Ente et al. 1990).
Relative to the melt index of the resins the highest melt strengths are measured for
autoclave LDPEs. Tubular reactor LDPE still had melt strengths about a factor of 2 higher
than LLDPEs and HDPEs which behave similar in melt strength experiments. As a result
the comonomer seems to have no influence on the melt strength properties of the
samples. The melt strength of LLDPE/LDPE blend systems can benefit from synergistic
effects. Especially for LDPE-rich blends higher melt strengths can be measured than for
the blend components (Micic, Bhattacharya et al. 1996). Similar results were reported by
Acierno and Schüle (Acierno 1986; Schüle and Wolff 1987)
Measuring the instabilities of the draw-down process is by far less covered by literature.
1987 White and Yamane evaluated the draw resonance by measuring the diameter of the
spin line at the position of the rotating wheels by an optical laser technique. They defined
the instability as the ratio of maximum and minimum diameter of the melt filament (White
and Yamane 1987).
A very interesting approach of quantifying results of Rheotens experiments is attempted
by Bernat and Wagner. They offer in their study a mathematical way to obtain Rheotens
curves without oscillations (Wagner, A.Bernat et al. 1998). They show that experiments at
different temperatures, die geometries and die exit velocities can be shifted to a master
71
_______________________________________________________________________
curve. After developing a way to calculate these mastercurves it is possible to calculate
force curves at different experimental conditions neglecting the occurring instabilities of
measured Rheotens curves (Figure 53).
Figure 53: Comparison of calculated and measured curves(Wagner, A.Bernat et al. 1998)
Starting from this approach an exact evaluation of occurring instabilities is possible. But
this combined experimental/theoretical approach proves to be too complex and some
variables too vague to apply this method to a large number of samples.
3.2 Experimental set-up of the melt-strength test and evaluation of the results
3.2.1 Experimental set-up
The Rheotens extensional experiment measures the occurring forces while an extruded
polymer strand is drawn at various draw-down velocities. This is achieved by extruding a
melt at a constant output rate through a circular die. In the following experiments the melt
is extruded by a capillary rheometer, where the output rate is determined by the geometry
and the speed of the piston. The extrudate is drawn with velocities v by an accelerating
pair of counter-rotating wheels in a distance d from the die (Figure 54).
72
_______________________________________________________________________
F
melt
counter-rotatingwheels
die
d
v
Figure 54: Schematic drawing of the Rheotens set-up: Melt is extruded through a circular die and drawn by counter-rotating wheels. The force is measured as a function of the velocity of the wheels.
The measured force F is recorded as a function of the draw-down velocity. The maximum
force of the drawn melt is defined as the melt strength (Figure 55).
The experimental results of the Rheotens experiments like the melt strength, the run of
the curve and the occurring draw resonance are strongly dependent on the experimental
set-up. Not only the distance of the wheels to the capillary plays an important role.
Moreover, the geometry of the capillary, the throughput and the temperature influence the
experimental results. For all experiments the geometry of the set-up used was the same
and the throughput was set by a constant speed of the piston of the capillary rheometer as
the feeding unit. To ensure a comparability to the experiments run on the elongational
rheometer, the experiments on the Rheotens were performed at a temperature of 150°C.
The parameters of the experimental set-up are compiled in Table 8. The variable that was
changed is the acceleration of the counter-rotating wheels. The effect of this parameter is
discussed in the next chapter.
73
_______________________________________________________________________
drawability
meltstrength
v0
velocity v
Forc
e F
Figure 55: Schematic sketch of a typical result of a Rheotens test at high acceleration.
capillary rheometer
diameter of the piston Dp 12 mm
piston velocity vp 0.32 mm/s
diameter of the die Dd 3 mm
length of the die Ld 30 mm
entry angle ad 90°
temperature T 150°C
Rheotens
distance d 120 mm
acceleration a 2.4 - 120 mm/s2
Table 8: Set-up of the capillary rheometer and the Rheotens
3.2.2 Influence of the acceleration on experimental results
The wheel acceleration can be varied over a wide range. As seen in Figure 56 the
variation of the wheel acceleration has a profound effect on the measured forces in the
experiment.
For high accelerations the force is steadily rising up to a point, where the melt brakes
(a = 120 mm/s²). For decreasing accelerations the melt breakes at lower forces till an
acceleration is reached, where the force runs through a maximum and starts to oscillate
74
_______________________________________________________________________
(a = 12 mm/s²). This oscillation runs through the more maxima the lower the acceleration
is chosen. For low accelerations a force level can be observed (a = 2.4 mm/s²), which
either is superposed by an oscillation like seen in case of LLDPE 22 or a constant force is
reached till a strong oscillation occurs at a critical draw-down velocity. Finally in both
cases the melt brakes. The melt strength (maximum force at high accelerations) and the
oscillation behaviour an small accelerations are both characteristic properties of the
sample.
0 10 20 30 40 50 60 70 80 90 100 110 1200
20
40
60
d = 120 mm
2.4 mm/s2
6 mm/s2
12 mm/s2
24 mm/s2
60 mm/s2
120 mm/s2LLDPE 22T = 150°C
velocity v [mm/s]
forc
e [c
N]
Figure 56: Rheotens curves at different acceleration of the counter rotating wheels in the Rheotens experiments.
3.2.3 Evaluation of melt strength and draw resonance
As shown in the previous chapter, the results of Rheotens experiments are sensitive to
the acceleration chosen. Usually the results desired are the melt strength and the
drawability of the sample. For both parameters the Rheotens experiment is carried out
with the highest acceleration of 120 mm/s2. A typical curve of an experimental result is
shown in Figure 55. The melt strength is defined as the maximum force in the experiment,
whereas the drawability is the draw-down ratio at the maximum force. Reasonable results
can only be expected, if the acceleration is high enough to prevent the force from
oscillation. A quantitative comparison of force curve obtained from Rheotens experiments
to the viscosity curves measured in elongational cannot be made. Elongational
75
_______________________________________________________________________
experiments measure the elongational viscosity at one defined deformation rate. In
contrast the Rheotens measures the occurring forces whilst deforming the sample at
different strain rates. The stability of the drawing process itself cannot be measured at the
high acceleration. As shown in Figure 56 the draw resonance can well be observed for
low acceleration rates. A qualitative evaluation and comparison of the draw resonance of
different samples seems to be possible, if the occurring forces are similar. When
comparing the investigated samples distinctly different force levels occur and the
evaluation of the intensity of the draw resonance turns out to be difficult.
In the following a method for a quantification of the draw resonance is introduced. It is
evaluated not only by the amplitude of the force oscillation but also with respect to the
occurring forces in the Rheotens experiment.
Due to the enormous differences in the occurring forces, the intensity of the oscillations of
different samples are considerably distorted by the scaling of the graphs. For an
evaluation of a relative draw resonance, which is aimed to be a measure of the
oscillations with respect to the occurring forces, a force level for the normalization
procedure of the measured curve must be defined. The procedure of the evaluation of a
relative draw resonance is presented by the example of mLLDPE 12.
The force curve of this sample shows the characteristic oscillation of the draw-down force,
which occurs before the drawn melt breakes (Figure 57). The Rheotens curves oscillate
around a force plateau for high draw-down velocities. However, due to the superposed
oscillation the force plateau must be approximated by taking the average of the last
minima and maxima as shown in Figure 57. This mean value of the force is taken to
normalize the Rheotens curve, as shown in Figure 58.
76
_______________________________________________________________________
0 50 100 150 200 2500
1
2
3
4
5
6
force level: 3.9 cN
mLLDPE 12T=150°C
v [mm/s]
forc
e [c
N]
Figure 57: Evaluation of an average force by taking the last three minima and maxima of the oscillations of the force curve of mLLDPE 12. The force level represents the average of the six
suprema.
0 50 100 150 200 2500,00
0,25
0,50
0,75
1,00
1,25 T=150°Cnormalized Rheotens curve
v [mm/s]
norm
aliz
ed fo
rce
Figure 58: Normalization of the Rheotens curve of mLLDPE 12
77
_______________________________________________________________________
In the next step of the quantitative evaluation of the draw resonance an envelope curve
and a pedestal curve are constructed for the normalized force curve (Figure 59) by
connecting the maxima of the oscillation for the envelope curve and vice versa the minima
for the pedestal curve. The difference between the envelope curve and the pedestal curve
is then defined as the relative draw resonance. It is a function of the draw-down velocity v.
In Figure 59 this value (black arrow) quantifies the force fluctuations in the Rheotens
experiment with respect to the occurring force. As instability phenomena tend to have a
remarkable scatter of the experimental data, the results are exhibited for several
experimental runs. In the case of Figure 60 the relative draw resonance is displayed as an
area following from four measurements.
0 50 100 150 200 2500,00
0,25
0,50
0,75
1,00
1,25 mLLDPE 12T=150°C
normalized Rheotens curve envelope curve pedestal curve
v [mm/s]
norm
aliz
ed fo
rce
Figure 59: Envelope and pedestal curve of mLLDPE 12 indicating the range of the force fluctuations.
78
_______________________________________________________________________
0 50 100 150 200 250 3000,00
0,25
0,50
0,75mLLDPE 12T=150°C
v [mm/s]
norm
aliz
ed d
raw
reso
nanc
e
Figure 60: Normalized draw resonance of mLLDPE 12. The scattered area covers four independent measurements.
3.3 Samples for Rheotens and film blowing experiments
To cover the broad range of polyethylene resins, the samples were chosen in such a way
that on the one hand a broad range of molecular structures is investigated, on the other
hand the influences of the molecular parameters can be separated. The first three
products that were chosen, were the autoclave LDPE, the Ziegler-Natta LLDPE 1, which
both have no HMW components and, a blend of 10% LDPE and 90% LLDPE 1 (see Table
9). The LDPE shows a typical strain-hardening behaviour in elongational flow. It is strong
for high strain rates and decreasing for lower strain rates. At a rate of 0.01 s-1 no strain
hardening can be detected (see Figure 22). However, as rates less than 0.1 s-1 play a
minor role in the film blowing process the sample characteristic can be regarded as strain
hardening. The LLDPE 1 shows no strain hardening. For the 10% LDPE blend a strain
hardening behaviour like that for LDPE is found, but not as pronounced.
79
_______________________________________________________________________
LDPE LLDPE 1Blend
LLDPE1/LDPE 90/10
LLDPE 21 LLDPE 22 mLLDPE 11 mLLDPE 12
density [g/cm3] .922 .924 not measured .921 .923 .921 .935
Mw [g/mole] 130,000 92,000 100,000 139,000 193,000 104,000 100,000
Mn [g/mole] 12,000 18,000 14,000 25,000 7,500 22,400 6,600
Mw /Mn 11 5 7 5.6 26 4.6 15
Table 9: Samples for Rheotens and film blowing experiments
Blending is a common way to realise a compromise between the good processing
behaviour of the LDPE resins and the good end product properties of LLDPE films. To
broaden the spectrum of samples with different molecular characteristics, two LLDPE
samples with high molecular weight components were investigated. LLDPE 22 has a
broad molecular weight distribution characterized by Mw/Mn = 26 and high molecular
weight components can be detected in the GPC up to 5⋅106 g/mole, whereas LLDPE 21
shows a high molecular mass tail up to 3⋅106 g/mole, whilst having a comparatively narrow
molecular weight distribution of Mw/Mn = 5.6. Both LLDPEs show strain hardening for all
strain rates investigated in elongational flow (Figure 36, Figure 41). The last two samples,
mLLDPE 11 and mLLDPE 12, are newly developed metallocene polyethylenes. Single
site metallocene catalysts enable new molecular characteristics as they allow a defined
polymerization of long-chain and short-chain branches. The mLLDPE 12, polymerized in a
two reactor process, has a bimodal comonomer content, whereas the mLLDPE 11 has
very few, but highly effective long-chain branches. The elongational behaviour of the
mLLDPE12 is similar to a classical LLDPE (Figure 51). However, the mLLDPE11 behaves
like a LDPE in elongational flow (Figure 32).
3.4 The melt strength test
The chosen samples which represent various low density polyethylenes can well be
differentiated by their different experimental results in the Rheotens test. Drawn with a
high acceleration of 120 mm/s2 the occurring forces are between 2.5 and 52.5 cN and
drawabilities of 91 up to 190 mm/s are measured (Figure 61). The error bars indicate the
standard deviation of the results of five measurements.
80
_______________________________________________________________________
0 50 100 150 2000
5
10
15
20
25
30
35
40
45
50
55
LLDPE 21mLLDPE 11
LDPE
mLLDPE 12Blend (10% LDPE)
LLDPE 1
LLDPE 22T=150°Ca=120mm/s2
v [mm/s]
forc
e [c
N]
Figure 61: Melt strength of the polyethylene samples measured at 150°C with an acceleration of 120mm/s2
The lowest melt strength is measured for the LLDPE 1. With only 2.5 cN the measured
force is clearly below all other samples investigated. This linear LLDPE has the lowest
molecular weight of all measured samples (Mw = 92,000 g/mole) and contains no high
molecular weight fractions. The addition of only 10 % of the long-chain branched LDPE to
the LLDPE 1 increases the melt strength up to 8.1 cN. As the molecular weight is only
slightly higher, but the melt strength increased by the factor of 3.3, it is obvious that long-
chain branching has a pronounced effect on the draw-down properties. This becomes
even clearer when the behaviour of the blend is compared to the melt strength of the
linear mLLDPE 12. Although its molecular weight is slightly higher than that of the blend
its melt strength of 5.9 cN is 30% lower. For the two long-chain branched samples
mLLDPE 11 and LDPE a similar melt strength of 28.8 cN and 28 cN can be measured.
The linear LLDPEs 21 and 22 have melt strengths of 29.8 cN and 52.6 cN. These high
forces in the melt-strength test can be explained by their diverse molecular weight
distributions compared to LLDPE 1 and mLLDPE 12. Whereas the latter contain no high
molecular weight fractions, LLDPE 21 contains traces of high molecular weight molecules
81
_______________________________________________________________________
up to 3 · 106 g/mol and LLDPE 22 has a broad molecular weight distribution reaching the
high molecular weight region.
LDPE LLDPE 1Blend
LLDPE1/LDPE 90/10
LLDPE 21 LLDPE 22 mLLDPE 11 mLLDPE 12
characteristic LCB SCB LCB HMW HMW LCB bimodal SCB
density [g/cm3] .922 .924 not measured .921 .923 .921 .935
Mw [g/mole] 130,000 92,000 100,000 139,000 193,000 104,000 100,000
Mn [g/mole] 12,000 18,000 14,000 25,000 7,500 22,400 6,600
Mw /Mn 11 5 7 5.6 26 4.6 15
melt strength [cN] 28 2.5 8.1 29.8 52.6 28.8 5.9
drawability [mm/s] 190 92 140 103 91 139 111
Table 10: Melt strength and drawability of the samples in Rheotens experiments compared with characteristic molecular properties of the samples.
More information about the deformation behaviour can be obtained investigating the
drawability of the samples in the Rheotens test. In case of the tested samples the long-
chain branched LDPE, the blend and the mLLDPE 11 show the higher drawability
compared to the linear samples. The LDPE, which has the most long-chain branches can
be drawn to the highest draw-down ratios of 190 mm/s. For the linear samples
drawabilities of 91 (LLDPE 22) to 111 mm/s (mLLDPE12) are measured. The
incorporation of long-chain branches seems to improve the drawability of the
polyethylenes. The effect can most significantly be seen by comparing the blend and the
LLDPE1. The addition of 10% LDPE improves the drawability by 40% from 92 mm/s to
140 mm/s. For a more elaborated evaluation of the drawing properties of the samples the
drawing instabilities are discussed in the next chapter.
3.5 The relative draw resonance of characteristic polyethylenes
In the following the method to evaluate a relative draw resonance (see Chapter 3.2.3) is
applied to a number of characteristic samples. The stability of the drawing process was
measured for 6 samples which will later be investigated in the film blowing process. The
seventh sample, the high molecular LLDPE 22 is excluded from this investigation as the
draw resonance of the LLDPE 22 is so intense, that the filament breaks after one
82
_______________________________________________________________________
oscillation. For this sample an evaluation of the relative draw resonance with an
acceleration of 6 mm/s2 fails as a force level cannot be calculated.
0 100 200 3000
5
10
15
20
T=150°Ca= 6mm/s2 LLDPE 21
mLLDPE 11 mLLDPE 12 LDPE Blend 10% LDPE LLDPE 1
v [mm/s]
forc
e [c
N]
Figure 62: Rheotens curves of the 6 chosen polyethylenes measured with an acceleration of 6 mm/s2 at 150°C
Figure 62 shows the Rheotens curves of the six selected polyethylenes. It is obvious, that
the highest forces are measured for the strain-hardening samples (LLDPE 21, LLDPE 22,
mLLDPE11, LDPE and its blend). When comparing the results of the relative draw
resonance, displayed in Figure 63 the performance of the chosen samples can clearly be
divided into three groups. The first group are the samples which contain the long-chain
branches catalyzed in the common autoclave process (LDPE and blend with 10 % LDPE).
The LDPE shows a small draw resonance over the full range of draw-down ratios. The
reproducibility of the results is very good which can be seen by the small area all
measured graphs cover. The blend of the LDPE and LLDPE1 shows the same low relative
draw resonance for draw-down velocities up to 270 mm/s. From 400 mm/s onwards the
relative draw resonance increases till the melt brakes at nearly 700 mm/s, a value which is
by far higher than for any other sample tested.
83
_______________________________________________________________________
The three LLDPEs mLLDPE 11, mLLDPE 12 and LLDPE 1 exhibit a distinct higher draw
resonance than the LDPE and the LLDPE/LDPE blend. The linear LLDPE 1 and
mLLDPE 12 show a strongly rising instability with increasing draw-down velocity.
0 100 200 300 400 500 600 7000,0
0,5
1,0
1,5
2,0
Blend (10% LDPE)LDPE
mLLDPE 11 mLLDPE 12
LLDPE 1
LLDPE 21T=150°Cd = 120 mma = 6 mm/s2
v [mm/s]
rela
tive
draw
reso
nanc
e [a
.u.]
Figure 63: Relative draw resonance of 6 polyethylenes measured with an acceleration of 6 mm/s2 at 150°C
The long-chain branched mLLDPE 11 does not show an increase of the draw resonance
with rising draw-down ratio, but the instabilities are more pronounced than in case of the
long-chain branched LDPE. The bimodal comonomer structure of the linear mLLDPE 12
has no distinct effect on the draw resonance properties. Its behaviour can be compared to
the linear LLDPE 1. The draw resonance of the LLDPE 21 is a lot more pronounced than
the draw resonance of the other samples.
Minoshima and White correlated the draw resonance with the molecular weight
distribution (Minoshima and White 1986) (White and Yamane 1987). They found a more
pronounced draw resonance for broader molecular weight distributions. LLDPE 21,
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_______________________________________________________________________
however, has a molecular weight distribution of only Mw/Mn=5.6, but contains high
molecular weight fractions. Hence, in this case the draw resonance seems to be sensitive
to the presence of high molecular weight fractions.
Up to now the relative draw resonance has been shown for an acceleration of 6 mm/s2.
However, resonance phenomena are highly sensitive to geometry and time scales. But it
can be shown that the unstable drawing behaviour is an inherent property of the sample.
As already described in Figure 56, where the drawing behaviour of LLDPE 22 is shown for
a broad variety of acceleration rates, the resonance behaviour stops at a threshold
acceleration. For higher accelerations the filament breaks before an oscillation can
develop. For small accelerations the oscillations increase distinctly before the filament
breaks.
0 50 100 150 200 250 300 3500,0
0,2
0,4
0,6
0,8
1,0
mLLDPE12
LLDPE 22LLDPE21
mLLDPE11
Blend10% LDPE
LLDPE 1
LDPE
T = 150°Cd = 120 mma = 2.4 mm/s2
v [mm/s]
rela
tive
draw
reso
nanc
e
Figure 64: Relative draw resonance of 7 samples measured with an acceleration of 2.4 mm/s2 at 150°C.
In Figure 64 the behaviour of the polyethylene samples is displayed for an applied
acceleration of 2.4 mm/s2. Once again the LDPE and the LLDPE/LDPE blend show the
least instabilities. Comparing the blend composition of LDPE and LLDPE 1 it can be
85
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stated that adding already 10 % LDPE dramatically improves the stability behaviour. In
contrast to the “classical” long-chain branched LDPE, the draw resonance of the LCB-
mLLDPE 11 is in between the LDPE and the LLDPE 1 for low draw down velocities
Starting at 80 mm/s the relative draw resonance strongly rises till the samples break at
about 120 mm/s. Clearly the worst resonance behaviour is exhibited by LLDPE 21 and
LLDPE 22, both containing high molecular weight fractions. Generally the shapes of the
curves have changed compared to the higher acceleration of 6 mm/s2. They show a
strong increase .of the resonance when a critical draw down velocity is exceeded
However, the relative behaviour comparing the samples remains.
Summing up the behaviour of the relative draw resonance as a function of draw-down
velocity, it can be said that samples containing high molecular weight components show a
distinct draw resonance. LLDPE 1, mLLDPE11 and 12, linear LLDPEs containing no high
molecular weight components, show a comparable draw resonance, but a different
drawability, i.e. they can be drawn to different drawing ratios. The long-chain branched
LDPE and the LDPE/LLDPE blend show the smallest relative draw resonance.
3.6 Conclusion on the Rheotens experiments
In the Rheotens experiments the samples were characterized according to the occurring
forces and their drawability at high draw-down velocities and to the oscillations at low
draw-down velocities. The molecular characteristics of the samples can be correlated to
the Rheotens experiments as follows:
• Linear low-molecular weight samples (LLDPE 1, mLLDPE 12) have a low melt
strength and can be drawn to moderate velocities (92 – 139 mm/s). Their instability
is characterised by an average relative draw resonance.
• The long-chain branched LDPE and the long-chain branched mLLDPE 11 show
significantly higher values of the melt strength than the linear samples LLDPE 1
and mLLDPE 12, although the difference in their molecular weights is moderate.
The molecular weight of the mLLDPE 11 is only 4% higher than the mLLDPE 12.
The long-chain branched samples can be drawn to higher draw-down velocities.
The relative draw resonance of the LDPE is distinctly lower than that of the linear
samples. In contrast, the mLLDPE 11, which has only very few long-chain
branches shows a stability behaviour comparable to the linear LLDPE 1 and
mLLDPE 12. The relative draw resonance does not seem to be influenced by the
branching structure.
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• The blend of LLDPE 1 and LDPE (90/10) has a 3.2 times higher melt strength than
the pure LLDPE 1. However it is still ten times lower than that of the LDPE and the
mLLDPE 11. The metallocene catalysed long-chain branches seem to be more
effective than the long-chain branches of the LDPE at least if the effect on the
force in uniaxial extension is compared to the amount of branches in the resin. The
different branching structure seems also to be reflected in the relative draw
resonance. On one hand the relative draw resonance of mLLDPE 11 behaves like
a linear LLDPE, on the other hand the blend shows a relative oscillation behaviour
like the LDPE.
• The samples containing high molecular weight fractions, LLDPE 21 and 22, have
high melt strengths and a limited drawability in the melt-strength test. The highest
force and the worst drawability is measured for the LLDPE 22. Their relative draw
resonance is the highest of all samples. High molecular weight fractions, either as
a high molecular weight tail, or as a broad molecular weight distribution with a
considerable amount of molecules with a high molecular weight, seem to have a
strong destabilising influence on the drawing process.
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4 Film blowing of polyethylenes
4.1 Introduction
Films made of polymers have gained a considerable importance in many branches. Films
are used for packaging, as farming films and in the building industry. In the packaging
industry more than one half of all polymeric packaging goods are films. Furthermore,
many special applications demand high quality films. Polyethylene (PE), polypropylene
(PP) and poly(vinyl) chloride (PVC) dominate the film market. There are two important
processes established in film production: the blown film process and the cast film process.
The cast film process is a high speed process for making highly orientated films in
machine direction. The extrudate of a flat die is rapidly stretched in machine direction by a
chill roll. Therefore the mechanical properties are different in machine and transverse
direction. The rapid cooling right after stretching freezes the molecular orientation. Films
can be drawn down to 7µm. The disadvantages of the mechanical properties of cast films,
which are highly sensitive to the orientation, can be overcome by the tenter process,
where a cast film is undergoing a defined biaxial orientation in a so-called tenter oven.
Especially the defined cooling enables an optimal crystallization characteristic. However,
the superior mechanical properties of these films come along with high costs of a tenter
line of several million dollars, even for small lines.
The most common film production process is film blowing. The film is produced by
extruding polymer through an annular die (see Figure 65). The extruded tube is taken up
by a pair of nip rolls and inflated by an internal pressure. The pressure inside the bubble
controls the so called blow-up ratio (BUR), the ratio between the diameter of the annular
die and the diameter of the bubble. For a constant output rate the speed of the nip rolls
determines the take-up ratio (TUR), defined as the ratio between the take-up speed and
the velocity of the melt at the die. Thus the internal orientation of the film is dependent on
the ratio of blow-up ratio and take-up ratio. The film blowing process is most widely used
for polyolefins, which have a rapid crystallization rate. As the cost of a single layer film
blowing line is moderate (350-700 thousand USD), film blowing is an economic way to
produce polymer films with a high output. Besides their mechanical properties the
performance of polyethylene resins on film blowing lines is judged by their maximum
output rate, the homogeneity of the film and the stability of the drawing process. The aim
of this investigation is to assess these properties of several polyethylene samples with
regard to their molecular structure and the way they were polymerized.
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Guide Rolls
Nip Rolls
Blown Film(Bubble)
Cooling Ring
AirSupply
AirSupply
Polymer Melt Spiral Mandrel Die
Frost LineCooling Air
Figure 65: Schematic figure of the film blowing process
4.2 Literature survey: The film blowing process
The performance of a polymer on a film blowing line must be discussed under two
aspects. On the one hand low pressures in the extruder and the absence of melt fracture
are desirable in the extrusion step, on the other hand a stable bubble and a good film
homogeneity even at high draw-down ratios should enable a high film quality and thus
good film properties at high outputs. Unlike pipe or sheet extrusion, the blowing of film
may give relatively high thickness variations. However, by optimising the polymer resin
and the film-blowing line for the desired product it is possible to achieve a good film
quality.
4.2.1 Extrusion step
In the extrusion step the properties of the polymer are dominated by the rheological
behaviour in shear deformation. Schüle and Wolf (Schüle and Wolff 1987) demonstrated
that samples showing a low shear viscosity at shear rates around 100 s-1 exhibit low melt
pressures in the extrusion step. Thus for the extrusion step not only the zero shear
viscosity but even more the shear-thinning behaviour of the resins at rates occurring in the
extrusion process is the important property.
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4.2.2 Film blowing step
In the last 30 years a significant effort has been directed to understand the correlations
between the processing behaviour in the film blowing process and the rheological
properties of the polymer. The investigations concentrated on the bubble stability in the
film blowing process. Although blown film is a commercial reality since the early fifties, the
first theoretical approach was taken 1970 by Pearson and Petrie (Pearson and Petrie
1970; Pearson and Petrie 1970). They elaborated a description of the bubble shape
assuming isothermal flow of a Newtonian liquid. They concluded, that the dominant factor
in the process is the balance between the viscous forces and the externally applied
forces. However, the restriction to the isothermal operation of Newtonian fluids fails to
represent the process adequately from a practical point of view. For the realistic
processing point of view, the cooling rate is one of the most important processing
variables. Moreover, the thermoplastics used for film blowing are non-Newtonian fluids at
processing conditions. Yeow (Yeow 1976) showed 1976 on the basis of the model
developed by Pearson and Petrie that the stability of the isothermal tubular film flow is not
directly relevant for the actual operation of the film-blowing process which is highly non-
isothermal. According to this model the film blowing process should be a stable process
for normal blow-up and take-up ratios. Both authors were well aware that the major
shortcoming of this model was the neglect of deviations from Newtonian behaviour,
effects of gravity and inertia and temperature variations. Y. Seo shows in his analysis of
the influence of the extrudate swell on the film blowing process that already at a take-up
ratio of 4 the influence of the extrudate swell on the blown film contour, the axial velocity
and the temperature profile of the film is negligible.
Latest theoretical approaches, also working with a simple isothermal Newtonian model but
with a more sophisticated stability analysis, like those of K.S. Yoon and C.W. Park (Yoon
and Park 1999) manage to predict the range of possible operation settings, like blow-up
ratio, take up ratio and frost line height for linear polymers like LLDPE. Housiadas
(Housiadas and Tsamopoulos 2000) shows the influence of the cooling on the process
stability. They find that additional cooling leads to increased regions of stability. But the
complexity of the cooling process, with its varying wall thickness, crystallisation kinetics
and thermal gradients in two directions prevented an exact description of the process up
to now. Although no developed theory is able to describe the whole process so far,
experimental findings have led to some interesting correlations. Another aspect of the film
blowing process is covered by Kuijk, Tas and Neuteboom. They developed a model which
is capable to calculate the mechanical and optical properties of blown films of LDPE and
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LLDPE/LDPE blends. Applying rheological models for the melt deformation in the process,
they correlated material properties like density and MFI with mechanical and optical
properties (Kuijk, Tas et al. 1998)
A by far lesser number of articles dealing with experimental work on the film blowing
process can be found. One reason might be the large amount of parameters one can deal
with but mainly it might be the effort which is necessary to get the result for just one
specific polyethylene resin. Moreover, a quantitative evaluation of the processing
behaviour is doubtful. It took up to 1975 until the first experimental investigation of the film
blowing process was published. Han and Park studied the film blowing process and
concentrated on the open questions of the theoretical studies of Pearson: Elongational
viscosities, heat transfer and deformation stability. First they proved, that the isothermal
film blowing process with an uniaxial deformation can rheologically be compared to the
uniaxial stretching in melt spinning (Han and Park 1975). However, only stability data of
film blowing experiments with a blow-up ratio of 1 can be correlated with data from melt
spinning experiments. The biaxial nature of film blowing (BUR > 1) cannot be simulated
with melt spinning experiments. Han and Park showed that for the real, non-isothermal
film blowing process bubble shapes do not match the theoretical predictions (Han and
Park 1975).
Figure 66: Different kinds of instabilities occurring in the film blowing process (Fleissner 1988)
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In the last part of their study, they reported different kinds of bubble instabilities for
uniaxial and biaxial deformations in the film blowing process (Han and Park 1975). In the
following years the stability of the process became the most interesting property for
experimental work on film blowing. It is possible to distinguish between 4 different bubble
instabilities like shown in Figure 66. These different types of instability, draw resonance,
bubble instability, helical instability and meta-stability have characteristic structure. The
metastable state is characterized by a varying frostline. Here the frost line height can be
stable at first, but it might happen, that after some time the frost line height suddenly starts
to vary. Thus it is called a metastable state. In case of a bubble instability the diameter of
the bubble pulsates. In contrast to the bubble instability the diameter of the bubble
remains constant in case of a helical instability. In this case the bubble shows a helical
movement. The instability is called draw resonance when the bubble shows an oscillating
occurrence of small bubble diameters, a behaviour that is also reported from the
Rheotens experiments.
As a next step correlations were established between the bubble stability, the melt
strength (Ghijsels, Ente et al. 1990; Field, Micic et al. 1999; Steffl and Münstedt 2000)
and elongational viscosity (Micic, Bhattacharya et al. 1998). In summary, stable bubbles
for samples with high melt strengths and high elongational viscosities can be found. As a
result it is favourable with respect to a stable blowing process to use resins with a high
molecular weight or a strain hardening behaviour in uniaxial extension (Ghaneh-Fard,
Carreau et al. 1996). However, another important parameter in the film blowing process is
hardly discussed, the film homogeneity.
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Figure 67: Blown film dimension variation as a function of time. An oscillating bubble diameter (also measured as layflat width) results in a varying weight per film tube length and a variation of the film thickness. All variation show the same amplitude (Fleissner 1988)
Fleissner (1988) investigated the film thickness variations. He found a relation of the
homogeneity and the bubble stability in the process. Figure 67 shows the influence of an
unstable bubble on the film thickness. The layflat width as a function of time is displayed
in the top graph. The periodic unstable bubble can lead to a pulsation in the layflat width.
As a result the film thickness is affected, too. The lower graph shows that the pulsation of
the bubble is also reflected in the film homogeneity. B. Feron investigated the film
homogeneity as a function of the way of cooling the bubble (Feron 1988). He found that
the air stream leads to a fluttering of the film which is reflected in the film thickness.
Kurzbeck has shown in his thesis that the homogeneity of the blown film and the stability
of the process are better for samples showing strain hardening in uniaxial deformation
(Kurzbeck 1999). Within the window of deformation rates relevant for the film blowing
process, the investigated LDPE shows a strain hardening behaviour which leads to a
stable film blowing process and due to its inherent self-healing effect to more
homogeneous films, than the used LLDPE. Marquardt (1998) investigated the deformation
behaviour of the bubble in the film blowing process. With the help of an ink-dot method
and video analysis the deformation rates in the deformation zone of the bubble were
investigated (Marquardt 1998). Figure 68 illustrates the deformation rates in take-up
direction as a function of the distance to the tool for different take-up ratios.
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Figure 68: Elongational rates of the film blowing processs. The elongational rate is plotted as a function of the distance from the die for several take-up ratios. (LDPE, BUR 2) (Kurzbeck 1999)
In the following part of the work, the processing parameters melt pressure, bubble
stability, and variation of film thickness will be discussed with respect to the rheological
properties of the samples. This should give further insight into the relations between
rheology, processing and film homogeneity.
4.2.3 Performance of different polyethylenes in film blowing
LDPE is the most widely used plastic in packaging. Beside the good transparency and
good heat sealing characteristics its good machinability makes it ideal for film production.
Especially as thin film can be processed on standard film blowing equipment it is the most
common material for polyethylene films. 55% of the US LDPE production is made into
films less than 300 microns (2000) (Hernandez, Selke et al. 2000).
Compared to the favourable behaviour of LDPE in the film blowing process LLDPE is a lot
more difficult to handle. To enable comparable output rates special cooling systems are
necessary (Kanai 1999). These increase the cost of a film blowing line and restrict the
94
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utility to a limited number of film blowing resin. The better mechanical properties
compared to LDPE justify, however, the effort for many products.
The distinct improvement of the bubble stability of LLDPE by adding LDPE is already
described in literature and moreover a commercial reality (Obijeski and Pruitt 1992;
Obijeski and Pruitt 1992). Hadjiandreou and Goyal have shown that it is possible to
process the blends with conventional LDPE equipment without problems (Hadjiandreou,
Bakar et al. 1987) (Goyal, Bohnet et al. 1995). The mechanical properties of the films
made of blends were better compared to films of LDPE (Yilmazer 1991). In addition, it is
possible to produce thinner films with the favourable properties for mechanically
demanding applications (Arch and Rogers 1982). To match both, the manufacturing
demands and the film properties, a compromise is necessary (Huizenga, Chornoby et al.
1990) (McNally, Bermingham et al. 1993).
In the last years metallocene catalyst technology has gained considerable attention in the
film industry. These resins proof to offer a very good balance of processability and film
properties and can be processed on a LLDPE film blowing line. (Sukhadia 1997; Whitte,
Beaulieu et al. 1998). Latest developments in the polymerisation technology open new
possibilities for the molecular engineering of the polymer structure. Metallocene catalysts
combined with a smart reactor technology enable the control of a bimodal molecular
weight or comonomer distribution. Forster and Scott demonstrate that it is possible to
develop tailored mLLDPEs which are superior to the HDPE/LDPE which are used up to
now, with respect to processing and mechanical properties. In addition, the optical
properties can match Ziegler Natta LLDPE grades (Forster and Wassermann 1997).
4.3 Experimental setup of the film blowing line
All film blowing experiments of this work are performed on a lab scale film blowing line
with exactly the same setup. It consists of a single screw extruder with a screw diameter
of DS = 30 mm and a length-diameter ratio of L/DS = 20. To ensure a homogeneous
throughput through the annular die a mandrel die is mounted between the 90° crosshead
and the annular die. The latter has a gap of 0.7 mm. The technical details of the extrusion
unit are displayed in Table 11.
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extruder
drive 4.5 kW
number of revolutions per minute N 0 - 80 U/min
screw diameter Ds 30 mm
screw length Ls 20 DS
heating zones 4
die
diameter of annular die Da 36 mm
gap h0 0.7 mm
land length 15 mm
heating zones 3
cooling system
diameter air ring 70 mm
gap 3 mm
air stream angle 45°
take-up gear
take up velocity vTU 0 - 0.53 m/s
Table 11: Technical specifications of the film blowing line
The heating is achieved by four heating zones for the extruder and three heating zones for
the die unit. The temperature profile for the following experiments is shown in Table 12.
Zone of the Extruder / Die 1 2 3 4 5 6 7
Die
Temperature [°C] 170 180 190 190 190 190 190
E x t r u d e r Crosshead
Table 12: Temperature profile of the extrusion process
The take-up gear consisted of a lab scale unit, modified by a balance for the take-up
forces. This setup included a single flux cooling ring supplied by a cooling air system
which is adjusted manually. The power of the cooling air system was set to a frost line of
the melt at a height of 7 cm above the die. This frost line height proved to be applicable for
all samples. The take-up gear consists of a lay-flat and wind-up unit. The wind-up drive
was able to run film velocities of 50 to 500 mm/s. The take-up ratio TUR was evaluated as
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the ratio between actual take-up velocity vTU and the extrusion velocity of the melt v0 which
was calculated from the mass flow.
0vv
TUR TU= (13)
vTU: take-up velocity vo: velocity at die exit
The second important parameter of the film dimension, the blow-up ratio BUR is defined
as the ratio of the annular die and the final bubble radius.
0rRBUR = (14)
R: radius of the bubble r0: radius of the annular die
The lay flat unit was mounted to a balance, which enables the measurement of the take-
up forces. A schematic drawing of the balance setup is shown in Figure 69. It is designed
in a way that the nip rolls do not contribute to the measured force. The calibration was
performed by Marquardt (Marquardt 1998).
Kraftmeßdose
Abquetschwalzen
Abzugswalzen
Ausgleichsmasse m 1
Ausgleichsmasse m 2
FA
force transducer
nip rolls
wind-up rolls
balance mass
balance mass m
m
Figure 69: Schematic setup of the take-up force balance. [Kurzbeck, 1999]
The reproducibility of the force has been shown to be 0,8%. The friction of the bearings of
the balance can be neglected. However, for low viscous samples, the air stream from the
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cooling system influences the force signal. For these samples, the balance was re-
calibrated with the cooling system running at the power used in the film blowing process.
During the tubular film blowing experiments the following parameters can be adjusted or
are measured (see Figure 70). The melt temperature in the extruder was set to 190°C.
The power of the extruder was adjusted to an output of 2 kg polymer per hour.
melt pressure
throughput
air pressure in the bubble
take up ratio
take up force
inhomogeneity of film thickness
blow up ratio
frost line / cooling power
stability of the bubble
temperature
Figure 70: Parameters of the film blowing process. (Experimental settings: black; experimental results: underlined).
It was measured by weighing the output. This was checked several times during the
experiment to ensure a constant mass flow. The pressure of the melt was measured in
three zones of the extruder and in the crosshead. A quantification of the bubble stability
proved to be very difficult. Like described in literature, the bubble stability is not only
dependent on the actual processing parameters, like temperature, take-up ratio, blow-up
ratio and frost line height, but also on prehistory of the parameters. The stability of the
bubble is time dependent. That means sometimes instabilities develop not before several
minutes. In the following, this will be defined as a meta-stable state. A quantitative rating
of the stability of the bubble which embraces all effects occurring proves to be nearly
impossible. Thus the stability of the bubble is judged in a qualitative rather than in a
quantitative way.
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The thickness homogeneity of the blown film was measured mechanically. For each
production parameter film samples were taken and the homogeneity was measured. 32
equidistant points along the take-up direction, often called machine direction, and 16
measurement points perpendicular to the take-up direction were taken to evaluate the
average film thickness and its relative standard deviation. On the basis of these
measurements the homogeneity of the produced films is discussed as a function of the
take-up ratio. It is worth mentioning that the film homogeneity is dependent on the design
and adjustment of the die and the air cooling system (Feron 1988; Vlachopoulos and
Sidiropoulos 2000). Therefore, the setup was kept constant for all experiments of this
work.
4.4 Film blowing
The polymers which were well rheologically characterized in the first part of this work are
investigated with respect to their processing behaviour in the film blowing process.
Therefore the parameters:
• Pressure in the extruder
• Take-up force
• Bubble stability
• Film homogeneity
are discussed as a function of take-up ratio for all samples. For all experiments, the
temperature (T=190°C), the blow-up ratio (BUR=2) and the throughput (2 kg/h) were kept
constant.
4.4.1 Melt pressures in the extruder
The first processing step in film blowing is the extrusion. To reach the goal of a high
throughput at low production costs a sample is favourable that can be extruded at low
temperatures, low melt pressures and thus low motor load whilst the extrudate shows no
melt fracture. The last point will not be discussed in this work. All samples are extruded
with a throughput of 2 kg/h and none shows signs of melt fracture. For the evaluation of
the pressures in the extrusion step melt pressures were measured in three zones of the
extruder and in the cross head at a temperature of 190°C and 2kg/h output. The first two
zones are in the feeding zone, whereas zone 3 is in the compression zone. The fourth
pressure sensor is located in front of the crosshead. The reproducibility of the melt
pressures was excellent. It proved that the melt pressure was a more sensitive measure
for the throughput than the revolutions per minute of the extruder which could not be
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adjusted with the necessary reproducibility. That means after adjusting the output to
2 kg/h it was easier to reach the working set-up again by adjusting the revolution per
minute with the help of the pressure than by the display of the extruder speed.
The investigated samples exhibit a distinct pressure behaviour as shown in Figure 71. For
a comparison of the investigated samples the pressure in the last two zones will be
discussed, as they determine the throughput of the melt through the die.
0 1 2 3 4 5
50
100
150
200
250
300
zone of extruder
mel
t pre
ssur
e [b
ar]
LLDPE 22 LLDPE 21 LLDPE 1 Blend (10% LDPE) LDPE mLLDPE 11 mLLDPE 12
Figure 71: Melt pressures during extrusion, zone 1 - 3 in the extruder and zone 4 in the crosshead
The highest melt pressures were measured for samples with a high molecular weight and
a broad molecular weight distribution i.e. LLDPE 22 and a high molecular weight tailing of
the molecular weight distribution, i.e. LLDPE 21. In case of the LLDPE 22 the high
molecular weight of this resin leads to a high viscosity and thus to a high melt pressure in
the extrusion process. Like the LLDPE 22 the high molecular weight of the LLDPE 21
leads to a higher viscosity of the resin and consequently to higher melt pressures. The
melt pressure of the LDPE is distinctly lower than for the LLDPE 1, although it has a
higher molecular weight in comparison with the LLDPE 1. The pronounced shear thinning
behaviour of long-chain branched products is known to result in lower pressures. But the
LLDPE/LDPE 90/10 blend does not show an improvement of its properties in extrusion by
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the added long-chain branched fraction. The two mLLDPEs 11 and 12 exhibit very low
melt pressures compared to their molecular data.
4.4.2 Stability of the bubble in the film blowing process
After the melt is extruded through an annular die, it is drawn by the take-up gear and
inflated by an internal pressure. Whilst inflated the melt is cooled down. In this film blowing
step the bubble shape must be in a stable state to achieve an optimum output and film
quality. The evaluation of the stability of the blowing process proved to be very difficult.
Several approaches were taken to quantify the arising instabilities. Han and Park tried to
measure the instabilities using high-speed motion pictures and defined the criteria of an
unstable system as a system that would not return to a stable state (Han and Park 1975).
Nevertheless, there is no exact definition of a stable and unstable bubble. Furthermore, it
was not reported that the history of parameters like frost line height and take-up ratio play
a role for the stability of the bubble. But an influence of the history is found by Kanai,
White and Minoshima (Kanai and White 1984; Minoshima and White 1986; White and
Yamane 1987).
Campbell and Sweeny used a CCD-camera and data analysis software to judge the
stability of the bubble. They neither discuss the way they approach the stable state, nor
they exactly define the states as stable or metastable, that means stable for a limited
amount of time. Last not least, Fleissner measured the instability by means of the layflat
width, the width of the film on the take up reel (Fleissner 1988). In this way helical
instabilities cannot be measured, as the diameter of the bubble does not change.
As neither the stability judgement by a qualitative pass/fail manner nor the quantitative
evaluation of the bubble stability by a camera system seem to be able to describe the
stability behaviour in practice, the bubble stability is assessed in the following by these
criteria:
How stable is the bubble at the given processing parameters?
How easy is it to reach the stable working state?
How long is the process running stable? Is it really a stable or only a metastable state?
How broad is the operating window of possible take-up ratios with a stable process?
Applying these criteria to the processing behaviour of the used polyethylene samples,
each sample can be characterized by its unique stability behaviour. Although being aware,
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that generalising the stability behaviour of different samples by creating a ranking might
neglect some effects during processing, a final ranking is a good base for further
discussions of the samples. In the following the particular characteristics of the samples
will be discussed.
The most stable processing behaviour was observed for the two LLDPEs with a content of
high molecular fractions, the LLDPE 21 and the LLDPE 22. These samples show a
completely static bubble for all take-up ratios (TUR=7-60). Even at highest take-up ratios,
holes or instabilities were not observed. A stable process can easily be adjusted.
Figure 72: Stable bubble of LDPE. Processing parameters: extrusion temperature 190°C, blow-up ratio 2; take-up ratio 28, frost line height 7 cm
The LDPE shows no instabilities at all take-up ratios (7 - 60). At TUR 60 the bubble
collapses after some time (average 8min) as inhomogeneities in the sample cause holes
in the film. Changing the experimental parameters like the cooling power or the take-up
ratio can lead to instabilities in the process, which can be eliminated by a careful
adjustment of the cooling power. These occurring instabilities are mostly of a helical
nature. Although the handling of this product is more difficult than the first two discussed
LLDPEs it can easily be processed at all take-up ratios.
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In contrast to the LDPE the LLDPE 1 is very difficult to process. When adjusting the
bubble varying instabilities at all take up ratios occur. At low take-up ratios it shows helical
instabilities, especially when the working setup is approached from a lower frost line. At
higher take-up ratios it shows all kinds of instabilities from draw resonance, helical
instabilities to a metastable behaviour. Nevertheless it can be processed with all possible
take-up ratios, when minor movements of the bubble are accepted. To reach a stable
working state a careful and often lengthy adjustment of the cooling power is necessary. At
high take-up ratios the process is metastable. After some minutes the cooling power must
be readjusted to keep the frostline constant and to prevent instabilities.
By adding only 10 wt.% of the LDPE to the LLDPE matrix, the processing properties are
improved significantly. In case of the 10 wt.% LDPE blend it is easy to adjust the frost line
and the cooling system without instability problems over a broad range of take-up ratios.
This distinct positive change in the processing properties goes along with an introduction
of strain hardening behaviour in elongational flow by adding 10 wt.% LDPE to the LLDPE
matrix (see Chapter 2.3.3), whereas the shear behaviour is not affected by the addition of
LDPE (see Chapter 2.3.2).
The third sample containing long-chain branches is the metallocene polymerized
mLLDPE 11. This sample exhibits a processing behaviour comparable to the LDPE. A
stable bubble can be achieved for all take-up ratios.
In contrast to the long-chain branched mLLDPE 11, a more critical stability behaviour of
the bubble was observed for the mLLDPE 12. The sample tended to helical instabilities,
when approaching the frost line from below, and to vertical oscillations, if adjusting the
frost line from above to the desired height. A meta-stable behaviour like for the LLDPE 1
was not observed. However, the adjustment of a stable bubble was difficult and time
consuming, especially for high take-up ratios.
LDPE LLDPE 1 Blend LLD/LD 90/10
LLDPE 21 LLDPE 22 mLLDPE 11 mLLDPE 12
viscosity characteristics
moderate η0
strain hardening
low η0
no strain hardening
low η0 , moderate strain
hardening
high η0
moderate strain hardening
high η0
moderate strain hardening
moderate η0
strain hardening
moderate η0
no strain hardening
bubble stability + -- O ++ ++ + -
Table 13: Qualitative comparison of the bubble stability in the film blowing process of the samples and their viscosity characteristics in shear and elongational rheology.
103
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Table 13 summarizes the bubble stability behaviour of the samples for film blowing. All in
all, samples showing strain hardening in uniaxial extension exhibit a better bubble
stability. The samples LLDPE 21 and LLDPE 22 containing high molecular weight
fractions exhibited the best bubble stability. Samples LDPE and mLLDPE 11 had a
comparable good film blowing behaviour. Both contain long-chain branches. The blend
shows that adding a small amount of long-chain branched LDPE leads to a remarkable
improvement of the film blowing behaviour. Non strain-hardening samples like the
mLLDPE12 and the LLDPE 1 were difficult to handle in the film blowing process.
4.4.3 Take-up forces in the film blowing process
It is well known that LLDPE is prone to give bubble instabilities in the film blowing process
(White and Yamane 1987; Ghijsels, Ente et al. 1990). But the preceeding study of the
stability behaviour shows that LLDPEs containing high molecular weight fractions or a
small amount of long-chain branches also show a very stable bubble. Moreover, these
samples exhibit a strain hardening behaviour in uniaxial extensional flow. This strain-
hardening behaviour should be reflected in the take-up force of the samples in the film
blowing process.
10 20 30 40 50 60 70 80
0,1
1
LLDPE 22
mLLDPE 12
LLDPE 1
Blend (10%LDPE)
mLLDPE 11 (LCB)LDPE
LLDPE 21
Forc
e [N
]
TUR
Figure 73: Take-up force of the bubble in the film blowing process as a function of the take-up ratio. BUR=2, throughput 2kg/h
104
_______________________________________________________________________
Figure 73 compares the occurring take-up forces of all samples as a function of take-up
ratio. The force values vary only slightly with changing take-up ratio. It must be taken into
account that on the one hand the deformation rate and the maximum strain is increasing,
but on the other hand the film thickness is decreasing with growing take-up ratio. A thinner
film is cooling more rapidly and thus the viscosity increases. The weighting of these
effects is the main issue of several theoretical considerations made by earlier mentioned
authors, which try to simulate the film blowing process. The experiment shows that the
influences of the different parameters nearly cancel out each other.
The two LLDPEs LLDPE 21 and LLDPE 22 which showed clearly the most stable
processing behaviour exhibit the highest take-up forces. The measured force level of the
LDPE is slightly lower than the one measured for the LLDPE 21. The forces occurring in
the blowing process for the mLLDPE 11 are in between the LPDE and the LLDPE/LDPE
90/10 blend. The lowest take-up forces are measured for the mLLDPE 12 and the
LLDPE 1 which both contain no long-chain branches or high molecular weight fractions.
They exhibit the worst processability in the film blowing process. Investigating the
LLDPE/LDPE blend with respect to the pure LLDPE matrix, the characteristic of the
introduced strain-hardening behaviour is reflected. At low take-up ratios the forces
occurring are the same. Low take-up ratios correspond to low strains. At these small
strains, like at the take up ratio of 5 (eH=1.6), no strain hardening behaviour is observed in
the elongational rheology. However, for higher strains due to the strain-hardening
behaviour the forces of the blend are distinctly higher than of the pure LLDPE.
105
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4.4.4 Homogeneity of the blown films
In contrast to the bubble stability, the homogeneity of blown film is only poorly featured in
literature. But as the film homogeneity is one of the dominating parameters for the
performance of the film it is worth taking a closer look at the homogeneity as a function of
take-up ratio for different polymer samples.
For the evaluation of the film homogeneity 16 equidistant measurement points
perpendicular to the take-up direction were measured twice, at two different positions
along the film. Moreover 32 points were taken in take-up direction. The average of all 64
measurement points was defined as the film thickness hav.
n
hh
n
ii
av
∑== 1 (15)
hi: film thickness at point i n: number of measurement points
Then the standard deviation sh is calculated which is defined as:
1
)(1
2
−
−=
∑=
n
hhs
n
iavi
h (16)
The given values for the homogeneity of the samples are the standard deviations divided
by the average sample thickness. The values are given in percent.
av
hh h
sr = (17)
An example for this procedure is given in Figure 74. The measured values of the film
thickness are displayed as a function of the position along the film in take-up direction.
The solid line represents the average film thickness hav of all measured points, the dotted
lines point out the standard deviation sh of the scattered results.
106
_______________________________________________________________________
0 10 20 30 40 50 60 702
4
6
8
10
222426283032343638
standard deviation 9.7%
TUR 47
TUR 12
Blend 90% LLDPE 1 10% LDPE standard deviation 7.0%
average film thickness
fil
m th
ickn
ess
[µm
]
position along the film, take-up direction [cm]
Figure 74: Film thickness along the take-up direction for take-up ratios 12 and 45, 32 measurements each take-up ratio.
The results of the blend in Figure 74 are measured only in take-up direction. But to
evaluate the final homogeneity of a film not only the homogeneity in take-up direction
must be taken into account, also the homogeneity in transverse direction must be
measured. For these two directions the homogeneity behaviour might be of different
nature as the occurring deformations in each direction are rather different. In take-up
direction deformations occur up to a Hencky strain of 4 (take-up ratio 55), whereas for the
given blow-up ratio of 2 the Hencky strain in transverse direction is 0.7. In Figure 75 the
homogeneity of the films of LLDPE 1 and the LDPE are plotted as a function of the take-
up ratio. It turns out that for the LDPE the direction of the measurement is not relevant.
However, the LLDPE 1 seems to be more homogeneous in take-up direction than in
transverse direction. As for a universal discussion of the film homogeneity the overall
homogeneity of the film is relevant, the thickness of the polyethylene films is measured in
take-up and in transverse direction.
107
_______________________________________________________________________
0 10 20 30 40 50 600
5
10
15
20
25
30
LLDPE 1: take-up direction transverse LDPE: take-up direction transverse
inho
mog
enei
ty n
umbe
r rh [
%]
TUR
Figure 75: Comparison of the homogeneity in take-up direction and transverse direction (BUR = 2)
So far it is obvious that both samples have a comparable film homogeneity at small take-
up ratios. Increasing the take-up ratio and thus the strain of the polymer has no influence
on the homogeneity of the LDPE film. However, the LLDPE 1 shows an increasing
inhomogeneity of the film, if the take-up ratio is increased. LDPE shows an improved
processing behaviour compared to the LLDPE 1. As shown by Kurzbeck the strain
hardening characteristics of the LDPE has a distinct positive effect on the homogeneity of
the deformation in elongational flow (Kurzbeck 1999). With increasing deformation the
self-healing effect of the strain-hardening behaviour comes more and more into play. As
can be seen in the present case, the strain-hardening behaviour improves the
homogeneity not only in take-up direction, but also in the transverse direction and thus
improves significantly the overall performance of the polyethylene resin. The positive
effect of long-chain branching on the homogeneity of processed films becomes even more
evident, when the performance of the 10 % LDPE blend is compared with its blend
components. Figure 76 shows the inhomogeneity number rh of the film thickness of the
blend and its components. In this graph the homogeneity of the films is displayed, i.e.
both, the transverse and the take-up direction are measured and averaged. Like in a
108
_______________________________________________________________________
previous work of S. Kurzbeck, the film homogeneity is fitted linearly as a function of the
take-up ratio (Kurzbeck 1999).
0 10 20 30 40 50 60
5
10
15
20
LLDPE 1 Blend (LLDPE 90%/ LDPE 10%) LDPE
inho
mog
enei
ty n
umbe
r rh [
%]
TUR
Figure 76: Homogeneity of film samples of LDPE, LLDPE 1 and their blend as a function of the TUR at a BUR of 2.
Although the rheological behaviour of the LLDPE 1 in shear is hardly changed by adding
small amounts of LDPE, the 10 % LDPE blend shows an obvious improvement in the
homogeneity behaviour of the film with respect to the LLDPE 1. The addition of 10 %
LDPE does not only improve the stability of the bubble in the film blowing process,
moreover, it results in a significant enhancement of the homogeneity of the blown film.
Comparing all measured films some findings can be generalized (Figure 77). At the lowest
take-up ratios the film homogeneity is between 4 and 7% nearly independent of the
sample. This is the variation caused by the film blowing equipment: The inhomogeneities
of the die, the air flow of the cooling system and the take-up gear. With rising take-up ratio
the film homogeneity becomes more and more dependent on the sample. Except for the
LDPE films the homogeneity of which proves to be independent of the take-up ratio, all
samples show a rising inhomogeneity with increasing take-up ratio. This effect is most
obvious for LLDPE 21 and LLDPE 22 which both contain high molecular weight fractions.
In contrast to former literature, where the film homogeneity was correlated with the bubble
109
_______________________________________________________________________
stability in the film blowing process (Fleissner 1988), these two samples exhibit a perfect
stable bubble, but their films are the most inhomogeneous. They are even more
inhomogeneous than the films made of LLDPE 1 and mLLDPE 12. These are very difficult
to process because of their instable bubbles. They show a considerable scatter of the
measured film homogeneities. But discussing the linear fits of the homogeneity behaviour,
the LLDPE without high molecular weight components (LLDPE 1) and the one with a
bimodal comonomer distribution (mLLDPE 12) show an identical behaviour in film
blowing. Compared to these LLDPEs, the samples containing a small amount of long-
chain branches show a clear improvement of the homogeneity behaviour. Both the
LLDPE 1 blended with a small amount of LDPE and the metallocene long-chain branched
mLLDPE 11 are less inhomogeneous with rising take-up ratio. The most homogeneous
film is made of the LDPE. It exhibits a good bubble stability in the film blowing process. In
addition, the self-healing effect of LDPE in elongational deformation is known to be
beneficial for the homogeneous deformation.
0 10 20 30 40 50 60 70 800
5
10
15
20
25
30
35
LDPE ( )
Blend (10%LDPE) ( )
mLLDPE 11 ( )LLDPE 1 ( )
mLLDPE 12 ( )
LLDPE 21 ( )LLDPE 22 ( )
inho
mog
enei
ty n
umbe
r rh [
%]
TUR
Figure 77: Linear fits of the inhomogeneity number of film samples as a function of the TUR at a BUR of 2.
Summing up, the bubble stability cannot be the dominating parameter for the homogeneity
of the film. In equal measure the molecular structure and the resulting drawing properties
seem to be responsible for a favourable homogeneous deformation of the melt in the film
110
_______________________________________________________________________
blowing process. Long-chain branched samples show a clearly better film homogeneity
than the linear samples. High molecular weight fractions seem to have a negative effect,
whereas comonomers have no effect on the film homogeneity. Summing up, long-chain
branching has a positive effect on film homogeneity, whereas high molecular weight
components seem to decrease the film homogeneity with increasing take-up ratios.
4.5 Conclusion on the behaviour of polyethylenes in the film blowing process
The performance of a film blowing resin in processing is judged by the extrusion
behaviour and the bubble stability. In the extrusion step the samples containing high
molecular weight fractions, and also the samples with a high Mw generated the highest
pressures in the extruder. The long-chain branched LDPE took advantage of its distinct
shear-thinning behaviour. Its melt pressure is clearly smaller than that of the LLDPE 1 and
the blend. The latter exhibited even higher pressures than the LLDPE 1. The two
polyethylene resins polymerized with metallocene catalysts exhibited unexpected low
pressures in the extrusion process which cannot be explained by their molecular data.
The properties of the samples in the film blowing process were judged by their bubble
stability. It is possible to correlate the bubble stability by comparing the forces which arise
in the take-up process. LLDPE 21 and 22 exhibited the highest forces in the take-up
process and both had a perfectly stable bubble. The long-chained branched samples
showed a good bubble stability. The worst bubble stability was observed for the LLDPE 1
and the mLLDPE 12. For both low forces were measured in the take-up process.
Finally the homogeneity of the processed film was evaluated as a function of the take-up
ratio. At low take-up ratios the homogeneity of the films was the same for all samples and
can be attributed to the inherent thickness variations of the film blowing line. For rising
take-up ratios the film homogeneity of the samples developed differently. They can be
divided into four different groups:
- The films of the samples containing high molecular weight components exhibited
the worst film homogeneity. In contrast to literature, where a good bubble stability
was correlated with a homogeneous film (Fleissner 1988), the films made of
samples LLDPE 21 and 22 were the most inhomogeneous.
- Films made of LLDPE, without high molecular weight components (LLDPE 1 and
mLLDPE 12) performed better than the ones with high molecular weight
111
_______________________________________________________________________
components, but their films were still rather inhomogeneous. An influence of the
comonomer structures cannot be observed.
- Films made of long-chain branched LDPE performed with the best film
homogeneity. Their film homogeneity is not dependent on the take-up ratio and not
worse than the inherent homogeneity of the film blowing line.
- Films of samples with a small amount of long-chain branches proved to be better
than purely linear LLDPE, whereby the LLDPE 1 / LDPE blend and the
metallocene catalysed mLLDPE 11 performed equally. For both films the
inhomogeneities are slightly dependent on the take-up ratio. They increase with
rising take-up ratio.
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_______________________________________________________________________
5 Correlations
In the previous chapters four different kinds of deformation have been studied. In
Chapter 2 the uniaxial deformation was investigated with well defined parameters like a
constant elongational rate or applied stress. These investigations were carried out with a
Münstedt-type elongational rheometer. The properties in shear flow were measured with a
shear rheometer. In addition in Chapter 3 the properties in uniaxial elongational flow were
investigated by Rheotens experiments. This laboratory setup is assumed to simulate the
deformation, which occurs in melt spinning. Elongational rate and applied stress are not
constant during an experiment. In Chapter 4 the film blowing process was studied. In the
course of this process shear deformation, uniaxial deformation and biaxial deformation
occurs. Having investigated a set of 7 samples with all described experiments correlations
should be established between the rhelogical behaviour and the properties in processing.
5.1 Correlation of draw resonance and inhomogeneous deformation in
elongational rheology
The strongly varying relative draw resonance of the different samples leads to the
question of the origin of these instabilities in melt spinning. Even if the origin of these
instabilities cannot be revealed, it should be attempted to show correlations of the
deformation behaviour in different experiments.
First of all there is the strain-hardening behaviour in elongational flow. In case of
inhomogeneities this effect leads to a healing of the inhomogeneous spot and to a more
stable deformation of the sample as shown in Figure 1. Therefore, it is called self-healing
effect like described in Chapter 1. Logically this effect can only have a positive
consequence on the deformation behaviour as long as the viscosity is growing with
applied strain. For deformations smaller than the onset of strain hardening it has no
positive effect on the deformation as well as for high strains, when the elongational
viscosity reaches a steady state.
This consideration can be applied to Rheotens experiments, too. Strain-hardening
samples should show a more stable deformation than non strain hardening samples. The
LDPE and the LDPE/LLDPE 1 (10/90) blend exhibit the least relative draw resonance of
the tested samples. Both samples show a distinct strain-hardening behaviour for strain
rates above 0.1 s-1 up to the maximum Hencky strain of εH = 3. Very meaningful is the
behaviour of the blend. The relative draw resonance of the pure LLDPE 1 is manifoldly as
113
_______________________________________________________________________
high as the blend at low draw-down ratios. At high draw-down ratios the draw resonance
of LLDPE 1 is strongly rising compared to that of the blend. Although only 10 % of the
LDPE is added, the drawing stability behaviour is like that of the pure LDPE. As the
molecular weight distribution of the blend and the LLDPE 1 are nearly the same, the
improved drawing behaviour can be attributed to the strain-hardening behaviour in
uniaxial elongational flow.
The relative draw resonance of LLDPE 21 and 22 is by far more pronounced as for all
other samples. Both LLDPEs show a weak strain hardening behaviour in elongational flow
for all measured strain rates. Contrary to the long-chain branched polyethylenes, the
samples deform inhomogeneously at high strains. The draw resonance starts at draw-
down velocities which correspond to Hencky strains of about εH = 1.5. At this Hencky
strain the samples still show a homogeneous deformation in elongation. But in Rheotens
experiments the overall deformation of the melt is the sum of the deformation in the entry
flow of the die, where elongational deformations occur and the uniaxial deformation of the
extruded melt in the spin line. The deformation in the entry flow of the die can be
calculated as follows. According to the law of a constant mass flow for the given ratio of
piston diameter Dp and die diameter Dd of 4 the melt suffers a pre-deformation ε of 16
which corresponds to a Hencky strain εH of 2.7:
0vAvA dpp ⋅=⋅ == > 162
20 ====
d
p
d
p
p D
DAA
vv
ε (18)
Ap: piston cross section Ad: die cross section Dp: piston diameter Dd: die diameter
The overall strain of the melt at a draw-down velocity of 25 mm/s corresponds to a Hencky
strain of 4.35 (strain of the entry flow + strain in the spin line). In elongation these samples
break before they reach a Henky-strain of 3. Summing up, these two samples show an
inhomogeneous deformation in both experiments, if they are drawn to strains of εH=3
(according to elongational experiments).
The two mLLDPE 11 and 12 show relative draw resonance values similar to the LLDPE 1.
The mLLDPE 12 can be compared to the LLDPE 1. Like the LLDPE 1 it has no high
molecular weight components and no strain-hardening behaviour. The bimodal structure
in its comonomer distribution did not show any impact on the rheological properties.
However the mLLDPE 11 shows strain hardening and thus the deformation should be
more stable than the deformation of the other LLDPEs. The value of its relative draw
114
_______________________________________________________________________
resonance can be compared to the LLDPE 1 and mLLDPE 12, however it breakes at
considerably less strain. Tested with the lower acceleration of 2.4 mm/s2 it shows slightly
less relative draw resonance than the other two LLDPEs. A satisfying explanation cannot
be presented. It can only be speculated that at higher strains, which cannot be measured
by the extensional rheometer, the mLLDPE 11 does not show strain hardening any more
and tends to break. Thus unstable deformation behaviour can only be observed with the
Rheotens, which reaches far higher strains.
Summing up, the instabilities in the drawing process can be explained by elongational
experiments, if they occur at low draw-down ratios, i.e. if the instabilities occur at strains
which can be reached with the elongational rheometer. In the uniaxial extension
experiments occurring inhomogeneities lead to a failure of the sample. In Rheotens
experiments the draw resonance is initiated by local inhomogeneous deformations similar
to the necking in elongational rheology. Due to the dynamics of the deformation in a
geometrically limited spinline a strong oscillation starts to develop till the strand breaks.
Inhomogeneity in elongational rheology
Draw resonance in the Rheotens experient
Figure 78: Inhomogeneities lead to a failure of the sample in elongational rheology and to draw resonance in Rheotens experiments
115
_______________________________________________________________________
Thus samples, which break at low strains show a strong oscillation in Rheotens
experiments. A similar observation is reported by White and Ide (1978). They studied the
instability phenomena of melt spinning of fibers and found parallels to the failure of
samples of experiments in uniaxial extension. Samples showing strong draw resonances
showed a failure at small deformations in elongational flow. (White and Ide 1978)
5.2 Correlation of results of film blowing experiments, rheological experiments
and Rheotens test
The results of the previous investigation of a broad variety of samples in the film blowing
process are partially contradicting results in literature. The blend of LLDPE/LDPE (90/10)
exhibits higher melt pressures than the pure LLDPE, although long-chain branches are
known to improve the extrusion properties, i.e. reduce the melt pressure in the extruder.
Moreover, it was found by Fleissner that a good bubble stability can be related to a good
film homogeneity which cannot be confirmed for the LLDPE 21 and 22 containing high
molecular weight fractions. As well the same two samples contradict the findings of
Kurzbeck, who correlated strain hardening behaviour in elongational flow with
homogeneous wall/film thickness in the film-blowing and thermoforming process. The
following chapter tries to provide an explanation which brings together the processing
behaviour of the samples in film blowing with the previously discussed findings in shear,
elongational flow and the Rheotens experiments.
5.2.1 Correlation of melt pressure in the extruder and shear viscosity
The first step of the film blowing process is the extrusion of the melt. The processing
properties of the polymer melt are mainly dependent on the behaviour in shear flow. For a
further discussion of the pressures in the extruder and the shear behaviour of the samples
it is necessary to estimate the shear rates occurring in the extruder. The shear rates in the
metering zone can be approximated by (Natti 1989):
HNDex ⋅⋅
=π
γ& (19)
Dex: diameter of the cylinder, H: flight depth, N: number of revolutions per second
For the given experimental setup, with a diameter of the cylinder of 30 mm and a flight
depth of 1.5 mm the number of revolutions per minute of about 30 was needed to realize a
throughput of 2 kg/h. The corresponding shear rate follows as
116
_______________________________________________________________________
11
4.315.1
min60
min3030 −−
=⋅
⋅⋅= s
mmsmmπγ& (20)
According to the Cox-Merz relation the shear viscosity at a given shear rate corresponds
to the dynamic shear viscosity of the same angular frequency:
)()( γηϖη &≡∗ ⇒ γω &≡ (Cox-Merz relation) (21)
This relation enables a comparison of the shear flow with a constant shear rate, like it is
presumed for the estimation of the shear rate in the extruder with dynamic shear
measurements performed with a plate-plate shear rheometer.
0,01 0,1 1 10 100
1000
10000
100000
0,01 0,1 1 10 100
1000
10000
100000T = 190°C
LLDPE 22
LLDPE 21
LLDPE 1
Blend
LDPE
mLLDPE 11
mLLDPE 12
shea
r vis
cosi
ty |η
*| [P
as]
frequency ω [1/s]
Figure 79: Shear viscosities as a function of frequency at 190°C
LLDPE 22 LLDPE 21 Blend LLDPE 1 mLLDPE 11 LDPE mLLDPE 12
melt pressure
[bar]279 239 221 201 185 176 142
Table 14: Melt pressures in the extruder measured in front of the cross head (heating zone 4, T=190°C)
117
_______________________________________________________________________
Figure 79 shows the dynamic shear viscosities as a function of the applied frequency. The
results of the experiments in shear flow at a temperature of 190°C can be compared to the
measured melt pressures in the crosshead of the extruder which are listed in Table 14.
The shear rheology verifies the high viscosity of LLDPE 22 and LLDPE 21 and explains
the distinct highest melt pressures. The measured pressure for LLDPE 1 is higher than
the pressure of the long-chain branched LDPE. The blend (10% LDPE / 90% LLDPE 1)
shows slightly higher pressures than the pure LLDPE 1 resin. Coming back to the results
in Chapter 2.3.2, where the shear-thinning behaviour of the blends was compared to the
blend components, it is obvious, that adding 10% of LDPE to the LLDPE 1 matrix does not
significantly improve the shear thinning behaviour. It can be seen in Figure 79 that at a
temperature of 190°C the shear viscosity of the blend is only slightly lower than the
viscosity of the LLDPE 1. The somewhat higher pressure values compared to the
LLDPE 1 might be explained by the influence of the strain hardening behaviour especially
at the die entry, where elongational deformations occur. Wassner has shown, that the
presence of strain hardening has a distinct effect on the die entry flow (Waßner 1998). In
the present case this influence is visible as the shear viscosities differ just slightly,
whereas the strain hardening acts as a resistance to the die entry flow and thus leads to
higher pressures in the extruder. In case of the pure LDPE the shear thinning behaviour
exceeds by far the influence of the strain hardening in the die entry flow. The low pressure
for the LDPE can be related to the pronounced shear thinning behaviour of long-chain
branching. In shear flow at high shear rates the viscosity of the LDPE is below all other
tested samples.
The metallocene catalysed LLDPEs mLLDPE 11 and mLLDPE 12 exhibit lower extrusion
pressures than the LLDPE 1. The shear viscosity as a function of the frequency of the
long-chain branched mLLDPE 11 does not indicate a distinct shear thinning behaviour like
the LDPE. Compared to the mLLDPE 12 the shear thinning behaviour is only slightly more
apparent. The small amount of long-chain branches seems to have just a small impact on
the shear behaviour. On the base of these viscosity functions (Figure 79), the pressures of
the metallocene LLDPEs 11 and 12 in the extrusion process are unexpectedly low. As
according to the producer no additives are added to the resin, the low pressures of the
mLLDPEs cannot be explained so far. It can only be assumed that wall slip effects might
play a role in the extrusion process.
Summing up, the melt pressures of the classical polyethylenes can be predicted by shear
rheological results. High molecular weights result in high viscosities and pressures in the
extrusion process. The shear thinning behaviour of long-chain branched LDPE has a
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_______________________________________________________________________
beneficial effect on the melt pressure. As high shear rates are dominating in the extrusion
process the melt pressure of the LDPE is distinctly lower compared to LLDPE 1. The new
metallocene catalysed LLDPEs generate unexpectedly low melt pressures which cannot
be explained on the base of the shear rheology data.
5.2.2 Correlation of bubble stability and take-up force in film blowing with
elongational behaviour and melt strength measured in Rheotens
experiments
In the literature the melt strength which is measured by the Rheotens experiment is
correlated to the bubble stability. Film blowing resins, with high melt strengths exhibit a
good bubble stability and thus a good processability in the film blowing process (Field,
Micic et al. 1999). The question arises, whether the melt strength and the elongational
viscosity of the polymer have a direct effect on the film blowing process and whether the
bubble stability can be correlated to the arising force.
Like in literature, a correlation of the melt strength with the bubble stability for the
measured samples can be found (Table 15). The melt strength values were obtained at a
temperature of 150°C which seems to be a good compromise for the non-isothermal film
blowing process. (see Chapter 3.4)
LLDPE 22 LLDPE 21 LDPE mLLDPE 11 Blend mLLDPE 12 LLDPE 1
bubble stability ++ ++ + + o - --
take-up force TUR=25 [N] 2.2 1.4 1.4 0.72 0.37 0.28 0.24
melt strength (a=120mm/s2 ) [cN]
52.6 29.8 28.0 28.8 8.1 5.9 2.5
Table 15: Comparison of melt strength (Rheotens), take-up force and bubble stability in the film blowing process
Samples with a high bubble stability have a high melt strength and high take-up forces,
whereas samples with an unstable bubble have a low melt strength. For all samples the
ranking of the bubble stability behaviour can be derived from the measured melt
strengths.
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_______________________________________________________________________
Although a qualitative correlation of the melt strength and the bubble stability can be
shown for the seven samples, a general prediction of small differences in the stability
behaviour must be handled with care. Several influencing parameters which are not
discussed so far are likely to have also an effect on the stability of the process. Cooling
and crystallisation effects cannot be simulated by the nearly isothermal Rheotens
experiment. In addition, the different development of the elongational viscosity as a
function of time and strain has a fundamental influence on the actual bubble shape and
thickness development in the deformation zone of the film blowing process. The influence
of these parameters on the bubble stability are unknown for the samples investigated.
Comparing the stability behaviour of the bubble to the results of the elongational rheology,
samples showing no strain-hardening behaviour and low viscosity levels in elongational
flow (mLLDPE 12 and LLDPE 1) have a poor bubble stability. With rising strain-hardening
behaviour the bubble stability can be gradually improved, as shown by the Blend (90%
LLDPE 1 / 10% LDPE) and the LDPE. The strain-hardening behaviour of the mLLDPE 11
leads to a stable bubble comparable to the LDPE. The best bubble stability is observed for
the LLDPE 21 and 22, whose strain-hardening behaviour is less pronounced than the one
of the long-chain branched samples. However their shear viscosity is higher than the one
of the other samples and thus their elongational-viscosity level is higher than that of the
long-chain branched samples. As a conclusion the bubble stability seems to be dependent
on the run of the elongational viscosity function at high strains. The higher the
elongational viscosity, the better is the bubble stability in film blowing. Of course strain
hardening clearly improves the bubble stability as it leads to high elongational viscosities
at high strains even if the samples have a lower shear viscosity level.
In contrast to Han and Park (Han and Park 1975), the bubble instability cannot be
correlated to draw resonance effects as seen in the Rheotens experiments. The samples
LDPE 21 and LDPE 22 showing clearly the strongest draw-resonance effects in uniaxial
deformation in the Rheotens experiments can be processed with a perfect stable bubble.
5.2.3 Correlation of film homogeneity with instability behaviour in uniaxial
elongation and Rheotens experiments
In contrast to the bubble stability very little attention has been payed to the film
homogeneity of the film blowing process in literature. Fluctuations in film thickness and
thus in the homogeneity of the blown film are explained by the instability behaviour of the
bubble in the film blowing process. In the work of Fleissner this investigation is made with
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one reference sample (Fleissner 1988). It is shown, that the pulsation of the bubble is
reflected in a variation of the film thickness. But in case of the samples investigated in the
present study, the bubble stability cannot be correlated to the film homogeneity. Sample
LLDPE 21 and LLDPE 22 can be blown with a perfect stable bubble, but their films are the
most inhomogeneous. Kurzbeck demonstrated on two polyethylenes that the sample
showing strain hardening in elongational flow could be blown to more homogeneous films
than the non strain-hardening samples (Kurzbeck 1999). Again, samples LLDPE 21 and
22 which show a strain hardening behaviour in elongational flow have a poor film
homogeneity. To obtain a more fundamental relation of rheological properties and the
homogeneity of blown films the previous results should be discussed under a new
perspective.
Fluctuations in the film thickness can be regarded as a kind of instability in the drawing
process. In the Rheotens experiments the instability phenomena is called draw
resonance. In elongational rheology the failure of the samples as a result of
inhomogeneous sample deformation can be regarded as a drawing instability, too. To
compare these instability phenomena it is necessary to quantify these effects. As
described before, the sample inhomogeneity in elongational rheology cannot be
quantified. Deformations by a slight density mismatch of the melt and the hot oil cannot be
excluded and these falsify the measurement of the inherent deformation homogeneity of
the sample. But in Chapter 3.2.3 a way to quantify the drawing instabilities in Rheotens
experiments was introduced, the relative draw resonance.
Comparing the defined normalized relative draw resonance in Figure 63 and Figure 64 to
the film homogeneity (Figure 77) and the bubble stability the following conclusions can be
drawn:
The bubble stability cannot be correlated to the draw resonance. Sample LLDPE 21
shows the highest draw resonance, but the best bubble stability. This observation
indicates that the bubble stability is independent of the drawing stability and only a
function of the melt strength. LDPE, LLDPE 21 and mLLDPE 11 exhibit high melt
strengths and thus a good bubble stability, but show a distinctly differing behaviour of the
relative draw resonance.
Assuming that the draw resonance and film inhomogeneity are both instability phenomena
the following conclusions can be made:
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_______________________________________________________________________
- LDPE with a low normalized relative draw resonance, nearly independent of the
draw-down velocity, shows the most homogeneous films. The homogeneity is
independent of the take-up ratio. From the rheological point of view it can be
assumed, that the LDPE can be drawn to very high strains with a good
homogeneity. This also indicates that a steady state of the elongational viscosity is
reached not until high strains. In elongational experiments the samples deform
very homogeneously up to a Hencky strain of 3.9 in creep experiments. Summing
up, the positive effect of strain hardening, the ability to be drawn to high strains
and last not least the good bubble stability of the LDPE result in its superior
processing behaviour.
- Contrary the normalized relative draw resonance of LLDPE 21 is high and rising
with increasing draw-down velocity and its films are the most inhomogeneous.
Comparing this result to the observations during elongational rheology
experiments, it is striking that the samples of LLDPE 21 become inhomogeneous
for Hencky strains of 3, although the samples show strain-hardening behaviour
and thus the deformation should be homogeneous. For sample LLDPE 22 similar
observations can be made. These observations indicate that the instabilities are
caused by a limited drawability that can be seen in elongational rheology
experiments. The limited drawability can be presumed as a result of reaching a
critical strain. This seems to be an inherent property of the samples containing
high molecular weight fractions. Due to dominant development of the
inhomogeneities in the drawing process, the good bubble stability of the samples
plays an inferior role for the final film homogeneity.
- The characteristic results in elongational and Rheotens experiments of the sample
mLLDPE 11 are in between LLDPE 21 and the LDPE. In elongational experiments
a critical Hencky strain is not reached within the possible strains, where the
sample shows a clear strain hardening behaviour, i.e. the samples deform
homogeneously up to a Hencky strain of 3. However, the Rheotens experiments
already indicate a limited drawability. Thus mLLDPE 11 cannot be processed as
homogeneously as the LDPE although is has a comparable bubble stability.
- Comparing LLDPE 1, LDPE and LLDPE/LDPE 90/10 blend it is obvious that
already a small amount of LDPE improves the film blowing properties of the resin.
According to the Rheotens experiments the relative draw resonance of the blend
can be compared to the LDPE. It can even be drawn to higher draw-down ratios.
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Its strain hardening is not as elaborated as that of the LDPE. Therefore the self
healing effect is not as distinct as for the LDPE and consequently the homogeneity
is decreasing with increasing take-up ratio.
- The three samples mLLDPE 11, mLLDPE 12 and the LLDPE 1 have a similar
relative draw resonance. In elongational rheology mLLDPE 12 and LLDPE 1 show
no strain hardening. Both samples contain no long-chain branches. As a result
their film homogeneity is comparable. The bimodal comonomer structure of the
mLLDPE 12 has no effect on the rheological properties and on the film
homogeneity. Conversely, mLLDPE 11 show the same instabilities in the
Rheotens experiment like mLLDPE12, but exhibit strain-hardening behaviour in
elongational flow, can be blown to more homogeneous films than the non long-
chain branched samples. All three samples have a better film homogeneity and
have less relative draw resonance and can be drawn to higher strains in
elongational experiments than the LLDPE 21 and LLDPE 22.
- Finally the blend (90% LLDPE / 10% LDPE) is compared to the long-chain
branched mLLDPE 11: Both samples contain small amounts of long-chain
branches, but their characteristics are different. On the one hand the blend shows
a very low normalized relative draw resonance and can be drawn to high strains. It
has only a moderate strain-hardening behaviour, mainly for the high rates in the
elongational experiments. On the other hand the mLLDPE 11 shows a more
distinct strain-hardening behaviour for all strain rates. The Rheotens experiments
indicate a worse drawing stability compared to the blend. In reality both samples
show the same homogeneity behaviour of the film, although its drawing
characteristics are different. The limited drawing stability of mLLDPE 11 and the
moderate strain-hardening behaviour of the blend seem to end up in a similar
inhomogeneity of the film for the given processing parameters.
Summing up these results, it is obvious that the film homogeneity in film blowing can be
explained by considering the behaviour in uniaxial elongational flow. The positive effect of
the strain-hardening effect which is measured with an elongational rheometer can well be
observed in these experiments. But besides this self-healing effect, the strain dependence
plays an important role for the homogeneity behaviour. Some samples show an
inhomogeneous deformation, if they are elongated more than a critical strain, although
they show strain hardening behaviour for deformations below this critical strain. As the
maximum strain of the elongational rheometer is limited, Rheotens experiments can
123
_______________________________________________________________________
quantify the stability of the drawing process at high strains which has been defined as a
normalized relative draw resonance. It has been shown that samples which show an
inhomogeneous deformation at high strains in the elongational rheometer reveal drastic
force oscillations in Rheotens experiments. Samples which deform homogeneously in the
elongational rheometer, but show strong relative draw resonance in Rheotens
experiments, reveal a worse film homogeneity than expected taking into account the
strain-hardening behaviour at small strains. With the help of the deformation
characteristics of strain hardening and deformation stability a description of the film
homogeneity of the samples is possible. The lower the relative draw resonance and the
stronger the strain hardening behaviour, the better is the measured film homogeneity.
5.3 Conclusions on correlations
The investigated parameters of the film blowing process can be correlated to rheological
properties of the film blowing resins. The behaviour in the extrusion process can be
explained by the behaviour in shear. It can be shown that the bubble stability is dependent
on the forces in elongational deformation and finally the film homogeneity can be
correlated to the stability and the homogeneity of an uniaxial drawing process.
The extrusion process was characterized by the melt pressures in the extruder. These can
be correlated to the shear viscosity measured at a shear rate that actually occurs in the
extrusion process. Samples with high shear viscosities generate high pressures in the
extrusion process. The strain hardening of the LLDPE/LDPE blend leads to a slight
increase of the melt pressure. As its dynamic shear viscosity matches the LLDPE 1 the
difference can be contributed to the different behaviour in elongation. The metallocene
catalysed mLLDPE 11 and mLLDPE 12 do not match the observations made for the other
samples. As their pressures are distinctly lower as expected wall slip effects might occur.
The bubble stability in the film blowing process is dominated by the forces that occur in
the take-up step. The higher the measured take-up forces, the better is the observed
bubble stability. These forces can be correlated with the forces that occur in Rheotens
experiments (i.e. melt strength) or in elongational rheology (elongational viscosity).
An inhomogeneous deformation in the film blowing process of a film resin can already be
observed in experiments in uniaxial deformation. Samples which break in elongational
experiments show a distinct relative draw resonance and their films are the most
inhomogeneous. The most homogeneous films are made of resins that deform
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_______________________________________________________________________
homogeneously in elongational rheology and show the least relative draw resonance in
Rheotens experiments.
6 Summary
The conclusions of this work can be divided into two parts. In a first part the molecular and
rheological properties of different polyethylenes are discussed. Molecular branching
structure and molecular weight of the molecules have proven to have a distinct impact on
the melt flow and film blowing of the samples. The number of samples allowed to set up
qualitative correlations of molecular structure and processing properties of the samples.
The second part of the conclusions discusses the results from a different point of view.
Correlations are summarised, which should enable to predict the film blowing behaviour
by laboratory experiments.
It could be shown that important processing properties of the samples investigated, like
extruder pressure, bubble stability, and film homogeneity can be correlated to rhelological
properties in shear and uniaxial extension. These are dependent on the molecular
structure of the samples.
• As known from literature the long-chain branched LDPE has a strong strain-hardening
behaviour in elongational flow, whereas linear LLDPE shows no stain-hardening
behaviour. Investigating LLDPE/LDPE blend series it could be shown that for a given
long-chain branching structure an increase in the concentration of long-chain
branches, i.e. a growing amount of LDPE in the blend, leads to a more pronounced
strain hardening behaviour. The viscosity of the linear matrix does not influence the
intensity of the strain-hardening behaviour, however, the strain rate dependence of the
strain-hardening behaviour is shifted to lower strain rates for a higher matrix viscosity.
Creep experiments show that the maximum elongational viscosity is shifted to lower
rates, when the viscosity of the matrix is increased. The distinct strain hardening of
mLLDPE 11 which contains a very low number of long-chain branches
(< 1 CH3/10000 C) cannot be derived from the results of the blend series. These long-
chain branches act very effectively in elongational flow and thus must have a
molecular architecture different from LDPE. Long-chain branched samples show a
good processability in the film blowing process. In Rheotens experiments
LLDPE/LDPE 90/10 blend and the LDPE can be drawn with the least instabilities up to
high strains. Due to their shear-thinning behaviour their melt pressures are low. As the
strain-hardening behaviour leads to an enormous increase in elongational viscosity the
bubble stability is distinctly improved, compared to linear samples of the same
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_______________________________________________________________________
molecular weight distribution. Films made of long-chain branched samples are the
most homogeneous.
• Experiments to introduce strain hardening by blending a high molecular weight
component to a low molecular weight matrix failed, because a sufficient molecular
weight difference could not be incorporated homogeneously by an extrusion process.
Another way to introduce strain hardening is the polymerisation of samples containing
a high molecular weight fraction. Due to their higher molecular weights and the less
pronounced shear thinning behaviour compared to LDPE the pressures in the extruder
are high. Their bubble stability in film blowing is excellent, however, they exhibit a
distinct relative draw resonance in Rheotens-experiments. Their films are the most
inhomogeneous ones of all samples. As the drawability of samples containing high
molecular weight fractions proves to be very limited in elongational measurements and
Rheotens-experiments it can be assumed that the limited drawability is an inherent
property of the samples containing high molecular weight components although they
show strain hardening at low strains. This reproducible ductile failure observed is also
reflected in the bad homogeneity of their films.
• The short-chain branching structure seems to have no influence on the rheological
properties. Neither the rheological experiments nor the film blowing experiments show
an effect of the short-chain branching structure on the experimental results.
• The metallocene LLDPEs (mLLDPE 11 and mLLDPE 12) exhibit some effects which
cannot be explained, yet. The strain hardening of mLLDPE 11 compared to the LDPE
and its blends is unexpectedly high taking into account the assumed low amount of
long-chain branches of the resin. Hence, the very few long-chain branches must act
very effective in elongational flow. Moreover, the pressures in the extruder are lower
than expected from shear rheology. The mLLDPE 12 which has a bimodal comonomer
structure behaves like a usual LLDPE (here LLDPE 1). In Rheotens-experiments the
relative draw resonance of these two metallocene samples behaves like the linear
LLDPE 1. The films of the strain hardening mLLDPE 11 are more homogeneous than
those of the mLLDPE 12.
Qualitative relations between processing properties on one side and Rheotens-
experiments and elongational rheology on the other could be established:
126
_______________________________________________________________________
• The pressures in the extruder can be correlated to the behaviour in shear. Shear
viscosities at shear rates matching the conditions in the extruder correspond
qualitatively to the pressures in the extruder. High viscosities result in high pressures
and thus lower maximum output rates of the extruder. The metallocene LLDPEs have
unexpected low melt pressures, which cannot be explained by their molecular data or
shear viscosity.
• High take-up forces in the film blowing process can be correlated with a good bubble
stability. Qualitatively these forces are in accordance with the melt strength and the
elongational viscosity of the samples. High elongational viscosities, e. g. high melt
strengths give a good bubble stability in the film blowing process.
• Samples showing ductile failure in elongational experiments exhibit very pronounced
draw resonances in the Rheotens experiment and break at low strains
• In case of a fixed experimental setup the film homogeneity is dependent on
rheological properties of the film blowing resins. The lower the normalized relative
draw resonance which is a measure of the drawing stability in elongational flow, and
the more pronounced the strain hardening behaviour the better is the homogeneity of
the blown film.
In the present work the rheological behaviour in shear and elongation of various
polyethylenes was investigated. Starting from the results of these laboratory experiments,
parameters of the film blowing process can be correlated with rheological properties of the
products. It has been shown that long-chain branching improves distinctly the bubble
stability and the homogeneity of the blown film. Already small amounts of long-chain
branched molecules have a pronounced, positive effect on the film blowing process.
However, high molecular weight fractions, which result in strain-hardening behaviour in
elongational flow similar to long-chain branching, have negative effects on the deformation
homogeneity, i.e. film homogeneity, as their homogeneous deformation is limited to small
strains.
From the processing point of view the ideal film blowing resin has long-chain branches
and no high molecular weight components. As blends of LLPDE and LDPE are a
compromise regarding the mechanical film properties compared to pure LLDPE, long-
chain branched mLLDPE might be a product combining the excellent processing
properties of LPDE and the good film properties associated with LLDPE resins.
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_______________________________________________________________________
Appendix A: Materials used for film blowing experiments
LDPE LLDPE 1Blend
LLDPE1/LDPE 90/10
LLDPE 21 LLDPE 22 mLLDPE 11 mLLDPE 12
characteristic LCB SCB LCB HMW HMW LCB bimodal SCB
density [g/cm3] .922 .924 not measured .921 .923 .921 .935
Mw [g/mol] 130,000 92,000 100,000 139,000 193,000 104,000 100,000
Mn [g/mol] 12,000 18,000 14,000 25,000 7,500 22,400 6,600
Mw /Mn 11 5 7 5.6 26 4.6 15
viscosity characteristics
moderate η0
strain hardening
low η0
no strain hardening
low η0 , moderate strain
hardening
high η0
moderate strain hardening
high η0
moderate strain hardening
moderate η0
strain hardening
moderate η0
no strain hardening
3η0 [Pas] at 150°C 3.5 . 104 1.5 . 104 1.6 . 104 11 . 104 32 . 104 4.3 . 104 3 . 104
µ [Pas] at ε0 = 0.5 s-1
εH= 3 and T = 150°C10 . 104 1.5 . 104 2.1 . 104 ~ 10 . 104 * ~ 50 . 104 * 7 . 104 3 . 104
melt strength [cN] (a=120mm/s2 )
28 2.5 8.1 29.8 52.6 28.8 5.9
drawability [mm/s] 190 92 140 103 91 139 111
melt pressure [bar] 176 201 221 239 279 185 142
take-up force TUR=25 [N] 1.4 0.24 0.37 1.5 2.2 0.72 0.28
bubble stability + - - o ++ ++ + -
film homogeneity + + o + - - + o
* Inhomogeneous deformation and sample failure at higher elongation
Mol
ecul
ar d
ata
Rhe
olog
yR
heot
ens
Film
blo
win
g
++ very good + good o average - bad - - very bad
Table 16: Characteristics and experimental results of materials used for film blowing experiments
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_______________________________________________________________________
Appendix B: Thermal stability
For all experiment its is essential, that the samples are not thermally aged and their
properties changed. As far as the thermal endurance property is concerned, the
elongational rheology is the most demanding experiment. Including the rod preparation,
annealing time, and the time in the elongational rheometer the sample must be stable at
the most for 70 minutes at 135 – 150 °C and either under oil or air atmoshere. In this case
the thermal stability is checked under air at 150°C. As a common way to evaluate the
stability the storage modulus G’ of the samples is plotted as a function of residence time
at 150°C at a low frequency. The frequency of 0.01Hz is chosen. However, samples with
a low viscosity were tested at higher frequencies as the scatter in the data was too high.
The samples are regarded as thermally unstable when the G’ value changes more than
5 % compared to the initially measured value. The results are displayed in Figure 82 -
Figure 84. All samples are stable for at least 5500 s. No molecular changes are expected
in the rheological experiments.
0 2500 5000 7500 10000102
103
5% tolerancef = 0.01Hz
f = 0.63HzLLDPE 1
LDPE multiplied by factor 2
Thermal stability T = 150 °C, air
G' [
Pa]
time t [s]
Figure 80: Thermal stability of the LDPE and the LLDPE 1 at 150°C under air.
129
_______________________________________________________________________
0 2500 5000 7500 10000102
103
5% tolerance
LLDPE 21
LLDPE 22
7100 s
6000 s
Thermal stability T = 150 °C, air, f = 0.01HzG
' [P
a]
time t [s]
Figure 81: Thermal stability of the LLDPEs LLDPE 21 and LLDPE 22 at 150°C under air.
0 2500 5000 7500 10000102
103
5% tolerance
mLLDPE 12
mLLDPE 11
5700 s
Thermal stability T = 150 °C, air, f=0.05Hz
G' [
Pa]
time t [s]
Figure 82: Thermal stability of the metallocene LLDPEs mLLDPE 11 and mLLDPE 12 at 150°C under air.
130
_______________________________________________________________________
0 2500 5000 7500 10000102
103
divided by 3LLDPE 4
divided by 2blend EX2
HDPE
blend POW
blend EX1 multiplied by 2Thermal stability T = 150 °C, air, f = 0.05Hz
G' [
Pa]
time t [s]
Figure 83: Thermal stability of the blend series investigating the influence of a bimodal comonomer structure at 150°C under air.
0 2500 5000 7500 10000200
300
400
1000
2000
3000
40005000
LLDPE 21 + 10% HMW
LLDPE 1 + 50% HMW
LLDPE 1 + 10% HMW
Thermal stability T = 150 °C, air, f = 0.05Hz
5500s
G' [
Pa]
time t [s]
Figure 84: Thermal Stability of the HMW - blend series at 150°C under air.
131
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Appendix C Reproducibility
The precision of the elogational rheometer is well documented by Kurzbeck (Kurzbeck
1999). In the following the reproducibility of the Rheotens experiments at two different
accelerations and of the film blowing results is shown.
Rheotens The investigations of the behaviour of the samples in the Rheotens experiments
concentrated on two acceleration rates. The melt strength was tested at an acceleration of
120 mm/s2 and the draw resonance was evaluated with an acceleration rate of 6 mm/s2.
In Figure 85 the reproducibility of 6 samples is shown. Samples LLDPE 22 is displayed in
Figure 86 to improve the scaling of the previous graph. In general, the reproducibility of
the results is dependent on the occurring forces in the experiment. Samples with a high
melt strength are measured with an accuracy of 0.8% (mLLDPE 11) up to 1.7 %
(LLDPE 22). Samples with a low viscosity show a worse reproducibility. Their deviation
can be up to 11.2 % for the LLDPE 1. With a melt strength of only 2.58 cN its forces are
very low and already close to the experimental limit of 1 cN.
0 50 100 150 200 250 3000
10
20
30
40
Reproducibility: 4 curves for each sample
blend LLDPE1 / LDPE 90/10
LLDPE 1
LDPE
mLLDPE 12
mLLDPE 11LLDPE 21a= 120 mm/s2
d= 120 mm
T=150°C
v [mm/s]
Forc
e [c
N]
Figure 85: Reproducibility of Rheotens experiments with an acceleration of a = 120 mm/s2 at 150°C.
132
_______________________________________________________________________
0 50 100 150 200 250 3000
10
20
30
40
50
60
70
80
melt strength 53.18 cNstandard deviation +/- 0.9 cNrel. deviation +/- 1.7 %
Reproducibility: 4 curves
LLDPE 22a=120mm/s2T=150°C
v [mm/s]
Forc
e [c
N]
Figure 86: Reproducibility of Rheotens experiments of LLDPE 22 run with an acceleration of a = 120 mm/s2 at 150°C.
LDPE LLDPE 1 Blend LLDPE 21 LLDPE 22 mLLDPE 11 mLLDPE 12
melt strength [cN] 28.2 2.58 7.62 29.7 53.18 28.84 5.93
standard deviation [cN] 0.26 0.29 0.30 0.31 0.9 0.24 0.04
rel. deviation +/- 0.9 % +/- 11.2 % +/- 3.8 % +/- 1.0 % +/- 1.7% +/- 0.8 % +/- 0.7 %
Table 17: Melt strength, standard deviation and relative standard deviation (given in percent) of the samples investigated in the Rheotens experiment measured with an acceleration of 120 mm/s2.
Due to the low viscosity of this sample the handling in the experiment is difficult.
Investigations of samples with a lower viscosity than the LLDPE 1 cannot be
recommended with the geometrical setup of the Rheotens experiment used in this work.
The attempt to measure the LLDPE 1 at 190°C failed as the handling of the sample is
impossible.
In addition to an acceleration of 120 mm/s2 samples were investigated with an
acceleration of 6 mm/s2. At this acceleration the forces tend to a strong oscillating
133
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behaviour. The reproducibility is shown for the LDPE which shows only slight oscillations
(Figure 86) and the LLDPE 1 which shows strong oscillations and has the worst
reproducibility of the experimental results. As within certain limits the onset of draw
resonance is a statistical process, the curves of different measurements do not overlay.
This is more obvious for samples with a low force level like the LLDPE 1. Figure 87 shows
4 curves of the LDPE. The force level and the intensity of the force oscillations is well
reproducible.
0 50 100 150 200 250 3000
5
10
15
20
Reproducibility: 4 curvesLDPET=150°Ca = 6 mm/s2
d = 120 mm
v [mm/s]
Forc
e [c
N]
Figure 87: Reproducibility of Rheotens experiments of the LDPE run with an acceleration a = 6 mm/s2 at 150°C.
In contrast to the LDPE the draw resonance of the LLDPE 1 shows a strong scatter and
thus its relative draw resonance covers a large area (Figure 88). But with respect to the
diversity of the behaviour of the samples in the Rheotens experiments the reproducibility
of the LLDPE 1 is sufficient to differ between the LLDPE 22, 21 on the one hand and the
blend and the LDPE on the other hand. A closer differentiation between the samples
mLLDPE11, mLLDPE 12 and LLDPE 1 is inappropriate.
134
_______________________________________________________________________
0 100 200 300 400 500 6000
1
2
3
4
5
6
Reproducibility: 4 curvesLLDPE 1T=150°Ca = 6 mm/s2
d = 120 mm
v [mm/s]
Forc
e [c
N]
Figure 88: Reproducibility of Rheotens experiments of the LLDPE 1 run with an acceleration a = 6 mm/s2 at 150°C.
Film homogeneity For the rating of the trustworthiness of the homogeneity of the film homogeneity the
results of two samples will be discussed. For the samples LLDPE 1 and the LLDPE/LDPE
90/10 blend two measurements are compared. Two film samples were taken from two
independent film blowing runs and their homogeneity was checked. Figure 89 shows the
average film thickness and the standard deviation as a function of take-up ratio. The
thickness of the film can be measured with good reproducibility. But standard deviation
tends to remarkable fluctuations which can amount to 50 %. These are reflected in the
relative standard deviation, too (Figure 90). But the linear fits show an acceptable
agreement for the qualitative evaluation of the results as done in this work. The bad
reproducibility of the homogeneity for single take-up ratios is another indicator of the bad
processability of the sample. It seems to be difficult to obtain a constant film quality in two
different experiments.
135
_______________________________________________________________________
10 20 30 40 504
6
8
10
12
14
16
18
20
22
24
measurement 1 measurement 2
Reproducibility: LLDPE 1
av
erag
e fil
m th
ickn
ess
h av [
µm]
TUR
1,0
1,5
2,0
2,5
standard deviation of film
thickness sh [µm
]
Figure 89: Average film thickness and its standard deviation as a function of the take-up ratio for the LLDPE 1; 2 independent measurements.
10 20 30 40 50 60
10
15
20 measurement 1 measurement 2
Reproducibility: LLDPE 1
rela
tive
stan
dard
dev
iatio
n of
film
thic
knes
s r h
[%]
TUR
Figure 90: Relative standard deviation of film thickness and its linear fit as a function of the take-up ratio for the LLDPE 1; 2 independent measurements.
136
_______________________________________________________________________
The reproducibility of the film thickness of the LDPE/LLDPE1 blend is shown in Figure 91.
Like in case of LLDPE 1 the film thickness of two independent film blowing experiments is
nearly overlapping. But in contrast to the LLDPE 1, the measurement of the standard
deviation can be done with a higher accuracy. A discrepancy of 30 % is an exception.
0 10 20 30 40 50 600
10
20
30
40
50
measurement 1 measurement 2
Reproducibility: Blend LLDPE1 / LDPE 90/10
aver
age
film
thic
knes
s h av
[µm
]
TUR
0
2
4
6
standard deviation of film
thickness sh [µm
]
Figure 91: Average film thickness and its standard deviation as a function of the take-up ratio for the LLDPE/LDPE 90/10 blend; 2 independent measurements.
As demonstrated in Figure 92 the reproducibility of the linear fits of the homogeneity as a
function of take-up ratio shows a sufficient reproducibility.
137
_______________________________________________________________________
0 10 20 30 40 50 600
5
10
15
20
25
30
measurement 1 measurement 2
Reproducibility: Blend LLDPE1 / LDPE 90/10
re
lativ
e st
anda
rd d
evia
tion
of fi
lm th
ickn
ess
r h [%
]
TUR
Figure 92: Relative standard deviation of film thickness and its linear fit as a function of the take-up ratio for the LLDPE/LDPE 90/10 blend; 2 independent measurements.
138
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Appendix D: Symbols and Abbreviations
AP cross section piston
AD cross section die
a acceleration of the wheels (Rheotens)
BUR blow-up ratio
c concentration
D diameter
Da diameter of annular die (film blowing)
Dd diameter of the die (capillary rheometer)
DS diameter of the extruder cylinder (film blowing)
Dp diameter of the piston (capillary rheometer)
d distance die – wheels (Rheotens)
EA activation energy
G’ storage modulus
G’’ loss modulus
h film thickness
H flight depth (film blowing)
h0 annular die gap
hav average film thickness
L Length of the extruder cylinder (film blowing)
Ld Length of the die
n number of measurements
N number of revolutions per minute
R radius of the bubble
Rfs ratio of force in film blowing and melt strength
r0 radius of the annular die
rh inhomogeneity number
sh standard deviation of film thickness
T temperature
TUR take-up ratio
v velocity of the wheels (Rheotens)
vp velocity of the piston
v0 initial velocity
vTU take-up speed (film blowing)
αd entry angle of a die
139
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ε strain
εH Hencky strain
ε& strain rate
sε& steady-state strain rate
γ shear deformation
γ& shear rate
ηo zero shear viscosity
η*(ω) complex dynamic viscosity
η (t) time dependent viscosity
µ(t) time dependent elongational viscosity
µs steady-state elongational viscosity
σ tensile stress
τ shear stress
ω angular frequency
140
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Danksagung Die vorliegende Arbeit entstand zwischen 10/1997 und 06/2003, wobei alle praktischen
Experimente während meiner Zeit als wissenschaftlicher Mitarbeiter am Lehrstuhl für
Polymerwerkstoffe der Universität Erlangen-Nürnberg durchgeführt wurden.
An erster Stelle möchte ich mich bei Herrn Prof. Dr. Helmut Münstedt bedanken, der mir
die Betreuung eines internationalen Projektes ermöglichte. Seine ausdauernde
Unterstützung trug maßgeblich zum Gelingen dieser Arbeit bei.
I thank Borealis Polymers Oy for the assistence and sponsorship of my project, especially
Dr. Anneli Malmberg and Juha Matti Levasalmi, who both were excellent partners for
discussions and external experiments. Kiitos!
Mein besonderer Dank gilt den technischen Mitarbeitern des Lehrstuhls, die mir jederzeit
hilfsbereit zur Seite standen. Nur durch ihre Unterstützung bei elektronischen,
konstruktiven oder experimentellen Problemen wurde die große Anzahl an Versuchen erst
ermöglicht.
Dank gebührt auch meinem Studienarbeiter Klaus Beisert und meinem Diplomanden
Martin Krogoll, deren Arbeiten zur Durchführung dieser Arbeit beigetragen haben.
Ich danke allen Mitarbeitern des Lehrstuhls für viele fachliche Diskussionen und ein
kollegiales Arbeitsklima.
Meinen Eltern danke ich für die andauernde Motivation und Unterstützung während dem
Entstehen dieser Arbeit.
Curriculum Vitae
Persönliche Daten Name: Thomas Steffl
Familienstand: verheiratet seit 10/2003 mit Julia Steffl (geb. Benker)
Nationalität: deutsch
Geburtsdatum: 18.12.1970
Geburtsort: Nürnberg
Schulbildung
08/1977 - 06/1981 Grundschule, Lauf a. d. Peg.
08/1981 - 05/1990 Staatliches Gymnasium Lauf a. d. Peg.
Wehrdienst: 07/1990 - 06/1991 Nachschubbataillon 4; Amberg, Regensburg
Studium: 11/1991 - 07/1997 Physik (Diplom) Friedrich-Alexander-Universität Erlangen-Nürnberg
09/1993 - 04/1994 Physik Imperial College of Science, Technology and Medicine,
London, England
05/1994 - 07/1997 Physik (Diplom) Friedrich-Alexander-Universität Erlangen-Nürnberg
Abschluss: Diplom - Physiker
Beruf 09/1997 – 12/2000 Wissenschaftlicher Mitarbeiter am Lehrstuhl für Polymerwerkstoffe
Institut für Werkstoffwissenschaften der Friedrich-Alexander
Universität Erlangen-Nürnberg
seit 10/2001 Forschung & Entwicklung, TEADIT International Produktions GmbH,
A-6330 Kufstein
