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Rijksuniversiteit Groningen

Improving the properties of polymer blendsby reactive compounding

Proefschrift

Ter verkrijging van het doctoraat in deWiskunde en Natuurwetenschappenaan de Rijksuniversiteit Groningenop gezag van deRector Magnificus Dr. F. van der WoudeIn het openbaar te verdedigen opvrijdag 12 juni 1998des namiddags te 2. 45 uur precies

door

Douwe Jurjen van der Wal

Geboren op 28 april 1964te Leeuwarden

Promotores Prof. dr. ir. L.P.B.M. JanssenProf. dr. ir. H.W. Hoogstraten

contents

CONTENTS

CHAPTER 0IMPROVED PROPERTIES OF POLYMERIC MATERIAL BY MEANSOF MIXING TWO POLYMERS 1

1 Introduction 11.1.1 Theory of compatibilisation 21.1.2 Mechanical properties of blends 31.2 What has been done in earlier work 32 This thesis 7

References 8

CHAPTER 1A NEW METHOD FOR REACTIVE BLENDING 10

Abstract 101 Introduction 102 Theory 112.1 Experimental set-up 132.2 Analysis 133 Experimental results 144 Concentration profiles 174.1 The materials formed in the dispersed phase 205 Conclusions 23

Nomenclature 23References 24

CHAPTER 2THREE DIMENSIONAL FLOW MODELLING OF A SELF WIPINGCOROTATING TWIN SCREW EXTRUDER, THE KNEADING SECTION

25

Abstract 251 Introduction 252 Mathematical method 263 Definition of the problem 283.1 Geometry and mesh 283.2 Boundary conditions 304 Results 314.1.1 The axial velocities 314.1.2 The axial backflow volume 324.2 The transverse velocities 344.3 The pressure difference over one kneading element 354.4 The shear and elongation rate 374.5 The influence of the stagger angle between the kneading elements

on the flow 394.6 The influence of the viscosity on the flow 43

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4.7 The adiabatic axial temperature rise 454.8 Experimental validation 465 Discussions and conclusions 47


CHAPTER 3THREE DIMENSIONAL FLOW MODELLING OF A SELF WIPINGCOROTATING TWIN SCREW EXTRUDER, THE TRANSPORTINGSECTION

51

Abstract 511 Introduction 512 Mathematical method 533 Definition of the problem 554 Results and discussion 574.1 The throughput 574.2 The flow profile 584.3 The backflow 614.4 The axial pressure gradient 634.5 The shear and elongation rate 644.6 The adiabatic temperature rise 674.7 The influence of viscosity 685 Conclusions 71


CHAPTER 4THREE DIMENSIONAL FLOW AND TEMPERATURE MODELLING INTHE CHANNEL OF THE COROTATING TWIN SCREW EXTRUDER

74

Abstract 741 Introduction 742 Definition of the problem 752.1 The geometric model 752.2 The flow problem 772.3 The temperature problem 782.4 The temperature profile for a larger length of the channel 793 Results 793.1 Three dimensional temperature calculation, an example 803.2 The influence of the heat conductivity coefficient 863.3 The influence of reaction heat on the temperature profile 884 Conclusions 90


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CHAPTER 5THE ROLE OF DIFFUSION AND REACTION IN REACTIVECOMPOUNDING

92

Abstract 921 Introduction 92

Diffusion 92Kinetics 93Modelling 93

2 Experimental set-up 942.1 The measurements of the diffusion coefficient with FRAP 953 Results 973.1.1 The diffusion coefficient 973.1.2 Variation of the temperature 983.1.3 Diffusion coefficients of binary diffusion in a polymer 1023.2.1 Kinetics 1053.2.2 Measurements of the reaction velocities 1064 Modelling the concentration profiles and Mn distribution of

the alloying agent 1075 Discussion and conclusions 112


CHAPTER 6MODELLING AND EXPERIMENTAL EVALUATION OF THETEMPERATURE IN A COROTATING TWIN SCREW EXTRUDER

115

Abstract 1151 Introduction 1152 Modelling of the average axial temperature in the corotating

twin screw extruder 1162.1 The geometry and the throughput of the extruder 1162.2 The temperature model 1192.3 The viscous dissipation 1192.4 The temperature profile 1203 Experimental 1223.1 Extrusion and viscosity 1224 Results 1234.1 The power 1234.2.1 The temperature profile in the partially filled section 1264.2.2 The fully filled section 1284.2.3 The temperature at the entrance of the kneading section 1304.2.4 The heat transfer coefficient calculated ; the kneading section 1324.2.5 The temperature of a blend (PS/HDPE) 1335 Conclusions 135


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CHAPTER 7

MODELLING AND EXPERIMENTAL EVALUATION OF MIXING IN ACOROTATING TWIN SCREW EXTRUDER

138Abstract 138

1 Introduction to mechanical properties of blends 1381.1 Mixing in the intermeshing corotating twin screw extruder 1392 Modelling of mixing in the corotating-twin screw extruder 1402.1.1 A simplified modelling of the average size of the dispersed phase of a blend

1422.1.2 Modelling of the average size of the dispersed phase of a blend 1443 Experimental set up 1464 Results and discussions 1474.1 Modelling of the axial development of the average size of the dispersed phase

1474.2 The influence of the rotation speed of the screws 1524.3.1 Comparison between measurements and modelling, PS/HDPE blends 1554.3.2 Comparison of our computer modelling with the measurements of others 1565 Conclusions 157


CHAPTER 8MODELLING AND EXPERIMENTAL EVALUATION OF REACTIVECOMPOUNDING IN A COROTATING TWIN SCREW EXTRUDER

161

Abstract 1611 Introduction 1612 Modelling reactive compounding 1642.1 The different steps taken in our modelling 1642.2 Measuring and modelling the reaction velocity of monomer in the melt,

an example 1662.3 Modelling and measuring the size of the dispersed phase, an example 1702.4 Modelling of the diffusion of monomer out of the dispersed phase

, an example 1712.5 Modelling of the conversion of monomer in the dispersed phase 1713 Experimental set-up 1723.1 Experiments with the Brabender mixing chamber 1733.2 Reactive blending in the extruder 1743.3 Reactive blending of PS/PP with MAH/S 1753.4 Experiments with an improved screw geometry 1764 Comparison between model and experiments 1784.1 The measured and modelled conversions of MAH in the

dispersed phase (HDPE) versus rotation speed and throughput 1794.2 The conversion of acrylates in the dispersed phase of PS/HDPE 1805 The grafted monomer on HDPE in the dispersed phase of PS/HDPE 182

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6 Conclusions 185Nomenclature 186References 186

CHAPTER 9IMPROVED TOUGHNESS VERSUS PROCESSING PARAMETERS

188

Abstract 1881 Introduction 1881.1 Theory, mechanical properties and morphology 1891.2 The conversion in the dispersed phase of a PS/HDPE blend 1902 Experimental set-up, the extruder 1922.1 Experimental set-up, the materials 1922.2 Analysis 1933 Results 1933.1 Material choice for the dispersed and matrix phase 1943.2 Material properties versus processing conditions 1943.3 Toughness and elongation at break 1973.4 The influence of rotation speed on the Notched Izod Impact values 1993.5 Impact values versus conversion and rotation speed 2023.6 The relation between elongation at break, and an efficient alloying agent 2034 Discussion 2075 Conclusions 209


CHAPTER 10THE LINK BETWEEN THE GLASS TRANSITION TEMPERATURE, THEALLOYING AGENT FORMED, AND THE MECHANICAL PROPERTIES OFTHE BLEND

211

Abstract 2111 Introduction 2112 Experimental 2152.1 Analysis 2163 Results 2173.1 The conversion of monomer in the dispersed phase 2173.2 The glass and melt transition temperature and toughness versus the rotation

speed of the screws 2204 The Notched Izod Impact value, Tg, and the alloying agent 2265 The influence of the type of dispersed phase 2296 Conclusions 2306.1 Theoretical considerations 231


Dankwoord

Het heeft even geduurd maar nu is het toch klaar. Direct nadat mijn contract bij het NWOafliep werd ik bij Philips gevraagd om te komen werken als kunststof specialist. Dit heb ikgedaan om op deze manier ook de toepassingen en de markt van kunststoffen te lerenkennen. Maar ja om dan ook nog een proefschrift af te maken bleek een zware klus. Omhet toch af te ronden ben ik een aantal hoogleraren dank verschuldigd. Als eersten wil iknatuurlijk mijn promotors prof. Dr. Ir. H.W. Hoogstraten en vooral mijn eerste promotorProf Dr. Ir. L.P.B.M. Janssen noemen. De grote vrijheid die ik heb gekregen om mijneigen methode te bedenken en te onderzoeken heeft geresulteerd in een patent op dezemethode (een publikatie met een gouden randje). Hun begeleiding bij het doen van ditonderzoek en het publiceren hiervan heeft (hun en mij) zeer veel tijd gekost, waarvoordank. Verder wil ik de hoogleraren uit mijn leescommissie bedanken die bestond uit Prof.dr. G. Hadziioannou, Prof. Dr. Ir. L.L. van Dierendonck, Prof. Dr. Ir. A.A.C.M.Beenackers. Maar ook andere hoogleraren hebben bijgedragen door apparatuurbeschikbaar te stellen of door middel van waardevolle discussies waarbij ik vooral Prof dr.G. Hadziioannou, Prof. dr. G. ten Brinke, en Prof. dr. A. J. Pennings wil bedanken.Van onschatbare waarde voor mij waren de technische medewerkers zoals LaurensBosgra, Luuk Balt, Harry Nijland, Gert Alberda v Ekenstein, Marcel de Vries, AdamsVerweij, Dirk Grijpma, Joop Vorenkamp, Karel van der West, Jan Henk Marsman, BerendQuant, Yannis Pappantoniou en al die anderen bij Technische Scheikunde zoals GerdaEverts en de ander dames van het secretariaat, en Polymeerchemie. Echt compounderenleer je in de praktijk en daarvoor dank ik Ben en Netty, Dermy en Erwin, Johan en Ilse,Lex, en Fred. Dit proefschrift was niet mogelijk geweest zonder al die afstudeerders dienaast goede studenten, erg leuke mensen en vaak ook nog komische duo's bleken te zijnaangezien ze vaak twee aan twee kwamen. Hierbij wil ik met name noemen Johan enCarel, Udo en IJeb, Johan en Jelle, Pieter, Eric en David, Jeroen, en Arnoud, Sylvia, EricJan, Carolien, Welmoed en Mildo. Jullie hebben ondertussen allemaal een eigen carrièremaar ik hoop dat jullie met veel plezier terug denken aan het onderzoek bij Technischescheikunde (Wiskunde en Polymeerchemie zijn trouwens ook goed vertegenwoordigd).Ze zijn voor mij het belangrijkste, mijn vader Jurjen (die mij leerde te fantaseren) en mijnmoeder Binnie (die mij leerde nuchter na te denken).Als je vrienden je ook nog door een promotie heen willen loodsen, dan moeten het welechte vrienden zijn. Buiten het onderzoek en buiten het werk ben ik ze tegengekomen aldie vrienden. Op het gevaar af er enkele te vergeten zijn daar mijn Paranimfen, GerardLemson (voorvechter van zuivere wetenschap, IT, en mijn vaste gesprekspartner). Het wasvooral een mooie tijd dankzij Roel, Perry en Margriet (mijn pleegouders), Dick (squashSM er) en Carolien, Arjen en Gerrie, Rob en Yolanthe, Douwe en (?) , Frank en Maran,Keimpe en Marie en Johan, Rixt, Jan en Linda de Boer, Yolanda, Ineke, Marga, Ellen enLeon, Anne, Jacco, Inge en Karin. Sporten is een feest met vrienden zoals Sven, Sander enJildou, Frank Derks, Frank Meeuwissen, Frank Wind en Fabienne, Mirjam, Richard en aldat volk van Amor zoals Vincent, Hans, Alex en ga zo maar door. Deze lijst is beslist nietvolledig en daarom wil ik allen bedanken die deze tijd voor mij tot een groot feest hebbengemaakt.

Maart 1998 Douwe Jurjen van der Wal

Dit proefschrift is tot stand gekomen met financieel hulp van het NWO

Aan Jurjen, Binnie, Keimpe, Marie, Johan, en Rixt

Voorwoord

Dit is het verhaal van een reis. Het is echter niet een gewone reis zoals je die tegenwoordighet liefst boekt bij een reisorganisatie. Je weet precies waar je heen gaat, hoeveel het kosten wat je er aan zult treffen. Voor mij was het een reis met een onbekende bestemming enhoeveel het zou kosten daar had ik ook nog geen idee van.Toch had ik wel nagedacht over het punt waar ik het liefste uit zou komen. Maar zoalsiedere reiziger weet moet je eerst door heel veel plaatsen heen voor je ergens komt. Iedereplaats had een reisdoel kunnen zijn en op iedere plaats loont het de moeite om eens goedrond te kijken. Er zijn mooie en vaak boeiende dingen om te zien en eigenlijk zou je opieder van die plaatsen kunnen blijven. Blijf je lang genoeg dan ken je na een tijd ieder detailvan die plaats, je begrijpt wat de mensen op die plaats beweegt en je voelt je er thuis.Helaas, ik moest verder. Met het einddoel in het achterhoofd was en niet genoeg tijd omgoed rond te kijken. Een snelle indruk opdoen en dan me weer klaar maken voor devolgende bestemming. Een reis kan vaak lang duren en erg vermoeiend zijn. Je steeds weerte verplaatsen, geen tijd om uit te rusten. Ik moest zoeken naar het juiste transportmiddelom weer verder te gaan. Als je zo'n reis alleen maakt dan is ie ook erg saai. Natuurlijk ishet leuk uit 't raam te kijken, de omgeving in je op te nemen en proberen rond te kijken hoede mensen op die plaats leven. Maar als je er met niemand over kunt praten dan mis je tochiets. Gelukkig zijn er altijd wel reisgenoten. Ze hebben niet altijd het zelfde einddoel maartoch kan ik altijd wel met ze praten, soms over hun einddoel, vaak over de omgeving en demensen om ons heen, soms ook over mijn einddoel. Het beste kunnen we praten over watons allemaal beweegt. Er zijn dingen om mee te maken. Op de haltes kunnen we wel eensde stad in gaan, naar de film, wat drinken of wat sporten. Er is altijd wel een ACLO waarontzettend veel verschillende sporten kunnen worden beoefend. Dat leid een beetje af vande vermoeiende reis en na het sporten is het erg gezellig om met zijn allen nog wat na tepraten.Maar dan weer verder. Het einddoel wacht en er moeten nog zoveel haltes wordenafgelegd. Als de reis echt zwaar wordt dan bel ik mijn ouders even, Jurjen en Binnie zijn eraltijd voor me. Dat ik op reis wou, dat hebben ze altijd gestimuleerd. Om de wereld te zienop mijn eigen manier, maar hoever ik ook ga ze blijven altijd bij me. Van wat ze zeggen alsik ze bel begrijp ik dat ze alles goed vinden als ik maar voorzichtig ben. Ze willen megezond terug hebben en het enige wat ze echt interesseert is dat ik gelukkig ben. Tja,samen met mijn broer Keimpe, en mijn zus Rixt vormen ze de beste thuis basis die eenreiziger zich maar kan wensen.Onderweg leer ik vrienden kennen, Sommige ken ik al vanaf de eerste halte. Het zijngeweldige mensen, net als ik op zoek naar hun reisbestemming en enorm nieuwsgierig watde reis te bieden heeft. Samen doen we dingen onderweg. We houden steeds contact, zelfs

als sommigen een andere route moeten nemen, uit stappen en verder reizen. Die vriendenbellen op, sturen een mailtje of we komen elkaar zo nu en dan weer tegen als onze routeselkaar toch weer kruisen. Als de reis zo nu en dan door een donkere tunnel gaat dan zijnwe er voor elkaar. Door met elkaar te praten lijkt de tunnel niet donker meer en we wijzenelkaar op het licht dat alweer te zien is aan het eind van de tunnel. Er is altijd licht aan heteind van de tunnel, en zo wordt dan eindelijk het reisdoel bereikt.Het reisdoel van dit proefschrift, dat had ik al bedacht na eerst een half jaar na te denkenover waar ik heen wou, is om een taaier plastic te maken door twee plastics te mengen.Om dit te doen moest ik bedenken wat mijn vervoersmiddel zou zijn. Dit is eenmeedraaiende dubbelschroefsextruder geworden. Dit type extruder is een apparaat mettwee lange schroeven die tegen elkaar aan draaien in een huis. Door dit draaien verpompenze plastic wat meteen ook wordt opgewarmd en gemengd. Door plastics te mengen endaarbij monomeer te laten reageren in dat mengsel kon ik mijn doel bereiken. Alle processtappen daar tussen in moest ik eerst bestuderen en die bewerkingen zijn de haltes die ikaan gedaan heb tijdens mijn reis. Het doel is bereikt en het wordt beschreven in hoofdstuk9 en hoofdstuk 10.Maar als ik nu terug kijk op mijn reis dan is het einddoel van de reis niet het mooisteresultaat. Het mooiste resultaat dat zijn de reisgenoten.

Douwe van der Wal, Groningen, Augustus, 1997.

Improving the properties of polymer blends, chapter 0

1

Since the contents of this chapter can mostly be found in other studies I called it chapter 0.

CHAPTER 0 IMPROVED PROPERTIES OF POLYMERIC MATERIALS BY MEANS OF MIXING TWO POLYMERS.

1 Introduction.

New properties, lower prices and reuse of polymers are needed to meet demands of today'ssociety and therefore of the polymer industry. Polymer is the technical name for what is moregenerally known as plastic. Plastics are used by almost everybody since (for example) mostdomestic machines have a housing, which is made out of it. The polymers commonly used inEurope are Polyethylene (PE), Polypropylene (PP), and Polystyrene (PS) (about 25% of themarket which is about 500,000 tons per year). These polymers can be extruded withoutexcessive degradation when they contain little impurities. Additives (such as antioxidants) areoften added for stabilisation. Other important plastics have more problems with degradationsuch as in the case of Polyacetals (POM) and Polyamide (PA 6 , PA 66, PA 4,6, PA 12, andPA 11). This thesis focuses mostly on reactive compounding of PS, Polyethylene (PE), and PPsince a relatively pure stream of PP, PE and PS is most easily obtained. Usually the mechanicalproperties of the pure blends obtained are poor. However a lot of research has shown thatthese properties can be brought back to their original level by adding an additional phase (1-17). This phase usually is called the compatibiliser. In this thesis the term alloying agent willbe used when a reaction takes place during the compatibilising step.Polymers are either amorphous or semi crystalline. A semi crystalline polymer has anamorphous and a crystalline part. The part, which is crystalline, has a more or less orderedstructure in which the chains of the polymer are often folded in a non random fashion. Themechanical properties of semi crystalline polymers are strongly determined by the crystallites,which usually enhance their stiffness (for example in polypropylene). Amorphous polymers areeither very brittle (polystyrene) or very tough (polycarbonate). It is quite difficult to predictthe mechanical properties of a semi crystalline material since it is determined by manyparameters (such as its percentage of crystallites). It is more feasible to understand themechanical properties of an amorphous polymer.Unfortunately the demands for many applications need a set of properties that no polymerscan fulfil. One method to satisfy these demands is by mixing two or more polymers. Mixingtwo or more polymers to produce blends or alloys is a well-established route to achieve acertain amount of physical properties, without the need to synthesise specialised polymersystems. This subject has been the focus of many papers, most of which was empirical. Part ofthe literature on blends is of academic rather than of commercial interest. Well knownexamples of commercial blends are high impact polystyrene (HIPS) and Acrylonitrilene-


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butadiene-styrene (ABS). These blends are tough and have good processability. Howeverwhen polymers are mixed the blend often is brittle. One of the most interesting examples of anamorphous polymer is polystyrene because of its brittleness. Adding a compatibiliser with thestructure of a copolymer, to PS/PE improves the toughness by a factor 3 (17).Improving the mechanical properties of polystyrene has been chosen as the aim of this thesissince brittleness is a large disadvantage of polystyrene in many applications. Anotherapplication for the results of this thesis is recycling. The first important step for recycling ispurification of the plastic stream. The second step is recycling by mixing polymers in such away that the required properties are reached.

1.1.1 Theory of compatibilisation.

Mechanical properties of polymers and polymer blends are very important in manyapplications. Significant for these properties is compatibility between the different polymerswhich is frequently defined as miscibility on a molecular scale of the components of the blend.Over 300 pairs of miscible polymers are known (14), from which only a few systems havebeen commercialised such as :Polyphenylether/Polystyrene (PPE/PS), Polycarbonate/Polyethylenterephtalate (PC/PET), andPolycarbonate/Polybutylterephtalate (PC/PBT).Another type of blend consists of incompatible polymers for which various morphologies canbe realised via processing, for instance droplets or fibres in a matrix and stratified or co-continuous structures. The structures induced are usually unstable. For example addition of arubber to a brittle polymer often creates an instable morphology, after processing this blendfor the second time because the morphology may change.In most cases, melt mixing two polymers results in blends, which are weak and brittle. Theincorporation of a dispersed phase into a matrix mostly leads to the presence of stressconcentrations and weak interfaces, arising from poor mechanical coupling between phases.Improving the mechanical properties of a blend is often done by compatibilisation whichmeans modification of normally not miscible blends by mixing a block-copolymer into theblend to improve the miscibility. The end-use performance has been improved many times bythis method. However this method is not the same as creating blends, which have miscibilityon a molecular scale, or even blends containing very finely dispersed phases. From a practicalpoint of view a blend often is considered to be compatible if a certain set of mechanicalproperties is achieved.Well known examples of blends are the impact modified, (rubber) toughened polymers, wherepolymers with different glass transition temperatures are blended. Many other blends areknown such as barrier polymers for packing, where specific polar or apolar polymers are


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combined in order to increase the resistance against transport of water and gas (oxygen,carbon dioxide).It should be kept in mind that several methods are known to improve the properties ofplastics. For many polymers additives are needed to improve for example processability andlifetime (lubricants or stabilisers), modulus and strength (mineral fillers such as glass beads,chalk, clay, mica or glass-fibre reinforcement), appearance and colour (pigments), conductivity(conducting fillers such as aluminium flakes or carbon) or flammability (flame retardants). Theword compatibiliser will sometime be replaced by alloying agent since a blend with improvedmechanical properties is also called an alloy. Therefore this name can also be used since theimprovement of the properties of the blend is the purpose of adding or creating acompatibiliser.

1.1.2 Mechanical properties of blends.

The incorporation of rubber particles within the matrix of brittle plastics may enormouslyimprove their impact resistance. Toughening in brittle plastics is also observed under otherloading conditions, such as simple low-rate stress-strain deformation and fatigue. When aforce is applied to a blend several deformation mechanisms of the major phase and of crackswhich are formed in the blend are important. Their relative importance may depend on thepolymer and on the nature of the loading. The effect of the quantity of rubber incorporatedand the method of forming the blend has been studied extensively forpolystyrene/polybutadiene blends. An optimum rubber concentration and phase domain sizeexists, the values depending on the rubber and polymer concerned. The importance of graft-type bonding and the finer, more complex morphology developed in graft copolymers shouldbe emphasised.

1.2 What has been done in earlier work.

Much work has been done on the blending (mixing) of polymers by many authors. A large partof these studies deal with attempts to obtain a combination of properties of different polymers.Unfortunately the mechanical properties of blends are usually worse instead of better for manycombinations of polymers. The conventional methods for improvement of these properties areoften expensive and do not always meet the required demands. A small part of the most recentresearch on compatibilisation and blending will be described shortly here. This is done toobtain some idea of the number of possible choices for application of the method described.In principle compatibilisation is influenced by the molecular weight distribution andconcentration of a compatibiliser in the dispersed phase in complex ways to influence finalblend properties.


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The best known effect from compatibilisation is reduction of the interfacial tension in the melt.This causes an emulsifying effect and leads to an extremely fine dispersion of one phase in theother. A second effect is to increase the adhesion at phase boundaries giving improved stresstransfer. For this effect the interaction between the compatibilising copolymer chain and thepolymer chains of the dispersed phase and the matrix phase will be important. A third effect isthe inhibition of coalescence of the dispersed phase by modifying the phase boundaryinterface. These and other effects (such as modification of rheology) may occur simultaneouslywhich complicates the ongoing of the whole process.

In the work of Lester and Hope (1) the complexity of the interaction of the compatibiliser withthe morphology of a blend was illustrated when high density polyethylene (HDPE) was mixedwith nylon 6, nylon 6-6, nylon 6-3T and polyethylene terephthalate (PET), with and withoutlow levels of various proprietary compatibilising agents. The blends were characterised interms of phase morphology (by scanning electron microscopy, SEM) and by tensile testing ofsamples cut from moulded plaques. The finest phase dispersion did not guarantee the highestvalues of ultimate elongation. Compatibilisation of PE/PS blends was studied by Barendsen etal (2) by addition of graft copolymers of LDPE with PS (PS-g-LDPE) to blends of LDPE andPS. Blends were produced by melt mixing at 195 °C on a laboratory mill, and the graftcopolymer was first melt blended with the polymer forming the dispersed phase before beingadded to the matrix polymer. Addition of 7.5 % by weight copolymer caused a substantialreduction in size of the dispersed phase. Heikens et al (3) showed that differences in thedetailed fine structure of copolymers gave rise to large effects on the impact strength, and onthe magnitude of the tensile modulus of the blends.Copolymers of Propylene and Ethylene (EP), displaying residual crystallinity because of longethylene sequences, could serve as compatibilising agents for polypropylene/low-density-polyethylene (PP/LDPE) blends (4). The purely amorphous copolymers were less effective ascompatibilising agents. To obtain a linear relationship between tensile strength andcomposition for HDPE/PP blends 5% addition of ethylene-propylene rubbers (EPR) isnecessary (5). However it must be noted that there are many examples in the literature whereblends prepared from the same types of polymer behave differently. This is hardly surprising inthe light of the high sensitivity of mechanical properties to variation of the temperature,composition, morphology of the blend, etc.A method commonly used to induce compatibility between polyamides and polyolefines is bychemical modification of the polyolefines. The polyolefines contains pendent carboxyl groups,often by grafting with maleic anhydride (MAH), which forms chemical linkage to thepolyamide via the terminal amino groups. The concept has been employed to producecompatibiliser by grafting MAH onto the polyolefine, and then adding the MAH-g-polyolefineas a third component in polyamide/polyolefine blends (6). The existence of a reaction between


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the MAH and the nylon 6 amino end groups was established by solvent extraction of the PPphase, estimation of the number of end groups and DSC analysis of the residue. Otherapproaches to enhance the properties of polyolefine/polyamide blends include the addition ofacrylic acid/butyl acrylate/styrene terpolymers to blends of nylon and polyethylene and theaddition of nylon 6-polybutene multiblock copolymer to nylon 6/HDPE blends (7-9). Alsocompatibilisation of nylon 6/PS blends was studied by addition of a Methyl-methacrylate-styrene (MMAS) copolymer (6). The use of a copolymer of styrene (S) and maleic acid(MAH) which is known as SMA was found to be more effective than styrene acrylonitrile(SAN) copolymer in compatibilising nylon 6/PS blends (10). Many studies have beenpublished in which the use of MAH led to interesting results.The success of using block and graft copolymers as compatibilisers accounts for some of thelarge number of the commercially available blends: high impact polystyrene (HIPS) andacrylonitrile butadiene styrene (ABS). Methyl-methacrylate (MMA)-graft rubbers and styrene-Methyl-mathacrylate copolymer (MMAS)-graft rubbers were blended with ABS increasingfracture toughness in MMA-graft rubbers and decreasing toughness in MMAS-graft rubber.This reduction for MMAS-rubbers increased with increasing Styrene content (11). An increasein toughness of polyamide-6 (PA6) in PA6/SAN blends was found by adding polystyrene-co-maleic anhydride (SMA) (12).The blend, which is studied most in this thesis, PS/HDPE, is one, which has been studiedextensively in the literature either as model of an immiscible blend or for the purpose ofdevelopment of an economic method for plastic scrap recycling. In the literature, studies of therheology of the blend showed that the steady state shear flow invariably led to shearsegregation of phases and irreproducible results. The dynamic-oscillatory tests werereproducible, indicating the presence of the apparent yield stress due to an interactivemorphology. It appeared that the concentration at which the yield stress was the largestdepends on the method of sample preparation. This means that the morphology of the blendswas not at equilibrium. The structure imposed by compounding was stabilised by the lowdiffusion rate. This may explain why in spite of the apparent yield stress it was possible toconstruct time-temperature master curves.The influence of addition of hydrogenated poly(styrene-b-isoprene) di-block copolymer (SEB)to a blend was studied by Utracki (13). Paul (14) and Barlow (15) reviewed the use of blockcopolymers and other copolymers to the compatibilisation of immiscible polymer blends. Theeffect of Kraton 1652G (containing PS and copolymer of ethylene and butane) or EPCAR 847(containing ethylene-propylene-ethyldiene norborene copolymer) are of particular interest.Addition to PET/HDPE blends variously affected the different physical properties, modulusand yield strength. In general, addition of block copolymers of the same chemical nature as thetwo homopolymers of a blend is an obvious choice which, when optimised, will lead toenhancement of properties. The disadvantage of this method is on one hand their


6

inaccessibility and the lack of flexibility in tuning the properties to specific applications. A wayof dealing with these problems is using multicomponent and/or multiphase material. Theirutility varies from system to system, as a function of their compatibilising efficiency and theoverall performance of the final product.Shilov et al (16) analysed the composition of an immiscible blend as a function of lineardimensions. Between a domain of polymer A and a domain of polymer B exists an interfaciallayer. For some blends this layer may have a final thickness as large as 4 nm. The interfacialregion can be considered as a third phase. This phase has been stabilised in many commercialpolymer alloys via selective crosslinking, resulting in reproducibility of performance,processability, and recyclability. The thickness of the interface layer depends on thethermodynamic interactions, macromolecular segment size, concentration, and phaseconditions. The interfacial tension, and the domain adhesion characterise the interface. Theinterfacial tension is the integral of the Helmholtz free energy change across the interface,which gradually changes over the interfacial area from phase A to phase B, due to a changingcomposition of the third phase between both phases.Much more systems as described here have been studied, but also a few other approaches havebeen used. One approach was to blend incompatible polymers in the presence of a free radicalinitiator, like a peroxide. The aim, for the radical from the initiator, is to attack the polymerchains of the dispersed phase of the blend. This only has a limited success because the additionof peroxide did not seem to have a significant compatibilising effect. In chapter 1 an idea isproposed which has a few of the same characteristics but will show to be more effective and tohave much more possibilities. In this (new) method the radical present on these chains in turnmay combine with monomers dissolved in the dispersed phase to form a copolymer which isthe "in situ" created compatibiliser. The elongation at break obtained with the methoddescribed in this thesis in chapter 9 and 10 will be compared with the results described in thethesis of E.Kroeze (17). More literature of PS/PE blends can also be found in (17).Polymer blends can be produced directly in several types of reactors. Production of a blend,on a macroscopic scale is done by coextrusion to produce multi-layered structures via casting,blowing, blow moulding and injection-moulding. Extrusion (melt) blending is in principle arather flexible method. Unless specific interactions exist phase separation of the major andminor phase of the blend occurs, which is the case for a very large part of the possiblecombinations of polymers. Many blend microstructures are possible for which only the simplecase of a spherical dispersed phase mixed in a major phase will be studied here.


7

2 This thesis.

This thesis deals with many subject such as incompatible pairs of polymers, processingconditions, compatibilisation and the morphology of the blends obtained. Aiming at controllingthe properties of the blend a special method of blending polymers has been studied. The phasemorphology will normally not be in thermodynamic equilibrium, however in most cases it willbe stabilised against de-mixing because the blend has been compatibilised. This blend then isstudied by quenching the blend to a temperature below the glass transition temperature of oneor both phases. Stabilisation of the blend could also been achieved via the occurrence ofcrystallinity in one or both phases, or sometimes by crosslinking. In chapter 1 of this thesis anew method, different from the ones investigated before, is proposed. To investigate thismethod particular attention will be paid to the polystyrene/polyethylene blend as a modelsystem. The same method can also be used for most combinations of bulk or engineeringpolymers, aimed at high performance applications (for instance aerospace products).The different subjects are treated separately in 10 chapters. In chapter 1 the idea developed inthis thesis is explained and some results are shown. The 3D-flow in the mixing andtransporting section and the 3D-temperature profile have been modelled to be able to developa computer code which describes how this method works in a continuous single-stepproduction process in the extruder. This is done by solving the Navier-Stokes and the energyequations in the geometry of the intermeshing corotating twin screw extruder (APV, MPF-50)(chapter 2, 3, and 4).During reactive compounding mass transfer by diffusion of monomers and initiators occurboth in the dispersed phase of the blend and in its neighbourhood. Some diffusion coefficientshave been measured which is described in chapter 5. They have been measured for moleculescomparable to initiators as Trigonox (peroxide, AKZO-NOBEL). Also the formation of agraft copolymer in the dispersed phase during mass transfer of monomer out of the dispersedphase is studied as described in chapter 5.The melting, heating, and mixing of polymers in an extruder have been studied experimentallyand theoretically in chapter 6 and 7. During mixing the minor phase deforms to a longstretched shape which after some time breaks up into small spheres. Usually deformation ofthe dispersed phase of the blend occurs rapidly. In our method of reactive compounding in theintermeshing corotating twin screw extruder, polymerisation of the monomer and modificationof the polymer chains of the dispersed phase and the matrix phase occur in the dispersedphase.A computer model has been developed, which will be described in chapter 8, enabling us todescribe the process of reactive blending in the extruder. To do so the size of the dispersedphase of a blend, the conversion of monomer added into the blend, and the molecular weightdistribution of the formed graft-copolymer are calculated. The models developed for reactive


8

compounding were used to establish the optimal screw geometry and working domain. Theseresults have been used to select the experimental conditions.In chapter 9 and 10 the production of a polystyrene/high density polyethylene (PS/HDPE) isdescribed for which the elongation at break improved by a factor 20. The blends producedalso showed an enormous improvement in their toughness and Notched Izod impact values. Itis remarkable that the properties of the PS/PE and PS/PP blends that are obtained by chemicalmodification of the dispersed phase are comparable with the properties of HIPS.The influence of the blending/extrusion parameters on the properties of the blend was alsostudied. Rheology, processing, compatibilisation, reactions and heat and mass transfer aresome of the subjects, which will be dealt with in the method developed and studied. Howeversince these subject are all of interest they have all been studied sufficiently for describing ourmethod of reactive blending in an extruder. Due to a lack of time it was not possible to dealwith all the subjects in more detail. Therefore additional studies are needed to further improvethe results which will be described in this thesis. The measured mechanical properties in thisthesis are average values of at least four samples usually with a range of experimental errorwithin 5%. The glass transition temperature, melt transition temperature and the conversionsusually are average values of 3 experiments. All percentages of the dispersed phase andmonomer are in weight percentage in this thesis. In chapter 8, 9 ,and 10 the conversion hasbeen calculated which means the conversion of the monomer inside the dispersed phase.From the results obtained it seems likely that the chemical adhesion between the matrix andthe dispersed phase of the blend plays a key role in the improvement of the mechanicalproperties of the alloys that have resulted from this investigation.

References.

(1) A.J. Lester, P.S. Hope, European Symposium on Polymer Blends, Strasbourg, May 25- 27, (1987).(2) W.M. Barentsen, D. Heikens, P. Piet, Polymer, 15, 19 (1974).(3) D. Heikens, D. Hoen, W. Barentsen, P. Piet, and H. Landan, J. Polym. Sci., Polym. Symp, 62, 309 (1978).(4) E. Nolley , J.W. Barlow, D.R. Paul, Polym. Eng. Sci., 20, 364 (1980).(5) W. J. Ho, R. Salovey, Polym. Eng. Sci., 13, 202 (1973).(6) F. Ide, A. Hasegawa, J. Appl. Polym. Sci., 18, 963 (1974).(7) R.V. Meyer, R. Dhein, Chem. Abstr. 87, 185771 (1977).(8) F. Wingler, L. Liebig, Chem. Abstr, 88, 8001 (1978).(9) K.A.H. Lindberg, M. Johansson, H.E. Bertilsson, Plast. Rub. Proc. Appl., 14, 195 (1990).(10) C. C. Chen, E. Fontain, K. Min, J.L. White, Polym. Eng. Sci.,28 (2), 69 (1988).(11) Keskula, D.R. Paul, Polym. Sci.Eng., 57, 674 (1987).


9

(12) J.C. Angola, Y. Fujita, T. Sakai, T. Inoue, J. Polym. Sci., Polym. Phys, 26, 807 (1989).(13) L.A. Utracki, P. Sammut, Polym. Eng. Sci., 28, 1405 (1988).(14) D.R. Paul, ed. S. Newman, Polymer blends, Academic Press, New York, (1978).(15) J. R. Barlow, D.R. Paul, Polym. Eng. Sci., 24, 525 (1984).(16) V.V. Shilov, V.V. Tsukruk, Y.S. Lipatov, Vysokomol. Soed. A26, 1347 (1984).(17) E. Kroeze, thesis, University of Groningen (1997).

A new method for reactive compounding, chapter 1

10

CHAPTER 1 A NEW METHOD FOR REACTIVE COMPOUNDING.

Abstract.

Dissolving (or absorbing) initiator and monomer in a polymer is the first step of a newmethod, which has been developed in this thesis. In general this mixture is then mixed withanother polymer in an extruder or other apparatus capable of mixing viscous fluids. If duringmixing the reaction takes place it is called reactive compounding. In this thesis reactivecompounding will be performed in an intermeshing corotating twin screw extruder.Since monomer is dissolved in the dispersed phase but not in the matrix it will diffuse out ofthe dispersed (minor) phase. If the dispersed phase is relatively large and the diffusioncoefficient is small mass transfer out of the dispersed phase is small and therefore the dissolvedmonomer has been polymerised inside the minor phase of a blend. One particular case is ifhydroxypropyl-methacrylate (HPMA) is dissolved and polymerised in high densitypolyethylene HDPE (the minor phase) and blended with polystyrene (PS) (the major phase).This results in a partial phase separation of PHPMA from HDPE and a new structure of themorphologies of blends.

1 Introduction.

Mixing two or more polymers together to produce blends or alloys is a well-establishedstrategy for achieving a specific combination of physical properties (1-9). Mixing in this thesismeans break-up of droplets of one polymer to obtain a dispersed phase with a very small sizein another polymer. This type of mixing will be called blending or if the mixture formed hasimproved mechanical properties it is called compounding (1). Break-up phenomena in liquids,which are of interest for blending of polymers, were already studied by Taylor (9) in 1932.Since then blending of polymers became increasingly important. Normally blending is used tocombine the properties of two or more polymers and is performed in extruders. However it isoften found that the material properties are not as good as expected due to a poor interfacialadhesion between the minor and the major component. Therefore a need arises to look forways to improve the material properties. In this thesis the focus will be on mechanicalproperties.

It will be investigated whether the following conditions are sufficient for an improvedtoughness of the blend :

- The polymer mixture must be stable under the normal conditions for its use and no de-mixingshould occur.


11

- The dispersed phase must have a strong bonding to the surrounding polymer.

Polymers are often referred to as compatible if the mechanical properties of a blend made bymixing them has a certain set of required values. This could mean that the blend is strongenough, tough enough or (for example) ductile enough. Compatibility is also frequentlyreferred to as miscibility on a molecular scale. In this thesis blends will be referred to ascompatible when they have a desirable set of properties. It will be investigated whether theadhesion between both phases in a blend is important for compatibility. Adhesion betweenboth phases in a blend can be achieved by addition of a compatibiliser. The compatibiliseroften is a block-copolymer consisting of monomers of the major and minor phase. The size ofthe dispersed phase also decreases by addition of compatibiliser. The copolymer is transportedto the interface of the dispersed phase by means of mixing and it decreases the interfacialenergy.Preparation of the samples before feeding the different polymers usually is donestraightforwardly without giving much consideration to the sequence of feeding the differentpolymers and compatibisers. Mixing the polymers is done in extruders since extruders are ableto process and mix highly viscous polymers continuously and high shear forces can be exertedon the material. Flow in the extruder affects the shape, size, as well as the orientation of thedispersed phase in the matrix (continuous phase). This may lead to a flow induced anisotropyin mechanical and other physical properties. The morphology of the blends after blending as afunction of material and processing parameters have been the subject of many publications, inwhich often scanning electron microscopy (SEM) was used to find the morphology (2,3).In reactive compounding chemical bonds are created across the interface. This is generallydone by functionalising one of the components with reactive groups. The method mostcommonly used in reactive compounding is the introduction of carboxylic acids andanhydrides on non reactive polymers by means of radically induced graft reactions (4,5). Thesegroups react with existing reactive sites of the other component. As an alternative, bothcomponents can be functionalised with mutually reactive sites. In reactive compounding by insitu compatibilisation compatibiliser is generated during the process. This may be achieved bythe formation of cross links between the both phases.

2 Theory.

The general idea in the method proposed here is that many monomers can be dissolved in awide spectrum of polymers, even if the resulting polymers are incompatible. Therefore,monomers of the major phase are absorbed in the minor phase together with an initiator. Inthis way the monomers polymerise during the blending "in situ" in the minor phase. Due to thefact that the mixture of polymers is generally non-compatible, partial phase separation will


12

occur forming entangled micro-phases of both polymers that can act as bonds between themacro-phases.In this chapter the influence of the addition of monomer and initiator on the morphology of theblend is investigated. The order in which reactive media, like monomers and initiators, are fedduring reactive compounding in extruders, is shown to have a very distinct influence on themorphology of the dispersed phase and therefore also on the material properties. The aim isthat the initiator radical or the monomer radical attacks the polymers, which in turn maycombine to form a copolymer in situ.In order to study the effect of dissolving a reactive component in the minor phase two types ofexperiments are performed.1 : Only the initiator is dissolved in the polymer of the minor phase.2 : A mixture of liquid monomer with the initiator is dissolved in the polymer of the minorphase.

figure 1 Morphology of a blend, without the use of reactive compounding


13

If a mixture of monomer and radicals is dissolved in the minor component the decompositionof the initiator will initiate radicals on the polymer chains, as well as initiate the monomer,forming major component polymer molecules within the minor component and phaseseparation will start. The extent of this separation can easily be estimated by comparing thediffusion distance with the final size of the minor component. Using a diffusion coefficient of10-14 m2/s and a residence time of 2 minutes will lead to a diffusion distance of:

? ? ?? ? ? ? ?Dt m. . *10 14 120 2 10 6 (1)

The penetration depth is in the same order of magnitude as the size of the spheres as found infigure 1. If only initiator is absorbed in the minor phase it is expected that the resulting radicalspartially will cause crosslinking in the minor phase polymer and partially will diffuse to theinterface to form compatibiliser between the minor and major phase. If diffusion of the radicalsinto the major phase occurs it is obvious that also crosslinking may occur in this phase.

2.1 Experimental set up.

The process studied is the blending of High Density Poly-Ethylene (HDPE) with poly-styrene(PS). Monomer and initiator are dissolved in the poly-ethylene. The choice of styrene asmonomer would be the most logical one. However since the grafted PS chains formed are thesame as the polymer of the matrix (PS) they can not be seen with SEM. Therefore otherexperiments have been performed where the absorbed monomer consisted of hydroxy-propyl-methacrylate (HPMA).The material was compounded on an intermeshing corotating twin screw extruder with adiameter of 50 [mm] and a length of 1200 [mm] (APV-Baker). The initiator (di-tertiary butylperoxide) or a mixture of the initiator and the liquid HPMA were dissolved into HDPE. Thismaterial was tumble mixed with PS (10 % HDPE in 90 % PS by weight) and successively fedto the extruder. The rotation speed of the extruder was for all samples shown here 200 rpmand the throughput was 0.3 kg/min. The mixture of monomer and initiator consisted of 5 w%initiator.After extrusion the samples were immediately quenched in liquid nitrogen.

2.2 Analysis.

Differential Scanning Calorimetry (DSC) was carried out on a mettler DSC TA4000 ThermalAnalysis System connected with a TC11TA processor and analysed with a method describedby Batch et al. (7). Extraction was done with a Soxtec system HT 2, 1045 Extraction Unit,Tecator Extraction thimbles (33*80 mm, Schleicher & Schuell). For the analysis Scanning


14

Electron Microscopy (SEM) was used in order to determine the morphology. Examination ofthe fracture surfaces with SEM shows whether a specimen breaks either by tough (ductile) orbrittle fracture or by some intermediate behaviour.

3 Experimental results.

In the first step only initiator is dissolved in polyethylene and blended into a matrix ofpolystyrene. Figure 2 shows the effect of the peroxide only, which was well known to causecrosslinking.

figure 2 Morphology of a PS/HDPE blend ; initiator was added in HDPE

Note that in the SEM photographs um means ? m = 10-6 m. Several spheres have a hole thatcan only be due to the effect of the cross linking agent. Because of the small length that theinitiator could travel due to the low diffusion constant the reaction will mainly occur in thepolyethylene (which is also shown in figure 6a). The resulting large macromolecule is more or


15

less rigid. Because of crosslinking the normal shrinkage (?2%) of HDPE is not uniform in thedispersed phase resulting in the peculiar shape shown in figure 2.In an additional experiment a blend of HDPE/PP was produced with reactive compounding forwhich a mixture of initiator and monomer (MAH) was absorbed in the PP. After extrusion atotally different morphology was observed as shown in figure 3. In this figure the dispersedphase is polypropylene (PP) which is connected to the matrix phase HDPE forming a verystable morphology.

figure 3 The morphology of a HDPE/PP blend (monomer : MAH)

However most of our experiments were done with a blend of PS/HDPE with HPMA dissolvedin HDPE. The resulting blend is shown in figure 4 where several spheres contain tails. Since


16

no pull out of the tails have occurred we conclude that the tails are connected to the dispersedphase. Some tails are also connected to the surrounding matrix. Some spheres seem to containa small, perhaps broken, tail.

figure 4 PS/HDPE blend, HPMA as monomer in HDPE

figure 5 Small tails sticking out of the dispersed phase


17

Due to the limited residence time in the extruder and the small diffusion coefficient of largegraft copolymers (formed by the reaction of monomer in the dispersed phase) phase separationof the tails and the spheres in figure 4 and figure 5 will only be partial. Details of the evidenceof the existence of a graft copolymer formed in the dispersed phase is shown in figure 5 wheretails of various shapes can be seen.

4 Concentration profiles.

Mass transfer out of the dispersed phase occurs after melting and blending in the extruder. Bysimple modelling it is possible to determine whether the polymerisation mainly occurs in thedispersed or in the continuous phase. The following two differential equations, containingdiffusion and a first order reaction are solved for a sphere.

??

??

??

??

??

??

Ct

Dr r

rCr

kC

r a

Ct

Dr r

rC

rkC

a r

A A AA

A A AA

? ?

? ?

??

? ?? ?

? ? ?

22

22

0

( )

( )

( )

( )

(2)

The ratio of the concentration of initiator and monomer at the interface is found by Henry'slaw.

CC

mA

Ar a

??

?

(3)

These partial differential equations are solved with the method of Baker and Oliphant [6]. Theother boundary conditions are :

C C

r a t

C

a r t

A

A

?

? ? ?

?

? ? ? ?

0

0 0

0

0

( , )

( , )

'

(4)

The flux at the centre of the dispersed phase is zero and therefore the concentration profile hasrotational symmetry. The diffusion coefficients used are determined experimentally by themethod described in chapter 5.


18

figure 6a The concentration profile of the initiator, m = 0.2.

The concentration outside the dispersed phase is very small due to a very small diffusioncoefficient and a small distribution coefficient (m) and therefore not visible in figure 6a. Thedecomposition kinetics of the initiator (Trigonox 145, AKZO-NOBEL) is given by :

k T e RT( ) .(

. *)

? ? ?

?

1 9 1015136 6 103

(5)

Diffusion of the initiator hardly has any influence on the initiator concentration in the dispersedphase, figure 6a. The decomposition reaction of the initiator does have a substantial influenceon the initiator concentration as can be seen from the decrease of Ci in time.


19

figure 6b The concentration profile of the monomer, m = 1.

A different picture is obtained when the concentration of monomer is observed. The diameterof the sphere is 10 mm in figure 6b where the concentration of monomer decreases 40 molewithin 2 minutes. The slope of the monomer concentration gradient Cm is very steep if thediffusion coefficient is very small. Note that the diffusion coefficient of the monomer is muchlarger than the diffusion coefficient of the initiator.Since the concentration of monomer and initiator is known the molecular weight distributionof the copolymer formed can also be calculated (see also chapter 5), figure 6c.


20

figure 6c The molecular weight distribution at three positions.

The ratio of monomer/initiator increases during the reaction because of the relative fastdecomposition of the initiator and because of diffusion of monomer and initiator out of thedispersed phase. The molecular weight distribution formed at increasing distance from thecentre of the dispersed phase also has shifted in comparison to the molecular weightdistribution formed inside because of a decreasing initiator concentration. The averagemolecular weight distribution as modelled increases with increasing distance from the centre ofthe dispersed phase. The three different molecular weight distributions are shown in figure 6c.

4.1 The materials formed in the dispersed phase.

It is clear from the SEM pictures that adding monomer to the minor phase results in a differentmorphology than that without monomer addition. Clearly visible tails originating from phaseseparation during the blending process can be detected. It is plausible from quantityconsiderations that the tail consists of the absorbed monomer, polymerised during theextrusion process and the spheres consist of the minor phase polymer. Proof of this contentioncan be found in figure 7.


21

figure 7 Morphology of the blend after treatment with xylene.

It can also be reasoned that the tails initially have grown mainly inside the dispersed phase andthat the size reduction of the minor component accelerated the separation process. Thetemperature profile and the position of the kneading section in the extruder will clearlyinfluence the part of the monomer and initiator that reacts in the dispersed phase and the partthat diffuses out of the dispersed phase and reacts in the matrix phase. From these and othercalculations we found that, if the dispersed phase is large enough, most of the monomer reactsin the dispersed phase.The sample, shown in figure 7 was treated with xylene for 20 seconds. It is clear that the tailsin this figure consist of the polymerised monomer since HDPE dissolves more easily in xylenethan PHPMA. Figure 8 shows the sample after treatment with chloroform for dissolvingPHPMA. Here it is clearly visible that polystyrene (the matrix) and PHPMA is extracted bythe chloroform. The structures in figure 8 are HDPE, which is not soluble in chloroform.During mixing in the extruder HDPE is deformed forming long stretched structures as shownin this SEM photo.


22

figure 8 Morphology of the blend after treatment with a solvent

figure 9 The conversion of S versus time (s)


23

Figure 9 shows the differential Scanning Calorimetry (DSC) data for the polymerisation ofStyrene in HDPE. This is much slower as polymerisation from pure monomer. Attemperatures of 130 oC the conversion of BMA to PBMA extends to 99 % within one minute.

The properties of the reactive blends will be given in chapter 9 and 10 which must becompared with the properties of pure PS in table 1.

Property Elongation at break Toughness (MPa) Stress at maximumload (MPa)

pure PS 2 % 0.4 40

table 1 The properties of pure PS (for references).

5 Conclusions.

Contrary to normal reactive compounding, where the reactive substances, like initiators, arefed separately from the polymers into the extruder, dissolving initiator and some monomer intothe minor polymer component leads to some unexpected results. Due to the usually very lowdiffusion coefficient, diffusion out of the dispersed phase will initially be small and thedissolved monomer will polymerise upon heating. This results in a partial phase separation.Moreover, apart from free homopolymer molecules of the major phase also graft copolymerswill be formed through combination of the growing chains with radicals on the polymer of theminor component. In both cases the partial phase separation will assure a good bondingbetween the minor and the major phase in the blend.The dissolved material can improve the blending considerably; the dispersed phase consists ofsmall spheres, in the range of 10-6 m and the reacted monomer manifests as small "tails". Themorphology obtained by SEM shows some structures that have not been reported so far.

Nomenclature.

a Radius of the spherical minor component [m].C Concentration [mole/m3].D Diffusion constant [m2/s].d Size of the dispersed phase [m].r Radial coordinate [m].R Gas constant (8.314) [J/mole K].k Reaction velocity [1/s].m Distribution coefficient [-].


24

M Monomer concentration [mole/m3]t Time [s].

Subscripts.

a Radius of the dispersed phase.A Component.0 At start of experiment.

References.

1. D.J. van der Wal, R. Hettema, L.P.B.M. Janssen, Operation for the manufacturing of mixedpolymers, Patent application number 1000994.2: S. Wu, Polymer, 26, 1855, (1985).3: L.A. Utracki, Inter. Polym. Proc. ,2, 3 (1987).4: V.J. Triacca, S.Ziaee, J.W. Barlow, H. Keskkula and D.R. Paul, Polymer, 32, 1401, (1991).5: K.J. Ganzeveld, and L.P.B.M. Janssen, Pol. Eng. Sci. 32, 467, (1992).6: G.A Baker, and T.A. Oliphant, Quart. Appl. Math. , 17, 361, (1960).7: G.L. Batch,. and W. Macosco, J. Appl Polym. Sci. , 44, 1711 (1992).8: M. Lambla, M. Seadan, Pol. Eng. Sci. , 32, 1687, (1992).9: G.I. Taylor, Proc. Roy. Soc. London, A138, 41 (1932).

3D modelling of the flow in the kneading section, chapter 2

25

CHAPTER 2 THREE-DIMENSIONAL FLOW MODELLINGOF A SELF-WIPING COROTATINGTWIN-SCREW EXTRUDER, THE KNEADING SECTION.

Abstract.

The average values of shear and elongation rate in kneading elements in anintermeshing corotating twin screw extruder depend strongly on processingparameters. The shear rate is found to be much larger than the elongation rate, even inthe kneading section. The ratio between the pressure drop and the viscosity isconstant. The results of the modelling will be used in the calculations in chapter 6, 7and 8. However it must be kept in mind that these results are only valid within thelimitations of the 3D modelling.

1 Introduction.

Controlling reactive compounding as described in chapter 1 can only be achieved if theflow characteristics and the temperature in the kneading and transporting elements isknown. Therefore these will be investigated in chapter 2, 3, and 4. Calculations of theflow profile in kneading elements in the intermeshing corotating twin-screw extruderhave been carried out by Yang et al (1). They show that the geometry of the volume inwhich the fluid flows changes during the rotation of the screw, as is described insection 3.1. Here a three-dimensional modelling of the flow profile in the kneadingsection of the intermeshing corotating twin-screw extruder is presented. By far themajority of the studies on the modelling of the twin-screw extruder have concentratedon 2D or quasi-3D modelling of the flow in the transport section in extruders (1- 3).In the intermeshing twin-screw extruder one screw wipes its mate and vice versa. Theself-wiping action makes the twin-screw extruder attractive for handling manypolymers. It eliminates dead spots where polymer can collect, stagnate, and degrade(4). In the kneading section the material flows from one element to the next. Usuallythe co-rotating twin-screw equipment comprises of a housing (called the barrel) andtwo identical parallel shafts equipped with identical screw or paddle elements. Thenumber of tips of the paddles can be chosen but the cross section of a paddle with 1, 2,3 or 4 tips must meet certain design specifications. These are well known and muchwork has been done by Booy (4) on the geometrical constraints of corotatingextruders.


26

The geometry of the kneading element in this work is shown in figure 1. Thecomputational mesh used (figure 1b) is part of the geometry as found in the corotatingtwin-screw extruder in figure 1a. The geometry will be described in more detail insection 3.1. The 3D flow profile is calculated with the boundary conditions given insection 3.2.

A number of assumptions will be made :

-The flow is laminar, isothermal and stationary.-The fluid is incompressible, Newtonian and, where relevant, has a viscosity of 100Pa.s. Although the Newtonian model is an obvious simplification for many situationsoccurring in practice, it is expected to provide a valuable first insight into the flowphenomena.-The elements are completely filled.-The outflow profile of an element is transformed into the inflow profile of the nextelement.

The backflow volume is an important parameter for mixing and it is computed byintegration of the axial (down channel) velocity component over the part of the cross-section where these velocities are negative. The pressure difference is dealt with insection 4.3. The shape of the flow profile, the backflow volume, the shear andelongation rate are calculated. The elongation and shear rate are defined in section 4.4.In this work, within the limitations of the calculations, results are obtained for theshear- and elongation rate as a function of rotation speed and throughput.

2 Mathematical method.

As mentioned before the simulation is based on a stationary model. The equations tobe solved are those for isothermal laminar flow of a Newtonian, incompressible fluidwithout body forces :

conservation of mass : div v→

= 0 (1)

conservation of momentum :

ρ( . )v v p div t→ →

∇ + ∇ = (2)


27

where p denotes the pressure, ρ the density, v→

the velocity, and t is the Newtonian

fluid stress tensor given by :

t v vT

= ∇→

+ ∇→

η( ) (3)

where η is the viscosity. The equations 1 and 2 are discretized. The Penalty method,described in Cuvelier et al (5), is used for the discretization of the incompressibilityconstraint. The continuity equation is adapted by adding a small term containing thepressure :

ε εp div v small+→

= 0 : (4)

By this method the pressure, p, is eliminated from the momentum equation. Thevelocity and pressure are then separated. The equations, after discretization byGalerkin's method are :

S u N u u L M L u

p M L u

TP

P

→ → → →

→ →

− − =

= −

−

−

( )1 1

1 1

0ε

ε

(5)

where S is the stress matrix, u→

the vector of the unknown velocity values, N u u( )→ →

the discretization of the convective terms, L the divergence matrix, Mp the pressure

mass matrix and p→

the vector of the unknown pressure values. In the numerical

solution, the non-linear terms in equation 4 and equation 5 are linearized with thePicard linearization and Newton iteration. In solving the 3D Navier Stokes equations atriquadratic isoparametic brick element is used. The velocity is approximated by a fulltriquadratic approximation based on the 27 nodes of an element. The pressure isapproximated linearly and is discontinuous.The numerical error in the velocity decreases quadratically with the mesh size, but theresults for the pressure are only first-order accurate (see Cuvelier et al (5)). However,the finite element mesh used in our computations has been chosen sufficiently fine toguarantee satisfactory overall accuracy. We emphasise that the Penalty functionmethod allows the extruder throughput to be prescribed whereas the required pressuredrop follows from the computations.

30 modelling of the flow in the kneading section, chapter 2

3 Definition of the problem.

3.1 Geometry and mesh.

During one rotation the geometry of the volume in the kneading section changes, as

shown in figure la. Changing the geometry and boundary conditions at every time

step in the calculations would be too time consuming for a fully three-dimensional

modelling. However in figure la it can be seen that part of the geometry remains the

same during a large part of the rotation.

j@re la Several orientations of the kneading paddles, cross set tion

The geometry that is used in these calculations is based on equations given by Booy

(4) and shown in figure lb. In order to obtain convenient boundary conditions a newco-ordinate system is chosen. In the geometry in figure lb the screw is at rest while

the barrel wall moves. The geometric parameters used in Booy’s equations (4) are Cl

and R,, where Cl (40 mm) is the distance between both axes of the screws and R,(25 mm) is the radius of the screw. The kneading elements have a width of 14 mm.

Screw diameter (= 2*R,) 0.05 [m]

Screw length 1.25 [m]

PC= Cl/R, 1.56

n 2

table 1 Extruder specifications (17)

28


30

3.2 Boundary conditions.

The boundary conditions are as follows: on the screw a zero velocity, on the barrel atangential velocity according to the rotation speed with a zero axial velocity (both dueto the no-slip condition).

figure 2 The transformation of the outflow profile to the inflow plane of the next element


31

On the inflow plane of the first kneading element we prescribe a uniform axial velocityfor the entire region. Part of the outflow plane is blocked because of the second screwelement, as shown in figure 2 for the case of a 900 stagger angle. In the non-blockedparts of the outflow plane no velocity is prescribed, but a free stress boundarycondition is imposed instead. The inflow plane of the second element is partiallyblocked by the first element (calculations are done for successive elements). The inflowvelocities to be prescribed in the two non-blocked areas follow from the transfer of theoutflow profile of the previous element, as indicated in figure 2. The boundaryconditions on the outflow plane are the same as those for the previous element. In thisway an arbitrary number of kneading elements can be joined together.The Reynolds number values used are small (Re @ 0.04). The materials usuallyprocessed in the corotating twin-screw extruder are polymers with high viscosity. Theviscosities vary, since during processing the polymers have changing, though highviscosity, due to temperature differences. Because the flow is assumed to beisothermal, the viscosity is assumed constant in the kneading element. However it ispossible to change the viscosity in the next kneading element which is of interest sincethe viscosity might influence the flow profile in the extruder, section 4.6.

4 Results.

First the symmetrical case with a stagger angle of 90 ° between the kneading elementsis considered, figure 1b. Calculations are performed for several rotation speeds,throughputs and viscosities, as defined in the previous section. The equations, given tofit the graphs, represent the results within 5 % (mean values are always calculated forthe second element).

4.1.1 The axial velocities.

In figure 3, axial velocity profiles in the first and the second kneading element areshown at five axial positions along the kneading element.


33

To characterise the flow profile the backflow volume will be used as a measure of theinfluence of the various extruder parameters on the flow profile. The backflow volumeis calculated at a number of axial positions along the kneading element, by integrationof the negative axial velocities in the transverse plane.

figure 4 The backflow volume along 8 kneading elements, N = 100 [rpm],Q = 80[ml/s], stagger angle : 90 0

The graph in figure 4 shows the absolute backflow, Qb , when eight kneading

elements are placed in series. The maximum values always appear at the outflow planewhich coincides with the inflow plane of the next element.

figure 5 The backflow volume, QB, as a function of rotation speed, length : 14 mmseveral throughputs ; stagger angle : 90 0


36

presence of the next element in the outflow profile causes a not completely linearpressure drop over the length of the kneading element.

figure 8 The pressure averaged over the cross section for five axial coordinates

The influence of rotation speed and throughput, for the pressure difference over oneelement, is illustrated in figure 9 and expression 8. The pressure difference, ∆P , isdefined as the difference between the average pressure in the inflow plane and theoutflow plane.

∆

∆

P c Q

pressure drop / kneading element

P [ m / s ]

c 408 . 5 10 [ kg / m s]

3

6 4

= ⋅

= ⋅

[Pa ], Q(7)

In this expression the constant c is dependent on the viscosity, the cross-sectional area,A, and the length of the kneading element, for Re = 0.039 : c f ( A l= −η, ,2 ) , which is

confirmed by calculations, performed in the geometry of several extruders withdifferent diameters, for which ∆P is found to scale with A-2 . It is interesting to notethat the pressure drop, in this particular case with stagger angle 90 0, is not influencedby the rotation speed. This is due to the lack of axial dragging action of the staggeredelements on the fluid. In those cases in which the stagger angle is different from90 0 the rotational speed has been found to influence the pressure build-down.


37

figure 9 The pressure drop over one kneading element ; stagger angle 90 0

4.4 The shear and elongation rate.

The two components of the deformation, the shear rate γ& and the elongation rate ε&,

are calculated. These quantities are computed with (6):

( )

)/())(

)()((

:21

222

222

wvuwvvw

wuuwvvuvwwvvuu

vv

vv

vv

yz

xzxyzyx

T

++++

++++++=

∇+∇= ρ

ρ

ρ

ρρρο

ε

(8)

γ⋅

= ∇→

+ ∇→

∇→

+ ∇→

= + + + + + + + +

2

2 2 2 2 2 2 2 2 2 1 2

( ):( )

(( ( ) ( ) ( ) ) /

v vT

v vT

ux vy wz uy vx uz wx vz wy

(9)

The integral mean values of the rates in each cross-section of the channel, γo

and εo

,

and the integral mean values for the complete volume, are also calculated for variousrotation speeds and throughputs (figure 10), in the kneading element.The increase of shear- and elongation rate due to variation of the rotation speed iscaused by two effects :-the influence of the backflow-the increase in transverse velocities.

Both effects cause an increase in local velocity differences in the flow profile andtherefore an increase in shear and in elongation rate.


38

For the case of a stagger angle of 90 0 the following equations have been fitted for themean shear and mean elongation rate as a function of rotation speed and throughput.

dependence on N and Q

Q A N

Q

AQ

N Q

N rpm Q ml s

:

. . (( )) ( )

. ( )

. ln( )

. .

:[ ], :[ / ]

γ

ε

=

=

= + ⋅ − − ⋅ −

+ ⋅ −

= ⋅

= ⋅ + ⋅

o

o

24 56 0 24 5 25

0 98 5

0 0725

0 0666 0 0337

1

1

(10)

figure 10a The average shear rate as a function of rotation speed and throughputFrom figure 10 a and b, it is clear that the rotation speed has a large effect on theshear- and elongation rate. In the limit for very large rotation speeds the shear fordifferent cases of throughput has the same value. It is concluded that in this limit theeffect of the throughput on the shear rate is small compared with the effect of therotation speed.


39

figure 10b The average elongation rate as a function of rotation speed and throughput

4.5 The influence of the stagger angle between the kneading elements on theflow.

In many geometries used in extruder technology the kneading section is designed withseveral configurations. Values of 30, 45, 60 o for forward pitch and 120, 135 and150 0 for backward pitch are commonly used as the stagger angles between thekneading paddles. For non-zero stagger angles part of the outflow plane in thegeometry of the kneading section is blocked.


40

figure 11 The pressure drop over one kneading element versus stagger angleN = 100 [rpm] ; Q = 80 [ml/s]

The influence of the stagger angle on the pressure drop over one kneading element isshown in figure 11. In most cases the pressure drop is found to increase when thestagger angle between the kneading elements increases.The elongation- and shear rate is calculated from the flow profile for different anglesbetween the kneading elements, figure 12. The size of the blocked part of the planegradually changes with increasing angle. Since the size of this plane reaches amaximum at 90 0 this influences the shear- and elongation rate as is visible in figure 12.

Dependence of the shear rate on the stagger angle,

exp( . )

90 150

4 58 1013

°< <

= ⋅ ⋅ ⋅= =

−

ϕ

γ γ ϕ

o

o o

(11)


41

figure 12 The shear rate versus stagger angle N = 100 [rpm], Q = 80 [ml/s]

A reasonably accurate value of the shear in the case with a stagger angle larger than

90 0 can be calculated by using the shear rate (γ&=) (equation 10) in equation 11.

The absolute backflow, Qb , has a minimum in the case of a stagger angle larger than

90 0 where the size of the blocked part of the outflow plane has a maximum, figure 13.The backflow volume is shown for varying stagger angles between the kneadingelements, in the case of N=100 [rpm] and Q=80 [ml/s]. For a better understanding ofthe influence of the blocked part of the plane on the flow profile the following must bekept in mind :As mentioned, the flow profile has a large backflow volume at small or large staggerangles. Changing the stagger angle means moving the blocked part of the outflowplane from a place where a negative outflow is found to a place with a positive outflow(or vice versa). The outflow plane is blocked at the position where normally thevelocities in outflow profile are negative when : ϕ = 15°, 30°, 45°, and 60°. Usingbackward staggered kneading elements on the other hand, the next screw elementblocks the positive outflow area, leaving room for a larger backflow to developϕ = 120 135 150 1650 0 0 0, , , . In this case the part of the outflow plane where normally the

axial velocities are positive is blocked and a larger backflow volume develops,figure 13.


44

DP = 4.085×Q×h [Pa] (12)Q [ml/s], h [Pa.s]

With equation 12 the pressure drop can be calculated. This may be of use in themodelling of the kneading section of reactive extrusion and mixing in corotating twin-screw extruders.

figure 16 The pressure drop for varying viscosities, the stagger angle is 90 °.

The influence of the viscosity on the shear- and elongation rate in the range from 100down to 0.01 [Pa s] is small. At high viscosities, the convective terms in the NavierStokes Equations are small, leading to a simple Stokes flow, in which there is no moreinfluence of viscosity. The shear rate decreases and the elongation rate increasesslightly with increasing viscosity, as shown in figure 17. At a viscosity of 1 [Pa.s] theserates have reached their limit values corresponding to Stokes flow.


45

figure 17 The shear and elongation rate for varying viscosities ; a, Shear rate ; b : Elongation rate

4.7 The adiabatic axial temperature rise.

The viscous dissipation due to the shear acting on the fluid causes a temperature rise.The shear rate as calculated in section 4.4 can be used to calculate the viscousdissipation for the Newtonian case. The viscous dissipation can be calculated from theaverage value of the shear rate and it is assumed that no heat leaves the extruder viathe walls. The adiabatic temperature rise has been calculated with Cp = 2000 [J/kg K]

as the specific heat of the material. The adiabatic temperature rise has been calculatedfrom the viscous dissipation W. To calculate the viscous dissipation the viscosity hasbeen calculated for the Newtonian case.

∆ TW

Q C p=

ρ(13)

In figure 18 the temperature rise (° C) over one single kneading element is shown as afunction of the rotation speed, for varying throughputs. The temperature increase overone short kneading element is small because the viscosity chosen here is 100 Pa.swhich is a relative small value.


46

figure 18 The adiabatic temperature rise as a function of the rotation speed

4.8 Experimental validation.

The pressure drop as calculated in section 4.3 is measured in an intermeshingcorotating twin-screw extruder. The experimental set-up is described in chapter 6 andthe experiments are done with polystyrene (SHELL, PS 7000), 7 kneading elementsand a barrel temperature of 200 0C . For all throughputs the viscosity was close to 180Pa.s at the rotation speed, throughput and temperature (measured with an IRthermometer) in the kneading section.

figure 19 The measured and calculated pressure drop versus throughput


47

The computed pressure drop is shown in figure 19 to be comparable with the measuredvalues, within the experimental error of 5 %. The temperature rise due to the viscousdissipation is calculated in (9) with the results for shear rate given in section 4.4. Sincein (9) it is found that the calculated temperature rise due to the shear is comparablewith measured values, within the experimental error (10 %) it can be concluded thatthe results for shear rate, found here, are also reasonable.

5 Discussion and conclusion.

The pressure gradient in the kneading elements is only found to be independent of therotation speed for a stagger angle of 90 0 . For other stagger angles pressure drop isinfluenced by rotational speed as it is also the case for transporting elements ascalculated in the next chapter. In the transporting element the pressure gradient isfound to be dependent on the rotation speed.

A number of conclusions can be drawn from our results :

-The average values of shear- and elongation- rate in kneading elements dependstrongly on processing parameters. Since mixing is dependent on the shear- andelongation rate (9) the results presented in this chapter can be used when two polymersare mixed in a corotating twin-screw extruder.-The shear rate is found to be much larger than the elongation rate, even in thekneading section.-The ratio between the pressure drop and the viscosity is constant.-The graphs and equations found can be used in other computer calculations to findparameters of interest, such as distribution in residence times (12) and axialtemperature profiles, in the kneading section. It must be kept in mind however that thisis only valid within the limitations of these calculations. A larger backflow volume willlead to a larger Residence Time Distribution. Variation of the backflow is found whenthe throughput or rotation speed is varied.-In the case of reactive extrusion or reactive compounding the expressions found canbe used in modelling of parameters, such as the pressure drop, to confirm experimentaltrends.The results in (13) show the resemblance and differences between transporting(chapter 3) and kneading elements. Here we find that the drop of pressure in the 90°kneading elements is independent of N and for the transporting elements it is foundthat the influence of N is prominent. Consequently, the length required for the build-upof pressure (and, so the residence time distribution) can be modified by changing N,


48

which will not influence the drop of pressure in the kneading elements with a staggerangle of 90°.The influence of the viscosity on the axial gradient of pressure is important (and∆P cη = onstant is found) and is similar for the transporting and kneading elements.

Nomenclature.

A : Area through which the fluid in the kneading section flows. [m2].A1 Fitted parameter.Cl: Centreline distance of the twin-screw extruder. [m].

d : Diameter of the screw [m].h : Channel depth without clearance. [m].L : Divergence matrix.l : Length of one kneading element (14 mm). [m].Mp: Pressure mass matrix.n : Number of screw threads. [-].N : Rotation speed. [rpm].

N u u( )→ →

Discretization of the convective terms.p−

: Pressures unknowns. [Pa].

P : Pressure. [Pa].∆P: Pressure drop over one kneading element. [Pa].ϕ : Stagger angle between the kneading paddles. [°].

Q : Throughput of the extruder. [ml/s].Q

B: Integral of the axial negative flow volume, also called backflow.

Volume, on a cross section. [ml/s].Q

B*: Q

B/Q : Relative backflow volume, on a cross section. [-].

Qr : Recirculation flux . [ml/s].Rs: Radius of the screw. [m].

Re : Reynolds number Re =. rvd/h [-].S : Stress matrix.∆T Temperature rise per kneading element, η=180 [Pa.s]. [oC].v→

: Velocity vector (with components u, v, w). [m/s].W : Width of the kneading paddle. [m].x, y : Transverse coordinates. [m].z : Axial coordinate. [m].γo

Local shear rate. [s-1].

εo−

Local elongation rate. [s-1].


49

γ=o

Shear rate averaged over the volume , equation 10. [s-1].

ε=o

Elongation rate averaged over the volume, equation 10. [s-1].σ Stress. [s-1].η : Viscosity. [Pa.s].ρ : Density of the fluid. [kg/m3].ρc : Ratio between centreline distance and radius of the screw [-].

References.

(1) H. H. Yang and I. Manas-Zlockzower, Polym. Eng. Sci., 2. 1411 (1992).(2) Y. Wang, J. Non- Newtonian Fluid Mech, 32, 19-32 (1989).(3) H. Werner, K. Eise, SPE ANTEC Tech Papers, 37 (1979) 181.(4) M.L. Booy, Polym.Eng. Sci. , 18 , p.973 (1978).(5) C. Cuvelier, A. Segal and A.A. van Steenhoven: Finite elements and Navier-Stokesequations, D. Reidel Publishing Co., Dordrecht, (1986).(6) J.M. Ottino, Chem. Eng. Sci. 35, p 1377 (1980).(7) K.J Ganzeveld, E. J. Capel, D.J. van der Wal, L.P.B.M. Janssen, Chem. Eng. Sci. (10), 1639 (1994).(8) K.J. Ganzeveld, LP.B.M. Janssen, Can. Journ. Chem. Eng., 71(1993).(9) Chapter 7 of this PhD thesis.(10) D. J. van der Wal, L.P.B.M. Janssen, Proc. ANTEC 94 conf. 1-5 may 1994 SanFransisco, Vol 1 P 46-49 SPE (1994).(11) D. Goffart, D.J. van der Wal, E.M. Klomp, H.W. Hoogstraten, L.P.B.M. Janssen,L. Breysse, and Y. Trolez, Polym Eng. Sci, Polym. Eng. Sci. , 7, 901 (1995).(12) Pinto and Tadmore, Polym.Eng. Sci., 5 ,10 (1970).(13) J. L. White, W. Szydlowski, K. Min, M. Kim, Advances in Polymer Technology,7 3, 295 - 332, (1987).(11) V. Bordereau, Polym. Eng. Sci.., 32 , 1846.(1992).(12) H.E.H. Meijer, P.B.M. Elemens, Polym. Eng. Sci, 28 , 275 (1988).(13) P.H.M. Elemans, Modelling of the processing of incompatible polymer blends,PhD thesis, Technische Universiteit Eindhoven (1989).(14) Z. Shi and L.A. Utracki, Polym. Eng. Sci., 32, 1834 (1992).(15) Z. Chen and J.L. White, SPE ANTEC Tech. Papers, 1332, (1992).(16) M. Fortin, Old and new finite elements for incompressible flows, Int. J. for Num.Meth, In Fluids, 347-364, (1981).(17) M.L. Booy, Polym. Eng. Sci., 18, 973 (1978).

3D modelling of the flow in the transporting section, chapter 3

51

CHAPTER 3 THREE-DIMENSIONAL FLOW MODELLINGOF A SELF-WIPING COROTATING TWIN-SCREWEXTRUDER, THE TRANSPORTING SECTION.

Abstract.

For understanding reactive compounding as described in chapter 1 three dimensionalflow-calculations of the fluid in the extruder are very useful. Therefore the results ofthese calculations will also be used for an improved understanding and process controlof the method developed in chapter 1. The influences of rotation speed of the screw(N), the throughput (Q), and the pitch of the screw (ϕ) on the build-up of pressure, theflow, the backflow volume and the shear and elongation rates have been modelled. It isfound that the shear and elongation rate are linked to the backflow and the pressurebuild-up which are, mainly, connected to the rotation speed. These parameters (alongwith the throughput) influence the mixing properties of the transporting elements andthe build-up of pressure necessary to pass through the kneading elements.

1 Introduction.

For controlling reactive compounding as described in chapter 1 we also need the flowcharacteristics and the temperature in the transporting elements. Therefore in thischapter we will focus on transporting elements in twin-screw extruders. This type ofextruder is used extensively in polymer processing. The transporting elements aregenerally considered for the action of building up pressure which pushes the polymerthrough the kneading elements, and the heating of polymers. In the twin-screwextruder, the channel of the transporting elements is interrupted by the flights of theother screw. The intermeshing zone is therefore of importance in the mixing. The self-wiping intermeshing twin-screw extruder is very attractive because of its wiping actionwhich provides the elimination of the dead zones. It is often said, but not proved, thatelongation affects mixing in the extruder more than shear. The extruder parametersinfluence the process optimisation, the residence time distribution and the screwdesign. It is therefore necessary to calculate the flow profile to find the shear andelongation rates, the axial (down-channel) pressure gradient, the backflow and to seehow these parameters vary with rotation speed, throughput, helix angle and viscosity.


54

momentum equations: ( ) tdivpvv =∇+∇⋅ρρ

ρ (2)

with the velocity, v, the pressure p, and Newtonian fluid stress tensor( )Tvvt

ρρ∇+∇=η . Equations (1) and (2) are discretized. The Penalty method

(Cuvelier et al. (3)) is used for the discretization of the incompressibility constraint.The idea of this method is to perturb the continuity equation with a small term containing the pressure:

0 =+ vdivpρ

ε (3)

with ε a small parameter. The main advantage of this construction is that p can beeliminated from the momentum equations. Thus the calculations of the velocity and thepressure are now separated.

After discretization by Galerkin's method, the non-linear equations for the solution ofstationary laminar flow of incompressible liquids are:

( ) 01 1 =−+ − uLMLuuNuS p

T ρρρρ

ε(4)

uLMp p

ρρ 11 −−=ε

(5)

with S the stress matrix, u→

the vector of unknown velocities, ( )uuNρρ

the discretizationof the convective terms, L the divergence matrix, M p the pressure mass matrix and p

ρ

the vector of unknown pressure values. In the numerical solution process, thenonlinear terms in (4) and (5) are linearized (Picard linearization and Newtoniteration).To solve the 3D Navier-Stokes equations, the Sepran (1) finite element package uses atriquadratic isoparametric brick element (Cartesian co-ordinates). The velocity isapproximated by a full triquadratic approximation based on the 27 nodes from anelement. The pressure is approximated linearly and is discontinuous from one elementto the next.The numerical error in the velocity results decreases quadratically with the mesh size,but the results for the pressure are only first-order accurate (see Cuvelier et al. (3)).However, the finite-element mesh used in our computations has been chosensufficiently fine to guarantee satisfactory overall accuracy. We emphasise that thepenalty function method is particularly suitable for our study since it allows theextruder throughput to be prescribed whereas the required pressure drop follows fromthe computations.


55


Geometry and mesh.

The 2D geometry of a cross section is based on an adaptation of Booy's (4) results byDenson and Hwang (5), who modified Booy's expression to account for the effect ofhelix angle ϕ and who included a term to account for the flight width. Therefore, the

cross-section is defined by equations that give the variation of the channel depthwithout clearance. In the 3D geometry used, the curvature of the screw and barrelhave not been neglected.

To simulate the complete channel of the transporting elements an iterative process withtwo different geometric problems was developed as shown in figure 1. The calculationsare done successively for problems Pb1, Pb1, Pb2, Pb1, Pb1, Pb2, etc. This processallows us to use a minimum number of elements and enables us to extend the length ofthe channel as far as we want. As shown in figure 1 and figure 2 (with Vb the velocitytangent to the barrel) a throughput is fixed at the inflow of the first Pb1 with the samedirection as the extruder axis. In this process, the values are taken at the end of eachgeometric problem and transferred to the beginning of the following. The first Pb1 isnot included in the iterative process because it is only used to establish an entry flowprofile for the subsequent iterations.

Pb1 represents a quarter of one screw rotation and Pb2 the intermeshing area with twochannels shifted in order to model the zig-zag motion of the fluid when it passes fromone screw to the other. Note that in Pb2 the cross-sections along the channel areparallel and not perpendicular to the curved axis as for Pb1, thus facilitating thegeneration of a computational grid for Pb2. In the intermeshing region of thecorotating twin-screw extruder the flight of one screw blocks part of the channel of theother screw. This small part of the cross-sectional geometry as used in our modelling isshown in figure 3, where it is depicted separately from the remaining cross-sectionalmesh.


57

provide a valuable first insight into the flow phenomena. Non-Newtonian fluidbehaviour should be incorporated in future work.A5. The rotation speed has a tangential direction to the barrel having an angle to thechannel axis (ϕ).

The boundary conditions used are the following:B1. A throughput Q is imposed on the plane inflow velocity profile of the first Pb1before the iteration (see Geometry and mesh).B2. A velocity Vb (related to the rotation speed N as seen in figure 2) is prescribed onthe barrel. On the screw surface and the small part of the mesh representing the screwflight that is blocked, see figure 3, the velocity is taken zero.B3. A free-stress condition is imposed at the outflow plane (Cuvelier et al. (3)).

4 Results and discussion.

Results will be presented for the flow profile, the pressure, the shear and elongationrates, while varying the throughput and the rotation speed for a fixed geometry. This isdone for two different helix angles. Because of a good convergence of thecomputations and of a fast establishment of the flow profile in the first Pb1, only oneiteration was sufficient. The values for N are 50, 150, 300 and 400 [rpm] and for Q 5,30 and 100 (ml/s). A backward transporting element is also presented with N varying,Q = 30 (ml/s) and ϕ = 10.9°. The influence of the viscosity is treated in the lastsection.

4.1 The throughput.

The two throughputs Qc and Qe are given in Table 1 for each of the two helix anglesconsidered. Qe corresponds to the calculated extruder throughput, which is slightly

different from the prescribed throughput Q because of the numerical discretization andQc is the throughput related to a stationary channel. Note that Qc varies when Qe isconstant because N varies. Indeed, the rotational speed imposed on the barrel has acomponent parallel to the axis of the channel which contributes to the generalthroughput in the channel.


64

anymore and a negative pressure gradient may occur. The larger ϕ will be, the smaller ∆P will be, which is one of the reasons why small ϕ is used in front of the kneadingelements and the die. Indeed, when the cross-section of the channel is smaller (ϕsmaller) the material requires a larger ∆P to move forward. The assumption of a fully-filled screw channel is realistic and even necessary to have a sufficient build-up ofpressure to balance, for example, the pressure drop in the die (7). For larger N, a largerdifference between both helix angles is calculated. It is also found that for very smallvalues of N , ∆P for ϕ = 14.3° is larger than ∆P for ϕ = 10.9° even though these valuesof N are not in current use in the industry. For backward elements the pressure drop islarger than the build-up, for the same Q, and the difference does not remain constantwhile N varies. The values are represented by the following functions (with ∆P alongthe extruder):

∆P [Pa/mm] = 16 05 10 2 45 102 2. * . *⋅ − ⋅− −N Q for ϕ = 10.9°, (11)∆P [Pa/mm] = 12 29 10 2 05 102 2. * . *⋅ − ⋅− −N Q for ϕ = 14.3°. (12)

For the backward element, ∆P [Pa/mm] = 19 347 10 73 41 102 2. * .⋅ − ⋅− −N forQ = 30 [ml/s] and ϕ = 10.9°. (13)

4.5 The shear and elongation rates.

The evaluation of deformations of the polymer is important in order to understand themixing and the heat transfer in the extruder. The two components of the deformation,

the shear rate γo

and the elongation rate εo

, are calculated. These quantities are

computed with (10):

( )

)/()(

)()((

:21

222

222

wvuwvvw

wuuwvvuvwwvvuu

vv

vv

vv

yz

xzxyzyx

T

++++

++++++=

∇+∇=⋅

ρ

ρ

ρ

ρρρ

ε

(14)

γ⋅

= ∇→

+ ∇→

∇→

+ ∇→

= + + + + + + + +

2

2 2 2 2 2 2 2 2 2 1 2

( ):( )

(( ( ) ( ) ( ) ) /

v vT

v vT

ux vy wz uy vx uz wx vz wy

(15)


67

γo

= ⋅ − − ⋅ −1 02 10 1 3 5 10 2. * . *N Q for ϕ = 14.3°, (18)

εo

= ⋅ − ⋅− −6 31 10 8 12 102 3. * . *N Q for ϕ = 14.3°. (19)

For the backward element γo

= +N 11 and εo

= ⋅ −−5 7 10 0 722. * .N for Q = 30 [ml/s]

and ϕ = 10.9°. (20)

4.6 The adiabatic temperature rise.

The dissipative action of the shearing forces acting on the fluid causes a temperaturerise. The shear rate values can be used to compute the viscous dissipation W by

integration of ηγo2

over the channel volume, for the Newtonian case. Assuming no

heat leaves the extruder via the screw and barrel walls, the overall adiabatictemperature rise is W/(rCpQe) [K/m³] with Cp the specific heat(Cp = ⋅2 103 [J/(kg.K)] ). The assumption of an adiabatic temperature rise is reasonable

if the volume-area ratio of the extruder is large, which occurs in the case of a verylarge diameter of the extruder. Figure 14 shows the temperature rise per millimeter ∆T [K/mm] along the extruder for η = 0.1 [Pa.s] (see following section for the changeof the viscosity).


71

The adiabatic temperature rise ∆T (previous section) is linearly dependent on η

because γ⋅ does almost not vary with η.

The following functions for DT include the viscosity:)10*(26.7** 895.1046.1 −− ⋅=∆ ηNQT for ϕ = 10.9° and Re ≤ 440,

)10*(74.6** 895.1038.1 −− ⋅=∆ ηNQT for ϕ = 14.3° and Re ≤ 440.For the backward element, )10*(66.2* 9936.1 −⋅=∆ ηNT for Q = 30 [ml/s], ϕ = 10 9. o

and Re ≤ 440.

5 Conclusions.

The influences of N and Q (and ϕ) on the build-up of pressure, the flow, the backflowvolume and the shear and elongation rates have been modelled. These results areimportant for the optimisation of melting and mixing processes in the extruder and thedesign of self-wiping intermeshing corotating twin-screw extruders.

It is noted that the shear and elongation rate are linked to the backflow and thepressure build-up which are, mainly, connected to the rotation speed. Theseparameters (along with the throughput) influence the mixing properties of thetransporting elements and the build-up of pressure necessary to pass through thekneading elements. The backflow volume also influences the residence timedistribution. This backflow, which can be related to the mixing, is linked to N/Q. Theshear rate is found to dominate the elongation rate by a factor 10 (the same is found inthe kneading element (9)). The adiabatic temperature rise along the extruder can bereasonably represented by a function of N2/Q

Nomenclature.

B: Minus the integral, over a cross-section, of the amount of flow volume in the opposite direction [ml/s].

B*: B divided by Qc [-].CL : Centreline distance of the twin-screw extruder [m].Cp : Specific heat [J/kg.K].

l: Lead of screw element [mm].L: Divergence matrix.M p: Pressure mass matrix.


72

n: Number of screw threads [-].N: Rotation speed [rotations per minute] [rpm].N u u( )r r : Discretization of the convective terms.

p Pressure [Pa].rp : Numerical vector of pressure unknowns in Galerkin's method [Pa].

P: Mean pressure over a cross-section [Pa].∆P: Build-up of pressure [Pa/mm].Pb1: Geometry and mesh for the channel.Pb2: Geometry and mesh for the intermeshing area.Q: Throughput in the extruder [ml/s].Qe: Throughput in the extruder computed with the mesh [ml/s].Qc: Throughput in the channel [ml/s].

Re: Extruder Reynolds number

=

ηρ SbRV2

[-].

Rs: Radius of the screw [m].S: Stress matrix.∆T Adiabatic temperature rise per unit length [K/mm].ru : Vector of velocity unknowns [m/s].rv : Velocity [m/s].

Vb: Barrel velocity

=

602 NRSπ

[Pa/s].

W: Viscous dissipation [Pa/s].

u, v, w: Components of v→

[m/s].

Greek

ρ: Density of the fluid [kg/m3].ε: Small quantity in equation 5 [m2/Pa s].η: Dynamic viscosity [Pa.s].ϕ: Helix angle [degree].

γo

: Shear rate [s-1].

εo

: Elongation rate [s-1].

γo

: Mean value of γo

for the cross section [s-1].

εo

: Mean value of εo

for the cross section [s-1].

γo

: Mean value of γo

for the channel [s-1].


73

εo

: Mean value of εo

for the channel [s-1].

References.

1. Sepran Package, Ingenieursbureau SEPRA, The Netherlands, (1992).2. Y. Wang and J.L. White, J. Non-Newton. Fluid Mech. ,32 19-38, (1989).3. C. Cuvelier, A. Segal, and A.A. van Steenhoven: "Finite elements and Navier-Stokes equations", D. Reidel Publishing Co., Dordrecht, The Netherlands (1986).4. M.L. Booy:, Polym. Eng. Sci., 18, No. 12, p. 973 (1978).5. C.D. Denson and B.K. Hwang Jr., Polym. Eng. Sci., 20, No. 14, p. 965 (1980).6. W.M. Davis, Chem. Eng. Progress, November, p. 35 ,(1988).7. D.M. Kalyon, C. Jacob, and P. Yaras Plast. Rubb.and Comp. Process. andApplications., 16, 193 (1991).8. Z. Chen and J.L. White, SPE ANTEC Tech. Papers, p1332, (1992).9. D.J. van der Wal, E.M. Klomp, D. Goffart, H.W. Hoogstraten and L.P.B.M.Janssen, Polym. Eng. Sci, 36, 912 (1996).10. J.M. Ottino, Chem. Eng. Sci, 35, 1377 (1980).

3D modelling of the temperature in the extruder, chapter 4

74

CHAPTER 4 THREE-DIMENSIONAL FLOW ANDTEMPERATURE MODELLING IN THE CHANNEL OFTHE COROTATING TWIN SCREW EXTRUDERS.

Abstract.

The temperature in the extruder is one of the most important parameters to controlreactive compounding as described in this thesis. Therefore the 3D-temperaturedevelopment in a viscous fluid flowing in the channel of an extruder has been calculatedalong the channel. The viscous dissipation is largest in the corners nearest to the barrel.This causes large temperature gradients in the calculated cross sectional temperatureprofiles.A more general solution has been derived by using dimensionless numbers. For this thePrandtl number, the Péclet and the Reynolds number are used. The boundary conditions atinflow have a distinct influence on the solution of the numerical problem while the viscousdissipation dominates the temperature profile at regions in the flow where the shear rate islarge.The solution has been investigated as a function of the heat transfer coefficient.

1 Introduction.

In chapter 2 and chapter 3 isothermal flow profiles in the geometry of the kneading sectionand the transporting section have been calculated (1, 2). Flow and temperature modellingis especially usefull for modelling of mixing (3-7). In this chapter we turn our attention tothe three-dimensional isoviscous modelling of the temperature based on similar three-dimensional flow profiles in single-screw and closely intermeshing corotating twin-screwextruders. The rectangular geometry of the channel is used as the geometry for ourcalculations as a reasonable approximation for the transporting section of the intermeshingcorotating twin screw extruder and also for the channel of the single screw extruder. Thenext step in developing a computer code is to model the 3D temperature profile now theflow in the kneading and transporting elements is know. This must help us in designing agood reactive compounding process. For some decades the simulation of flow andtemperature profiles in the fully filled part of the intermeshing co-rotating twin screwextruder has been an area of research. In most of this research flow and temperatureprofiles have been computed for simplified two-dimensional or quasi three-dimensionalmodels. Much of this work was based on lubrication theory (8, 9).


75


2.1 The geometric model.

Mixing of two polymers in an extruder is strongly influenced by the temperature and shearrate in the extruder. Therefore the temperature profile and shear rate in extruders will beinvestigated as well as the influence of the cross sectional geometry of the channel and theboundary conditions of the flow.

figure 1a The geometry of the channel

The geometry of the channel of the corotating twin screw extruder has been shown infigure 1a. The channel is curved and if we want to calculate the flow in this channel thisimposes complicated boundary conditions.For computational reasons, simplifications of the basic geometry have to be made, themost important one being the neglect of the curvature of the channel. Furthermore theleakage gaps will be neglected. Another assumption is that the screw is at rest whereas thebarrel wall is moving. The presence of the intermeshing regions will be ignored in the caseof the intermeshing corotating twin screw extruder. We assume that this is reasonable sincein chapter 3 it has been found that the shear rate in these regions turned out to differ


78

In equation 1a and 1b the coordinates x, y, z are made dimensionless with the screwdiameter (D). The components of the velocity,

rv , of the fluid are u, v, w, and are made

dimensionless with the characteristic velocity V =πDN where N is the number of screwrotations per unit of time. The velocities u, v, w are in the x, y (transverse), and z (downchannel) direction. The pressure p has been scaled by ρV2, where ρ is the fluid density.The Reynolds number is defined by Re = ρVD/η where h is the dynamic fluid viscosity.The helix angle of the flights on the screw (φ) determines the prescribed transverse velocityVsinφ and the down channel component Vcosφ at the barrel wall. The no-slip boundarycondition (

r rv = 0) has been prescribed at the other wall(s). A flat velocity profile has been

prescribed at the inflow plane while a stress-free outflow condition has been imposed onthe outflow plane.To simulate the flow and the temperature profile in the complete channel of thetransporting elements an iterative process with a sequence of geometric problems wasdeveloped, each problem corresponding to a segment of the complete channel. Thecalculations are done to find the flow profile in the channel. The outflow profile isinfluenced by the free-stress outflow boundary conditions. The flow profile at 2/3 of thelength of the segment is imposed as the inflow profile on the next segment, etc. Thisprocess enables us to extend the length of the channel as far as we want. A throughput isfixed at the inflow of the first segment with the same direction as the extruder axis. Theflow problem has been solved numerically by making use of SEPRAN in the same way asin chapter 2 and 3.

2.3 The temperature problem.

To obtain real temperatures from the values given for the temperature in this chapter thebarrel temperature must be added. In dimensionless form the energy balance for a three-dimensional stationary flow of an incompressible Newtonian isoviscous fluid reads asfollows :

222222

2

(2) RePr1

++

++

++

+

+

=

+

++=++

wy

vz

wx

uz

vx

uy

wz

vy

ux

W

Wzzyyxxz

wy

vx

u

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

τ∂∂

∂∂

τ∂∂

∂∂

τ∂∂

∂∂

τ∂∂

τ∂∂

τ∂∂

The scaled energy equation has been solved by use of the finite element package SEPRAN.In equation 2, Pr is the Prandtl number, Pr=ηCp/λ, where Cp is the specific heat of thefluid, and λ is the thermal conductivity coefficient of the fluid. W is the dimensionlessviscous dissipation function. The characteristic value for the temperature is V2/(CpRe),with V the characteristic value for the velocity. Note that 1/(Re Pr) equals λ/(ρVDCp)


79

which is independent of the viscosity, η. In the above formulation of the temperatureproblem the dimensionless temperature profile, τ, is related to its dimensional counterparttemperature profile minus the barrel temperature (Tb), ∆T , by :

∆TV

CV

DC VDCp p p=

⋅=

2

Re( )τ

ηρ

τλ

ρ(3)

In this chapter we will show the temperature profiles corresponding with the averagetemperature T (∆T in equation 3 but it is the difference from zero) as calculated from τ(the right hand side of equation 3). The velocities u, v, w in equation 2 are independent ofthe viscosity since the flow is practically Stokes-flow. From equation 3 it is obvious thatthis solution of the temperature problem is linearly proportional to the viscosity, for a zerotemperature prescribed on the barrel and the inflow plane and adiabatic conditions on thescrew. However, ∆T T T= − =( )0 is not linearly dependent on the viscosity, h, if the

dimensionless temperature profile of the fluid at the inflow plane is not equal to zero (inwhich case τ is dependent of h). The same computational grid has been used to solve thetemperature problem as for the flow problem.

2.4 The temperature profile for a larger length of the channel.

The temperature at the barrel is fixed. The barrel temperature must be added to thetemperature values shown in this chapter. On the inflow plane of the first channel segmentwe prescribe a uniform temperature profile (taken as zero) while the screw is adiabatic.The temperature to be prescribed on the inflow plane of the second segment follows fromthe transfer of the temperature profile of the previous element at 2/3 of the total axiallength of that element which is a comparable procedure as used in chapter 2, and 3. Bypositioning an arbitrary number of segments in a row an arbitrary length of the channel canbe modelled (this is called the number of iterations).The energy balance in equation 2 can usually not be solved with the real value of l (=0.2)because of numerical limitations. Therefore the calculations were usually done with l = 10or 20. However it will be investigated whether realistic temperatures can be calculatedfrom the solutions by scaling with l. The results of our calculations are the temperature onthe left hand side of equation 3 or its average value. The values have not been scaled butreal temperatures can be calculated from the temperatures in section 3 by scaling andaddition of this temperature to the temperature of the barrel.

3 Results.


90

4 Conclusions.

The fluid in the channel is heated by viscous dissipation (which is due to friction of thepolymer which flows through the channel) and cooled by the barrel. In the transportingelements a cooler area was found in the middle of the channel. The development of thetemperature distribution and the cooling by the barrel has been modelled. In order tocalculate the temperature in the real world from these results some rules for scaling thetemperature profiles have been developed.The calculations were done with an unrealistic high value (in most calculations 20) for theheat transfer coefficient because the calculations otherwise did not converge. Scaling ruleswere found by doing calculations with different values of λ and fitting the averagetemperature in the channel. Reasonable values for the average temperature rise withrespect to the barrel for a realistic value of λ of 0.2 have been obtained. This shows thatthe model presented can predict a reasonable temperature profile for the isoviscous casewith the restrictions mentioned in section 2.3.

Nomenclature.

iteration The number of channel elements placed after each other.τ Dimensionless temperature profile (right hand side in equation 3)[-].T Average temperature difference with the barrel temperature [K].Tb Temperature of the barrel [K].l Heat transfer coefficient [W/m K].Cp Heat capacity [J/kg K].η Viscosity [Pa s].


91

References.

1 Chapter 2 of this PhD thesis.2 Chapter 3 of this PhD thesis.3 Chapter 6 of this PhD thesis.4 L.P.B.M. Janssen, G.H. Noomen, and J.M. Smith, Plastics and Polymers,135 ,

August (1975).5 P.H.M. Elemans, PhD thesis, Eindhoven University (1989).6 J. Janssen, PhD thesis, Eindhoven University (1993).7 Chapter 8 of this PhD thesis.8 J.L. White, W Szydlowski, K Min, and M-H Kim, Adv. Polym Techn., 7 , 295

(1987).9 J.A. Speur, PhD thesis, Groningen University (1988).

The role of diffusion and reaction in reactive compounding, chapter 5

92

CHAPTER 5 THE ROLE OF DIFFUSION AND REACTIONIN REACTIVE COMPOUNDING.

Abstract.

During reactive compounding diffusion plays an important role. Monomer and initiator areabsorbed in the dispersed phase of a blend while no monomer is present in the major phase.Monomer and initiator diffuse out of the dispersed phase and simultaneously reaction of themonomer and initiator takes place. The kinetics of the reaction is diffusion limited. Diffusioncoefficients have been measured with FRAP (Fluorescence Redistribution After Pattern Photobleaching). The size, weight, and shape of the diffusing material and the number averagemolecular weight of PS were varied. A computer modelling of diffusion and simultaneouslyreaction of monomer in a sphere has been developed. With this model we investigate whethermost of the monomer reacts inside or outside the dispersed phase. It is calculated that thisdepends strongly on the size of the dispersed phase. The monomer concentration inside asphere with a diameter of 5 mm decreases mainly because of the reaction. In these calculationsthe reaction velocity of pure styrene has been chosen. However, if the dispersed phase consistsof spheres with diameters smaller than 5 mm, the monomer concentration inside the spheredecreases mainly because of diffusion of monomer out of the dispersed phase.

1 Introduction.

Chapter 2, 3, 4, 6, and 7 describe mixing of polymers in an extruder. However, we also needto describe diffusion and reaction which takes place in the dispersed phase of the blend todescribe reactive compounding in the extruder. Therefore, in this chapter the measureddiffusion coefficients and reaction velocities are discussed. These parameters are needed in themodelling which is explained in chapter 1. Section 2 describes the diffusion coefficients and insection 3 the reaction velocities are given. In section 4 the concentration profile of themonomer and the number average molecular weight distribution of polymer formed by thereaction have been modelled. In chapter 8 the computer code which models reactivecompounding will be described which is used in chapter 9, and 10 as a tool to improve themechanical properties of PS/HDPE or PS/PP blends.

Diffusion.

FRAP means Fluorescence Redistribution After Pattern Photo bleaching and was used tomeasure the diffusion coefficient. The experiments were set up in the same way as describedby B.A Smith (1). Use is made of fluorescent dyes, which can be irreversibly photochemically


93

bleached by intense light. A mask is placed on a hot polymer melt in a Mettler Hot Stageholder. This is placed under a microscope (with a 32/0.40 objective) in front of a beam with awavelength of 488 nm. The light is produced by a Spectra-Physics Beamlok A-12 argon ionlaser.Initially, the fluorescent dye is uniformly distributed throughout the sample. An intense burstof light destroys the dye molecules in selected regions, which are not covered by the mask.After the intensity of the light has been lowered the small fluorescent molecules diffuse fromthe shaded into the open areas between the mask. Due to this diffusion the fluorescent signalincreases. From the slope of this line the diffusion coefficient can be calculated.It is obvious that FRAP suffers from the disadvantage that only the diffusion coefficients ofsome specific fluorescent molecules can be measured. However the diffusion coefficient is notvery sensitive to the detailed structure of the small molecule but depends primarily on its sizeand shape (1). Since the fluorescent dye can be detected in very low concentrations, itspresence does not disturb the structure of the polymer matrix. Therefore, it is assumed that thediffusion coefficient of the dye at this low concentration is not a function of its concentration.Since the polymer molecules are much larger than the dye they are virtually immobile on thetime scale in which the dye diffuses. Therefore, the measured value is a dye-solvent mutualdiffusion coefficient within the polymer matrix, which functions as a model system fordiffusion of the initiator. In chapter 1 our system has been described which contains amonomer which reacts and diffuses in the dispersed phase of a blend. The diffusion coefficientof the monomer has been fitted from the literature. The monomer, when heated, also reactswhich also is studied. Unfortunately the conventional theories for the kinetics of additionpolymerisation in the bulk are only valid for homogeneous low viscous liquids and can not beapplied for our system where monomer and initiator is dissolved in polymer (3, 5).

Kinetics.

Reaction velocities of monomer were investigated with Differential Scanning Calorimetry(DSC) on a mettler DSC TA4000 Thermal Analysis System connected with a TC11TAprocessor and analysed. A similar system was described by Batch et al. (4).

Modelling.

The differential equations describing diffusion of monomer out of the dispersed phase andsimultaneous reaction are already given in chapter 1. Diffusion coefficients in the range of 10 -15 m2/s, as measured in section 3.1, and reaction velocities, as measured in section 3.2,will be used in the modelling. With these values the differential equations have been solvedwith the method of Baker and Oliphant [6]. From the calculations the concentration profiles of


94

monomer and initiator are found inside and outside the dispersed phase of a blend. Thenumber average molecular weight distribution of the graft-copolymer formed has beenmodelled with equations, which were derived for the conventional route of additionpolymerisation in the bulk.

Pn Akp aCM Akt aCRtot A

Pn Bkp bCM Bkt bCRtot B

,, ,

, ,

,, ,

, ,

=

=

2

2

(1a)

monomersiwithchainspolymeroffractionn

PPn

i

n

i

ni

:

111

1

−=

−

(1b)

In our calculations it is assumed that only termination by disproportionation takes place. Thewell-known equations of Flory are given in equation 1a and equation 1b. The viscoussurrounding imposes strong limitations on the mobility of the growing chain as well as on themonomers (7). If a large concentration of radicals is present in the melt the radicals on apolymer chain can also react with other polymer chains in the neighbourhood.

2 Experimental set up.

The diffusion coefficients of monomers such as styrene or butylmethacrylate and of initiatorssuch as Trigonox 145 in polystyrene are needed. Fluorescent molecules such as7 (diethylamino)-4-nitrobenz-2-oxa-1,3-diazola (NBD) or N-methyl-4-(pyrrolidininyl)-styrylpyridinium iodide (M 1329) are used as model materials, figure1.The number average molecular weight of 7 (diethylamino)-4-nitrobenz-2-oxa-1,3-diazola(NBD) is 240 g/mole, and the number average molecular weight of N-methyl-4-(pyrrolidininyl)-styrylpyridinium iodide (M 1329) is 394 g/mole. The polystyrene, PS, usedwas STYROL 2000, STYROL 7000, and a third type of PS (produced by us) with a numberaverage molecular weight (Mn) of 90000. The structure of the fluorescent molecules is shownin figure 1.


96

The pattern of light on the sample is shown in figure 2a. Note that, in reality, this is not aperfect square wave due to fundamental diffraction limitations. This leads to a reduction in theamplitude of the higher frequency terms.An assembly of beam splitters, attenuators, and shutters was used to provide the high-powerbleach and low power observation beams, figure 2b. A photon counting system was operatedin the chopped mode (automatic background subtraction) to measure fluorescence intensity.

figure 2b. Block diagram of the experimental set-up for FRAP


97

3 Results.

3.1.1 The diffusion coefficient.

As described in section 1 the light from the laser initially has a very large intensity and destroysthe fluorescent molecules in the melt between the mask forming alternating bands of high andlow dye concentration. After this first step the beam is set to a lower energy, which no longerdestroys the molecules in the melt. The light falling on the molecules creates a fluorescencesignal. A filter, for a wavelength 520 nm and up, has been used to detect this fluorescencesignal. The laser light when absorbed by NBD or M1329 causes a fluorescence signal whenthese molecules diffuse into the non-covered area. In figure 3 this signal coming from NBDabsorbed in PS increases due to diffusion.

figure 3. Graph of fluorescence intensity vs. time for photo bleached sample, NBD in PS.

By fitting the curve in figure 3 to equation 2 the diffusion coefficient of the molecules infigure 2 have been calculated. The intensity of the fluorescence signal can be fitted, from theconventional diffusion theory, to the, for FRAP well known equation (1) :

i A e C

Da

rt

r= − +

=

( )/1

12

τ

τ

(2)


98

where t is the time constant, which can be fitted with equation 1 from figure 3. The width ofthe part of the mask which is not covered (a in equation 2) is well known from the geometryof the mask (which is shown as a in figure 2b). Fitting equation 2 to measurements, such asshown in figure 3 may cause large deviations depending on the procedure of fitting. Thereforefigure 3 has been fitted to equation 2 with a standard procedure that assures that the relativevalues of the diffusion coefficients are good (1).

3.1.2 Variation of the temperature.

The temperature is expected to have a large influence on the diffusion coefficient of thefluorescent molecule (NBD and M1329) in a polymer melt. All measurements have been donewith a temperature above Tg (PS: Tg : 96 °C) since below Tg hardly any diffusion takes placeand therefore no increase in the fluorescent signal will be measured.

T (°C) D (m2/s), *10-15 D (m2/s), *10-15

first series second series

105 2.87

110 4.67

129.9 13.4

135.2 11.8

150 28.8

150.2 28.5

table 1. The diffusion coefficients of NBD in PS, number average molecular weight(Mn =: 40000).

The diffusion coefficients of NBD in PS have been measured for three types of PS with adifferent number average molecular weight (Mn). From table 1 it can be concluded that thediffusion coefficient of NBD in a melt of PS (Mn : 40000 g/moll) depends on temperaturewith an Arrhenius type of equation. A comparable increase of the diffusion coefficient of NBDis found in PS with a larger number average molecular weight, Mn = 100000 with increasingtemperature, table 2a. The resulting diffusion coefficients of two samples (A and B) have beenshown in table 2a and for each a measurements and its duplo are given. It can be seen that thereproducibility is reasonable.


99

T (°C) D (m2/s), *10-15 D (m2/s), *10-15

first series(A1)

first series(duplo : A2)

second series(B1)

second series(duplo : B2)

109.8 5.32 4.65

110.0 4.52 6.08

120.3 5.48 6.03

130.0 10.4 12.4

130.3 8.43 10.5

140.0 13.5 12.6

140.2 18.2 13.3

150.0 14.8 13.3

150.1 19.6

160.0 12.1

170.5 23.1 24

190.0 23.1

table 2a Diffusion coefficients of NBD in PS (Mn : 100000).

The diffusion coefficients of NBD in PS with Mn 100000 (table 2a) are comparable with thediffusion coefficients of NBD in PS with Mn = 40000 (table 1).In table 2b the averaged diffusion coefficients of NBD in a melt of PS with Mn = 100.000 andin a melt of PS with Mn = 140000 are equal within experimental accuracy. Only for the lowermolecular weight PS (Mn = 40.000) the diffusion coefficients were larger. The amount of freevolume may have been larger for the lower molecular weight PS. According to free volumetheory diffusion takes place because the smaller molecules jump into voids. This offers apossible explanation why the diffusion coefficients of the probes were the same in the PS withMn = 100.000 and 140.000. For this it is assumed that the numbers and sizes of the "freevolume" voids for the PS with a Mn larger than a critical value are not influenced by the Mn ofPS.


100

T (°C) D (m2/s), *10-15 D (m2/s), *10-15 D (m2/s), *10-15

Mn = 40000 Mn = 100000 Mn = 140000

115.0 2.87

119.9 4.81

120.0 3.36

120.1 4.22

130.0 4.67

130.3 5.67

134.9 8.2

139.9 13.4

140.1 11.2

140.2 10.1

145.2 11.8

150.1 14.4

159.0 12.8

159.7 15.7

160.0 14.1

160.1 28.1

165.1 18.9

170.0 21.1

170.1 21.0

180.3 22.8

190.3 33.5

200.o 36.8

table 2b Average values of the diffusion coefficients of NBD in three types of PS.

The values of table 2b have been plotted in figure 4a. The diffusion coefficients of NBD can becompared with the diffusion coefficient of M 1329, which is a larger molecule. At 180 °C thediffusion coefficient of the smaller molecule is four times the diffusion coefficient of M 1329(table 3). Therefore, for modelling purposes, the most important observation when comparingtable 3 with table 2a is that the diffusion coefficient of M1329 is smaller than the diffusioncoefficient of NBD.


101

figure 4 The diffusion coefficients of NBD in three types of PS as a function of thetemperature.

From the measurements diffusion coefficients for the PS with the large Mn (100.000 and140.000) have been fitted to an Arrhenius equation, figure 4. The activation energy and preexponential factor of the diffusion coefficient of NBD in PS are respectively 1000 (J/mole K)and 1.4*10-13 (m2/s).

T ( °C) D (m2/s), *10-15

140.0 0.97

160.0 2.16

180.0 5.02

199.9 6.84

table 3. The diffusion coefficients of M1329 in PS , Mn = 100000.


102

3.1.3 Diffusion coefficients of binary diffusion in a polymer.

When two small molecules diffuse in a melt of PS they share a limited amount of free volumefor diffusion. Therefore their two component diffusion coefficient will have a mutualinteraction. The response curve to FRAP is shown in figure 5 of a sample in which both NBDand M1329 is dissolved in PS. The molecules, which diffuse the fastest (that is NBD), willcause an increase of the intensity of the fluorescent light in the first period of themeasurement. After this period no further increase of the signal from NBD is expected.However the recovery curve still increases due to the diffusion of M1329 since a difference inconcentration for M1329 is still present. By fitting figure 5 with equation 3 it is possible todetermine the diffusion coefficients of both molecules for the case when both are diffusingsimultaneously in PS (binary diffusion). In a simple approach the recovery curve is found :

I A e B e C

Da

Da

rt a

rt b

r

aa

bb

= − + − +

=

=

− −( ) ( )/ /1 1

1

1

2

2

τ τ

τ

τ

(3)

T ( °C) D (m2/s), *10-15

140 3.07

160 16.9

180 20.3

table 4a. The two component diffusion coefficients of NBD in PS , Mn = 100000.

T ( °C) D (m2/s), *10-15

140 0.02

160 0.51

180 0.68

table 4b. The two component diffusion coefficients of M1329 in PS , Mn = 100000.

In table 4a the two component diffusion coefficients of NBD are much larger than those foundfor M1329 in table 4b.


103

figure 5. Graph of fluorescent intensity versus time for a two component diffusion.

T (° C) ratio [-] ratio [-]

binary unary

140 153.5 10.4

160 33.1 6.5

180 29.9 4.5

table 5 Ratio of the diffusion coefficients of M1329 and NBD in PS, Mn : 100000.

In figure 5 the response curve for a system in which two probes diffuse simultaneously isshown. In table 4b the two component diffusion coefficient of M1329, as calculated by fittingequation 3 to figure 5, is shown. This probe is a model material for the initiator Trigonox 145.The ratio between the one and two component diffusion coefficient is calculated with the onecomponent diffusion coefficients calculated in the previous paragraph. In the right handcolumn of table 5 the ratio between the diffusion coefficient of NBD and M1329 has beencalculated for single component diffusion.


104

figure 6a The values for the diffusion coefficients of M1329 for binary (that is the twocomponent diffusion coefficient) and unary (one component) diffusion.

Comparing the two component diffusion coefficients with those of the one componentdiffusion coefficients it is clear that the diffusion coefficient of M 1329 has decreased,figure 6a.The ratio between the diffusion coefficients of NBD and M1329 in the first column of table 5is much larger than in the second column.If we compare figure 6a with figure 6b it is remarkable that only a negligible difference isfound between one and two component diffusion for NBD. An explanation can be found fromthe free volume theory, which is often used, for diffusion in polymer (7). The one and twocomponent diffusion for NBD is the same while it differs for M1329 because of the fact thatthe molecular volume of M1329 is larger than that of NBD.


105

figure 6b One and two component diffusion of NBD.

It is well known that the diffusion coefficients of a certain material can be enlarged if astripping agent is added to a polymer (the stripping agent usually is a small molecule). Thisenhancement of diffusion has been explained by an increase of free volume in the polymer. Themolecules investigated here are much larger than Oxygen, Nitrogen etc. of which the diffusioncoefficients has been described in the book of Crank (2). NBD and M1329 have noresemblance in their chemical structure to PS. Their concentration is very low and it isassumed that in this case the free volume in PS in which NBD and M1329 has been absorbedremains the same as the original free volume in PS. Let’s assume that diffusion of the smallermolecules is independent of diffusion of the larger molecules. Diffusion takes place becausemolecules jump into the free volume voids. The diffusion coefficient of two-componentdiffusion of NBD remains the same because NBD jumps into the voids before M1329. Sincepart of the free volume in PS is occupied by NBD the two-component diffusion coefficient ofM1329 is smaller than the one-component diffusion coefficients in table 3.

3.2.1 Kinetics.

The reaction heat of Butylmethacrylate, BMA, absorbed in HDPE is measured after a sampleis heated in a seal cup in a DSC. The reaction is initiated by radicals due to decomposition ofTrigonox 145 (AKZO-NOBEL). The temperatures increase 10 °C per minute. From the heatof reaction the conversion has been calculated, figure 7.


106

Figure 7 The conversion of BMA measured with DSC (scanning).

The final conversion is only 65 % in figure 7 because of diffusion limitations when part of themonomer is captured between the polymer chains.

3.2.2 Measurements of the reaction velocities.

From the slope of conversion curves such as shown in figure 7 the reaction velocities of thepolymerisation have been calculated. An example of the calculation of the reaction velocity ofBMA is shown in figure 8. The conversion of BMA to PBMA or PE-g-PBMA extends to 50% within a few minutes (when the temperatures exceed 160 oC).The reaction velocity, vp, decreases after 140 s as shown in figure 8. Simultaneously themonomer and initiator concentration decreases and the propagation reaction velocity decreaseto zero. The overall reaction velocity, kov, decreases at a temperature of 180 °C (figure 9).This is due to the experimental method used in which monomer probably evaporates from thepolymer if heated above 170 °C. Hamielec (3) already noted that the reaction velocities foraddition polymerisation in a viscous surrounding differs from the reaction velocities in lowviscous fluid. Probably this is also found here since the reaction velocity decreases before 30% conversion is achieved due to diffusion limitations.Unfortunately, because of a lack of experimental accuracy, it was not possible to find a gooddescription of the reaction velocities which take place in a flowing viscous melt. More


107

extensive kinetic research was outside the scope of this thesis. For use in our computermodelling fitted equations were derived from the measurements.

figure 8 The reaction velocity of BMA dissolved in HDPE versus time, [M]= 6.5 moll/m3.

figure 9 kov of BMA dissolved in HDPE versus time.

4 Modelling the concentration profiles and Mn distribution of the alloying agent.

In the modelling the position where the initiator decomposes is assumed to be the positionwhere radicals cause a reaction.

DaIIk C R

D

DaII k C t

dispp A M A

A

matrix p B M B r

=⋅ ⋅

>

= ⋅ ⋅ ⋅ >

, ,

, ,

2

1

1π

(4)


108

This is justified if the reaction of the radicals is much faster than the diffusion of the radicals.The Damköhler number for the dispersed phase and the matrix phase was found to be largerthan one for the conditions chosen in our calculations.The diffusion coefficient of the initiator has been found by measuring diffusion coefficients ofmolecules with a comparable molecular structure. The diffusion coefficient of styrene in PS orHDPE is estimated to be 10-12 [m2/s] from the literature (2).

In chapter 1 the concentration profile of one component was found to depend mostly on thesize of the dispersed phase. In this chapter the concentration profile of two components will becalculated. The initiator T145 and monomer (S) is absorbed in the dispersed phase at the startof the modelling. The concentration profile of monomer and initiator has been found bysolving the differential equations in equation 5 containing diffusion and a first order reactionfor component Ca and Cb in a 3-D sphere, figure 10.

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

Ct

Dr r

rCr

kC

r a

Ct

Dr r

rC

rk C

a r

Ct

Dr r

rCr

kC

r a

Ct

Dr r

rC

rk C

a r

a a aa

a a aa

b b bb

b b bb

= −

≤ ≤

′=

′ ′− ′ ′

≤ ≤ ∞

= −

≤ ≤

′=

′ ′− ′ ′

≤ ≤ ∞

22

22

22

22

0

0

( )

( )

( )

( )

( )

( )

( )

( )(5)

Mass transfer out of the dispersed phase takes place after heating. The value of k isdetermined by both the concentration of radicals (a) and monomer (b). ratio of theconcentration of initiator and monomer at the interface is found by Henry's law.

C

Cm

C

Cma

aa

b

bb′ = ′ =; (6)

These partial differential equations are solved with the method of Baker and Oliphant [6]. Theboundary conditions are :


109

t 0 s :

Ca 0 mole / m 0 < r < a Ca = 0 a < r <

Cb 0.69 mole / m 0 < r < a Cb = 0 a < r <

3

3

=

= ∞

= ∞

210 (7)

The flux at the centre of the dispersed phase is zero and therefore the concentration profile hasa symmetrical shape. The decomposition kinetics of the initiator (Trigonox 145, AKZO-NOBEL) is given by:

k T e RT( ) . * *(

. *)

= 1 9 1015136 6 103

(8)

For the model calculations a monomer concentration of 2100 [mole/m3] and an initiatorconcentration of 0.69 [mole/m3] was chosen.

figure 10 Monomer concentration profiles versus distance from the centre of thedispersed phase, radius : 0.05 mm, Cm=2100 [mole/m3], CI = 0.69 [mole/m3], t = 300 s.

Figure 10 gives the monomer concentration after 300 seconds. A large initiator concentrationis present in the dispersed phase. The initiator concentration determines the reaction velocityof the monomer, which dominates the diffusion inside the dispersed phase. Therefore theconcentration profile inside the dispersed phase is constant. The shape of the monomerconcentration profile outside the dispersed phase can be understood from a relatively largeinitiator concentration outside the dispersed phase close to the interface of the dispersedphase. This initiator causes a rapid decrease of the monomer concentration outside close tothe interface. The concentration of the initiator further away from the interface is very smalland therefore the concentration profile is determined by diffusion.


110

figure 11 The molecular number distribution inside the dispersed phase and at the interface(the numerical accuracy is checked by doing two calculations with 10 (1) and 30 numericalsteps (2)), radius : 0.005 m, Cm=89.6 [mole/m3], CI = 0.069 [mole/m3], t = 300 s.

figure 12 The development of the molecular number distribution in time, d = 0.005 m..


111

From the profile of the monomer (figure 10) and initiator concentration (not shown) we cancalculate the molecular number distribution with the equations of Flory (equation 1a and 1b)as shown in figure 11, 12, 13, and 14.A concentration gradient for the monomer and for the initiator is present on the interfacewhich determines the molecular number distribution shown in figure 11. The number averagemolecular weight distributions are larger at the interface than inside (at 95% from the middleof) the dispersed phase because of the smaller initiator concentration (at the interface the M/Iis larger). The M/I ratio increases in time due to decomposition of the initiator. Thereforepolymer formed by the reaction starts with a large concentration of polymers with a relativelyshort chain in figure 12. Longer chains are formed if the initiator concentration has decreased.Also after some time part of these chains recombine forming a smaller concentration of muchlonger chains. Therefore the number of small chains decrease while the number of largerchains increase. The Mn distribution shifts in time because the concentration of monomerdecreases relatively fast.

figure 13 The molecular number distribution at the interface, for twodifferent sizes of the dispersed phase.

The concentration of long chains formed in a dispersed phase of 50 µm is larger than theamount of long chains in a dispersed phase of 5 millimetre in figure 13. Therefore the averageMn of the chains formed in the smaller dispersed phase is largest. This is found in spite of thefact that in the intermediate region of polymer chain lengths the concentration of chainsformed is largest in the dispersed phase of 5 millimetre. The explanation for this is that thelong chains have a much larger weight factor.


112

In figure 14 we show that the resulting copolymer from a reaction shifts to a higher numberaverage molecular weight if the initiator concentration is a factor ten lower.

figure 14 The molecular number distribution, [I]=0.00064 (high),[I] = 0.000064 (low).

5 Discussion and conclusions.

Diffusion of a small fluorescent molecule (a solvent or monomer analogue) in a polymer-monomer system can be observed over any distances accessible to optical systems using visiblelight. The diffusion coefficients in a melt of PS have been measured. At increasing temperaturethe diffusion coefficients increase as could be expected.At higher molecular numbers of the PS hardly any influence of the number average molecularweight of PS on the diffusion coefficients has been found. This indicates that the free volumesavailable for the diffusion of small molecules is not dependent on the Mn of the matrix, in thiscase polystyrene. However for a larger type of diffusing molecule it is more difficult to jumpinto free volumes present in a polymer melt at temperatures exceeding Tg. Therefore thediffusion coefficient is strongly dependent on the size of the diffusing small molecules.Binary diffusion differs from single component diffusion. In our measurements the diffusioncoefficient of the larger molecule drops in value while the diffusion coefficient of the smallermolecule remains roughly the same.The diffusion coefficient in PS of large molecules, comparable in size with MAH andTrigonox 145, have very small values ( ]/[10 215 sm− ) compared to values for the diffusion of

S in PE as found in the book of Crank (2) (D = ]/[10 212 sm− ).


113

The reaction of monomers, such as S, BA, BMA, HPMA, and HEMA reach their finalconversion (which usually is smaller than 50 %) within 5 minutes at a temperature of 160 oC.It is not yet known in what way the formation of a graft-copolymer is influenced by the factthat the polymerisation occurs in a (viscous) melt of another polymer. Because of a lack ofexperimental accuracy it was not possible to obtain data on kt. (instead we assume thatkt = 0.1*kp). The results of the calculations in our modelling are therefore not yet accurateenough. For a sufficiently accurate modelling the kinetics of graft-polymerisation reactions in aflowing melt must be studied in great detail.The Mn of the alloying agent formed due to reactive compounding increases in our system ifthe M/I ratio increases or if the reaction time increases.From our calculations we found that the number of time steps in our calculations must belarger than 100 to obtain a result which is independent of the number of time steps. This isvalid if the process time exceeds 60 seconds and the size of the dispersed phase is smaller than10⋅10-5 m.


114

Nomenclature.

a Radius of the sphere [m].Ca Concentration in the minor phase [mol/m3].Cb Concentration in the major phase [mol/m3].

D Diffusion coefficient [m2/s].I (au) Intensity of measured light (arbitrary units).k Reaction constant [m3/mol.s].Mn Average molecular number [g/mol].Mncr Critical average molecular number [g/mol].Me Average molecular weight between entanglements [g/mol].m Partition coefficient [-].[M] Monomer concentration [mol/m3].r Radial coordinate [m].R Gas constant [J/mol.s].t Time [s].tr Half value time of the reaction [s].T Absolute temperature [K].kov Overall reaction rate constant [mol/m3.s].wi Weight of formed graft-copolymer with polymerisation i [g/mole].d Penetration depth [m].

References.

1 : B.A. Smith, Macromolecules, 15 , 469 (1982).2 : J. Crank and G.S. Park, Diffusion in Polymers, Academic Press (1968).3 : F.L. Marten, A.E. Hamielec, ACS Symposium series 104, Amer. Chem. Soc. (1979).4 : G.L. Batch, C.W. Macosco, J. Appl. Polym. Sci, 44, 1711, (1992).5 : E. Trommsdorff, H. Hohle, P. Lagally, Macromol. Chem.,1, 196 (1947).6 : G.A. Baker, and T.A. Oliphant, Quart Appl Math, 17, 361, 1960.7 . J.A. Wesselingh, J. Controlled Release, 24, 47 (1993).

The temperature in a corotating twin-screw extruder, chapter 6

115

CHAPTER 6 MODELLING AND EXPERIMENTAL EVALUATION OF-THE TEMPERATURE IN A COROTATING- TWIN SCREW EXTRUDER.

Abstract.

Following the modelling of the 3D-flow and 3D-temperature in the kneading andtransporting section of the extruder we now will calculate and measure the averagetemperature along the extruder. For processing of polymers in the extruder thetemperature in the melt is an important parameter which will be used in chapter 7, and 8.The temperature of Polystyrene (PS) has been measured in the fully filled section and in thepartially filled section of a self wiping corotating twin screw extruder. The axialtemperature profile obtained for pure PS has been compared with the temperature profileof a blend of PS mixed with High Density Polyethylene (HDPE) processed in the sameextruder. The influence of rotation speed and throughput on the power consumption andon heating of the polymer in the extruder have been investigated. A heat transfer model forthe kneading section in the closely intermeshing corotating twin screw extruder isproposed based on the temperatures measured.

1 Introduction.

With the calculated flow profiles as modelled in chapter 2, 3, and 4 we now are able todevelop a model for the temperature and mixing of reactive compounding in the extruder.Therefore a computer code of reactive compounding will be developed in this chapter andchapter 7 and 8.The final goal of this thesis is to improve toughness and impact values of a PS/HDPEblend. Process control is very important for a good homogeneous product quality of theblend. In many cases of blending controlling the temperature may be a problem due to alack of knowledge of the axial and radial temperature profile. This can be prevented bypredicting the axial temperature profile (neglecting the melting process) for which acomputer program, written in Turbo Pascal, has been developed.Depending on screw design the barrel temperature for the melting of Polystyrene (PS) ormixing of PS and High Density PolyEthylene (HDPE) ranges from 180 to 210 0C .Temperatures above 2400C can cause a loss in the desired physical properties of theextrudate due to degradation. Temperatures below 110 0C can cause high extruded-instress and a loss in the desirable physical properties of the extruded part. Therefore it isimportant to determine the relation between the actual temperature of the polymer in theextruder and the temperature profile of the extruder wall.


116

The heat transfer coefficient in the partially and fully filled part of the transporting andkneading section of the extruder is needed to calculate the heat exchanged with the barrel.Several models for the heat transfer coefficient in the completely filled sections have beendeveloped in which the emphasis was mainly on the metering section in single-screwextruders. In 1953 Jephson (1) considered the wiping action of the flight of a rotatingscrew responsible for the heat transfer in the extruder. During a rotation of the screw, afresh layer of polymer becomes attached to the barrel surface just after passing of theflight. The amount of heat penetrated into this layer by conduction is distributed over thechannel by mixing at the next passage of the flight. The temperatures at different radialpositions in the channel were measured by Janssen et al (2) and Schlaffer et al (3). VanLeeuwen et al (4) have measured the temperature rise at the tip of a thermocouple due toviscous dissipation in PS. In the heat transfer model of Todd (5) the viscosity has a smallinfluence on the heat transfer coefficient. However no influence of the viscosity is expectedat creeping flow conditions. The processing of polymers and blends is strongly influencedby processing conditions and the viscosity and has been the subject of much work of whichsome can be found in Reference 6-18.

2 Modelling of the average axial temperature in the corotating twin screw extruder.

2.1 The geometry and the throughput of the extruder.

In fact the extruder is a pump for viscous liquids and sufficient pressure build up is neededfor a stable transportation of polymers in the extruder. In general the screw layout is suchthat the polymer or polymer mixture is melted and transported into a pressure build up orin a kneading section and then pushed through a die by a transporting section, figure 1.

Therefore the following four sections are distinguished here :

-Solids transport section : before the first kneading section. In this section frictional forcesare experienced by the solid particles, however, no shear on molecular scale is present. Inthis zone the effective heating of the polymers will not be very efficient since only part ofthe barrel is in contact with the polymers. Powder particles are assumed to have a muchlower flow resistance than molten polymers and a constant is fitted for the frictionaldissipation in the powder transporting section.-Melting zone : Melting of the polymer occurs mostly in the part of the transportingsection which is fully filled just before the kneading section or for very large throughputs inthe first part of the kneading section.


117

-The kneading section, which may partially overlap with the melting zone. The large shearin the kneading section causes a large increase in temperature due to viscous dissipation.-The melt transport section. From this section material is pushed through the die.

figure 1 Transporting and kneading elements in the intermeshing corotating twin-screw extruder, number of kneading elements : 8,upper figure : front view, below : side view.

In the transporting elements and pressure build up elements the pressure, needed for thematerial to be pushed through the kneading section, must be built up. After the kneadingelements, transporting elements or pressure build up elements are used to supply thepressure needed to transport the material through the die. Experiments have been donewith 7, 8, 9, 10, 11, and 18 kneading elements.The temperatures are measured in the partially filled transporting section before thekneading section and in the fully filled kneading section of a screw extruder as shown infigure 1. The positions where the temperature has been measured in the kneading sectionare at the first (T1) and the seventh paddle (T2) along the extruder. The temperatureincreases in the fully filled sections. This is mostly determined by the relation betweenviscous dissipation and cooling of the barrel.In our modelling a large number of general equations are used of which a few will be givenhere. The following expressions are valid for the self-wiping twin screw extruder and canbe found in the work of Elemans (11). The number of independent channels in a corotatingtwin-screw extruder are (2n-1). The channel width in a corotating twin-screw extruder isgiven by equation 1.

W = ((2n-1)/n)∗πDsinϕ(1-ne) (1)


118

e = Wf/Wtot = Wf/(πDsinϕ) (2)where W is the width, D is the diameter, e is the relative width, ϕ is the pitch of the screw,and the index f means of the flight. The throughput, the specific energy, and the degree offill are of interest for the temperature modelling. The geometry of the solid particles in thepartially filled section, the degree of fill in the partially filled section and the energyconsumption of the melt are used in the modelling and will be described in this section.The theoretical throughput yields:

Qth = ½VcosϕHW (3)

where V is the velocity of flight and H is the height of the channel. According to Elemans(11) the local throughput, Q, that must be transported to the die is larger than the metered(real) throughput (Qm), due to leakage flow (QL) through clearances over the flights :

Q = Qm + QL (4) with : QL = ½Vδ π Dsinϕcosϕ(1-ne) (5)

-The degree of fill equals:

f = Q

12

D HNcos sin (1- n e)

m

2 2π ϕ ϕ

δ+

H(6)

where j is the pitch angle, n is the number of channels per screw, and d is the distancebetween flight and barrel. It has been assumed that the amount of fill of the channel in theself wiping corotating twin screw extruder determines the contact surface with the barreland therefore the heat transferring area. The fully filled length, preceding the kneadingsection and die is calculated. The kneading section is totally filled as has been verified byvisual observations.

The area of the barrel which cools the melt in the channel of a twin screw extruder hasbeen modelled with :

A D D L= −( ) *π θ2 (7)

The effective surface area for the flights equals:

Af = neA [m3] (8)

The surface area which cools the melt in the transporting channel is assumed to depend onthe degree of fill :

Ac = f(1-ne)A [m3] (9)


119

2.2 The temperature model.

The temperature of the melt in the fully filled section is mostly determined by the viscousdissipation, which is a function of the shear rate in the fluid. The polymer in thetransporting elements experiences a relatively small shear stress. In the kneading sectionlarger shear stresses are applied. Part of the heat generated by viscous dissipation istransferred to the barrel. An expression for the heat transfer coefficients will be derivedboth in the partially filled and in the completely filled sections. This is needed for modellingthe temperature of the melt in the transporting section and the kneading section

2.3 The viscous dissipation.

A number of assumptions are used in these calculations

For the transporting section it is assumed that:

-The solid particles are heated by direct contact with the barrel or the screw both havingthe same uniform temperature.-The heat from the barrel penetrates directly into the solid.If the surface of the solid particles has a temperature higher than the glass transitiontemperature the solid becomes sticky and the frictional forces increase. This increase isassumed to be linear with the percentage of material within a particle having a temperaturehigher than the glass transition temperature.

For the kneading section the following is noted :

-The kneading section is assumed to be completely filled because it is a pressureconsuming section (the stagger angle used is 1500 ).-The influence of the pressure on density and viscosity of the polymers has been neglected.-The dominating term in the overall heat balance is the viscous dissipation which iscalculated with the average values of the shear rate (6-11) and elongation rate from 3-Dflow calculations in chapter 2 and chapter 3. It is assumed that the average value of theshear rate calculated can be used to calculate the viscous dissipation. A constant has beenfound which represents the fact that the temperature increase is slightly delayed becauseenergy is consumed when granules melt.-An experimentally measured viscosity model for PS and HDPE has been used in themodelling


120

-The screw surface is considered to be adiabatic

As a model for the shear stress in the flight gaps we use :

τ ηδf fV

= (10)

where h is the viscosity, as calculated from the experiments with a Cross Carreau model(12-14), and d is the flight gap. The Torque, To, is needed to calculate the averagetemperature rise due to the viscous dissipation :

To DF

with

F DL f l f f

t

t t

=

= + +⋅

12

1 2 3 4 12

(11)

:

( ( ) / ) ( )ηγ π

Where Ft is the total force and f is the (local) degree of fill (equation 9), and lt is the totallength. The power consumption depends on the screw element, the degree of fill of theelements and the viscosity of the material. The total power consumption consists of thepower consumption over the flights and the power consumption in the channel. The forces(F) acting on the wall are the product of shear stress and surface area where the stress isactive. The power consumption (Watt) equals torque times screw speed :

NDflfLf

P to 2

)/)43(21( 2++=

γηπ & (13)

2.4 The temperature profile.

The overall energy balance has been solved, providing an average value for the axialtemperature of the materials in the self wiping corotating twin screw extruder :

Q CdTdx

dPdx

hO T Tm po

w= − −( ) (14)

Where Qm is the throughput, Cp is the specific heat, O is the circumference, and h is theheat transfer coefficient. The energy needed for phase changes and pressure changes of thepolymer is generally small and has been neglected for the screw geometry without apressure build up section in front of the kneading section. The influence of heat exchangewith the screw has been neglected. The following solution has been derived to calculate thechange in melt temperature one step further along the channel (from equation 14) :


121

T TP

hO xe T T ew

o

hOQmCp

x

w

hOQmCp

x

= + − − −− −

[ ( ) ( ) ]∆

∆

∆ ∆

1 0 (15)

The temperature of the melt in equilibrium with the barrel is :

TP

hO xTo

w= +[ ]∆

∆(16)

Since the power Po depends on the screw speed, N, also the equilibrium temperaturedepends on the screw speed. The axial position of this equilibrium is within the kneadingsection in most of our experiments because of a relatively small throughput, Qm. Withequation 15 the temperature profile over the length of the screw can be calculated for eachscrew speed and throughput. For the modelling of the energy balance in the extrusionprocess two different models for the heat transfer coefficient have been compared. Themodel of Todd implies a dependence of the heat transfer coefficient on N, Q and D.

hD

D N Cp b

w= 0 94

20 28 0 33 019. [ ] [ ] [ ]. . .λ ρ

η

η

ληη

(17)

The model of Jephson (1) is based on the penetration theory :

NTCTTh

NTTCT

zerf

zzT

h

p

hzp

)()()(57.0

:casethisin

:

)()()(

2

)(

ρλ

ρλ∂

∂λ

=

=

=

(18)

The viscosity and the screw diameter influence the heat transfer in the model of Toddwhich is not the case in the Jephson model. The heat conductivity of PS (l) can be writtenas :

λ

λ

( ) . ( . ( ) ( . ))

( ) . ( . ( ) ( . )) ( )

TTT

T T

TTT

T T

gg

gg

= + − <

= − + + >

0 228 0 375 1 0 375

0 228 0 2 1 0 2 20

(19)


122

Both models are combined with the computer model and the results are compared withmeasured axial temperatures. From these measurements the heat transfer coefficient in thekneading section has been determined.

3 Experimental.

The torque, measured during processing with a Brabender plasticorder, is a direct measureof the viscosity. Therefore the torque has been measured during processing of PS, HDPE,and a mixture of HDPE with maleic acid (MAH), figure 2. From figure 2 it is possible tocalculate the ratio between the viscosity of PS and HDPE.

figure 2 The torque measured with a Brabender plasticorder, Tb = 200 °C.

The viscosity of the HDPE/MAH mixture (MAH is not grafted) is very small because ofthe porous structure of the HDPE granule. The material flows easily due to the presence ofMAH. The torque as measured when pure accurel (porous HDPE) is melted hardlydepends on the rotation speed.3.1 Extrusion and viscosity.

Extrusion of PS and PS/HDPE was performed on a Baker Perkins, 50 mm, self-wipingcorotating twin-screw extruder. The screw geometry has one kneading section (figure 1).In the first series of experiments this kneading section consisted of 7 kneading elements,with a stagger angle 150 0 . Our goal is to determine which heat transfer model is valid inthe fully filled kneading section and in the partially filled transporting section. Threedifferent barrel temperatures are used, 160, 180 and 200°C. The extruder parametersvaried are one of the screw speeds and one of the throughputs in table 1.


123

N [rpm] Q [kg/h]0.66

57 1.32107 3.3162 6.54214 8.59269 10.2314 12.7

table 1 The rotation speed, N [rpm] and throughput Q [kg/h] used in the experiments.

figure 3 The measured and modelled viscosity of PS.

The viscosity of the commercial grade PS (Styron 7000, SHELL) used in the experimentshas been measured and fitted to this model, as shown in figure 3. This viscosity has beenmodelled with a generalised Cross-Carreau model. Data sets for the viscosity of pureHDPE have been taken from the literature and verified for the PE used (13,14).

4 Results.

4.1 The power.

Under normal operation conditions the temperature of the melt in the extruder is stronglyinfluenced by viscous dissipation. The power of the motor is a direct measure of the


124

viscous dissipation. This power consumed by the extruder is measured when a PS fromShell is extruded, shown in figure 4a.The power consumed by the extruder as modelled for Styron 7000 corresponds very wellwith measured values. The influence of the length of the kneading section has been studiedand therefore also experiments with a new screw geometry with 11 kneading paddles havebeen done. From the calculations of the power consumption along the extruder it wasfound that most of the power is consumed in the kneading section.

figure 4a Comparison between calculated and measured Power of the extruder.PS, Tb = 200 oC, Q = 0.3 kg/h, PS : Styron 7000 (SHELL)

For the successive experiments a PS from Atochem was chosen because it appeared to bemore suitable for our blending experiments, figure 4b. In this case the screw geometry has7 kneading paddles. For processes such as mixing the specific energy is an important factorfor extrusion of viscous fluids. This energy decreases with an increase of throughput asshown in figure 5.


125

figure 4b The power versus rotation speed, various throughputsPS, Tb = 180 oC, PS : Lacquerene (ATOCHEM)

figure 5 The specific energy consumed by a melt of polystyrene, N = 267 rpm,Tb : 200 °C.

Figure 5 shows the specific energy consumed by the melt :

Espec = Po/Qm [kW/kg] (21)


126

4.2.1 The temperature profile in the partially filled section.

The melting mechanism in the single screw extruder has been the subject of much work inthe past but is expected to differ from the melting mechanism in a twin screw extruder. Inthe barrel two openings are present in the partially filled zone before and after the kneadingsection. This allows us to measure the temperature of the polymer in the partially filledzone by use of an IR thermometer, Scotchtrac Heat tracer (3M). The temperatures alongthe axial length in the fully filled part are measured at three axial positions with an IRthermometer suitable to measure in the melt (DYNESCO).PS or a polymer mixture of PS-HDPE is fed into the transporting section at 20 °C. Thebarrel has a temperature of 150°C, 160 °C, 170 °C, 180 °C or 200 °C. The heat from thebarrel penetrates into the granules transported in the partially filled section.

figure 6 The geometry of the granules in the partially filled section (side view).

Heat penetration from the barrel into the granule in the partially filled section has beenmodelled with Fourier theory, figure 6. The temperature profile has been calculated in ageometry completely consisting of transporting elements.


127

figure 7 The temperature profile in the partially filled transporting section.PS, Tb = 200 °C, Q = 8 kg/h, N = 107 rpm

If the temperature of the outer layer of the granules exceeds the glass transitiontemperature (96 0C) the outer layer of the granules becomes sticky leading to an increaseof friction. The temperature development of the granules in the partially filled section isshown in figure 7. This temperature profile shows a strong initial increase which levels offalong the transporting section.

figure 8 The temperature dependency on the rotation speed and throughput in the partially filled section ; PS, Tb = 200 °C, l = 0.4 m.


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The temperature of the melt decreases when more material is heated, figure 8. The degreeof fill increases with increasing throughput. Heating and cooling by the barrel increaseswith an increase of the degree of fill because an increase of the part of the barrel surfacehaving direct contact with the granules. Therefore the power consumed increases ascalculated with equation 11.

figure 9 Calculated and measured temperature and degree of fill (f) versusthroughput, partially filled section ; PS, Tb = 200 °C, N = 107 rpm

The temperature of the material measured with the IR thermometer in the partially filled(transporting) zone before the kneading section for various throughputs, Q, shows areasonable agreement between theory and experiments as shown in figure 9.

4.2.2 The fully filled section.

The temperature profile has been calculated for a screw geometry with transportingelements and one fully filled kneading section with a stagger angle of 150° (figure 10a).The radially averaged temperature in the melt of the extruder has a maximum near theentrance of the kneading section. This maximum occurs due to the interaction between theviscous dissipation and the heat transfer to the barrel. When entering the kneading sectionpart of the material is not melted yet and therefore the viscosity is very large. The phasetransition is not taken into account at the position in the extruder where the temperature ofPS reaches the glass transition temperature. Therefore the temperature of the materialentering the kneading section is expected to be slightly overestimated.


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figure 10a The modelled temperature development along the length of the extruder.PS : Styron 7000 (SHELL), Tb = 180 °C, Q = 3.5 kg/h

In figure 10b an additional pressure build up section is present in front of the kneadingsection and melting is taken into account. In the pressure build up section the temperatureis almost constant because the energy dissipated is consumed by the phase transition.

figure 10b The temperature development along the length of the extruder.PS : ATOCHEM, Tb = 150 °C, Q = 8 kg/h, pressure build up section = 10 cm

For all measurements the temperature in the melt in the fully filled kneading section has ahigher value than the temperature of the barrel due to the relatively large viscousdissipation. The viscosity of the melt entering the kneading section is relatively high anddecreases when it enters the kneading section. The comparison between calculated and


130

measured values is good, figure 11. The temperature decreases with increasing throughput,figure 11.

figure 11 Calculated and measured temperature versus Q [kg/h].PS, Tb = 180 °C, N = 107 rpm

4.2.3. The temperature at the entrance of the kneading section.

In figure 12a the temperature of the melt decreases with increasing throughput in the (fullyfilled) kneading section.

figure 12a The measured temperature of the melt versus throughput ; PSfrom Atochem ; Tb = 180 °C, position : first kneading paddle.


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It is obvious that a large resemblance in the shape of the lines is found for the differentrotation speeds of the screw.

figure 12b Calculated and measured temperatures of the melt versus rotation speed[rpm], Tb = 200 °C, Q = 0.3 [kg/h], position : seventh kneading paddle.

Since only an overall energy balance is solved it is difficult to accurately calculate theaverage temperature and the average viscosity in the melt. Nevertheless the comparisonbetween calculated and measured average temperatures in the kneading section isreasonable, as can be seen in figure 12b. The measurements shown are the temperatures inthe melt at the end of the kneading section. The temperature at the exit of the kneadingsection decreases with increasing throughput, figure 13a.

figure 13a The measured temperature of the melt at the seventh paddle, Tb = 200 °C.


132

4.2.4. The heat transfer coefficient calculated, the kneading section.

At a large rotation speed the measured temperatures in figure 13b all are the same. Thismeans that T1=T2 in equation 22, and for relative small throughputs the temperature of themelt is constant along the kneading section. From this figure it is clear that, at lowthroughputs and large rotational speeds, the temperature is almost independent of thethroughput. Therefore Q⋅ρ⋅Cp⋅(T1 - T2) in equation 22 is small in the kneading section.

figure 13b T1 and T2 of the melt in the kneading section, Tb : 200 °C.

If the temperature is constant along the kneading section the following overall energybalance is valid :

0 1 2

1 2

= − − − +

=

=−

Q C T T hS T T H

H heat due to viscous dissipation

if T T

hH

S T T

p av barrel e

e

e

av barrel

ρ ( ) ( )

:

:

( )

.

(22)

To calculate the heat transfer coefficient from the energy balance the viscosity of the PSmelt in the kneading section as a function of shear rate and temperature (and therefore alsothe viscous dissipation) has been found by iteration. The average shear rate in the volumeof one kneading paddle has been calculated in chapter 2 and 3 and has been used in thismodelling for the shear thinning behaviour to calculate the viscosities.


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figure 14 The heat transfer coefficient, theory : penetration theory.

Figure 14 gives a comparison between the experimental values for the heat transfercoefficient in the kneading section and the models proposed by Todd (5) and Jepson(1). Itis clear that the penetration theory (Jepson) shows a reasonable comparison with themeasured values for the heat transfer coefficient in the fully filled kneading section. Fromthe 3D temperature modelling, in chapter 4 it was also found that penetration theoryprovides a reasonable value for the power law (a function of N) to which the heat transfercoefficient in the transporting section has been fitted.The model of Todd, equation 18, as shown in figure 14 was found to be slightly differentfrom the heat transfer coefficients as we measured them in the kneading section.

4.2.5 The temperature of a blend (PS/HDPE).

The temperature of a blend of PS and HDPE has also been measured and modelled. Themeasured values at the end of the kneading section for different rotation speeds are shownin figure 15.The temperature of the melt is relatively low compared to the measurements for pure PS.The measured values of the temperature in the melt of a blend of PS/HDPE above thefourth kneading elements for increasing rotation speeds are shown in figure 16.The differences between the temperature of the melt of pure PS and of a PS/HDPE blendare mostly attributed to the differences in the viscosity between PS and PS/HDPE.


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figure 15 The temperature of a blend of PS/HDPE versus N [rpm].fully filled section.

figure 16 The temperature of PS/HDPE versus rotation speed [rpm].fully filled section , Tb = 160 °C.

The modelling of temperature and mixing will be used in chapter 8 in a modelling ofreactive compounding in the extruder.


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5 Conclusions.

With the operating conditions used here there is little difference between the heat transfermodels as proposed by Todd and Jepson. The Jepson model shows a slightly betteragreement with the experiments.In our 50 mm extruder viscous dissipation has a much stronger influence than the heatingand cooling effects of the wall. This is expected to be even more prominent when theextruder is scaled up.A strong increase in temperature occurs when the material enters the kneading section.Therefore kneading zones are effective for increasing the melting capacity of twin screwextruders.The rotational speed of the extruder was varied between 57 and 450 rpm. When therotation speed of the screw increases the viscous dissipation in the melt increases.Therefore the temperature of the melt increases.-The modelled average temperature and the power consumed has been validated withmeasured values.-The heat transfer coefficient in the kneading section could be calculated from an energybalance and the measurements fitted reasonably to penetration theory.-The results in chapter 4 will be combined with the results in this chapter which allows usto obtain both an average temperature and a maximum temperature in the channel of thecorotating twin screw extruder.-The temperature modelling can be improved by refining the work in chapter 4 byincluding the Cross-Carreau viscosity in the 3D modelling and combining this with themodelling in this chapter.More attention should be given to :- The viscosity of the powder in the powder transporting section and the heat transfer ofthe powder to the barrel.

Nomenclature.

A Area [m2]Cp Heat capacity [J.kg-1.°C-1]D Diameter [m]Espec Specific energy [kW.kg-1]f Degree of fill [-]F Force [N]H Channel depth [m]He Heat generated by viscous dissipation in the channel [W]


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h Heat transfer coefficient [W.m-2. C-1]L (axial) Length along the channel [m]2n-1 Number of independent channels [-]N Screw speed [rpm]Nspec Specific energy [kW.kg-1]Po Power [W]Q Throughput [m3.s-1]S Surface of the barrel [m2]T (average)Temperature [°C]T1 Temperature at the first paddle of the kneading section [°C]To Torque [N.m]V Circumferential speed [m.s-1]W Width of the channel [m]x Axial coordinate [m]z Radial coordinate [m]

Greek symbols

γ& Shear rate [s-1]

δ Space between flight and barrel [m]∆ Difference [-]λ Heat conductivity [W m-1 C-1]h Viscosity [Pa.s]ρ Density [kg.m-3]ϕ Pitch [rad]θ Angle (not covered) between the screws [-]τ Shear stress [Pa]σ Surface tension [N.m-1]

Subscripts

b Barrelc Channelf Flight clearanceg Glasstransition temperaturem Melt transition temperaturek Kneading elementtot Total


137

References.

1 C.H. Jephson, Ind. Eng. Chem., 45 992 (1953).2 L.P.B.M. Janssen, G. H. Noomen, and J.M. Smith, Platics and Polymers, 43, 135-

140, (1975).3 W. Schlaffer, J. Schijf and, H. Janeschitz-Kriegel, Plastics and Polymers, 39, 193-

199, (1971).4 J. van Leeuwen, Polym. Eng. Sci., 7, 98 (1967).5 D. B. Todd, Proc. ANTEC 88 conf. , Vol 1 P 54-58 (1988).6 D.J. van der Wal, E. Klomp, D. Goffart L.P.B.M. Janssen, H. Hoogstraten, Pol.

Eng. Sci., 36, 912 (1994).7 D. Goffart, D.J. van der Wal, L.P.B.M. Janssen, H. Hoogstraten, Pol. Eng. Sci.,

36, 901 (1996).8 Chapter 4, this thesis.9 Chapter 7, this thesis.10 D. J. van der Wal, L.P.B.M. Janssen, Proc. ANTEC 94 conf. 1-5 may 1994 San

Fransisco, Vol 1 P 46-49 SPE (1994).1 P.H.M. Elemans, Ph.D. thesis, Eindhoven, (1989).12 H.H. Hieber, C.H. Chiang, Rheol Acta 28:321 (1998).13 H.F. Mark, Encycl. of Polym. Science and Technology, Interscience Publ., New

York, Vol. 10.14 J.E. Mark, Physical properties of polymers handbook, (1996).15 L.P.B.M. Janssen, Twin-screw extrusion, Elsevier, Amsterdam (1987).16 M.L. Booy, Pol. Eng. Sci., 18, 937 (1978).17 K.J. Ganzeveld, PhD thesis, University Groningen (1992).18 C.A. Hieber, H.H. Chiang, Polym. Eng Sci, Vol. 32, Vol. 14, 931 (1992).

Mixing in an intermeshing corotating twin-screw extruder, chapter 7

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CHAPTER 7 MODELLING AND EXPERIMENTAL EVALUATION OF-MIXING IN AN INTERMESHING COROTATING TWIN SCREW EXTRUDER

Abstract.

Using the temperature modelling described in the previous chapter, mixing of twopolymers in the extruder has been modelled in this chapter. Coalescence is included in themodelling. This model and the model in chapter 6 (temperature and mixing) will be used inchapter 8 to model reactive compounding in the extruder. Finally this will be used toimprove the process control of reactive blending, as described in chapter 9. The size anddeformation of the dispersed phase of a blend mixed in the intermeshing corotating twinscrew extruder have also been measured. By comparing the measured and calculated sizeof a blend for several extruder parameters the model developed will be validated. Theinfluence of most of the processing parameters will be determined. The throughput, thetemperature of the barrel, the geometry of the screw and the screw speed have been varied.

1 Introductionto mechanical properties of blends.

The model developed in this chapter is a one dimensional model for the average size of thedispersed phase. It is obvious that the final size distribution can only be predicted when allparameters of interest to mixing are known at every 3D-position of the extruder, which isnot done here. Mixing, as will be described in this chapter, is of vital importance forimproved mechanical properties of blends (which is the final goal of this thesis).Sometimes combination of the properties of two polymers can be achieved by merelymixing. However improving the mechanical properties of a blend is often needed since inmany applications of blends the properties get worse instead of better. Especially themorphology of the blend has been investigated in the literature (1-10) as well as blendingand extrusion (11-24). In the conventional way the mechanical properties of a blend areimproved by improving the mixing of the different parts of the blend. However in doing sofor PS usually the mechanical properties were very poor. Therefore we first need tounderstand what determines the mechanical properties of an amorphous polymer. In asecond step we also need to understand what determines the mechanical properties of ablend. In the literature it has been stated that for optimal mechanical properties of PSblends the dispersed phase has an optimal size (14). This has been found for blends wherethere was no chemical adhesion between PS and the dispersed phase. A small size means alarge stress concentration but also a larger interface.


139

For a pure polymer it is well known from the literature that the structure of the chain of anamorphous polymer has a large influence on its mechanical properties. Kramer et al (7)ascribed the transition between brittle and ductile behaviour to a low value forentanglements resulting in a higher surface tension (see also chapter 10). Wu (6) studiedthe effects of the size of the dispersed phase for blends with rubber as the componentadded. He found that the distance between the particles of the dispersed phase of a blendshould be smaller than a certain critical inter-particle distance. This was shown to be one ofthe determining factors, whether a blend was tough or brittle. The minimum adhesionrequired for toughening was also discussed. It was found that the critical size of thedispersed phase of a blend depends on the rubber contents. PS is the matrix phase in mostof the blends studied in this thesis. The toughness increases with decreasing particle size ofthe dispersed phase for a blend with a matrix of this type of polymer. The highesttoughness was found for blends of PS and rubber at an optimum particle size of 2- 5 µm.With the results of the previous chapter where the temperature modelling has beendeveloped (and verified with measurements) we now are able to develop a computer codeto model dispersive mixing of two polymers in the extruder.

1.1 Mixing in the intermeshing corotating twin screw extruder.

In the intermeshing corotating twin screw extruder mixing mostly takes place in thekneading section due to shear and/or elongation. The dispersive mixing performance of thekneading elements in the intermeshing corotating twin screw extruder has been studiedonly by a few investigators. The minor component in many blends is the dispersed phase ofa blend (drops or filaments) mixed in a continuous phase of the major component. Heating,deformation and break-up of the dispersed phase occur during mixing. An elementary stepin the mixing process is the deformation of a dispersed drop in a flow field. An increase inthe interfacial area between the two components is accompanied by a decrease in localdimensions perpendicular to the flow direction (the striation thickness). Drop deformationis mainly governed by the capillary number and the ratio of the viscosities of both phases.Any mixing model should incorporate the governing mechanisms in a principally transientway in order to be applicable to a practical situation.A number of papers have been published dealing with morphology development duringprocessing. Most working models developed measure morphology development in asingle-screw extruder. Not many models for mixing in a corotating twin screw extruderswith these break-up models are known so far.Elmendorp (8) has reported most of the expressions needed to model the deformation andbreak-up time of the dispersed phase of a blend during mixing of immiscible fluids. Thesize of the dispersed phase of a blend in a 2-zone mixing model with an estimated value for


140

the shear rate has been modelled by Janssen (17). The results of his calculations showed adecrease in size of the dispersed phase of a blend to approximately 1 µm after passing 6kneading elements. However, the values of the elongation and shear rate were not basedon real-case values for twin screw or single screw extruders. Sufficiently accurate values ofthe shear and elongation rate can be calculated from 3D modelling (20, 21) which is usedin our calculations .The time needed for deformation and break-up of the dispersed phase of a blend intosmaller spheres has been studied for a number of decades. In particular the time scales ofthe rheological processes must be considered to determine whether the available processtime in the extruder suffices for a specific event to occur.Wu (6) published a dimensionless master curve of the Capillary number, γ.η.d/s, versus theviscosity ratio, p, for melt extrusion in a corotating twin screw extruder for several blendsof PET, nylon, and EP rubbers. From these curves it is clear that the size of the dispersedphase of a blend can only decrease due to elongation for a viscosity ratio larger than 3.5.From our earlier calculations shear rate was found to dominate elongation rate in the flowof the twin screw extruder used in our experiments except for in the intermeshing regions.Both, the shear and elongation rate, have been incorporated in our calculations.

2 Modelling of mixing in the corotating twin-screw extruder.

The 3-D flow and temperature profiles were calculated in chapter 2, 3, and 4 and partiallyvalidated in chapter 6. Deformation, break-up, the break-up time of the dispersed phase inthe melt, the residence time, and the occurrence of coalescence have been calculated.

The effectiveness of mixing of two polymers is influenced by several processes :

-The heating or cooling of the polymers by the barrel wall and heating by viscousdissipation determines the melting of the mixture of polymers and therefore the positionwhere they start to mix.-The shear rate in the melt determines the deformation of the dispersed phase in the fullyfilled sections.The model to describe mixing in the extruder has been based on the followingassumptions :

A subdivision of the mixing process can be based on the local capillary number in theextruder. The capillary number decreases continuously along the extruder due to thedecreasing size and is calculated at every axial position at the modelled temperature andviscosity.


141

The extended lamellar pattern of striations becomes unstable due to periodic distortionsand striations rupture into fibrils and later into globules. Depending on their size thesedrops may eventually be stretched and broken again unless the interfacial tension, σ(T),protects them against further deformation. The parameters which are calculated at everytemperature and position along the extruder are :

timeessdimensionl:tt

spheretheofdiameter:

(1) numberReynolds:

density:

We/Re :number ycapillaritthe:Ca..

phase)2(continuousand(1)dispersed;betweenratioviscositythe:

r

b

2

2

2

1

d

vd

d

p

ηρρ

σηγ

ηη

&

=

Formation of thin layers occurs mostly in kneading sections in the corotating twin screwextruder. Due to the layer-forming mechanism the phase size decreases tremendously inthe first minute.

Note that :

-Little mixing occurs in the powder transport section. Also little mixing is expected in themelt transporting section where shear rate will be very low in comparison to the kneadingsection. In the initial stage, under conditions where both polymer components are melting,the pellets produce fine lamellar structures. In the direction of the die of the extruder, thethickness of these striation layers is reduced due to stretching when Ca>>Cacrit.-The kneading section in the extruder is completely filled.-In the first set of kneading elements the dispersed phase has not been melted and thereforeno deformation occurs on this location. This delays break-up of the dispersed phase anddecreases the mixing efficiency.-The transporting elements are not completely filled, which makes the heating of themixture less efficient.-Mixing takes place mostly in the fully filled kneading section of the extruder due to highshear- and elongation rates. The flow of material between the flights and the barrel hasbeen neglected.-It has been assumed that the average size distribution of the dispersed phase of a blendresults from the average residence time and the average shear in the kneading elements.


142

These assumptions have been validated and found to be reasonably accurate in chapter 2,3, and 4.-If no break-up of the dispersed phase takes place, the average diameter of the dispersedphase of a blend will relax to its original size. This is the case when the residence time isshorter than the time needed for break-up.-After break-up, the dispersed phase of a blend consists of deformed droplets that relax(within less than one second) to spherical shapes. The spherical shape results in amaximum volume/surface ratio of the dispersed phase of the blend.-Coalescence of the dispersed phase has been taken into account even when only verysmall amounts of the dispersed phase of a blend are used.-Although most polymers exhibit viscoelastic behaviour, our modelling has been based onan analysis for Newtonian liquids.

2.1.1 A simplified modelling of the average size of the dispersed phase of a blend.

In a simplified approach it can be assumed that the sphere breaks up into two spheres. Therate of deformation has been taken into account by dy/dz, figure 1a. If the shear rate issmall the deformed sphere in figure 1a will have only a small angle with the vertical axis.

figure 1a Deformation and break-up of the dispersed phase.

The deformation and break-up mechanism of the dispersed phase of a blend is independentof the size of the dispersed phase and can be found by calculating the volumetricdeformation in a shear field, as shown in equation 4.For this simplified approach it is assumed that the surface tension is zero and the totalvolume of the sphere stays the same while the dispersed phase deforms. The volume of thedeformed sphere is constant. The deformation is the ratio between dz and dy in figure 1a.The volume of the dispersed phase is constant as long as no break up occurs for which d1

is the diameter of dispersed phase before deformation. The simplified approach leads toequation 2 and 3 while a detailed approach provides equation 4 :


143

if deformation is linear in shear :

(2)

factor which takes break up into two spheres into account :

(3)

(4)

∂∂

γ

∂∂

γ

γ

γ

dt

C d

C

Elmendorpdt

d

11

3

1 0 51

112

≅ −

= −

≅

* *

: * *

.

..

where &γ is the shear rate while the dispersed phase changes as dv/dz (in the flow field as a

function of the axial parameter z). From equation 4 an approximation of the final size ofthe dispersed phase can be found. However this is only valid in a pure shear flow. Underthe assumption made an estimation of the deformation of the sphere can be calculated. In amore extensive research the deformation as described in the thesis of Elmendorp has beenfound which is therefore used in our modelling.


144

2.1.2 Modelling of the average size of the dispersed phase of a blend.

The opposing force against deformation is the surface tension. Therefore the force due tosurface tension is subtracted from the deformation force, resulting in the following semi-empirical equations for the size of the dispersed phase which can be used as an estimation :

constants:,

:

)**(

21

..

2

5.0

1

CC

CdCtd

d

mmddm

d

ηη

γγττ

ησ

γ∂∂

==

−−= &

(5)

At the start of the break-up process the surface tension usually is small compared to thefirst term on the right hand side in equation 5. In the computer calculations the shear andelongation rate at every rotation speed and throughput are calculated for the extruder (11,18). From chapter 4 it could be concluded that the elongation is small in the channel. Theequations used for the average shear- and average elongation rate in a kneading paddlewere derived in chapter 2, 3, and 4. Equation 3 is a strongly simplified version of thereality of mixing. Elmendorp gives the equations for the deformation and mixing of thedispersed phase in a blend (equation 6).

d ≅

−

γo

1 2/.

(6)

After deformation break up of the dispersed phase takes place after some time. The totalstrain (elongation and shear) applied to the dispersed phase in the extruder can beexpressed as :

γ γ γ= +( )

: , :

:

:

. .

f f c cr

r

t tt N

f flight c channel

N rpm

t residence time at the actual throughput

260

(7)

At every axial position in the kneading section of the extruder, the deformation and thetime for break-up of the dispersed phase is calculated with expressions from the literature(8, 17). The time for break-up has been calculated with :

))(10

ln()()( 2

023

0

TRT

TRT

t cb

σση

Ω= (8)


145

Where Ω is a constant which is calculated with the expressions of Tomotikata (10), and R0is the thickness or minor axis of the long slender body formed during deformation. Thetime needed for break-up in a simple flow has been studied elsewhere (8). If the timeneeded for break up is too long, compared to the average residence time, the average sizeof the dispersed phase of a blend will not decrease over the axial position in the extruder.The algorithm in the modelling at every axial step along the extruder is therefore :

-Evaluate the average residence time in the (kneading and transporting) channel.-Compare the residence time with the break-up time.-Dispersive flow can be obtained if the residence time in a high shear flow is longer thanthe time for break-up and the viscosity ratio is smaller than 3.5, since the flow is mostlyshear flow in the extruder and break-up and deformation is mostly due to shear rate.The deformation of the dispersed phase of a blend leads to a large length over width ratio(L/B). The long slender bodies formed will break-up into spheres with a diametercomparable in size with B.In many cases the equilibrium size (when d is not anymore changing in time as shown inequation 6) is never reached because equilibrium between coalescence and break-up of thedispersed phase is reached at a larger size of the dispersed phase. This size was describedby Favis (5, 22, 23) as :

dP T

T

P E

T

r r dk%( )

( )(

( )). .= +

241

4ϕσ

πη γ

ϕ

πη γ(9)

where Pr is the probability that a collision between two spheres will result in coalescence, jis the volume fraction of the dispersed phase, and Edk is the bulk breaking energy.With increasing shear (and/or elongation) the average size of the dispersed phase of ablend decreases. This size of the dispersed phase decreases until equilibrium in equation 6ais reached.Mixing has been investigated by many authors such as Chella and Ottino who presented ananalysis of mixing in cavity flows and in single screw extruders (24)


146

3 Experimental set-up.

PS/HDPE mixtures are extruded with a Baker Perkins 50 mm, self wiping corotating twin-screw extruder (figure 1b). Two different screw configurations were used as also describedin (2). Samples were taken at the die and studied with SEM (figure 1c, In the figures ummeans µm = 10-6 m. ).

figure 1b screw geometry.

figure 1c Morphology of the blend measured with SEM

The experimental procedure contained the following measurements :


147

-Pressures are measured at the die and 80 mm before the die and were in reasonablecomparison with the calculated values. The temperature of the polymer in the melt at thekneading section is measured with an IR thermometer.-Visually the degree of fill is estimated in the partially filled transporting section.Directly after a sample is taken it is cooled with liquid nitrogen. With S.E.M themorphology of the blend is made visible from which the average length and thickness ofthe dispersed phase is measured, figure 1c.

4 Results and discussion.

The average size of the dispersed phase of a blend, calculated with our computer model,has been validated. Only the calculated size of the dispersed phase in the kneading sectionwill be shown since little mixing is found in the partially filled section. The influence ofseveral processing conditions on mixing are studied such as the temperature of the melt,residence time, and shear rate. For the matrix Styron 7000 (PS, SHELL) was chosen. Thebarrel temperature was 200 °C and the number of kneading elements 7.

4.1 Modelling the average size of the dispersed phase in the kneading section.

The thickness of the dispersed phase of a blend is chosen as the best measure for itsdeformation since often the length of the dispersed phase can not be determined with SEMIn figure 2a the development of the thickness of the dispersed phase as calculated in thekneading section is shown. The thickness of the dispersed phase is constant in the partiallyfilled section and decreases in the kneading section.

figure 2a thickness versus axial position in extruder.


148

figure 2b Length of dispersed phase versus axial position in the extruder.

The length of the dispersed phase increases to a value which is very large relative to thesmall volume of the channel in the kneading section, figure 2b. Since the thickness of thedispersed phase decreases the Capillary number also decreases along the axial position inthe extruder, figure 3.

figure 3 Capillary number versus axial position in the extruder.


149

Usually it is assumed in the literature that small perturbations in the flow cause waves atthe interface of the dispersed phase. These waves can grow and cause break-up of thedispersed phase. The time for break-up depends on this wave but also on the type of flowin the extruder. A sudden change of thickness of the dispersed phase causes a jump in thecapillary number in figure 3. After the material leaves the kneading section at 0.47 m the(effective) shear rate drops to a smaller value resulting in a jump in the Ca number. The

thickness of the dispersed phase (B), figure 2a, decreases resulting in figure 3, Ca = σγη B&

.

Average values of the shear rate have been used. In order to properly describe mixing inthe extruder a complicating factor is that all the processes take place in a very complicated3-D flow. Folding of the dispersed phase, which has the shape of a long slender body, maycause an enhancement of the break-up especially in the intermeshing region of the twinscrew extruders (4). However no proof was found in the literature that this phenomenaneeds to be included in our modelling. Therefore reorientation and details from the 3-Dflow in the extruder were not taken into account in the calculations.When the capillary number in figure 3 is decreasing it will become smaller than the criticalcapillary number. Only when the thickness of the dispersed phase is small enough, the timeneeded for break-up of this long slender body is shorter than the residence time availableand break-up can take place.

figure 4a The time for break-up versus axial position in the extruder.

The time for break-up decreases due to the decrease of the thickness of the deformeddispersed phase along the axial position in the extruder, figure 4a. An important parameter


150

in these calculations is the average temperature (Tb = 200 °C) as modelled earlier inchapter 6. The time needed for break-up decreases with increasing rotation speed becausethe diameter of the thread decreases with increasing rotation speed, figure 4b.

figure 4b the time for break-up after 7 kneading elements, Q = 3 kg/h, varying N.

figure 4c the time for break-up after 7 kneading elements, N = 60 rpm, varying Q.

Increasing the rotation speed usually causes an increase of the deformation and therefore adecrease of the thickness of the deformed dispersed phase. However other parameters suchas the temperature of the melt, are also influenced when the rotation speed increases. Thedistribution in size of the dispersed phase is measured with SEM, figure 5.


151

figure 5 The distribution of the size of the dispersed phase , experimental,N = 269 rpm, Q= 3.3 kg/h (um = µm).

figure 6 The average diameter of the dispersed phase versus the axial position in theextruder, calculated, N = 57 rpm, Q = 1 kg/h.

Usually a broad distribution of the size of the dispersed phase is found, figure 5. Thediameter of the dispersed phase as calculated suddenly drops by a factor 1000 in a veryshort length in figure 6. This occurs in the kneading section because the shear rate and


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residence time is relatively large. The dispersed phase first has a large deformation beforebreak up occurs.

4.2 The influence of the rotation speed of the screws.

One of the most important parameters for mixing is the rotation speed of the extruder.With increasing rotation speed the shear rate increases, the viscosity decreases and thetemperature of the melt increases (18). The size, the thickness, and the length of thedispersed phase will be calculated at the position of the seventh paddle of the kneadingsection.

figure 7a Equivalent diameter (6V/π)0.33 versus rotation speed ;Q = 3 kg/h, Tb = 200 °C, number of kneading elements :7.

As can be expected the average size of the dispersed phase decreases with increasingrotation speed, figure 7a. If the rotation speed increases the length of the dispersed phasedecreases if break-up occurs. When no break up occurs the length of the dispersed phaseincreases due to an increase in deformation. In figure 7b break up is delayed for N smallerthan 270 rpm. This is because the residence time is smaller than the break-up time at N<270 rpm and therefore the dispersed phase did not break up.


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figure 7b The length of the dispersed phase versus rotation speed ,Q = 3 kg/h.

Increasing the throughput causes a decrease of the residence time which causes a decreaseof the length of the dispersed phase and a decrease of the temperature of the melt as shownin figure 8a. With decreasing length of the dispersed phase the thickness of the dispersedphase increases. This increase in thickness results in an increase of the break up time.Combined with a shorter residence time this leads to less break up and a larger size of thedispersed phase, figure 8b.

figure 8a Length (L [m]) and temperature (Tmelt) versus the throughput of theextruder, N = 60 rpm.


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figure 8b Thickness (B [µm]) , break up time (tbr) versus throughput (Q), N : 60 rpm.

figure 9 tbreak-up - Temperature of the barrel, N = 107 rpm, Q : 3 kg/h.

The time for break up of the dispersed phase at the last paddle of the kneading section hasbeen calculated. From the calculations it is found that the break up process is stronglyinfluenced by the temperature (equation 8) and the thickness of the dispersed phase. Wefind that the size of the dispersed phase is determined by coalescence if the blend containsto much of the minor phase.


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4.3.1 Comparison between modelling and measurements, PS/HDPE blends.

The calculated size of the dispersed phase will be compared with the average values of thesize of the dispersed phase as measured. Calculation of the distribution of the size of thedispersed phase is possible with the results from chapter 4. However due to a lack of timeno 3-D residence time distribution was calculated (11). For simplicity it will be assumedthat the average size distribution of the dispersed phase in figure 5 results from the averageresidence time and average shear in the kneading elements. The extruder has vent ports attwo axial positions before and after the kneading section. The vent ports are at the top ofthe extruder, above a partially filled transporting element.

figure 10 Thickness of the dispersed phase (calculated and measured) versus Q,N = 314 rpm. Tb = 200 °C, 7 kneading paddles.

The average thickness of the dispersed phase as calculated at a position directly after thekneading section is comparable with the measured values, figure 10. With increasingthroughput the residence time and temperature decrease, both having an influence on thesize of the dispersed phase. Usually an increase of the throughput has the opposite effect,as an increase in rotation speed on the deformation of the dispersed phase. The mostimportant reason for this is the decrease of residence time, specific energy, and shear.


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4.3.2 Comparison of our computer modelling with measurements of others.

Favis et al (23) measured the size and size distribution of the minor phase in melt blendedpolypropylene/polycarbonate blends in a ZSK30 with a barrel temperature of 240 [°C] anda rotation speed between 100 and 300 [rpm].

figure 11 Calculated results and measurements by Favis (5).

figure 12 Calculated results and measurements versus viscosity ratio, p by Favis (5).

Little influence of the rotation speed was found, figure 11. The line represents values fromour computer calculations for which the rheological data and surface tensions were used as


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given by Favis (22). From our calculations it became clear that, due to a very long mixingsection used and the very large rotation speeds, the size of the dispersed phase isdetermined by the equilibrium between mixing and coalescence (5 % PP was mixed in).

figure 13 Calculated results and measurements (by Favis (5)) versus volume of the dispersed phase.

The calculated size of the dispersed phase as a function of the viscosity ratio again shows avery good resemblance to the measured values of Favis, figure 12. Mixing efficiencydecreases if the viscosity ratio increases. Mixing is obviously determined by shear, but alsoa little by elongation. If the flow was purely shear no mixing would have been found forP>4, according to Grace (16).An increasing viscosity ratio causes an increase in the size of the dispersed phase infigure 12. Increasing the volume of the dispersed phase increases the minimum attainablesize due to an increasing coalescence. The size of the dispersed phase is calculatedcorrectly with the computer calculations, figure 13.

5 Conclusions.

For optimising polymer blend properties it is essential to control and to predict the size ofthe dispersed phase of a blend during mixing in the extruder.The shear rate in the extruder, due to the rotating movement of the screw, causes theshape of the dispersed phase of a blend to deform. Due to the break-up of the deformed


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dispersed phase of a blend its average size decreases. From the comparison of themeasured and the calculated values of the size of the dispersed phase a number ofconclusions are found :

-The calculated values are found to be in reasonable agreement with the measured ones.-The time needed for decreasing the size of the dispersed phase by break-up is very shortfor thin threads. Nevertheless a dispersed phase with the shape of a thin thread is found formany practical situations of extrusion where polymers are mixed.-If the kneading section is long enough the size of the dispersed phase of the blend is inequilibrium with the surface tension. For a higher shear rate the equilibrium value for thesize of the dispersed phase is smaller.-To calculate the size of the dispersed phase coalescence is a very important process totake into account.

Nomenclature.

A Area [m2]B Thickness of the dispersed phase [m]Cp Heat capacity [J.kg-1.C-1]D Diameter [m]d Size of the dispersed phase [m]f flight clearance [m]L (axial) Length [m]N Screw speed [rpm]Q Throughput [m3.s-1]RT Residence time [s]t Time [s]

Greek symbols

∆ differenceh viscosity [Pa.s]ρ density [kg.m-3]s surface tension [N.m-2]τ shear stress [N.m-2]

γ.

shear rate [s-1]

ϕ pitch anglel Heat conductivity coefficient [W.m-1.C-1]


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Subscriptsb breakupr residencec channelf flightk kneading element

References.

1 D. J. van der Wal, L.P.B.M. Janssen, Proc. ANTEC 94 conf. 1-5 may 1994 SanFransisco, 1, P 46-49 SPE (1994).

E.H. Merz., G.C. Claver, and M.J. Bear., Polymer.Eng. Sci., 22, 325, (1956).3 C.G. Gogos, M. Esseghir, D.W. Yu, D.B. Todd, J.E. Curry, p 270, ANTEC '94

(1994).4 P.H.M. Elemans, Ph.D. thesis, Eindhoven University, (1989).5 B.D. Favis, J.M. Willis, J. Polym. Sci., Polym Physics, 28, 2259 (1990).6 S. Wu. Polym. Eng. Sci., 30, 753 (1990).7 E.J. Kramer, L.L. Berger, Adv. Polym. Sci. 91/92, 1 (1990).8 J.J. Elmendorp, Ph. D. thesis, Delft University of Technology (1986).9 Lord Rayleigh, Proc. Roy. Soc. (London), 29, 71 (1879).10 S. Tomotika, Proc. Roy. Soc. (London), A150, 322 (1935).11 Chapter 4, this thesis.12 L.P.B.M Janssen, Twin-screw extrusion, Elsevier, Amsterdam, (1978).13 S. Wu, Polym. Eng. Sci. 27, 335 (1987).14 S. Wu, Polymer, 26, 1855 (1985).15 D. B. Todd, Proc. ANTEC 88 conf. , Vol 1 P 54-58 (1988).16 H.P. Grace, Chem. Eng. Comm. 14, 225 (1983).17 J. Janssen, PhD thesis Eindhoven, (1993).18 Chapter 6, this thesis.19 L.A. Utracki, Z.H. Shi, Polym. Eng. Sci. 32 (24), 1824 (1992).20 D.Goffart, D.J. van der Wal, E.M. Klomp, H.W. Hoogstraten, L.P.B.M. Janssen,

Pol.Eng. Sci., mid april, 36, 901, (1996).21 D.J. van der Wal, D.Goffart, E.M. Klomp, H.W. Hoogstraten, L.P.B.M. Janssen,

Pol.Eng. Sci. mid april, 36, 912, (1996).22 B.D. Favis, J.P. Chalifoux, Polym. , 29, 1761 (1988).23 B.D Favis, D. Therrien, Polym. 32, 1474 (1991).


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24 R. Chella, and M. Ottino, Ind .Eng. Chem. Fund, 24, 170 (1985).

Reactive compounding in the extruder, chapter 8

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CHAPTER 8 MODELLING AND EXPERIMENTAL EVALUATION OF-REACTIVE COMPOUNDING IN THE EXTRUDER.

Abstract.

With our new method of reactive blending (as described in chapter 1) an alloying agent hasbeen produced in situ in the dispersed phase of the blend. Monomer is absorbed in thedispersed phase where it reacts to form the alloying agent. In our experiments monomerslike styrene (S), acrylates (such as butylmethacrylate, BMA), or maleic anhydride, MAH,are used. Polystyrene (PS) forms the matrix phase and high density polyethylene (HDPE)the dispersed phase.A computer model has been developed which describes most of the processes relevant tothe new method. From the calculations it was found that grafting of monomer in thedispersed phase should occur in the pressure build up section before the polymers aremixed in the kneading section.It is preferred if the reaction takes place in the dispersed phase. However monomer candiffuse out of the dispersed phase if mixing is good before the conversion of the monomeris large. Therefore the conversion of monomer in the dispersed phase is large if thereaction starts in the pressure build up section since here the size of the dispersed phase isalmost constant. This has been confirmed by our modelling where the conversion is almostindependent of the rotation speed if the screw geometry is transporting-pressure built up-kneading-transporting.The conversion of styrene (S) or maleic anhydride (MAH) in the dispersed phase either isconstant or decreases with increasing rotation speeds if the screw geometry istransporting-kneading-transporting. This is due to an increase of mixing and mass transfer(of monomer out of the dispersed phase) in the kneading section with increasing rotationspeed. The conversion of monomer in the dispersed phase is larger if the temperature andinitiator concentration is larger. It has a maximum or is almost constant as a function of therotation speed if a pressure build up section is present before the kneading section.

1 Introduction.

Following the modelling of the mixing and temperature in the kneading and transportingsection of the extruder we will now calculate the concentration of the monomer and theconversion of the monomer in the dispersed phase along the extruder. The results inchapter 6 and 7 are important since for reactive processing in the extruder the temperatureand mixing in the melt is an important parameter (1). The computer code developed in this


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chapter will be used in the next chapters to improve mechanical properties of a blend, suchas elongation at break and notched Izod impact strength.The mechanical properties of a blend made with reactive compounding must be comparedwith those of a blend made with the conventional method of compounding in which acompatibiliser is mixed in a blend. Adding a compatibiliser is often expensive since it mustbe produced in a separate production process and mixed into the blend, (sometimes analloying agent is used instead of a compatibiliser). These methods usually are also quiteexpensive due to the need of either a sequence of complicated processes or expensivematerials. Barendsen and Heikens (2) describe the addition of graft-copolymers of LDPEwith PS (PS-g-HDPE) to PS/HDPE blends. Addition of 7.5% by weight copolymer causeda substantial reduction in size of the dispersed phase.As an alternative method, Locke and Paul (3) grafted styrene to LDPE by radiation withcobalt 60 γ-radiation. The copolymer produced in advance was melt blended with PS andHDPE in a Brabender plasticorder. The effectiveness of the alloying agent was controlledduring the production process by the competition between grafting and crosslinking. Bakerand Saleem (4) produced blends of acid modified LDPE and oxazoline modified PS in amelt mixer giving materials with improved mechanical properties over unmodified PS/PEblends. The increase of elongation at break was attributed to the formation of an "in situ"alloying agent due to the interaction between the two components.

A less expensive alternative for the conventional method is to create the alloying agent "insitu". In this method the alloying agent will be produced by a reaction occurring at theinterface between both polymers. In the model presented here, the main interest is theongoing reaction in the interfacial region or in the dispersed phase during processing in theextruder. Some experiments were performed with the grafting reaction of BMA or MAHon HDPE in a blend of PS/HDPE.As described in chapter 1 the general idea in the method is that many polymers can bedissolved in a wide spectrum of monomers, even if the resulting polymers are incompatible.Monomers are mixed with an initiator and then absorbed in a polymer. After thetemperature increases monomer polymerises and is grafted on the polymer chains. Graftcopolymers are formed, forming "in situ" an alloying agent in the minor phase, during theblending process.So an essential process for the "in situ" production of an alloying agent is grafting orfunctionalizing the polymer chains of the dispersed phase. A popular route offunctionalizing polyolefins is the use of unsaturated carboxylic derivatives. For free radicalgrafting some of the most interesting monomers are unsaturated carboxylic derivatives,such as maleic or itaconic anhydrides, and vinylic or acrylic substances containing a secondfunctionality. Maleic anhydride, MAH, has a superiority over other monomers because it


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can hardly homopolimerize, but is also reluctant to free radical grafting, due to a deficiencyof electrons in its double bond. This is due to the electron-attracting nature of the carbonylgroup, the symmetry of the double bond, and a steric hindrance due to di-substitution.Because of the limited space available only a small part of the investigations to graft MAHon HDPE reported in the literature will be described in this chapter. For the "in situ"generation of a grafted polymer chain the grafting of BMA or MAH on HDPE isreasonably well known. Bonner et al (5) have investigated the reactive blending of Maleicanhydride grafted Nitrile Rubber (MAH-g-NBR) by melt mixing MAH with NBR in thepresence of a free radical initiator. By subsequent reactive blending with other polymersthe alloying agent is produced at the interface. Free radical grafting was used (8) for the insitu generation of an alloying agent in a blend. An important choice as monomer to begrafted on HDPE is styrene, since HDPE-g-PS may form an alloying agent for a HDPE/PSblend. Another possibility is grafting of MAH on HDPE which is known to cause anefficient adhesion of the grafted chain (HDPE-g-MAH) to other polymers, such as in ablend of HDPE/Nylon (PA). However usually the grafted chain contains only onemonomer per graft when MAH is the monomer. In the literature it is often stated that inmost cases no homopolymerisation of MAH takes place. Lambla et al (8) state thatgrafting of MAH in the presence of styrene (St) is a way of maximising grafting MAH onHDPE or PP while minimising chain degradation which seems a good choice for oursystem. It is also known that copolymerisation of S and MAH is a relatively fast alternatingpolymerisation reaction (10, 11).

Hogt (10) has pointed out that if the local concentration of MAH is larger than 4%, phaseseparation of MAH and polyolefins takes place. If the concentration of MAH increases toa value larger than 4% the phase separation increases and the conversion of grafted MAHdecreases.Lambla (8, 11) has investigated the stabilisation of a blend of polyethylene (LDPE) andpolyamide (PA) by in situ grafting of BMA or MAH in the presence of styrene. However itmust be noted that in our case monomers were dissolved in HDPE before feeding it in theextruder. Lambla et al fed monomer and initiator into the extruder in a separate stream(essentially into the matrix) which is an essential difference from our approach. Thereaction of S together with BMA or MAH was much faster than the grafting of MAHonly, which can be attributed to the formation of a charge transfer complex CTC, of anelectron donating monomer such as Styrene with MAH. Ganzeveld and Janssen alsoinvestigated grafting of MAH on HDPE in the counter rotating twin screw extruder (12,13).


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2 Modelling reactive compounding.

Free radical grafting on HDPE in the dispersed phase of a PS/HDPE blend is studiedduring reactive compounding in an intermeshing corotating twin screw extruder. Otherblends are also possible for the method proposed here. The blend PS/HDPE is chosensince PS and HDPE have an excellent processability and are widely applied, while thematerial properties of the uncompatibilised blend are usually brittle. If the properties of thePS/HDPE blend can be improved, it is likely that the method will also be successful formany other blends, since usually it is very difficult to improve the toughness of a PS/HDPEblend.

2.1 The different steps taken in our model.

The influence of the processing parameters on the conversion of the reaction in thedispersed phase will be determined both theoretically and experimentally. As described inchapter 1 generation of an alloying agent from monomer and initiator starts in thedispersed phase. The model is based on calculation of the following parameters along theaxial length of the extruder (6, 7, 9, 14, 15, 16):

-Reaction in and outside the dispersed phase (chapter 5)-Diffusion out of the dispersed phase (chapter 5)-The temperature of the melt (chapter 4 and 6)-The size of the dispersed phase (chapter 7)-The average residence time of the blend in the channel.

The following three sections in the extruder have been distinguished :

-The solid transporting section, before the first kneading section. In the partially filledtransporting elements directly after the feeding point friction between the granule particlesgenerates dissipation. The material is also heated by contact with the barrel.-The fully filled melting section. Melting of the polymer mostly occurs in the first fewcentimetres of the kneading section. The large shear rates in this section cause a largetemperature increase due to viscous dissipation.-The partially filled melt transporting section. Material in the partially filled melttransporting section has a higher temperature than in the feeding section. Part of the meltwill be scraped between the flight and the barrel and the average shear rate in this sectionwill be larger than the shear rate in the powder transporting section.


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Plug flow is assumed in our model for the melt in the extruder. Because of this assumptionwe can model reactive compounding in the extruder by calculating the average value for allthe processes of interest. Therefore in each step along the extruder the following factorsare calculated in the model :

-Mass transfer of monomer out of the dispersed phase.-The reaction velocity of monomer in the dispersed phase.-Decomposition of the initiator.-The temperature of the melt.


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A number of assumptions have been used in the calculations :

-The flow in the channel of the extruder is plug flow. Therefore the average residence timeis used in the calculations instead of the residence time distribution in the extruder. Valuessuch as the temperature of the melt and the size of the dispersed phase are average values.-The kneading section with a stagger angle of 150 ° is completely filled. This has beenverified by opening the extruder and visual observations.-Above the glass transition temperature of PS diffusion as well as reaction occurs in theminor and major component of the blend.

2.2 Measuring and modelling the reaction velocity of monomer in the melt.

In the calculations addition polymerisation kinetics have been used. The main reactions inthe grafting process are :

initiator decomposition ROOR ® 2RO* (1)hydrogen abstraction RO* + P ® P* + ROH (2)graft initiation P* + M ® PM* (3)intramolecular proton abstraction PM* ® P* + M (4)graft propagation PMn* + M ® PMn+1* (5)homopolymer initiation RO* + M ® RO + M* (6)propagation Mn* + M ® Mn+1* (7)depropagation Mn+1* ® Mn* + M (8)termination Mn*+ M* ® Mn+1 (9)

The reactivity of polyolefins originates from hydrogen abstraction along the hydrocarbonskeleton. A problem for a high grafting efficiency is the competition between grafting andhomopolymerisation, crosslinking, and chain scission due to hydrogen abstraction alongthe hydrocarbon skeleton. After decomposition of the initiator, its radicals are capable ofhydrogen abstraction of the polymer chains leading to radicals on the HDPE chains.Unfortunately little is known about the stability of a radical in a melt, and even less isknown about the stability of radicals during processing in extruders. Monomers in theneighbourhood of radicals on HDPE chains will react with these radicals. At the same timemonomer and initiator diffuses out of the dispersed phase. The decomposition velocities kd

of initiators are generally well known. For the initiator Trigonox 145 (AKZO-NOBEL)was chosen for which the data are given in datasheets :


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kov =

=

= − ⋅

Ae m mol s

A m mol s

E J mol

EaRT

A

[ / ]

[ / ]

. [ / ]

3

12 3

5

10

1 2 10

(1)

Monomer styrene (S) or, as an alternative, both S and BMA or MAH may react byhydrogen abstraction in the dispersed phase and is grafted on HDPE chains. This graftedpolymer forms an alloying agent in the dispersed phase. The amount of monomer graftedonto high density polyethylene in the dispersed phase has been modelled and comparedwith experiments. For example if MAH is absorbed in HDPE crosslinking of HDPE,HDPE-g-MAH or reactions forming HDPE-MAH-PS may occur.The overall reaction velocities were measured with DSC. In order to determine the kineticsa few milligram of a mixture (1:1) of HPMA:BMA was mixed with initiator (T145,AKZO-NOBEL) and absorbed in a porous granule HDPE (accurel). A scanningmeasurement is done in which the temperature increases with 10 °C per minute. The heatof reaction is measured in figure 1. The reaction heat if one mole monomer reacts must beknown. The overall reaction velocity, kov, has been calculated from this. With an increaseof the conversion a reduced propagation velocity is found from the DSC graphs.

figure 1 DSC measurements, HPMA/BMA versus temperature (also figure 1c)

Before being placed in a sealed cup in the DSC monomer and initiator are absorbed inHDPE. The reduced propagation velocity can be calculated with the method described in(19) (figure 3) :

R k C C Fp t p Rtot t M t active, ' , ' , '=

⋅(2)


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Where CRtot is the total concentration of free radicals, CM is the monomer concentration,and Factive is the fraction of active radicals after initiation. Marten and Hamiliec (17) havecalculated the reduced propagation velocity, Rp , and the propagation velocity, kp. Aftersome time the reaction is diffusion limited at conversions larger than 40 % for thepolymerisation of MMA , figure 2.

figure 2 Reaction velocities of MMA (Marten (17)), see also figure 8, chapter 5

Even relatively slow propagation reactions involving small monomer molecules becomediffusion-controlled well below the limiting conversion (17). In their article Marten andHamielec found that kp already begins to drop in value at a conversion of about 50 %,figure 2.In our case monomer is present in a highly viscous surrounding which is placed in a DSCafter which the temperature has been increased with 10 °C per minute. The reactionvelocity increases with temperature but after some time the monomer is not able to diffusetowards a reactive site which slows down the reaction. The overall reaction velocity, vp isrelatively small and the reactivity per radical (kp, figure 3) decreases after an initialincrease (this is comparable with Rp in figure 2).


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figure 3 Reaction velocity (vp) versus time, DSC, HPMA/BMA absorbed inHDPE, Trigonox 145; reactivity per radical : kp= vp/radicals.

figure 4 DSC, conversion and reaction velocity of the reaction of BMA in HDPE.

The reaction velocity of BMA absorbed in HDPE "vp" has a maximum in time, figure 4.

The conversions are below 40 %. This low value assures that no depletion of monomer caninfluence the reaction kinetics, figure 4. The kinetics of the reaction of monomer in theswollen system have been fitted with an Arrhenius equation. Complications arise from the


170

fact that many reactions can take place, and that the efficiency of the initiator, and diffusionlimitations of the reactions are unknown.

2.3 Modelling and measuring the size of the dispersed phase, an example.

When the rotation speed increases the size of the dispersed phase decreases which has beenmodelled for pure PS/HDPE in chapter 7. It has also been measured for the reactive blend.When the rotation speed of the screw increases the measured diameter of the dispersedphase of a reactive blend decreases almost linearly, figure 5. This size is much smaller thanwhen PS and HDPE are mixed without the use of reactive compounding (for which thesize was in the range of 0.8 µm, figure 10, chapter 7).

figure 5 The size of the dispersed phase, reaction MAH/St, Tb = 200 0C,Q = 6.3 [kg/h], 7 kneading paddles.

Improved mixing for reactive blending in comparison with the results in chapter 7 is due toa decrease of the surface tension if an alloying agent is formed in the dispersed phase dueto reactive compounding. In chapter 9 some equations will be given allowing the modellingof the size of the dispersed phase in reactive blending.Now we will show the results of the computer modelling of the conversion of monomer inthe dispersed phase. In this modelling the results of the previous chapters have been used.Therefore in the computer code the temperature (chapter 6) and the size of the dispersedphase (chapter 7) have been modelled. The diffusion coefficients of monomer (≅10-12) andinitiator (≅10-15) as measured have been fitted to Arrhenius equations in chapter 5.


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2.4 Modelling of the diffusion of monomer out of the dispersed phase, an example.

The screw used in this modelling consists of a transport section (of which the last part isfully filled), a fully filled kneading section (7 paddles), and a second transporting section ofwhich the last part before the die is again fully filled.

figure 6 The flux of MAH out of the dispersed phase versus position in the extruder

The flux increases strongly at a position 0.38 m from the hopper because the kneadingelements here are fully filled (figure 6). The decrease of the monomer concentration in thedispersed phase after the blend has passed the kneading section is small and theconcentration remains almost constant. Note that the residence time of the melt in theextruder at the position of the peak is long while it is short in the section before and afterthe peak. An alloying agent will be formed in the dispersed phase when copolymer isgrafted on polymer chains of HDPE. A graft copolymer MAH-g- HDPE can be formed ifMAH starts to react in HDPE (the dispersed phase). The amount of grafting will decreasewhen mass transfer of monomer out of the dispersed phase increases. In this case masstransfer of monomer out of the dispersed phase is relatively fast compared to reaction ofmonomer inside the dispersed phase.

2.5 Modelling of the conversion of monomer in the dispersed phase, an example.

In our model it will be assumed that diffusion, reaction of monomer and decomposition ofthe initiator starts at temperatures above 130 °C. The reaction velocity of monomer in andoutside the dispersed phase increases along the length of the extruder since also thetemperature of the melt increases along the length of the extruder (figure 7). Theconcentration of monomer in the dispersed phase, MAH and S, decreases in the kneading


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section. The concentration of monomer in the dispersed phase decreases partly because ofthe reaction of monomer but mostly because of mass transfer of monomer out of thedispersed phase. The screw geometry has a kneading section and transporting elements.

figure 7 Calculated concentration of S and MAH in the dispersed phase, and kpversus axial position of the extruder, blend : PS/HDPE; Tb=180 oC, Q = 1.3 kg/h

Note that both concentrations, of MAH and styrene, in the disperse phase have beencalculated and are shown in figure 7. If the size of the dispersed phase is large, masstransfer of monomer out of the dispersed phase is small. From our model calculations wefind that in this case the concentration of monomer in the dispersed phase decreases mainlybecause of the reaction of monomer inside the dispersed phase. The combination of MAHand S has been chosen because the copolymerisation of MAH with Styrene (S) is very fastcompared with the homopolymerisation of S. MAH has very reactive radicals with a highchain transfer constant. It is well known that the reaction velocity is large if the radicalsformed are relatively stable. Styrene will polymerise relatively slow while MAH hardlyhomopolymerises under most conditions.

3 Experimental set up.

The samples were purified by extraction with Tetrahydrofuran (THF, from ACROS) toremove the materials which did not react, and dried for several days in a vacuum oven. Theamount of oxygen in the dispersed phase of a sample could be measured with elementanalysis. The concentration of monomer (such as MAH, BMA, or HPMA) grafted onHDPE can be calculated from the amount of oxygen. The percentage of MAH grafted onHDPE could also be measured by titration with a water free 0.1 N tetra-butyl-ammonium


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hydroxide solution using a thymol blue indicator. The conversion in the dispersed phase ofthe graft- copolymerisation reaction is measured (BMA, HPMA/BMA, BMA/S, BA orMAH) assuming that all the monomer which has not reacted is washed out. Theexperimental error is +/- 3 %.

3.1 Experiments with the Brabender mixing chamber.

PS, or a mixture of PS/HDPE (95/5), is mixed in a Brabender mixing chamber in order tostudy the ongoing of the reaction in time. Monomer and initiator have been absorbed in PSor in the dispersed phase (HDPE) of a PS/HDPE blend. After melting of the polymermixture in the Brabender chamber, monomer is grafted on the polymer backbone as foundfrom analysing the samples.

figure 8 The torque measured with and without reaction PS/HDPE (95/5), 25% MAH,M/I=100, Tb= 180 oC, N =100 rpm, sample 30 gram.

The average viscosity of the blend increases in time in the case where a monomer wasadded in the dispersed phase. One possible explanation for the average viscosity of theblend to increase is when the molecular weight distribution of PS shifts to the highmolecular weight. Simultaneously, the size of the dispersed phase decreases while Mw andMn of the dispersed phase-polymer increase. It is plausible that the viscosity of a blendincreases with increasing compatibilisation between the dispersed phase and the matrixphase. The resulting increase of viscosity causes an increase in the torque. The torque of


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the blend in which MAH was added in the dispersed phase increases while the torque ofthe blend in which no monomer was added in the dispersed phase decreases, figure 8. Thedecrease of the torque when no monomer has been added is due to degradation andorientation of the polymer chains. In the other cases due to (graft) polymerisation ofmonomer (mostly in the dispersed phase) the molecular weight of the copolymers formedby the grafting and adhesion between both phases increases, figure 8.

3.2 Reactive blending in the extruder.

A mixture of PS/HDPE-MAH is fed into a Baker Perkins, 50 mm, self wiping corotatingtwin-screw extruder. For our experiments three values for the temperature of the barrelwere used, 160, 180 and 200 °C. The most important part of the screw geometry used isshown in figure 9. The rest of the screw geometry consists of transporting elements. Theextruder is open at two axial positions before and after the kneading section abovetransporting elements.

figure 9 Part of the screw geometry

N [rpm] Q [kg/h]57 0.66

107 1.32162 3.3214 6.54269 8.59324 10.2

table 1 The extrusion parameters

By visual inspection the degree of fill is estimated. Samples are taken at the die. Within afew seconds these samples are quenched in liquid nitrogen after which they are analysed.After the samples are taken from the extruder and cooled in liquid nitrogen PS and HDPE


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have been separated by soxlet extraction. From analysing the amount of oxygen in thedispersed phase the conversion of monomers such as BMA or MAH in the dispersed phasehas been measured.

3.3 Reactive blending of PS/PP with MAH and S.

In our experiments MAH, BMA, or BA are grafted in the dispersed phase (((NourimixMA-901 (HDPE or PP), AKZO-NOBEL)) in the presence of styrene. It is well known thathomopolymerisation by a free radical reaction of monomer S as well as BMA or MAH isslow while the copolymerisation of these monomers is very fast. With increasing rotationspeed mass transfer out of the dispersed phase increases and the conversion of monomer inthe dispersed phase decreases.

figure 10 The measured conversion of MAH, monomer added : MAH/St = 1/1.

The conversion of MAH at a barrel temperatures of 160 °C (Q= 1 [kg/h]) in figure 10(MAH : S = 1:1) decreases from 20 to 2 % while at Tb=180 °C it decreases from 40 to 5%with increasing rotation speed in figure 11a (MAH : S = 1:2).At small rotation speeds the size of the dispersed phase is relatively large and MAHremains long enough in the dispersed phase to graft on PP. Some model calculations weredone with a constant overall reaction velocity (kov=10-5) and a barrel temperature of160 °C. In figure 11b it can be seen that the calculated conversion also decreases with therotation speed as in the case with the measured values. The differences between theexperimental and the calculated values can be attributed to inaccuracies of the microkinetics model in the dispersed phase.


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figure 11a The measured conversion of MAH versus rotation speed ; MAH/St = 1/2

figure 11b The calculated conversion of MAH versus rotation speed ;kov=10-5

3.4 Experiments with an improved screw geometry.

Several combinations of monomers such as BMA/S, HEMA/BMA, and HPMA/BMA areabsorbed in porous HDPE and fed into the extruder with a geometry as shown infigure 12.

figure 12 The geometry of the screw, kneading section : 12.5 cm,pressure build up section : 32.5 cm.


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First experiments are done with the HDPE and PP version of accurel. The percentagemonomer grafted in the HDPE phase is analysed after removing PS and unreactedmonomer with a soxlet.The conversions measured are of samples made with three different barrel temperaturesand a pressure build up section of 20 cm. This conversion of the monomer in the dispersedphase is shown in figure 13 as a function of the rotation speed (N). The reaction velocitiesof the copolymerisation of HEMA/HPMA, HEMA/S, HEMA/BMA and HEMA/BA arelarger than the reaction velocities of the homopolymerisation of BA or BMA.

figure 13 Measured conversions; copolymerisations with HEMA ; M/I = 1000, Tb=150 °[C].

In the pressure build-up zone, before the mixing section, little mixing occurs (the size ofthe dispersed phase is comparable to the size of the granule). The melt has a relatively longresidence time and has a high temperature in this section. Therefore we expect that mainlyreaction and only little mass transfer of monomer out of the dispersed phase occurs in thepressure build-up section. The dependence of the conversion of HPMA/BMA in thedispersed phase on rotation speed is shown in figure 14.In the case of HPMA/BMA the largest conversions are found for measurements done witha barrel temperature of 160 °C and 180 °C. It is not clear why the conversion is lowerwhen the barrel temperature is set to 170 °C.


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figure 14 The measured conversion of HPMA/BMA in PP : PS/PP ; M/I = 1000

figure 15 The measured conversion of HPMA/BMA in HDPE :PS/HDPE : Tb = 160 °C

The conversion of HPMA/BMA is between 8 and 12 % in figure 15 and is almostindependent of the rotation speed. The influence of the rotation speed on the conversion ofHPMA/BMA in the dispersed phase is small because the reaction mostly occurs in thepressure build-up section where mixing is hardly influenced by the rotation speed.

4 Comparison between model and experiments.

The kinetics of the reaction in a flowing melt are not the same as the kinetics measuredwith DSC because of less diffusion limitations. Yet an attempt has been made to fit thereaction velocity and to model reactive compounding with our computer model. In thissection we will compare the results of the modelling with the results measured.


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4.1 The measured and modelled conversion of MAH in the dispersed phase(HDPE) versus rotation speed and throughput.

The reaction of MAH (at the time when the blend enters the kneading section) (figure 16)is much slower than the reaction of BA/S and therefore the conversion in the dispersedphase is smaller then the conversion of BA/S in the dispersed phase.

figure 16 The total conversion of MAH grafted in the dispersed phase, Q = 3.2 [kg/h]

figure 17 The conversion of MAH versus the throughput

It has been calculated in the next paragraph that the conversion of BA/S (figure 20)already has achieved the maximum value in the pressure build-up section in front of thekneading section. Therefore the conversion of BA/S in the dispersed phase is much larger


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than the conversion of MAH in figure 16 with increasing rotation speed. Due to goodmixing in the kneading section MAH leaves the dispersed phase before it reacts. Mixingincreases with increasing rotation speed causing a decrease of the conversion of MAH withincreasing rotation speed. The conversion of MAH without a pressure build up section inthe screw geometry shown in figure 16 is small compared to the conversion of MAH/S infigure 10 and figure 11a.The conversion of MAH in the dispersed phase decreases when N increases. Withincreasing rotational speed the interfacial area and therefore the mass transfer out of thedispersed phase increases. Yet some monomer is grafted on HDPE before all the monomerdiffuses out of the dispersed phase. The combined effect of the increase of mass transferout of and reaction in the dispersed phase is that the conversion of MAH decreases withincreasing throughput, figure 17.

4.2 The conversion of acrylates in the dispersed phase of PS/HDPE.

The conversion of BMA in the dispersed phase at various M/I ratios is shown in figure 18.The conversion of the monomer is larger at larger initiator (and radical) concentration ifother processing conditions remain the same which is expected.

figure 18 Conversions of BMA versus M/I.


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figure 19 The measured conversion of BA and BA/S in a blend of PS/HDPE,Tb = 150 °C, M/I = 10000.

The conversions of BA when also S is present is usually larger than the conversion of BAonly (measured in the dispersed phase). However, in figure 19, the measured conversion(of BA/S) at a rotation speed of 107 rpm is unexpectedly large. Unfortunately this can notbe explained from the computer modelling.

figure 20 The calculated conversion of BA/S in the dispersed phase, M/I = 100,kov : A : constant in equation 1, EA = 140 kJ/mole, 10 kneading paddles.


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figure 21 The calculated conversion of BA in the dispersed phase, M/I = 10000.kov : A = 1.4*109, EA = 140 kJ/mole, initiator is T101

In figure 20 the conversion has been calculated for a screw geometry with a pressure buildup section of 10 cm and 10 kneading elements. The conversion increases slightly with therotation speed because the temperature of the melt and the reaction velocity of monomerincreases. In figure 21 the conversions of BA with M/I = 10000 are much smaller andalmost constant as a function of rotation speed. The conversions are this small due to thevery small initiator concentration used in the case shown and the small value for thereaction velocity (kov) of BA.

5 The grafted monomer on HDPE in the dispersed phase of PS/HDPE.

In order to determine the presence of grafted monomer in the dispersed phase we haveanalysed it in more detail. With extraction, the dispersed phase (in most cases HDPE orPP) has been separated from the matrix phase (PS). An important parameter for themechanical properties to be improved is the adhesion between the dispersed phase and thematrix. The adhesion between both phases originates from the formation of a graftedcopolymer in the dispersed phase which may act as an alloying agent.The sample analysed in table 1 was made by reactive compounding with the followingmixture. Initiator (Trigonox T, AKZO-NOBEL) is mixed in a 1:1000 ratio with a 1:1mixture of HPMA/BMA. This mixture of HPMA/BMA is absorbed in porous HDPE. Themixture of HDPE, initiator and monomer is blended with PS. The extruder has a barreltemperature of 160 °C and the screw a rotational speed of 214 rpm. After analysing theextracted (HDPE) phase the following IR spectrum is found :


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position of peak [ cm-1] material type of bond

3386 THF or poly-n-BMA O-H vibration

2912 PE or PBMA C-H3, C-H2vibration

2851 PE C-H3, C-H2 vibration

2657 PE unknown

1729 can only be PBMA C=O vibration

1473 PE or PBMA C-H3, C-H2

1368 PE or PBMA C-H3 vibration

1299 PE unknown

1174 PBMA C-O-C

729 PE C-H vibration 'out ofplane'

table 1 Peaks found in IR measurement of PS/HDPE/ (BMA/S)

In another sample as shown in table 2 proof is found again that grafted monomer is firmlyattached to the dispersed phase HDPE. The sample was produced with our method forwhich Trigonox T (AKZO-NOBEL) has been mixed in a 1:1000 ratio with a 1:1 mixtureof BMA/S. This mixture of BMA/S is then absorbed in porous HDPE. The extruder has abarrel temperature of 160 °C and the screw a rotational speed of 214 rpm. After analysingthe extracted (HDPE) phase the following IR spectrum is found for the dispersed HDPEphase :

Comparable results were obtained for many more samples for which a grafted part of themonomer was found. In table 2 it can be seen that even after extraction for several daysBMA is not washed out of the HDPE. Since PBMA is still present in the HDPE phase thisis proof that PBMA has been grafted on the HDPE. Additional proof was also found withNMR but attempts to find the molecular structure of the graft-copolymer failed. It wasalso not possible to find the Mw with GPC due to experimental problems.


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position of peak [ cm-1] material type of bond

3082, 3026 PE, PS combinations of

2919 PE-PS Ø-H (benzene)

1942 PS combinations benzene

1870 PS

1802 PS benzene vibration

1734 PS or PBMA vibrations C-O

1069,1028 PS unknown

1181 PS or PBMA unknown

1154 PS or PBMA unknown

906, 756, 703 PS (benzene part) C-H bend vibrations

table 2 Peaks found in IR measurement of PS/HDPE/ (BMA/S)


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6 Conclusions.

A graft copolymer is formed in the dispersed phase because of monomer present in thedispersed phase during reactive compounding. The screw geometry has an influence on theproduct made with reactive compounding because there is a competition between masstransfer of the monomer out of the dispersed phase and reaction of the monomer inside thedispersed phase.

The following conclusions have been found from our experiments and calculations :

-Reactive compounding will mostly take place in the fully filled sections. Therefore thelength of the fully filled sections should be well controlled. The conversion of BMA,HPMA, BA or HEMA is almost constant if a pressure build up section is present beforethe kneading section.-Mass transfer out of the dispersed phase is strongly influenced by the reaction in thedispersed phase.-MAH, BMA, BA, HPMA, and HEMA are very useful monomers when chosen asmonomer absorbed in the dispersed phase. This is remarkable since these monomers differfrom the monomer of the major and the minor component of the blend.-The conversion of BMA, HPMA, BA or HEMA in the dispersed phase increases withincreasing temperature. The conversion of monomer in the dispersed phase decreases withincreasing M/I ratio. In chapter 5 we found an increase of the average molecular weightwith a decrease of the initiator concentration. In chapter 9 and 10 we will determine whatthis means for the mechanical properties of the blend.-In section 2 and 4 the size of the dispersed phase, and the reaction velocity as modelled inchapter 6 has been used to calculate the mass transfer out of the dispersed phase. It wasfound that the calculated values of the conversion of monomer in the dispersed phase arecomparable with the measured values.Despite simplification of the complex kinetics a reasonable agreement between the modeland experiments has been obtained. The kinetics of the reaction of monomer in the swollensystem have been fitted with an Arrhenius equation. Complications arise from the fact thatmany reactions can take place, and that the efficiency of the initiator, and diffusionlimitations of the reactions are unknown. Further research is needed into the kinetics ofgrafting monomer onto flowing polymer. A first conclusion can be that mass limitations ofmonomer reacting in a flowing melt is less than mass limitations in a quiescent melt.


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Nomenclature.

A Kinetic constant [-]CM,I Concentration of monomer, initiator [mole/m3]CRtot The total concentration of free radicals [mole/m3]d The size of the dispersed phase [m]EA Activation energy [J]Espec Specific energy [kW.kg-1]Factive The fraction of active radicals after initiation [-]kov Overall reaction velocity of monomer [mole/m3 /s]kd The decomposition constant [1/s]kp The propagation constant [m3/mole s]Rr,t The reduced propagation velocity [1/s]kp The propagation constant [m3/mole s]N Screwspeed [rpm]Vp The propagation velocity [mole/m3 s]P Power [W]Q Throughput [m3.s-1]RT Residence time [s]t Time [s]

Greek symbols

t Shear stress [Pa]&γ Shear rate [s-1]

h Viscosity [Pa.s]ρ Density [kg.m-3]

References

1 D. J. van der Wal, L.P.B.M. Janssen, Proc. ANTEC 94 conf. 1-5 may 1994 SanFransisco, Vol 1 P 46-49 SPE (1994).

2 W.M. Barentsen, and D. Heikens, Polymer, 14 ,579 (1973).3 C.E. Locke, and D.R. Paul, J. Appl. Polym. Sci. 17 ,2791 (1973).4 W.E. Baker, M. Saleem, Polym. Eng. Sci. 27 (20), 1634 (1987).5 J.E. Bonner, P.S. Hope and A.S. Jackson, preprint.6 Chapter 6, this thesis.7 Chapter 7, this thesis.


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8 M.L. Lambla, M. Seadan, Macromol. Chem., Macromol. Symp. 69, 99-123 (1993).

9 Chapter 5, this thesis.10 A. Hogt, Proc. ANTEC 88, conf. Vol 1, P 1478 SPE (1988).11 G. Hu, J Flat, M Lambla, Macromol. Chem., Macromol. Symp. 75, 135-157

(1993).12 K.J. Ganzeveld, 1992, thesis, University of Groningen.13 K.J. Ganzeveld, J.E. Capel, D.J. van der Wal, L.P.B.M. Janssen, .Chem. Eng. Sci,

49, 1639-1649 (1994).14 Initiators for polymer production, Product catalogue AKZO NOBEL, (1994).15 D.J. van der Wal, D. Goffart, E.M. Klomp, H.W. Hoogstraten, L.P.B.M. Janssen

Pol. Eng. Sci., 36, 912 (1996).16 D. Goffart D.J. van der Wal, E.M. Klomp, H.W. Hoogstraten, L.P.B.M. Janssen,

LL. Breysse, Y. Trolez, Pol. Eng. Sci., 36, 901 (1996).17 F.L. Marten, A.E. Hamiliec, ACS Symposium series 104, American Chem. Soc.,

Washington (1979).18 G. A. Baker,T. A. Oliphant, Quart, Appl. Math., 17, 361 - 373 (1960).19 G.L. Batch, C.W. Macosco, J. Appl. Polym. Sci, 1711 44, (1992).20 J. Crank, and G.S. Park, Diffusion in Polymers, academic press, London and New

York, (1968).

Improved toughness versus processing parameters, chapter 9

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CHAPTER 9 IMPROVED TOUGHNESSVERSUS PROCESSING PARAMETERS.

Abstract.

The mechanical properties of the blend made with our new method have been investigated as afunction of the processing parameters. By changing the parameters of the process we bothchange the conversion of the monomer in the dispersed phase and the mechanical properties ofthe blend. In this chapter we have to determine which parameters are critical for improving themechanical properties of the blend formed by reactive compounding.All the (PS/HDPE and PS/PP) blends formed with our new method of reactive compoundinghave an elongation at break which is much larger than the elongation at break of pure PS foralmost all sets of processing parameters. Imperative to this was that a pressure built up sectionwas present in front of the kneading section. The mechanical properties did not improve if thedispersed phase consisted of PMMA or PET (possibly because of the absence of a graft-reaction). No increase of elongation at break and impact value is found if HDPE is mixed withPS without adding other materials (such as reactive materials).

1 Introduction.

In the previous chapters some of the most important parameters for reactive compoundinghave been studied. For the reactive compounding process the temperature profile and theposition of a pressure build-up section, a kneading section, and a transporting section in theextruder influence the formation of an alloying agent. Part of the monomer and initiator reactsin the dispersed phase and part diffuses out of the dispersed phase and reacts in the matrixphase. This has been measured and modelled and the molecular number distribution of thealloying agent formed has been calculated in chapter 5. The parameters needed such as thetemperature of the melt in the extruder as a function of the processing parameters have beendescribed in chapter 6. The morphology obtained in the intermeshing corotating-twin screwextruder has been studied in chapter 7. Computer modelling of the conversion of monomer inthe dispersed phase during reactive compounding in an intermeshing corotating twin screwextruder has been described in chapter 8.In chapter 7 it was mentioned that the size of the dispersed phase has an optimal value fortoughness of the blend if the matrix is PS. From the literature it is known that someamorphous polymers tend to deform by crazing and some are ductile. Kramer et al (1)ascribed this transition to the fact that an increasing network density results in a higher surface


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tension which hampers the void formation process of crazing. The other factor whichdetermines the toughness of polymer-rubber blends is the adhesion between the dispersedphase of a blend and the matrix. Wu (2) found that the distance between the particles of thedispersed phase of a blend should be smaller than a certain critical inter-particle distance. Theminimum adhesion required for toughening was also discussed. It was found that the criticalsize of the dispersed phase of a blend depends on its elastomer contents. The highesttoughness was found to occur at an optimum particle size of 2- 5 µm.

1.1 Theory, Mechanical properties and morphology.

When looking at the mechanical properties of polymers it is useful to classify the existingpolymers such as thermoplastics with respect to their physical composition. In all cases exceptthe single phase material the morphology comes into play. The continuous phase isdetermining the general behaviour, but the dispersed phase will contribute in various ways.This depends on the volume fraction and the distance between the dispersed entities. Onlyamorphous polymers can be single phase while semi-crystalline polymers are always two-ormore phase systems. In the rubbery state the material has little structural strength unless thematerial is cross linked chemically. A material is a thermo-plastic elastomer (TPE) if the cross-links are not of chemical but of physical nature (crystallites and/or a second solid phase in acopolymer). The stability of the physical network in a TPE is often achieved by the phaseseparation of the different segments.Comparable considerations are valid for the mechanical properties of mixtures of polymers(blends). Yet there still is a lot of dispute about the mechanical properties, such as elongationat break and notched Izod impact strength and the relation with the morphology of blends.Two important aspects that have been stated in the literature are the need for a small size ofthe dispersed phase and adhesion between both phases. The influence of the size of thedispersed phase on the mechanical properties of polystyrene blends have been studied by vander Sanden (3). It was claimed that in this case only the Inter particle Distance (ID) betweenthe dispersed phase particles in a blend determines whether a blend of PS with anotherpolymer will have a brittle fracture or ductile fracture. If the value of ID is larger than the'critical inter particle distance' (IDc) brittle fracture of the ligament will occur. If brittle fracturecannot occur complete deformation of the ligament will take place, eventually leading to afully ductile macroscopic fracture behaviour. The calculations of van der Sanden indicate thatthe material chosen for the dispersed phase will have no influence on the effectiveness ofreactive blending. In this thesis it will be investigated whether the blends described in thisthesis have improved mechanical properties because both phases have adhesion with eachother by chemical linking of the dispersed phase to the matrix, figure 1a, b chapter 10. Thiswill be investigated in the next chapter. Such a structure is also found in TPE's such as


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styrene-ethylene-butadiene-styrene (SEBS) where the EB part of the chain is chemically linkedto the S part. The physical properties and the theories needed for calculations of the propertiesof the polymers used in this thesis can be found in the handbook edited by Mark (4).

1.2 The conversion in the dispersed phase of a PS/HDPE blend.

The conversion of the reaction in the dispersed phase is shown in figure 1a. The reactionvelocity is modelled with an Arrhenius equation (the constants are shown in the figure):

kov = Ae m mol sEaRT [ / ]3 (1)

Several effects influence the reaction velocity such as the temperature in the melt whichincreases with increasing rotational speed. However mass transport out of the dispersed phasealso increases with increased mixing. Therefore the conversion has a maximum as a functionof the rotational speed of the extruder in figure 1a.

figure 1a The modelled conversion, Tb = 170 °C, M/I=100, [M] = 2100.5 [mole /m3]number of kneading elements : 10, pressure buildup : 10 cm, Q = 1 kg/h.

Note that :

For a slow reaction the measured conversion is constant or decreases (figure 1a) and for a fastreaction the conversion increases with increasing rotation speeds (figure 1b). Thesephenomena are due to the fact that with increasing rotation speed the size of the dispersedphase decreases (chapter 7) and the temperature of the melt increases (chapter 6).


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The conversion of the reaction is relatively large if the screw geometry has a long pressurebuild up section, figure 1b. The temperature and the reaction velocity in this pressure build upsection increase with rotation speed. Therefore the conversion of the monomer in the minorphase increases with rotation speed. The modelled conversions in figure 1a have the sametrend as the three lower lines (measured values) in figure 1c.

figure 1b The modelled conversion in the dispersed phase, Q =1 kg/h,M/I =1000, number of kneading elements = 10, pressure build up section : 18 cm.

figure 1c The measured conversion, M/I = 1000, Tb=150 °C, Q = 1 [kg/h], number ofkneading element : 10, length of the pressure build up section = 32 cm.


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2 Experimental set up, the extruder.

Polystyrene and high density polyethylene or polypropylene are mixed in an intermeshingcorotating twin screw extruder with a diameter of 50 mm and a length of 1200 mm (APV-Baker), figure 2. The extruder is operated at a rotation speed between 50 and 400 rpm and hasa solids feed port in the first section. In most cases we focus on PS/HDPE (95 % / 5 %)blends.

2.1 Experimental set up, the materials.

The process studied is reactive compounding of high density polyethylene (HDPE, accurel,AKZO-NOBEL) or polypropylene (PP) with polystyrene (A in figure 2) (PS, ELF-ATOCHEM). Monomer and initiator (Trigonox 145) are dissolved in HDPE or PP (B infigure 2). In our first experiment Butylmethacrylate (BMA) has been chosen to be dissolved inHDPE (figure 3).

figure 2 Reactive compounding in the extruder

Additional experiments have been performed where the dissolved monomer consisted ofhydroxy-propyl-methacrylate (HPMA), Butylacrylate (BA), Hydroxy-ethylene-methacrylate(HEMA), and Styrene (S), and mixtures of these monomers. Unless stated otherwise thebarrel temperature of the extruder is 150 °C, the rotational speed is 57 rpm, M/I ratio is 1000,the concentration of monomer in the dispersed phase (HDPE or PP) [m] is 30 % by weight,and the throughput is 1 kg/h. The first transporting section is 40 cm, the pressure build up


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section 32.5, the kneading section 12.5 cm, and the last transporting section 37.5 cm. Samplesare cooled directly in liquid nitrogen when the blend leaves the extruder to prevent furtherchanges (such as reaction of the monomer or changes of the morphology).The initiator or the mixture of the initiator and the liquid monomer is dissolved into HDPE.This material was tumble mixed with PS ( for example 10 mass % HDPE in 90 mass % PS byweight) and successively fed to the extruder.

2.2 Analysis.

In order to separate PS from HDPE we dissolve the samples, which are taken directly fromthe die of the extruder, in THF. We can separate the PS, which is solved in THF, from theHDPE, which is not solved. For the extraction we use a Soxtec system HT 2, 1045 ExtractionUnit, Tecator Extraction thimbles (33*80 mm, Schleicher & Schuell). The grafting ofmonomer on HDPE is determined by measuring the amount of oxygen present in the separateddispersed phase of the blend. The tensile tests were done according to ASTM D1708 at acrosshead speed of 10 mm/min on a tensile tester Instron tensile tester at room temperature.Tensile specimens of the obtained blends were prepared by compression molding at 180 °C.Since the material made with our method might replace high impact polystyrene (HIPS)impact test are also of interest. Since impact properties are important in many applications ofmaterials Notched-Izod (NI) values have been measured with a Zwick impact tester. Note thatthe values for impact strength must be multiplied by 1/0.03 due to sample dimensions. Itappeared that the results from impact tests are very sensitive to small changes in themorphology of the material as well as small changes in the test piece. A NI measurement of0.15 in the graphs in this thesis corresponds to a Notched Izod value of 5 which is comparablewith the NI value of HIPS.

3 Results.

For improved toughness and impact strength of the blend the reaction is found to be of vitalimportance. In order to gain a better understanding the conversion of the monomer in thedispersed phase will be studied further. Rotational speed is one of the most important extruderparameters since it influences the conversion of monomer in the dispersed phase but alsodirectly the size of the dispersed phase.A blend of PS/HDPE with BMA monomer has been produced with the method described inchapter 1. From observations with SEM (figure 3) we find that the blend produced withreactive compatibilsation differs from the blend which has been described in chapter 7 becausethe size of the dispersed phase is smaller.


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figure 4a Stress (F)-strain curve of a reactive blend with 1 and 5 % HDPE as thedispersed phase (in HDPE 10% monomer BMA has been absorbed), Tb= 180 oC, Q = 1.3kg/h.

figure 4b Elongation at break - rotation speed , HDPE : 5%, HPMA/BMA (30 %) , Q= 1.3kg/h .

In a few cases the maximum stress increases with the rotation speed of the screws (figure 4c).We found that this only is the case if the elongation at break decreases with increasing rotationspeed. The influence of the percentage dispersed phase, the conversion of monomer in the


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dispersed phase, the structure of the alloying agent formed and the size of the dispersed phasehave been investigated.

figure 4c Stress at maximum load - rotation speed [rpm]; HDPE : 10% BA/S 10%, M/I = 10000, Q = 1.3 kg/h.

figure 4d Elongation at break - rotation speed (N), M/I = 500, HPMA/BMA (30 %) , Q= 1.3 kg/h, blend PS/HDPE, Tb = 170 °C, Trigonox T .

The blend with 1 percent HDPE in figure 4a has a much smaller elongation at break as theblend with 5 percent dispersed phase (figure 4a and figure 4d). The elongation at breakdecreases with increasing percentage dispersed phase if more than 5 % dispersed phase ismixed in. Coalescence increases if the dispersed phase is more than 5 % HDPE.


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Toughness of a blend is found by calculating the area under the tensile curve (figure 4a). Thetoughness of reactive blends has a maximum as a function of the rotation speed as shown infigure 5. However the most important observation is that all materials have a stronglyimproved toughness compared with polystyrene (pure PS : T=0.4).

figure 5 Toughness - rotation speed [rpm] ; HPMA/BMA, 10% , M/I : 10000, Q = 1.3 kg/h,Tb = 170 °C, HDPE = 15 %.

3.3 Toughness and elongation at break.

In the literature it is usually found that for radical polymerisation the molecular weightincreases when the monomer/initiator ratio increases. We expect the same to be valid for theformation of the graft copolymer (the compatibiliser to be formed) in the dispersed phase. Toobtain an improvement of the toughness of the blend it is important that the alloying agent isformed in the polymer of the minor phase and more specific is present in the interfacial area.Its molecular weight must be larger than a critical value of the molecular weight betweenentanglements (Me) as described by Creton, Kramer and Hadziioannou (5).Larger Toughness at lower initiator concentration in figure 6a can only be explained by a moreeffective alloying agent. For this we assume that the reaction velocity decreases and the lengthof the graft copolymer increases (forming a more effective alloying agent) when themonomer/initiator concentration increases. Note that the samples with the lowest initiatorconcentration have the largest toughness (T). This is expected since the Mw of the alloyingagent must exceed Me as mentioned by Creton et al (5) and the Mw is larger when M/I islarger. In the previous chapters we have found that the conversion of the reaction decreaseswith increasing M/I but a higher concentration of alloying agent does not cause a larger


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toughness. This is confirmed by the fact that also no influence of the conversion in thedispersed phase on the Notched Izod impact values is found in figure 10 (this chapter).

figure 6a Toughness - rotation speed [rpm], Tb = 170 °C, HDPE = 15 %, HPMA/BMA.

figure 6b Toughness - rotation speed [rpm] for several material choices of the dispersedphase, PP, PET, PMMA.


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To determine whether the material choice of the dispersed phase is important PET and PMMAhave been used for the dispersed phase in figure 6b (instead of HDPE or PP). In this case(PET, PMMA : Tg > 20 °C) no improvements in mechanical properties have been found.From what we found so far we might conclude that the toughness and impact value of a blendprobably is influenced by a combination of parameters such as the size of the dispersed phase,the molecular weight, and the concentration of the alloying agent in the polymer of the minorphase. No improvement is found when PET or PMMA is the dispersed phase which may bedue to the fact that HDPE and PP are (partially crystalline) rubbers while PET and PMMA arenot. Another possibility could have been that the dispersed phase was not small enough in thecase of PET or PMMA. Therefore the size of the dispersed phase of the PS/PET andPS/PMMA blend has been measured with SEM (table 1, chapter 10) but was found to becomparable with the size for PS/HDPE and PS/PP blends. Possibly another condition forimproved mechanical properties of the blend is that the dispersed phase must have a Tgsmaller than 20 °C. Moreover the chemical bonding between the minor phase and the majorphase must be sufficiently strong.

figure 7 Elongation at break - rotation speed [rpm], blend PS/PP, MAH/S (ratio 1:1)

The elongation at break, Notched Izod impact strength and toughness of the blend werealmost constant as a function of the rotation speed of the extruder, figure 7 and 8a. Probablythe graft-copolymerisation has a sufficiently high conversion and the alloying agent formed inthese experiments is effective enough.

3.4 The influence of rotation speed on the Notched-Izod impact values.

In figure 8a both toughness and impact value increase. The large improvement is remarkablesince only a small monomer concentration and a small amount of HDPE is used. Probably


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there is a relation between the length of the alloying agent in the dispersed phase and themechanical properties such as toughness and impact value.

figure 8a (NI) Impact and toughness - rotation speed [rpm] , 5% HPMA/BMA,Tb = 170 °C, PS (95%)/HDPE (5%), [m]=5%.

It is of great practical use if a product made out of a plastic does not break when it falls. Thechance for a product to break is determined by its response to a fast impact force andtherefore the (Notched) Impact value is at least as important as the elongation at break.

figure 8b Notched Izod values, Tb = 150 ° C, Q : 1.3 kg/h, HEMA/BA and HEMA,M/I = 1000, PS/HDPE (90 % / 5 %), [m]= 30 %.

The Notched Izod value of the reactive blend is at least three times as large as the NotchedIzod value of PS, figure 8a and 8b. For most combinations of reactive mixtures it is almost


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constant as a function of rotation speed of the screw (figure 9). It is also remarkable that theNotched Izod values for reactive blends made with different monomers have only slightlydifferent values. The NI value of pure PS is between 0.03 and 0.04 depending on the barreltemperature.

figure 9 ; Notched Izod - rotation speed [rpm] , pure PS and reactive blends , monomers : BA/S and S , (M/I = 1000).

figure 10 Notched Izod Impact value versus the conversion of BMA/S in the dispersedphase.

The impact strength is almost constant as a function of the conversion of the monomer in thedispersed phase, figure 10. Since this has no influence on the impact values it is possible thatthe interface is already saturated with compatibiliser. With increasing rotation speed the


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notched Izod impact value decreases and the conversion increases as shown in figure 11.Again the interface is already saturated with compatibiliser and a further increase of theconversion means a less efficient alloying agent.

figure 11 Impact strength and conversion - rotation speed [rpm], HEMA/BMA.

Again the most plausible explanation for the relative large NI value relative to PS is that achemical link between the matrix phase (PS) and the dispersed phase (HDPE) is formed.However note that some unreacted monomer is still present if the conversion is low, figure 11.

3.5 Impact values versus conversion and rotation speed.

From figure 12a we might conclude that the Notched Izod impact value of our blend increasesbecause the conversion increases and a graft copolymer is formed in the dispersed phase.Unfortunately it is not this simple since the Notched Izod impact strength does not alwaysincrease with increasing conversion of HPMA/BMA in the dispersed phase of the blend,figure 12b. In the samples made with small rotation speed the conversion usually was smalland mixing poor which in many cases means poor compatibilsation. This might explain thesmall NI values at small conversions in figure 12a. This also is due to a large concentration ofunreacted monomer which is still present in the dispersed phase.


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figure 12a The Notched-Izod impact strength versus the conversion ofHPMA/BMA, PS (95%)/HDPE (5%), [m]=30%.

figure 12b The Notched-Izod impact strength versus the rotation speed, HPMA/BMA,PS (95%)/HDPE (5%), [m]=10%.

In contrast with figure 12a the Notched Izod impact strength in most cases is constant withincreasing rotation speed (figure 12b).

3.6 The relation between elongation at break, conversion, and an efficient alloying agent.

Both an increase and a small decrease of the elongation at break can be seen in figure 13.


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figure 13 The elongation at break - the conversion of BMA/S PS (95%)/HDPE (5%).

When BMA/S is absorbed in the dispersed phase the elongation at break is almost constant atconversions larger than 10 % and smaller than 50 %, figure 13. If the conversion is larger than50 % more graft-copolymer has been formed. Clearly a less effective alloying agent has beenformed causing a decreased toughness of the blend at a conversion exceeding 50 %.The influence of the processing conditions and the choice of monomer on the elongation atbreak will be described below. Usually it is found that the elongation at break increases withincreasing rotation speed (figure 14a, 14b, and figure 14 c).

figure 14a The elongation at break - rotation speed [rpm] , monomer : HPMA/BMA,M/I=1000, Q = 0.5 kg/h, Tb = 170 oC, 10 and 30 % monomer absorbed in the dispersedphase, PS (95%)/HDPE (5%).


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In figure 14a the elongation at break increases with increasing rotation speed if 10 %HPMA/BMA is absorbed in the dispersed phase while the M/I is relatively small (1000). Atthis initiator concentration the elongation at break is large for all rotation speeds if 30 %HPMA/BMA is absorbed in the dispersed phase.

figure 14b The elongation at break - rotation speed [rpm], monomer : HPMA/BMA,M/I=10000, Tb = 160 oC, 30 % monomer absorbed in the dispersed phase, PS (95%)/HDPE(5%).

In figure 14b the elongation at break increases with increasing rotation speed and reaches avalue of 30 %. In this case the barrel temperature (Tb ) is 160 °C which is lower than thebarrel temperature used to make the blends shown in figure 14a. Because the barreltemperature is lower in figure 14b the temperature in the melt which is measured in thepressure build up section is determined by viscous dissipation. It increases with increasingrotation speed. The reaction and increase of Mw of the alloying agent formed by the reactiontakes place in the pressure build up section. The compatibilsation due to the alloying agent andtherefore also the mixing increases when the barrel temperature is set to higher values. Sincethe efficiency of the alloying agent formed increases the elongation at break also increases.In figure 14c the barrel temperature is again 160 °C and the initiator concentration has beenvaried. The temperatures in the pressure build up section were measured and were found toincrease with increasing rotation speed. This is important since in this case the temperature ofthe melt determines the concentration and Mw of the graft copolymer formed.Because the temperature in the melt determines the structure of the alloying agent the initiatorconcentration has no effect on the elongation at break in figure 14c.


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figure 14c The elongation at break - rotation speed [rpm], HPMA/BMA, Tb = 160 °C 30 %monomer absorbed in the dispersed phase, influence of the M/I ratio, PS (95%)/HDPE (5%).

Normally the M/I ratio must be large and is a very important parameter because it determineswhether the alloying agent is effective, figure 14d. This is in contrast with figure 14c wherethe effect of the initiator concentration is not very clear.

figure 14d The elongation at break - rotation speed [rpm], BMA/S, M/I=1000 and M/I=10000, Tb = 160 °C, 30 % monomer absorbed in the dispersed phase, PS (90%)/HDPE (10%).


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The choice of monomer is also important for the efficiency of the alloying agent since normallyit is expected that HPMA/BMA-g-HDPE is a less efficient alloying agent than BMA/S-g-HPMA. Note that the styrene part of the copolymer can penetrate PS forming a bondingbetween matrix and dispersed phase. The influence of the Mw of the alloying agent is that alarge difference in the elongation at break for different M/I ratio's is found in figure 14d.

figure 14e The elongation at break - rotation speed [rpm], HPMA/BMA, M/I=1000, Tb = 150 °C and 170 °C, [m]=30 % monomer absorbed in the dispersed phase.

In figure 14e the blend (with HPMA/BMA as monomer) has a large elongation at break for allrotation speeds when the barrel temperature is 170 °C. This is not the case when the barreltemperature is 150 °C and the rotation speeds are small. This can be explained by the fasterdecomposition of the initiator at higher temperatures. Due to this the initiator concentrationdecreases faster at higher melt temperatures. A small initiator concentration means a largerMw of the graft copolymer and a more efficient alloying agent.

4 Discussion.

It can be concluded that our method is fairly successful in improving the mechanical propertiesof the blend PS/HDPE and PS/PP. However more work is needed to better understand therelation between material properties, blend morphology, and reactive compounding.Many more measurements were done for which also the concentration of monomer absorbedhas been varied between 0.1 % and 30 % with respect to the mass % HDPE. On the averagethe influence of the monomer concentration was found to be relatively small. In all cases themechanical properties were improved sufficiently. Because of this it seems profitable to use a


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minimum amount of monomer in the dispersed phase which is easier for processing (feeding awet sticky mixture of polymer and monomer into the extruder with the hopper is difficult). Itis also better if we want to keep the amount of monomer remaining in the blend after reactivecompounding to a minimum. So far we found that reactive compounding should be designedsuch that first the grafting of monomer in the dispersed phase occurs. This is done to makesure that most monomers react in the polymer of the minor phase. Therefore the screwgeometry is designed such that the polymer mixture has a long residence time and a hightemperature in the pressure build up section before entering the kneading section. Because ofthis, a large part of the monomer can react to form grafted-copolymer on the polymer chainsof the dispersed phase. After passing through the pressure build-up section the blend passesthrough a kneading section decreasing the size of the dispersed phase. If the conversion ofmonomer in the dispersed phase is large enough the toughness of a PS/HDPE blend can beimproved with reactive compounding. The influence of processing conditions andmonomer/initiator ratio provides opportunities for optimisation.Van der Sanden (3) has claimed that the distance between dispersed particles must be below 1 µm which was found to be difficult when more than 15 mass % HDPE was the dispersedphase due to coalescence during mixing. From SEM. it was found that in our blends thedistance between the several spheres of the dispersed phase was much larger than the criticalinterparticle diameter. Possibly the properties of our blends can be further improved byforming a blend with a smaller interparticle distance between the several spheres of thedispersed phase and good adhesion between the matrix and the dispersed phase.As a conclusion for most cases favourable conditions for tough mechanical properties aresufficient mixing, a higher temperature, larger M/I ratio, and a smaller monomerconcentration. Because of the large amount of parameters which have an influence on themechanical properties of the blend (conversion, molecular weight, size of the dispersed phase,choice of monomer) a general explanation of trends is not available yet.The following theory can be considered for blends in which the major phase is amorphous :The unreacted monomer in the neighbourhood of the dispersed phase also may have atoughening influence. The improvement of our new method of reactive compounding is not aslarge for NI measurements because the soft part of the blend (which is a monomer/polymermixture) is to weak when the tests take place at much larger velocities. When under load, thePS part of a blend can deform but the stress must also be passed on to the dispersed (HDPE,or PP) phase by the adhesion between the matrix and the dispersed phase. Brittle breakageoccurs if the stress can not be passed on at some interface (because of poor adhesion or a hardparticle).


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5 Conclusions.

The blends of PS/HDPE and PS/PP have strongly improved mechanical properties for allsamples. The elongation at break of PS/HDPE blends made by reactive compounding isalways very large. Also the Notched-Izod value of PS/HDPE blends is large (4 times as largeas pure PS) because the reaction of monomer with the polymer of the minor phase improvesthe chemical bonding between the dispersed phase and the matrix phase while the size of thedispersed phase decreases. Unfortunately no direct evidence of the chemical bond between thedispersed and matrix phase was found.The toughness of PS/HDPE and PS/PP blends is much larger than the toughness of PS. Thestress at maximum load is about 30 MPa which is smaller than the value of pure PS. Themorphology of the blend and the molecular weight and concentration of the alloying agent arelikely candidates to directly influence the mechanical properties of the blend.The molecular weight distribution of the graft copolymer formed is very important but notknown in sufficient detail. The thermodynamics of monomers and graft copolymers capturedin the dispersed phase is also not known. More experimental results are needed.For application of these blends their material properties must be well defined and variances inimpact values are usually not allowed. Therefore controlling the processing parameters and theconversion of the monomer in the dispersed phase is essential for the improvement of thetoughness of the blend. The influence of extrusion parameters on the properties of the blendcan be understood from the concentration and structure of the alloying agent in the polymer ofthe minor phase. The reactions of monomer and initiator of the minor phase will mostlyinfluence this. The concentration of alloying agent in the polymer of the minor phase willdecrease when less monomer is present in the polymer of the minor phase.For practically all combinations of polymers it has great advantages to determine if the methoddescribed in this thesis can be applied. This is more cost effective than most conventionalmethods because it uses only the cheapest material such as monomers and initiators and insmall amounts. The method is flexible and can therefore also be used for the recycling of manydifferent polymers. However more research is needed. Part of this research should focus onmethods to keep the amount of unreacted monomer (which is already small) below the ppmlevel.


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Nomenclature

[m] Monomer concentration in the dispersed phase [mole /m3 /s]Conv. Conversion of the reaction in the dispersed phase (grafted monomer) %Mw Average molecular weight [g/mole]Mwcr Critical average molecular weight [g/mole]Me Average molecular weight between entanglements [g/mole]M/I Monomer over initiator ratio [-]N Screw speed [rpm]NI Notched Izod impact value (relative value) [-]Stress Maximum stress at Yield [MPa]T Toughness (surface under the tensile test curve ) [MPa]]Tb Temperature of the barrel [°C]Q Throughput [kg/h]elong, break. Elongation at break during a tensile test (velocity 10 mm/min) [%]Q Throughput [m3.s-1]

References

(1) E.J. Kramer, J. Appl. Polymer Sci., 14. 2825 (1970).(2) S. Wu, Polym. Int. 29, 229-247 (1992).(3) M.C.M. van der Sanden, PhD thesis, University of Eindhoven (1993).(4) J.E. Mark, Physical properties of polymers, American institute of physics, Woodbury,

New York, (1996).(5) C. Creton, E.J. Kramer, G. Hadziioannou, Macromolecules, 24, 1846 (1991).(6) R. Kroeze, PhD thesis, University of Groningen (1997).

Bulk plastics

Verreweg de meest gebruikte plastics zijn polyetheen en polypropeen. Deze materialen zijnrelatief makkelijk te verwerken en te vormen in een gewenste vorm. Populairetoepassingen zijn verpakkingen, behuizingen van huishoudapparatuur, kinder speelgoed,stoelen, opslagvaten etc.Een belangrijke stroom die voor herverwerking belangrijk is wordt gevormd doorverpakkingsmaterialen. Zo worden er enorme hoeveelheden polyetheen en polypropeenverzameld die ingezet zijn in shampoo flessen. Na gebruik worden de flessen verhaktwaarna het materiaal opnieuw wordt opgesmolten en in een nieuwe toepassing wordtingezet. Door de extra verwerking worden de eigenschappen echter minder waardoor deprijs van het materiaal ook lager wordt. Er is vrijwel geen marge op de kiloprijs van dezematerialen omdat er enorme hoeveelheden van dit materiaal worden gebruikt. Om de prijsop een acceptabel niveau te kunnen stellen wordt het nodig de eigenschappen van dematerialen naar hun oorspronkelijke niveau (of naar een hoger niveau) terug te brengen. Eris dus een methode nodig waarbij de eigenschappen van een plastic worden verbeterd.Om aan alle randvoorwaarden te voldoen is in dit promotiewerk een goedkope methodegezocht waarmee het mogelijk is de eigenschappen van een plastic of een mengsel vanplastics te verbeteren.

Dit proefschrift.

In hoofdstuk 1 wordt de methode beschreven die bedacht is om een chemische verbindingte maken tussen twee plastics als deze door elkaar heen worden gemengd. Hierbij wordtaangenomen dat een chemische hechting tussen beide fases van een mengsel van plasticseen noodzakelijke voorwaarde is voor goede eigenschappen van het resulterende product(dit zal een blend worden genoemd).

De bolletjes die in figuur 2 te zien zijn moeten hierbij dus via een chemische reactie wordengehecht aan het omliggende materiaal. Een mengsel van polystyreen en polyetheen wordtgebruikt als voorbeeld. De eerste stap in de bedachte methode is om het polyetheen op tezwellen met monomeren. Deze monomeren kunnen na verhitten reageren waarbij ze ookals zijgroep kunnen vast reageren op de polyetheen ketens. Tijdens het proces waarbij hetpolyetheen wordt gemengd in polystyreen reageert het monomeer zowel met polyetheenals met polystyreen. Hierdoor ontstaat een verbindende keten tussen de beide materialenwat voor de benodigde chemische hechting zorgt tussen de plastics die gemengd worden.De bolletjes in figuur 2 zijn het polyetheen en het omliggende materiaal is polystyreen.Het eerste doel van dit proefschrift is om uit te zoeken of een chemische binding wordtgevormd tussen beide fases van de blend. Het tweede doel om de procesconditieshiervoor te optimaliseren. Het derde doel is te bepalen hoe de mechanische eigenschappenvan de resulterende blends worden bepaald door de procescondities.