Reactive Extrusion Systems Leon P. B. 1\11. Janssen University of Groningen Groningen, The Netherlands M A R C E L MARCEL DEKKER, INC. m D E K K E R NEW YORK - BASEL Although great care has been taken to provide accurate and current information,neither the author(s) nor the publisher, nor anyone else associated with thispublication, shall be liable for any loss, damage, or liability directly or indirectlycaused or alleged to be caused by this book. The material contained herein is notintended to provide specic advice or recommendations for any specic situation.Trademark notice: Product or corporate names may be trademarks or registeredtrademarks and are used only for identication and explanation without intent toinfringe.Library of Congress Cataloging-in-Publication DataA catalog record for this book is available from the Library of Congress.ISBN: 0-8247-4781-XThis book is printed on acid-free paper.HeadquartersMarcel Dekker, Inc., 270 Madison Avenue, New York, NY 10016, U.S.A.tel: 212-696-9000; fax: 212-685-4540Distribution and Customer ServiceMarcel Dekker, Inc., Cimarron Road, Monticello, New York 12701, U.S.A.tel: 800-228-1160; fax: 845-796-1772Eastern Hemisphere DistributionMarcel Dekker AG, Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerlandtel: 41-61-260-6300; fax: 41-61-260-6333World Wide Webhttp://www.dekker.comThe publisher oers discounts on this book when ordered in bulk quantities. Formore information, write to Special Sales/Professional Marketing at the headquartersaddress above.Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.Neither this book nor any part may be reproduced or transmitted in any form or byany means, electronic or mechanical, including photocopying, microlming, andrecording, or by any information storage and retrieval system, without permission inwriting from the publisher.Current printing (last digit):10 9 8 7 6 5 4 3 2 1PRINTED IN THE UNITED STATES OF AMERICAPrefaceOne of the earliest concepts of screw extrusion is found in a 1873 drawingowned by Phoenix Gummiwerke A.G. in Germany. Since then manyengineers and scientists have been fascinated by the use of this type ofmachine in the polymer industry and for food processing. Even morefascinating is the use of extruders as chemical reactors for high-viscosityliquids. In recent years extruders have been used as polymerization reactors,modication reactors, and degradation reactors and knowledge oftheir operation has expanded considerably. The main advantage of usingextruders instead of conventional reactors is the ability to work withoutsolvents. An extra separation step thus becomes superuous, and theprocess becomes more energy ecient and environmentally friendly. Otheradvantages are continuous operation, the relative insensitivity to viscositychanges, a large heat-transfer area, and well-dened shear levels.This book approaches reactive extrusion from a phenomenologicaland engineering point of view. It is divided into three parts. The rst part(Chapters 2 to 6) describes phenomena that are important for understandingreactive extrusion, such as the dierent types of extruders and their specicadvantages, polymerization kinetics in highly viscous media, the rheology ofreacting monomerpolymer mixtures, mixing in extruders, and heat-transferand energy balances. These are not subjects of a hidden textbook ontransport phenomena, but they are always treated with a direct link toreactive extrusion processes. Although the chapters are more or less self-contained, the normal basic knowledge of transport phenomena andreaction engineering will be helpful. The second part of the book (Chapters7 to 11) considers several types of reactions that can be performed inextruders, including homo- and copolymerizations and multicomponentreactions. It further includes modication reactions and reactive compound-ing of immiscible polymers. The chapters in this part are accompanied byexamples from research projects, illustrating the theories with experimentalcases. The last part of the book (Chapters 12 to 14) treats some advancediiiengineering problems including scale-up from laboratory equipment toproduction size, the stability of the process, and economic aspects ofreactive extrusion, compared with conventional processes.The book is intended for engineers, scientists, and technologistswho are interested in or working with reactive extrusion, but it can alsobe used as a textbook for courses on this subject. The main objective isunderstanding the complex interactions that make reactive extrusion work.In this book we take a practical point of view, avoiding lengthy calculationsand theoretical derivations that are not relevant to applications and can befound elsewhere.Many theories and much experimental work described in this bookwere developed and performed by Ph.D. students who worked on reactiveextrusion at the Department of Chemical Engineering of the University ofGroningen. I thank the doctores Jan Speur, Ineke Ganzeveld, RandellPieters, Atze van der Goot, Robbert de Graaf, Hetty Jongbloed, Douwevan der Wal, Rienk Hettema, Eric-Jan Troelstra, Mario Cio, and VincentVerhoeven, who by continuously asking me why? have drawn me moreand more into the secrets of reactive extrusion. I also especially thank Dr.Ineke Ganzeveld for the critical way she read the manuscript and the manysuggestions for improvement and Professor Arend-Jan Schoutedn for thediscussions and suggestions on hard-core polymer chemistry. Finally, Ithank my family; Rene e, Camiel, and Dorata, for their patience while I waswriting this book.Leon P. B. M. Jansseniv PrefaceContentsPreface iii1. Introduction 1THE BASICS2. Extruders 113. Chemical Kinetics 414. Rheology and Rheokinetics 615. Mixing and Reactions 756. Heat Balances and Heat Transfer 99APPLICATIONS7. Chain-Growth Homopolymerizations 1158. Copolymerizations 1419. Step-Growth Polymerizations 15710. Modication Reactions 16911. Reactive Compounding 179ADVANCED PROBLEMS12. Scale-Up 193v13. Stability 21314. Economic Feasibility 231Index 243vi Contents1IntroductionI. HISTORYThe possibilities to use an extruder as a polymerization reactor were alreadyrecognized in 1950. A patent of Dow Chemical Company (1) described apolymerization unit in which a single-screw extruder was used as the mainpolymerization device. For the rst part of the polymerization process,when low viscosities prevailed, a continuous stirred-tank reactor with aresidence time of 90 h was used as a prepolymerizer, after which the materialwas transferred to the single-screw extruder for the high-viscosity part ofthe reaction. In this extruder a residence time of 18 h was necessary forthe thermal polymerization of styrene. The rst polymerizations describedin open literature were the polymerization of nylon (2) and severalpolycondensation reactions (e.g., Ref. 3). In the mid-1970s, the rsttheoretical considerations concerning reactive extrusions appeared.Meyuhas et al. (4) stated that an extruder is the best plug ow reactor forviscous materials, but that some distribution in molecular weight of thepolymer formed can not be prevented. In this study, a prepolymerization isadvised to avoid low viscous material to be fed to the extruder. Mack andHerter (5) proposed twin-screw technology for reactive extrusion because ofdiculties in scaling up single screw extruders that could be avoided in twin-screw extruders. Residence times of half an hour were possible in self-wipingtwin-screw extruders. Mack and Herter also concluded that a combinationof a stirred-tank reactor, a single-screw extruder, and a twin-screw extruderwas most suitable for the production of polyesters.In more recent years, the radical polymerization of several methacry-lates was studied in a counterrotating twin-screw extruder (69). Stuber andTirrel (6) and Dey and Biesenberger (7) studied the radical polymerizationof methylmethacrylate, Ganzeveld and Janssen (8) described the poly-merization of n-butylmethacrylate, while Jongbloed et al. (9) also studied acopolymerization of butylmethacrylate and 2-hydroxy-propylmethacrylate.1Both Jongbloed and Ganzeveld found maximum conversions of roughly96% in one step based on gravimetric analyses, while Dey claimed completeconversion after pre-polymerization, as measured by gas chromatography.Similar dierences in conversion are sometimes found in literature. Apossible explanation for this was given by Van der Goot et al. (10), whopointed out that the method of analysis can have a distinct inuence on thenal conversion found. They measured the conversion during reactiveextrusion of styrene in the same samples both with a gravimetrical methodand by using gas chromatography. It was found that the conversions withgas chromatography were up to 3% higher than that when measured bygravimetry. Jongbloed et al. (11) compared a self-wiping corotating twinscrew with a counter rotating closely intermeshing twin-screw extruder forthe copolymerization of n-butylmethacrylate with 2-hydroxy-propylmeth-acrylate. Apart from the polymerizations already mentioned, thecounterrotating extruder was also used for the polycondensation ofurethanes (12) and the anionic polymerization of c-caprolactam (13). Thepossibilities for reactive extrusion of urethanes were also recognized byseveral other authors (1416).Other reactions have been described in various types of extruders, likethe use of corotating twin-screw extruders for the anionic polymerizationof c-caprolactam (1719). The anionic polymerization of styrene wasinvestigated by Michaeli et al. (20), who also published work on thecopolymerization of styrene with isoprene (21). The radical polymerizationof styrene and several copolymerizations with styrene as the maincomponent were described in a patent by Kelley (22). This patent alsodescribes the synthesis of high-impact polystyrene (HIPS). Van der Gootand Janssen (10) investigated the polymerization of styrene and theinuence of prepolymerization on the maximum stable throughput. Acomprehensive overview of reactive extrusion is given in a monograph,edited by Xanthos (23). In this work Brown gives a listing of over600 reactive extrusion processes that have appeared in open and patentliterature between 1966 and 1983. The most surprising conclusion from thissurvey is that during that period more than 600 patents on reactive extrusionwere granted to 150 companies, but only 57 technical papers were found.Only three of them were from companies holding ve or more patents.Most of the research on reactive extrusion is performed in twin screwextruders, although a single-screw co-kneader has denite advantages ifmicromixing plays an important role. Franz (24) gave an overview ofapplications of reactive extrusion with a Busskneader in a paper discussingthe polycondensation reaction of silanoles to produce silicon oils. Aeppli (25)2 Chapter 1describes the ionic polymerization of acetals in the same type of machinesand Jakopin (26) reports on reactive compounding, where the good mixingaction of a co-kneader is an advantage.Foster and Lindt developed models for devolatilization in connectionwith reactive extrusion (27,28). In later work it has been described that in areux ask reactor a signicant acceleration of a transesterication reactioncould be achieved if a boiling inert hydrocarbon solvent was present (29).The same signicant enhancement was found in reactive extrusion withsimultaneous devolatilization, during a monoesterication reaction betweenstyrene-maleic anhydride copolymer and alcohol (30).Reactive extrusion is also attractive for grafting or modicationreactions, where micromixing is an important factor for obtaining ahomogeneous end product. Typical examples are the free-radical grafting ofmaleic acid, glycidyl methacrylate, or acrylic acid onto polyolenes (3134).The resulting functionalized polymers can be used for blending with otherpolymers; also the adhesive properties of these polymers to metals or glassbers improve (35). Apart from the desired grafting reactions, unwantedside reactions such as cross-linking of polyethylene and chain scission inpolypropylene may occur (36).Little is known about the stability of the reactive extrusion process.Especially if a transition of very low to very high viscosities occurs, as is thecase during polymerizations starting from low-molecular-weight monomers,a sharp transition between high conversion and low conversion of thereaction can occur as a result of very small changes in operating conditions.This may be accompanied by severe uctuations in throughput andconversion. Van der Goot et al. (37,38) noted that stability can be increasedby increasing reaction speed or viscosity buildup, which later could beexplained qualitatively by multiplicity in stability of the length over whichthe extruder is fully lled with material (39).II. ADVANTAGES AND DISADVANTAGES OF REACTIVEEXTRUSIONDue to its specic properties, the extruder has certain advantages as areactor for polymerization and modication reactions:+ The extruder is a stable pump for highly viscous media. Thisguarantees a constant throughput which is vital for its operation asa continuous reactor.Introduction 3+ The process is continuous in contrast to various conventionalprocesses that operate batchwise.+ The mixing can be adjusted to the requirements for optimalreaction conditions by a judicious screw design.+ Devolatilization of the reaction product in the extruder makes itpossible to remove and recycle unreacted components.+ No or only a small amount of solvent has to be used in anextruder-polymerization process; therefore, no expensive extraseparation steps are needed. Due to the absence of volatilesolvents, the process is also more environmentally friendly. This isimportant as legislation increases strongly in this area.However, there are also some restrictions to the use of extruders aspolymerization reactors as well as to the type of extruder to be used.+ As the extruder is a reactor with a relatively expensive volume, theresidence time needed for the reaction should be short. Therefore,the reaction kinetics have to be sufficiently fast to acquire aneconomically feasible process.+ There is a limitation to the reactions that can be performed inextruders based on the heat of reaction and the viscosity reached.If the reaction enthalpy is very large, the temperature rise in theextruder is too large to control. Moreover, the viscosity of thereaction product has to be sufficiently high to be able to obtain astable transport of the material and to make the use of an extruderprofitable.+ On scaling up the equipment, the surface-to-volume ratiodecreases, which limits the heat removal in production machines.Moreover, in production-size machines thermal inhomogeneitiesmay occur that do not exist in laboratory equipment. This requiresa careful design of the experiments on laboratory scale in order toassure a reliable scale-up procedure.+ Due to the large viscosity changes that arise during mostpolymerizations, instabilities may occur, resulting in very lowconversions or fluctuating throughput. These instabilities can bedependent on the scale of the equipment, and therefore they poseextra restrictions to the scaling up of the process.From an economic point of view, it should also be realized that most of thepolymer produced in classical reactors has to be pelletized before furtheruse, which involves an extrusion step anyway.4 Chapter 1III. MAIN REACTIONS IN REACTIVE EXTRUSIONReactions involving polymers that have been performed in extruders cangenerally be divided into ve categories (40):1. Bulk polymerizations2. Graft or functionalization reactions3. Interchain copolymerizations4. Coupling or branching reactions5. Degradation reactions1. Bulk Polymerization. In bulk polymerization reactions, a polymer isformed from a monomer or a low molecular prepolymeric material. Duringthe polymerization, a polymer is formed that, in general, is soluble in themonomer. The viscosity of this polymermonomer mixture increasessharply as the reaction progresses. Due to this increase in viscosity bothmixing and heat transfer become restricted.Bulk polymerizations are traditionally subdivided into additionreactions and condensation reactions. During addition reactions a polymerchain is formed in a very short time, until it terminates and stops growing.During condensation reactions, all polymeric chains keep growing during thewhole reaction time and often a low-molecular-weight by-product is formed.The removal of this by-product by devolatilization is often the limiting factorfor the reaction speed. Also, polymerization reactions exist of which thereaction kinetics shows aspects of both addition and condensation reactions.On the basis of reaction kinetics, a division in step reactions and chainreactions is therefore more correct. This division will be used in this book.2. Graft and Functionalizing Reactions. The production of both graftpolymers and functionalized polymers involves the reaction of a polymericchain with molecules of a monomer or a mixture of monomers. Infunctionalizing reactions, single units of the monomer are chemically linkedto the backbone polymer. In grafting reactions, short chains of the monomerunits are linked to the main chain polymer. Both the single units and thechains may be capable to react with other chemicals. Graft and functionali-zation reactions lead to a change in physical and chemical properties of thepolymeric material, thereby increasing the industrial value. Due to thelonger side chains, the viscosity of the reacting mixture increases moredrastically during grafting reactions than during functionalizing reactions.3. Interchain Copolymerization. This is a reaction between two or morepolymers to form a copolymer. This type of reaction often involves theIntroduction 5combination of reactive groups of the dierent polymers to form a graftcopolymer. However, contrary to normal graft reactions, no monomers areused in this process.4. Coupling or Branching Reactions. These reactions involve the increaseof the molecular weight of homopolymers by coupling the polymeric chainsthrough a polyfunctional coupling agent.5. Degradation Reactions. are used to decrease the molecular weight ofpolymers in order to meet a specic product performance. The degradationis often achieved by simple shear heating or by the addition of chemicalsubstances like peroxides. Because large chains have a bigger chance beingcut, degradation often occurs together with a narrowing of the molecularweight distribution.Table 1.1 gives some examples of reactions that have actually beenperformed in extruders (40,41).Besides polymerization reactions and modication reactions ofpolymers, other types of reactions can also be performed in extruders(41,42):+ Cyclization of chemical components+ Isomerization of chemicals+ Depolymerization of polymers to their monomers+ Hydrolysis of wood, esters, and polyurethanes+ Salt formation in high-viscosity media+ Neutralization reactions+ Modification of starches like benzylation, ethoxylation, andacetylationIV. SINGLE-COMPONENT VERSUS MULTICOMPONENTREACTIONSFrom a processing point of view all reactions can be divided into two maingroups: single-component and multicomponent reactions.Single-component reactions can occur throughout the bulk of thematerial. At the start of the reaction only one component, monomer orprepolymer, is present, or the components used are well miscible andpremixed. For this group of reactions the temperature of the mixture playsan important role, as well as macromixing over the length of the extruder,which is related to the residence time distribution. Both parametersdetermine the progress of the reaction.6 Chapter 1Multicomponent reactions, on the other hand, occur predominantlybetween immiscible components. Because the reaction proceeds mainly atthe interface between the components, micromixing plays an important role.Normally, this type of reactions becomes diusion limited as the reactionprogresses due to the buildup of reaction products at the interfacebetween the components. To overcome this diusion limitation, extensiveTable 1.1 Reactions Performed in ExtrudersType of polymerization End productStep polymerization Polyetheremide(condensation reactions) PolyestersPolyethylterephthalate (PET)Polybutylterephthalate (PBT)Polyamide 6.6PolyarylatePolyurethanesPolyamide 6Chain polymerization Polyoxymethylene(addition reactions) Polymethyl methacrylate (PMMA)Acrylic polymersPolystyrene and styrene copolymersWater soluble polyamideGraft reactions andfunctionalizationreactionsGraft copolymer of polystyrene and maleic anhydrideGraft copolymer of polyolenes and vinylsilanesGraft coplolymers of polyolenes and (meth) acrylicmonomersGraft copolymer of EVA with acrylic acidGraft copolymer of polyolenes and maleic anhydrideHalogenation of polyolenes or EVAInterchain copolymerformationCopolymers of reactive polystyrene and polymers withamide, mercaptan, epoxy, hydroxy, anhydride orcarboxylic acid groupsCopolymer of polypropylene grafted with maleicanhydride and nylon 6Copolymer of polyolenes and polystyreneCopolymer of EVA grafted with methacrylates andgrafted polystyreneCoupling reactions Coupling of PBT with diisocyanate and polyepoxide orpolycarbodiimideCoupling of PET with bis(2-oxalzoline)Degradation reactions Degradation of polypropylene by shear-heatingDegradation of PET with ethylene glycolIntroduction 7micromixing is necessary. In addition to micromixing, these reactions areinuenced of course also by temperature and macromixing.V. CONCLUDING REMARKSExtruders have denite advantages for their use as chemical reactors. Theyprovide good mixing, a reasonable heat transfer, and good pumping abilitiesfor highly viscous materials. This opens the possibility to utilize them as apolymerization or modication reactor for macromolecular materialswithout the use of large amounts of solvents, which has well-recognizedadvantages from environmental point of view. In addition, the lack ofsolvents also results in economical advantages; no expensive separation stepis necessary and the process becomes more energy ecient. Also theexibility due to the scale is an advantage of reactive extrusion. Whereasin classical solution polymerization batch times of several hours are quitecommon, the residence time needed in an extruder reactor is of the order ofminutes. Changes in operating conditions are generally eective within avery short period of time and fast changes in product specications can bemade during the process, without producing large amounts of o-specmaterial. Finally, reactive extrusion gives the opportunity to polymerizeunder constant high shear. This opens possibilities for new processes in theeld of reactive mixing and blending.However, the extruder as reactor has also some disadvantages: it is anexpensive apparatus per unit reactor volume. In order to be economicallyattractive, this requires for relative fast reaction kinetics, while the coolingcapacity of the extruder limits the amount of reaction enthalpy that can betolerated. Especially this last phenomenon can limit the scalability frompilot plant to production size equipment.REFERENCES1. K.E. Stober, J.L. Amos, Dow Chemical Co. U.S. Patent no. 2,530,409 (1950).2. G. Illing, Modern Plast 46 (1969), 7076.3. W.A. Mack, Chem Eng 79 (1972), 99102.4. G.S. Meyuhas, A. Moses, Y. Reibenbach, and Z. Tadmor, J Polymer Sci., Pol.Let. Ed 11 (1973), 103111.5. W.A. Mack and R. Herter, Chem. Eng. Progress 72 (1976), 6470.6. J.A. Stuber and M. Tirrel, Polym. Proc Eng 3 (1985), 7183.7. S.K. Dey, J.A. Biesenberger, Proc 45th ANTEC, Soc Plastic Eng, 133135(1987).8. K.J. Ganzeveld and L.P.B.M. Janssen, Can J. of Chem. Eng., 71 (1993), 411418.8 Chapter 19. H.A. Jongbloed, R.K.S. Mulder, and L.P.B.M. Janssen, Polym Eng Sci 53(1995), 587597.10. A.J. van der Goot and L.P.B.M. Janssen, Adv Polym Techn 16 (1997), 8595.11. H.A. Jongbloed, J.A. Kiewit, J.H. Van Dijk, and L.P.B.M. Janssen, Polym EngSci 35 (1995), 15691579.12. K.J. Ganzeveld, and L.P.B.M. Janssen, Polym Eng Sci 32, no. 7 (1992),457466.13. J.A. Speur, Polymerisation Reactions in a Twin Screw Extruder, PhD thesis,University of Groningen, The Netherlands (1988).14. A. Bouilloux, C.W. Macosco and T. Kotnour, Ind Eng Chem Res 30 (1991),24312436.15. S. Coudray, J.P. Pascault, and M. Taha, Polym Bull 32 (1994), 605610.16. E. Uhland, and W. Wiedman, Macromol Symp 83 (1994), 5975.17. P.R. Hornsby, J.F. Tung, and K. Taverdi, J Appl Polym Sci 53 (1994),891897.18. H. Kye, and J.L. White, J Appl Polym Sci 52 (1994), 12491262.19. W. Michaeli, A. Grefenstein, and U. Berghaus, Polym Eng Sci 35 (1995),14851504.20. W. Michaeli, U. Berghaus, and W. Frings, J Appl Polym Sci 48 (1993),871886.21. W. Michaeli, H. Hocker, W. Frings, and A. Ortman, Proc 52nd ANTEC, SocPlastic Eng 6267 (1994)22. J.M. Kelley, U.S. Patent no. 5,270,029 (1993).23. M. Xanthos, Reactive Extrusion, Principles and Practice, Munich: HanserPublishers (1992).24. P. Franz, Polymerreaktionen und reactives Aufbereiten in kontinuierlichenMachinen. In: Kunststofftechnik, Dusseldorf: VDI Verlag (1988).25. H.D. Aeppli, Plastverarbeiter, 40 (1989), 108.26. S. Jakopin, Adv Polym Techn 11 (1992), 287.27. Foster, R.W. and J.T. Lindt: Polym Eng Sci 29 (1989), 27828. Foster, R.W. and J.T. Lindt: Polym Eng Sci 30 (1990), 621.29. Chen, L., G.H. Hu and J.T. Lindt, AIChE J 39 (1993), 653.30. Chen, L., G.H. Hu and J.T. Lindt, Intern Polym Proc XI (1996), 329.31. M. Xantos, M.W. Young and J.A. Biesenberger, Polym Eng Sci 30(1990), 355.32. K.J. Ganzeveld and L.P.B.M. Janssen, Polym Eng Sci 32 (1992), 457.33. N.G. Gaylord, In: Reactive Extrusion, Principles and Practice, M. Xantos, ed.,Munich: Hanser Publishers (1992).34. Y.J. Sun, G.H. Hu and M. Lambla, J Appl Polym Sci 57 (1995), 1047.35. C.W. Lin, J Mat Sci Lett 12 (1993), 612.36. D. Suwanda and S.T. Balke, Polym Eng Sci 33 (1993), 1585.37. A.J. van der Goot, R. Hettema and L.P.B.M. Janssen Polym Eng Sci 37(1997), 511.38. A.J. van der Goot, S.A. Klaasens and L.P.B.M. Janssen, Polym Eng Sci 37(1997), 519.Introduction 939. L.P.B.M. Janssen, Polym Eng Sci 38 (1998), 2010.40. S.B. Brown, C.M. Orlando, Reactive extrusion, In: Encyclopedia of PolymerScience and Engineering. Vol. 14. New York: John Wiley, 1988: 169.41. L. Wielgolinsky and J. Nageroni, Adv Polym Techn 3 (1983), 99.42. Graaf, R.A. de, A Broekroelofs and L.P.B.M. Janssen, Starch 50 (1998), 198.10 Chapter 12ExtrudersI. INTRODUCTIONAlthough there exists a variety of dierent types of extruders, a main divisionthat can be made is between single-screw extruders and twin-screw extruders.The most important dierence between those two types of machines is thetransport mechanism. A single-screw extruder consists of one screw rotatingin a closely tting barrel; the transport mechanism is based on frictionbetween the polymer and the walls of the channel. If the polymer slips at thebarrel wall, it is easy to envisage that the material will rotate with the screwwithout being pushed forward. This makes these types of machines stronglydependent on the frictional forces at the wall and the properties of thematerial processed. Therefore, single-screw extruders are less suitable forreactive extrusion processes, like polymerizations, where large viscositydierences occur. However, application for grafting reactions is still apossibility. An exceptional machine is the co-kneader. In this special type ofsingle-screw extruder the screw consists of elements with interrupted ightsthat rotate in a barrel with stationary pins. Due to the rotation of the screwand a superimposed axial oscillation good conveying capacities and a goodmixing action are achieved, although the pressure built up is rather poor.Twin-screw extruders consist of two screws, placed in an gure-8-shaped barrel. In case of intermeshing extruders the ights of one screw stickin the channel of the other screw. Because of this, the polymer cannot rotatewith the screw, irrespective of the rheological characteristics of the material.This indicates the most important advantage of intermeshing twin-screwextruders: the transport action depends on the characteristics of the materialto a much lesser degree than in the case of a single-screw extruder.Figure 2.1 represents the main types of extruders.+ The single-screw extruder (a) is most common in polymerprocessing. Its working characteristics are strongly dependant on11the material properties. In reactive extrusion single-screw extruderscan only be used if the viscosity changes of the material are limited.+ Co-kneaders (b) have one single screw, while the barrel is equippedwith kneading pins. The screw rotates and oscillates giving a verygood mixing action. Different pin geometries can provide differentmixing actions. The pins can also be used for monitoring thetemperature or as injection points. Moreover, the pins prevent thematerial from rotating with the screw and therefore ensure a morestable operation than can be provided in an ordinary single-screwextruder+ Tangential twin-screw extruders (c and d) are not closelyintermeshing; they can be envisaged as a parallel connection oftwo single-screw extruders with mutual interaction. A model basedon three parallel plates is often used to describe this type of twin-screw extruder. This model shows a strong resemblance to thetwo-parallel-plate model that is used for single-screw extruders.The screws can be arranged in two different ways, a mixing mode(c) or a transport mode (d). All commercial tangential twin-screwextruders are counterrotating.+ The closely intermeshing twin-screw extruders, both counter-rotating (e) and corotating (f ), can best be modeled as series ofC-shaped chambers. Due to the rotation of the screws thesechambers transport the material from hopper to die, whileFigure 2.1 Dierent types of extruders: (a) single-screw, (b) co-kneader, (c) non-intermeshing, mixing mode, (d) nonintermeshing, transport mode, (e) counter-rotating, closely intermeshing, (f ) corotating, closely intermeshing, (g) conicalcounterrotating, and (h) self-wiping, corotating.12 Chapter 2interactions between the chambers occur via leakage flows. Ingeneral these leakage gaps are larger in corotating machines thanin counterrotating ones. Due to the large resistance to back flowthrough the narrow gaps, these extruders possess a strong positiveconveying character and their stability is large.+ The screws and the barrel of closely intermeshing twin-screwextruders can also be conical (g). This has advantages for thefeeding process if the material has a low bulk density. Whilepassing through the extruder, the chambers gradually decrease insize and compress the material. Moreover, conical screws providea larger space for the bearings of the screws and they can easilybe removed from the barrel.+ Depending on the exact geometry, self-cleaning corotating twin-screw extruders (h) can be described in two ways. They can bemodeled as series of C-shaped chambers with very wide leakagegaps, or which is more common, they can be considered to beconstructed as continuous channels with some flow restrictions atregular intervals. This type of machinery imposes high-shear forceson the material, and to increase shear even further special shearingelements are common. Both screw configurations with two or threelobes or thread starts per screw exist. Two lobe screws possessa better conveying capacity and provide a higher throughput;three lobe screws have a larger mechanical strength and highershear rates in the channel. Most modern machines have two lobescrews.Closely intermeshing extruders, as well corotating as counterrotating,have in general deeply cut channels and narrow leakage gaps. Theirrotational speeds are generally low, due to the large shear forces on thematerial in the gaps. Therefore the average shear level imposed on thematerial in the chambers is low. Selfwiping extruders, on the other hand,have shallow channels (especially if equipped with triple ighted screws).They operate with high rotational speeds and the transport eciency (theamount of material transported per revolution) is lower than in closelyintermeshing machines. In these machines the material is subjected to highaverage shear forces and the viscous dissipation is much larger than inclosely intermeshing machines.Conical twin-screw extruders have the advantage that the spaceprovided for bearing is large. Moreover, by moving the screws axially it ispossible to compensate for wear of the screws. A disadvantage of this typeof machine is that screw elements with dierent geometries are not easilyinterchangeable.Extruders 13Tangential extruders are often used in situations where the elasticity ofthe material would pose problems in the leakage gaps. This type of extruderis often found in the rubber industry.In general, it can be concluded that because of the large shear forces inthe channel and the simple application of mixing elements, self-wipingextruders are often used in compounding processes. In reactive extrusiontheir high shearing action is particularly convenient if intensive mixing ordevolatilization is required. For plasticating extrusion the low average shearin closely intermeshing extruders is an advantage when working withmaterials that are sensitive to degradation. Moreover, because of the lowshear levels the heat generated by viscous dissipation is low, allowing for agood temperature control. This type of extruders is often found in proleextrusion and lm blowing as well as in PVC extrusion where a smalldistribution in residence times is important. Some closely intermeshingextruders are also provided with screws with large leakage gaps. Whenoperating at high rotational speeds these machines can also be used forcompounding. In reactive extrusion the positive displacement action of aclosely intermeshing twin-screw extruder can be an advantage when low-viscosity monomer has to be transported. As will be shown in Chapter 13this type of machine has certain advantages when slow reactions areperformed or if the viscosity buildup during the reaction is poor. On theother side, self-wiping extruders generally possess a better mixing action andhigher throughput at comparable screw diameters.II. SINGLE-SCREW EXTRUDERSSingle-screw extruders can be used in reactive processes where the viscositychanges remain within acceptable limits, like in some grafting reactions.Their working mechanism and the modeling is well covered in literature, andan extensive description can be found in various books like those byRauwendaal (1) and Tadmor and Klein (2). The basis of the uid ow insingle-screw extruders can also be generalized to other types of extruders.Therefore we introduce here a simple analysis based on Newtonian behaviorof the liquid. For this analysis the channel of the screw is simplied intoa at plane geometry. The single-screw extruder consists of a barrelcontaining a rotating screw. As a rst step in the simplication we will keepthe screw stationary and let the barrel rotate. The next step is to unwind thescrew channel into a straight trough. Figure 2.2 shows the results. Therotation of the screw can now be transformed into the movement of a plateover the channel. The velocity of this plate is of course the circumferentialvelocity of the screw and equals pND, while its direction relative to the14 Chapter 2trough equals the screw angle f. N is the rotation rate of the screw, and D isthe screw diameter.A. Fluid FlowThe movement of the plate has a component in the down channel directionand a component in the cross-channel direction; both drag the liquid alongand introduce ow proles with components parallel and perpendicular tothe direction of the channel.Uz = pNDcos fUx = pNDsin f (2.1)The ow in the down-channel direction can be calculated from a forcebalance:vz = pND cos c yHH22mdPdzyH yH 2 (2.2)where dP/dz denotes the pressure gradient in the down-channel direction. Acloser look at this equation reveals that the right-hand side consists of twoterms. The rst part (apart from geometrical parameters) only depends onthe rotational speed and the second part is a unique function of the pressure;so the eects of screw rotation and pressure can be separated. This is shownin Fig. 2.3. The actual ow prole is a superposition of the (linear) drag owand the (parabolic) pressure ow. However, strictly speaking this separationis only valid for Newtonian liquids.From the velocity prole in the down-channel direction thethroughput of the pump zone of a single-screw extruder can be obtainedby integration:Qv = W

H0v(z) dy =WH2 pND cos f H3W12mdPdz (2.3)Figure 2.2 The channel in a single-screw extruder.Extruders 15Also in this equation the eects of drag ow and pressure ow can beseparated; the drag ow is proportional to the rotational speed of thescrews, and the pressure ow is proportional to the ratio of pressuregradient and viscosity.For the transverse direction of the channel too, an analogouscalculation can be set up, and if the ow across the ights of the screwcan be neglected (which is generally the case for the hydrodynamics insingle-screw extruders), the velocity prole in the direction transverse to thechannel can easily be calculated.vx = 3UxyH+ 23 yH (2.4)The cross-channel ow forms a circulatory ow as sketched in Fig. 2.4. Thecenter of circulation, where vx equals zero, lies at two thirds of the channelheight. This cross-channel prole must of course be combined with thedown-channel prole; the cross-channel ow should be superimposed on theow in the channel direction. As a result the polymer elements follow ahelical path through the channel. The center of rotation of this helical owlies at two thirds of the channel height. Particles in this location followa straight line through the channel without being interchanged withparticles at other locations. Therefore these uid elements will neverapproach the wall closer than one third of the channel depth if no mixingelements are used in the screw design. This will appear to be particularlyFigure 2.3 Superposition of drag ow and pressure ow in a single-screw extruder.Figure 2.4 Rotating ow in the cross-channel direction.16 Chapter 2important when considering heat transfer and thermal homogenizationfor reactions where a large amount of reaction heat is released (seeChapter 6.IV).B. Correction FactorsStrictly speaking Eqs. (2.2) and (2.3) are only valid for straight extruderchannels of innite width. To account for the curvature of the channel andthe nite width, correction factors can be used and Eq. (2.3) can be written asQv =WH2 pNDcos f fd H3W12mdPdz fp (2.5)The correction factors follow from an analytical solution of a two-dimensional stress balance:fd =16Wp3Hoi=1,3,51i3 tanh ipH2W fp = 1 192Hp5Woi=1,3,51i5 tanh ipW2H (2.6)For practical purposes (H/W-0.6) these factors can conveniently beapproximated byfd = 1 0.57 HWfp = 1 0.62 HW(2.7)III. CO-KNEADERSA particular type of single-screw extruder that can be used as apolymerization reactor is the co-kneader. Traditionally this machine isoften used for processing of rubbers and foods. Though discovered in 1945and commonly used in industry, its application is far ahead of theoreticalunderstanding.The co-kneader consists of a single screw with interrupted ights (3). Aschematic representation is given in Fig. 2.5. Its working principle is basedon the rotation and axial oscillation of the screw, causing transportationand mixing. The mixing is enhanced by stationary pins in the barrel. Duringone passage of the pin, the material is subjected both to high-shear stressExtruders 17and to reorientation. The dispersive mixing process is promoted by the localweaving action of the pins and screw ights, where the distributive mixing isenhanced by the reorientation that is introduced by the pins. Figure 2.6displays an unrolled screw and barrel. The trajectories of the kneading pinsare visualized in relation to the rotating screw. It is clear that all surfaces aresubjected to wiping actions.The temperature can be controlled by the thermostated barrel andscrew. The large area-to-volume ratio as well as the radial mixingcontributes to good heat transfer capacities. These characteristics makethe co-kneader well suited for exothermic polymerization reactions, whereFigure 2.5 The co-kneader (from Ref. 3).Figure 2.6 Path of the kneading pins with respect to the screw ights (from Ref. 3).18 Chapter 2good dispersive mixing is required. Due to the large interruptions of theights it is not possible to use this machine for pressure buildup. If pressureneeds to be built up, a normal single-screw extruder is generally placed inseries at the end of the kneader.The mixing mechanism in the co-kneader is rather complex. Itprovides both distributive and dispersive mixing. The distributive mixing iscaused by the geometry of the screw ights. The interruptions in the ightsdivide material in each screw channel into two streams. The following screwight recombines and divides the material again. The kneading pins providefurther divisions. Due to these two eects the distributive mixing of theco-kneader can be regarded as a moving static mixer. This distributivemixing process requires relatively low energy.By the rotating and oscillating movement of the screw, the screwights slide along the pins and barrel. This results in high-shear stresses anddisperse mixing. It also leads to good self-cleaning properties.IV. CLOSELY INTERMESHING TWIN-SCREW EXTRUDERSIf the chambers of a closely intermeshing twin-screw extruder are fully lledwith material, the maximal throughput of a zone, Qth, can be written as thenumber of C-shaped chambers (Fig. 2.7) that is transported per unit of time,multiplied by the volume of one such chamber:Qth = 2mNV (2.8)Figure 2.7 The C-shaped chamber (from Ref. 4).Extruders 19Here N is the rotation rate of the screws, m is the number of thread starts perscrew, and V is the volume of a single chamber. In reality the output ofa twin-screw extruder is, of course, smaller than the theoretical throughputbecause the chambers are not completely closed. Four dierent kinds ofleakage ows can be distinguished (4) (see Fig. 2.8):+ A leakage (Qf) through the gap between the flights and the barrelwall. This leakage shows clear parallels with the leakage thatoccurs in a single-screw extruder. The gap through which thisleakage flows is called the flight leak.+ A leakage (Qc) between the flight of one screw and the bottom ofthe channel of the other screw. Because the flow through this gapresembles the flow in a calender, this leak is called the calenderleak.+ A leakage (Qt) through the gap between the sides of the flights,which is called the tetrahedron leak. In principle, this leak is theonly leak that leads from one screw to the other. In closelyintermeshing counterrotating twin-screw extruders, this gap isgenerally very narrow. In self-cleaning counterrotating twin-screwextruders this gap is very wide and the major part of the materialpasses this gap regularly.+ A leakage (Qs) through the gap between the sides of the flights,normal to the plane through the two screw axes. This leak is calledthe side leak. In its behavior this leak resembles the calender leakmost.The throughput through the dierent leakage gaps partly consists of dragow and partly of pressure ow. The pressure ow in its turn, is aFigure 2.8 Leakage gaps in a counterrotating, closely intermeshing twin-screwextruder (from Ref. 4).20 Chapter 2consequence of the internal pressure buildup in the chambers and of thepressure that is built up at the die, resulting inQf = AfN BfPm Qs = AsN BsPmQc = AcN BcPm Qt = AtN BtPm(2.9)here the subscripts f, s, c, and t stand for ight, side, calender, and side gap,respectively. The total amount of leakage through a section of the extruderis the sum of the individual leakage ows. For a screw with m thread startsthis can be written as (4)Ql = 2Qf Qt2m QcQs( ) = AN BPm (2.10)in which P is the pressure drop between two consecutive chambers, m theviscosity, and N the rotation rate of the screw. Numerical values for A and Band for the chamber volume V follow from the geometrical parameters ofthe screws only and are given in Section IV.C of this chapter. The realthroughput of a pumping zone in a twin-screw extruder, completely lledwith polymer, can now be determined easily.Q = QthQl = 2mV A ( )N BPm (2.11)For Newtonian liquids the use of dimensionless numbers for throughputand pressure drop leads to simple relations:Q = Q2mNV P =PNm (2.12)Here P is the pressure drop per chamber, caused by the pressure in front ofthe die, and m is the Newtonian viscosity. These two dimensionless groupsfor throughput and pressure are very powerful. When these groups are used,the characteristics for the completely lled pumping zone of twin-screwextruders are straight lines that are independent of viscosity and speed ofrotation of the screws. Figure 2.9 presents an example of these lines andtheir dependence on the size of the calender gap. As these lines are onlydependent on geometrical parameters, they keep their validity when thepumping zone of a twin-screw extruder is scaled up geometrically. If,for instance, the screw diameter, the pitch, the chamber height, and thedierent leakage gaps are all enlarged by the same factor, the lines do notchange.Extruders 21A. The Different ZonesIf a twin-screw extruder is stopped and opened, several zones can bedistinguished clearly (Fig. 2.10). Depending on whether the extruder is fedwith a solid or a liquid material two dierent situations occur. In case of asolid feed (a polymer or solid monomer) the chambers near the feed hopperare more or less lled with solids. This material melts, and a zone with onlypartly lled chambers can be seen. At the end of the screw, close to the die,the chambers are completely lled with polymer.If the extruder is fed with a liquid monomer, the rst part notnecessarily needs to be partly empty. However, as will be explained later, forreasons of stability it is advisable to create a zone where the chambers arenot fully lled. Especially the fully lled zone is very important for a properfunctioning of the extruder. In this zone the pressure is built up, mixingand kneading mainly takes place, and the major inuence of viscousdissipation also occurs. In reactive extrusion, changes in the length ofthe fully lled zone are associated with changes in reactor holdup andresidence time.In order to explain the existence of the fully lled zone, we will have torealize that the dierent zones in a twin-screw extruder cannot be viewedseparately, but are interconnected. This can be shown by the throughput.The actual throughput of a twin-screw extruder is determined by the feedingFigure 2.9 Dimensonless pressure-throughput characteristics of a counterrotatingtwin-screw extruder.Figure 2.10 The dierent zones in a twin-screw extruder when fed with solidmaterial: (a) solids transport; (b) partly empty; (c) fully lled.22 Chapter 2zone. What comes into the extruder here will also have to leave the extruderat the other end. Because the chambers are only partially lled, no pressurecan be built up in this zone, and the leakage ows will be limited to the dragcomponent only. Under normal circumstances, the throughput of this zoneis therefore independent of pressure at the die end of the extruder. In the lastpart of the extruder, where the pressure that is needed for squeezing thepolymer through the die is built up, the chambers are fully lled withmaterial, a pressure gradient is present, and considerable leakage ows aredependent on this gradient.The eect of the throughput is as follows: As derived, the actualthroughput through the completely lled zone is given byQ = 2mNV Ql (2.13)but the real throughput is determined by the feeding zone:Q = 2mvNVvc (2.14)in which c is the degree of lling of the chambers in this zone and the index vindicates that volume and number of thread starts of the screws relate to thegeometry in this zone. Because of continuity, the dierence betweentheoretical throughput and real throughput should equal the sum of theleakage ows:Ql = 2N mV mvVvc ( ) (2.15)As the degree of lling c does not depend on the nal pressure and all otherparameters in the right term of this equation are also independent ofpressure, it becomes clear that the sum of the leakage ows in a twin-screwextruder must be independent of pressure. However, if the equation for theleakage ows is taken into considerationQl = AN BPm (2.16)the pressure drop per chamber is xed and dependent on viscosity andgeometry only. If geometry and viscosity would not change, the pressuregradient would be constant over the whole completely lled zone. Also axed pressure is built up in the die of the extruder, which depends onthroughput, viscosity, and die geometry. Therefore, within reason, there willbe a point in the extruder at which the actual pressure becomes zero.Between this transition point of partly and fully lled chambers and the diethere exist pressure gradients, there are leakage ows, and the chambers arecompletely lled with polymer. Between this transition point and the feedhopper, there is no dierence in pressure between consecutive chambers, theExtruders 23leakage ows are zero or only consist of drag components and the chambersare only partly lled with material.For reactive processing, the length of the completely lled zone is oneof the most important factors and for good process control, knowledge ofthe dierent parameters that inuence the length of the completely lledzone is indispensable. Table 2.1 gives this inuence schematically.+ If, for instance, for the simplified case that the extruder is filledwith an isoviscous liquid, the resistance of the die is doubled, thepressure in front of the die will also double because the outputremains constant. However, the leakage flow is not influenced bythe die pressure, so that the pressure gradient in the extruderremains constant. Ergo, the completely filled length increases asindicated in Fig. 2.11.+ If the rotation speed is doubled while keeping the specific through-put (throughput per revolution) constant, the throughput willalso double, and consequently the die pressure will do so too. Asthe leakage flows also double, the pressure gradient will double,and the length of the completely filled zone will remain the same(Fig. 2.11).If the viscosity is not constant, the ability to build up pressure is pro-portional to the viscosity. If a monomer is polymerized by reactiveextrusion, this means that in the region where conversion is low hardlyany pressure can be built up. Also the inuence of the temperature in thisscheme is based on a change in the local viscosity and, because of that, onpressure drop.B. Corotating Versus Counterrotating Closely IntermeshingExtrudersBoth corotating and counterrotating twin-screw extruders can be modeledby means of a C-shaped chamber model. However, there are someTable 2.1 Influence of Extrusion Parameters on the Filled LengthInuence of Q P Ql dp/dx Filled lengthDie resistance 0 0 0 Rotation speed 0Filling degree Wall temperature 0 0 0 Die temperature 0 0 0 Gap size 0 0 0 24 Chapter 2dierences. Because of reasons of construction (the screws must t into eachother) the tetrahedron gap in corotating machines is generally bigger than incounterrotating machines. Moreover, the drag ow in the tetrahedron gap isin corotating extruders parallel to the direction of this gap. Where incounterrotating extruders the direction of internal pressure generationfavors the ow through the calender gap, in corotating machines thispressure generation favors the tetrahedron ow (Fig. 2.12). Since thetetrahedron leakage is the only leakage connecting the chambers on onescrew with the chambers on the other screw, the mixing between material onthe dierent screws is better in corotating machines. In counterrotatingextruders both drag ow and internal pressure generation favor thecalender leak. Since in the calender gap the material is elongated andkneaded, it can be concluded that counterrotating extruders favor a goodkneading action.Figure 2.12 Internal pressure generation in (a) a counterrotating and (b) acorotating twin-screw extruder.Figure 2.11 Pressure buildup: (a) changing rotational speed and (b) changing dieresistance.Extruders 25C. The Mathematics of the Counterrotating Twin-Screw ExtruderThe equations for the dierent leakage gaps are mathematically simple (4).The variables are dened in Fig. 2.13. For the tetrahedron gap in acounterrotating twin-screw extruder an empirical equation exists:Qt = 0.0054 HR 1.8c 2 c o tan cH 2+PR3m (2.17)The derivation of the ight leakage is similar to that for the ight leakage ina single-screw extruder:Qf = 2p a ( )R NBd2 d36mB 3mNBH2BmB P (2.18)The equation for the calender leakage follows the classical derivation forthe throughput of a two-roll calender with the only dierence that thevelocities of the two calender surfaces are dierent because of the dierentradii:Qc = 4B3m2mPs36pm2R H ( )s2 Np 2R H ( )s (2.19)Figure 2.13 Geometrical parameters.26 Chapter 2For the side leak a semiempirical equation is used:Qs=pN 2RH ( ) Hs ( ) cstanc ( ) mP Hs ( ) cstanc ( )2cosc212mRsina2 10.630cstancHs cos2c0.052 cstancHs cos2c 5 (2.20)From the equations above it can simply be deduced that every leakage owhas two components: one drag component that is proportional to therotational speed and one pressure component that is proportional to thepressure dierence between two consecutive chambers and inverselyproportional to the viscosity. The proportionality factors are onlydependent on geometrical parameters. The only exception is the tetrahedrongap that only depends on pressure dierences. The total amount of leakagecan now be written asQl = AN BPm (2.21)in which, as can be seen from the equations, A and B are constants that onlydepend on the geometry of the screws.Also the volume of a C-shaped chamber can easily be determined bystraightforward calculations. Therefore, we subtract the volume of the screwover the length of one pitch from the free volume of the barrel over the samelength. The volume of the barrel follows from Fig. 2.13:V1 = p a2 R2 R H2 RH H24 S (2.22)The volume of the screw root isV2 = p R H ( )2S (2.23)and the volume of the ight isV3 =

RRHb(r) + 2 pr dr (2.24)For a screw with straight-sided ights yieldsb r ( ) = B 2 R r ( ) tan c (2.25)Extruders 27and the integral can be written asV3 = 2p RH H22 B RH223H3 tan c (2.26)The total volume of one chamber can now be calculated fromV =V1V2mV3m (2.27)V. SELF-WIPING TWIN-SCREW EXTRUDERSAn important dierence between closely intermeshing and self-wiping twin-screw extruders is the way the screws t into each other. In self-wipingextruders the screw geometry is such that in the plane through both screwaxes there is a very close t between both screws (Fig. 2.14). This requires aspecial geometry with, as a consequence, a very large tetrahedron gapbetween the chambers. Due to this special character of most self-wipingextruders the C-shaped chamber concept has to be abandoned; a modelbased on continuous channels can better be used. Therefore, the self-wipingextruder acts more as a drag pump than as a displacement pump. Figure2.15 shows, analogously to single-screw extruders, the unwound channel.Each time when the material changes screw during its transport through achannel, there exists a certain ow restriction. This can give an extrapressure buildup, which is however in general very minute, and for practicalpurposes this eect is often neglected.Screws of self-wiping extruders consist of one, two, or three threadstarts. At an increasing number of thread starts the distance between thescrew axes has to increase and as a consequence the maximum channeldepth decreases, which in turn inuences the maximal throughput per screwrotation. For this reason extruders with four or more thread starts are notFigure 2.14 Transport elements in a self-wiping extruder.28 Chapter 2common. Because there exist hardly any parallel planes close to each otherin the geometry of self-wiping machine, their rotational speed can be chosenmuch higher than for closely intermeshing twin-screw extruders. Combinedwith the shallow channels this leads to a high average shear level, which is inpractice ve to 10 times higher than in closely intermeshing machines. Theshear levels can be increased further by the use of so-called mixing orkneading elements. Changes in the angle between these elements determinethe kneading action as will be seen later.A. Screw GeometryBecause the screws have to t closely in the plane through the axesthe degrees of freedom in screw geometry are very limited. Due to therequirement of close tting in a cross section perpendicular to the axes,the surfaces of the screws must always (nearly) touch. This is shown inFig. 2.16. The channel depth as a function of the angle c can be written in itsmost elementary form asH c ( ) = R 1 cos c ( ) c2R2sin2c

(2.28)Figure 2.15 Unwound channel in a self-wiping extruder.Figure 2.16 Cross section through the screws.Extruders 29where c is the center line distance (5). More complicated geometries existwith dierent radii of curvature to obtain geometries with a larger ightwidth or deeper channels. The cross section of the screw elements is the sameas the cross section of the kneading elements. If extra pressure buildup isrequired, elements with a more narrow pitch (pumping elements) are used.Nearly all self-wiping extruders consist of screws with separate screwelements, and depending on process requirements, dierent screw lay outscan be constructed.B. Transporting ElementsBecause the working of self-wiping twin-screw extruders is mainly based ondrag in an open channel, the equations derived for single-screw extrusioncan be used. Combination of drag ow and pressure ow in a single channelleads to an equation for the throughput per channel:Q =12WH0Uz fdsWH3012mdPdz fps (2.29)Here fps and fds are correction factors for the channel geometry, and H0 isthe maximum channel depth. In case of rectangular screw channels thecorrection factors can be calculated analytically [Eqs. (2.6) and (2.7)]; for thecomplex geometry of self-wiping extruders they can be approximated byEq. (2.32) or they can be calculated numerically (6). The number of parallelchannels in a screw with m thread starts equals 2m1. This leads to athroughput for a self-wiping twin-screw extruder of (6,7)Q = m12 WH0Uz fds 2m1 ( )WH3012mdPdz fps (2.30)Apart from this, an extra pressure buildup will occur in the intermeshingregion. This can be expressed by means of a correction factor k that is afunction of the relative ow area in the intermeshing region, leading to thenal equation:Q = m12 WH0Uz fds 2m1 ( )kWH3012mdPdz fps (2.31)In practical situations this factor k is close to 1 and its inuence is oftenneglected. For shallow channels the shape factors fds and fps can beapproximated by (7)fds =

W2W2H x ( )WH0dx and fps =

W2W2H x ( )3WH30dx (2.32)30 Chapter 2C. Elements for Pressure BuildupBy constructing screws with a large overlap in the intermeshing region thepressure buildup abilities can increase considerably. In the limiting casethe self-wiping prole will be lost and C-shaped chambers will emerge.Figure 2.17 shows these so-called pressure built-up elements. The pitch isgenerally chosen smaller than in transport elements. A model based onC-shaped chambers (Section IV.C) leads to good results for this type ofelements.D. Kneading ElementsThe third type of elements present in self-wiping twin-screw extruders is thekneading element (Fig. 2.18). These elements consist of kneading disks thathave the same cross-sectional shape as the transport elements. The anglebetween the individual kneading disks, the so-called stagger angle,determines the kneading action. Stagger angles of 30

, 60

, 90

, 120

, and150

are frequently used. The last two angles (120

and 150

) are alsosometimes referred to as 60

and 30

. As a general rule, it can be statedthat the larger the angle between the disks (30

, 60

, 90

, 120

, 150

), thelarger the kneading action, but this results, of course, also in a larger energydissipation in the element. Furthermore, the pressure drop over the kneadingelement is dependant on the stagger angle. At moderate throughputs akneading element with a stagger angle up to 60

can still build up somepressure; in all other situations a pressure is needed to transport the polymerthrough the element. This dependence on the stagger angle can beunderstood if we consider the kneading element as an interrupted screwight.Figure 2.17 Pressure-generating elements.Extruders 31At angles of 30

and 60

there exists a certain pumping action thatdepends on the rotational rate. At larger throughputs, the pressure dropover the element will decrease or, as stated, even become negative. Inkneading elements with a stagger angle of 90

the pumping action is absent.This implies that the pressure needed to pump the polymer through thekneading element is independent of the rotation rate but proportional to thethroughput. At stagger angles larger than 90

the kneading element acts asa screw element with reversed pitch. The transport elements in front of thekneading element have to pump against the reversed pumping action of thekneading element, and high-shear levels and large energy dissipation will beattained. Figure 2.19 shows an example of the pressure drop over thekneading elements as a function of the stagger angle at two dierentrotation rates at large and at small throughput. At increasing throughputFigure 2.18 Kneading elements.Figure 2.19 Pressure losses over kneading elements: (a) low rotational speed,(b) high rotational speed, () low throughput, ( ) high throughput.32 Chapter 2the curves will be shifted upward, resulting in higher pressure drops at largestagger angles and a disappearing of the pressure generation at low staggerangles. For reactive extrusion the kneading elements have two functions:they improve the mixing and, as will be seen in Section IV.E, they increasethe lled length in front of the element and therefore the hold-up in theextruder-reactor.E. The Fully Filled LengthSimilar to closely intermeshing twin-screw extruders, in self-wipingextruders dierent regions can be distinguished where the screws are fullylled with material or only partially lled. Again in the fully lled regionpressure is built up; in the partially lled zone the pressure gradient equalszero. This implies that a fully lled zone must be present before the die andbefore pressure-consuming kneading elements. The pressure gradient in thefully lled zones can be calculated from the equation for the throughput andequals for an isoviscous processPZ =dPdz = WH02 pNDcos f ( )fps Q2m1 + 12mkWH30 fds(2.33)As a consequence the fully lled length before the die in axial direction isLf = Zsin y = kWH30 fdsP12m (WH02) pNDcos f ( )fps(Q(2m1)) sin y(2.34)For kneading elements the pressure drop can be written asP = m AQxBN ( ) (2.35)in which A and B are geometrical constants and x denotes the dependence ofpressure on the stagger angle. x is negative for angles smaller that 90

, zerofor 90

, and increases with increasing stagger angle. If the pressure is zeroafter the kneading element, indicating a partially lled zone in that region,an expression for the lled length in front of the kneading element can beobtained:Z = 2m1 ( ) + AQxBN ( )2m1 ( )WH0 pNDcos f ( )fps2QkWH30fds6 (2.36)Z is the lled length in the channel direction. The axial lled length Lf caneasily be obtained fromLf = Zsin f (2.37)Extruders 33The equations above can be used to quantify the inuence of dierentextrusion parameters on the lled length. Striking is that the lled length isindependent of viscosity. This is due to the simplication we have made inassuming an isoviscous process: if the viscosity changes, a relative viscosityfactor has to be introduced. The fact that the lled length is independent onthe absolute value of the viscosity can be understood if we realize that boththe pressure-generating abilities of the transport elements as well as thepressure drop in the die or over the kneading elements are proportional tothe viscosity; the absolute viscosity therefore has no inuence on the lengthof the fully lled zone. In reactive extrusion, where the viscosity in front ofthe kneading element is generally lower than that in the kneading element,the fully lled length as calculated here will be an underestimation.Moreover, the equations show that if we change the rotational speedand the throughput in the same way, or in other words we keep therelative throughput constant, the fully lled length does not change.If the throughput increases at constant rotation speed the lled length willincrease and if the rotation rate increases at constant throughput the lledlength decreases. Finally, an increase of the stagger angle in kneadingelements (increasing s) will also increase the lled length. Application ofkneading elements with a more severe kneading action (larger staggerangles) will not only increase the kneading action in the elements themselves,but will also result in a larger lled length resulting in extra mixing.Figure 2.20 shows an example of the pressure prole in a screw,consisting of transport elements, followed by pressure buildup elements, akneading zone, transport elements, and nally pressure buildup elementsbefore the die. At location A the material is pressureless and the channel isnot necessarily fully lled. This location can be used, for instance, fordevolatilization or for an easy feeding of an extra component. However, itshould be realized that at increasing throughput the lling of the extruderincreases and the pressureless zone will disappear.Figure 2.20 A possible screw layout and the pressure prole. At location Amaterial can be added or removed.34 Chapter 2VI. NONINTERMESHING TWIN-SCREW EXTRUDERSNonintermeshing twin-screw extruders can as a rst approximation be seenas two parallel single-screw extruders. This would be accurate if the openarea that connects the two barrel halves (the apex area) would be zero.Because of the existence of the apex area, the screws interact with eachother, and the throughput of the nonintermeshing twin-screw extruder willbe less that that of two single-screw extruders. The screws can be arranged intwo dierent ways (Fig. 2.21): in the staggered conguration mixing isenhanced, but pressure buildup abilities are low; in the matched congura-tion a better pressure buildup is achieved at the cost of some mixing abilities.A model for the conveying action of this type of machine consists of a three-parallel-plate model, where the outside plates represent the screw surfacesand the middle plate (with zero thickness) represents the barrel. The apex isaccounted for by parallel slots in the middle plate, perpendicular to thecircumferential velocity. Using this model Kaplan and Tadmor (8) derivedan expression for the throughput for Newtonian ows:Q = WHUz fdnWH36mdPdz fpn (2.38)This throughput is of course twice the throughput for a single-screwextruder, except for the correction factors, which can be written in theirsimplest form asfdn = 4f1 3f fpn = 41 3f (2.39)Figure 2.21 Two dierent congurations for nonintermeshing twin-screwextruders: staggered conguration (top) and matched conguration (bottom).Extruders 35where f is the ratio between the uninterrupted barrel circumference and thetotal barrel circumference, orf =ap (2.40)(See Fig. 2.22). A more accurate description of the correction factors arebased on a model, where the middle plate has a nal thickness (9):fdn = f fd fp 2 WaH ( )3f 2 WaH ( )32fp 1 f ( )fpn = fp 2 WaH ( )3f 2 WaH ( )32fp 1 f ( )(2.41)Wa is the apex width and fp and fd are the shape correction factors, as theyare dened for single-screw extruders [Eqs. (2.6) and (2.7)].VII. INFLUENCE OF LOW VISCOSITY MONOMERIC FEEDIn the simplied case of an isoviscous process, the pressure built up alongthe lled length appeared to be constant. In reactive extrusion, however, thematerial is generally far from isoviscous, which inuences the lled lengthconsiderably. Figure 2.23 shows the inuence of an increasing viscosity onthe pressure built up in the extruder. For a simple screw with uniformgeometry this pressure buildup is uniform in the simplied case of anisoviscous material (Fig. 2.23a). For reactive extrusion the viscosityincreases in the direction of the die, and the low viscosity in the llingregion results in poor local pressure buildup abilities (Fig. 2.23b). Thismakes the extruder more sensitive to disturbances, and small uctuations inFigure 2.22 Cross section through a nonintermeshing twin-screw extruder withstaggered conguration.36 Chapter 2pressure may result in large changes in the fully lled length and therefore inresidence time. Moreover, overlling of the extruder can easily occur.A low-viscosity feed stream also inuences the working of the feedzone. In this partially lled zone, material with low viscosity is not likely tobe dragged properly along the channels of the screw but tends to ow on thebottom of the extruder because gravity forces predominate rather thanviscous forces. A dimensionless parameter that relates gravity and viscousforces is the Jereys number:Je =rgDmN (2.42)where g is the gravitational acceleration. This Jereys number equals theratio between the Reynolds number and the Froude number. De Graaf et al.(10) described experiments where the pattern of the uid in the chamberswas correlated to the Jereys number and to the degree of ll. Threedierent patterns could be distinguished (Fig. 2.24):1. At low filling degrees and high Jeffreys numbers the materialremained basically at the bottom of the channel and was notcarried over the screws.2. At low filling degrees and low Jeffreys number the materialcollected at the pushing flight.3. At high filling degrees the material sticks to both flights.VIII. CONCLUDING REMARKSVarious types of extruders exist, all with their specic characteristics.Typical for many reactive extrusion processes are the large changes inFigure 2.23 Pressure generation with (a) an isoviscous and (b) a reacting uid.Extruders 37viscosity, in the most extreme case varying from monomer viscosity topolymer viscosity, which can easily be six orders of magnitude. This requiresfor good pumping abilities, preferably independent of viscosity. For thisreason single-screw extruders have limited possibilities in reactive extrusion.Their application can be found in modication reactions, provided theextruder is equipped with good mixing elements.A special type of single-screw extruder is the co-kneader. This type ofextruder is provided with mixing pins through the barrel wall and the ightsof the screw are interrupted. This extruder provides a very good mixingaction, good transporting characteristics but poor abilities to build uppressure. Especially when extensive micromixing is required this extruder isa good alternative.Twin-screw extruders can be divided into dierent classes: noninter-meshing (counterrotating), closely intermeshing (counter- or corotating), andself-wiping extruders (corotating). Especially the last two types have goodpumping capabilities. Specic for twin-screw extruders is the occurrence of afully lled zone and a zone where the screws are only partially lled withmaterial. The operating conditions and screw geometry determine the lengthof the fully lled zone and as a consequence the holdup in the reactor.SYMBOL LISTa Apex anglec AngleFigure 2.24 Inuence of viscosity and lling degree on the material distribution inpartially lled chambers.38 Chapter 2c Degree of chamber or channel llingd Flight gap width (m)k Pressure correction factor for the intermeshing zones Calender gap width (m)x Pressure factor for kneading elementsf Screw anglec Tetrahedron width at the channel bottom (m)m Viscosity (Pas)iP Pressure dierence (Pa)Ql Total of leakage ows (m3/s)A Geometry parameter (m3)B Chamber width (m)B Geometrical parameter (m3)c Distance between screw axes (m)D Screw diameter (m)fd Drag ow correction factor single-screw extruderfp Pressure ow correction factor single-screw extruderfds Drag ow correction factor self-wiping extruderfps Pressure ow correction factor self-wiping extruderfdn Drag ow correction factor nonintermeshing extruderfpn Pressure ow correction factor nonintermeshing extruderg Gravitational acceleration (m/s2)H Channel depth (m)H0 Maximum channel depth (m)Je Jereys numberLf Filled length in axial direction (m)m Number of thread starts of one screwN Rotation rate of the screws (1/s)P Pressure (Pa)P Dimensionless pressureQ Dimensionless throughputQf, Qc, Qt, Qs Leakage ow through the ight gap, calender gap,tetrahedron gap and side gap (m3/s)Ql Leakage ow (m3/s)R Screw radius (m)S Pitch of the screw (m)Ux Wall velocity in the cross channel direction (m/s)Uz Wall velocity in the down channel direction (m/s)v Local velocity (m/s)V Volume of a C-shaped chamber (m3)W Width of the channel (m)y Height coordinate in the screw channel (m)Extruders 39z Down-channel coordinate (m)Z Length of the extruder channel (m)REFERENCES1. C. Rauwendaal, Polymer Extrusion, Carl Hanser Verlag, Munchen, 1986.2. Z. Tadmor and I Klein, Engineering Principles of Plasticating Extrusion,New York: Van Nostrand Reinhold, 1970.3. P. Franz, Polymerreaktionen und reactives Aufbereiten in kontinuierlichenMachinen. In: Kunststofftechnik, Dusseldorf: VDI Verlag, 1988.4. L.P.B.M. Janssen, Twin Screw Extrusion, Amsterdam: Elsevier, 1978.5. M.L. Booy, Polym Eng Sci 18 (1978), 973.6. C.D. Denson and B.K. Hwang, Polym Eng Sci 20 (1980), 965.7. M.L. Booy, Polym Eng Sci 20 (1980), 1220.8. A. Kaplan and Z. Tadmor, Polym Eng Sci 14 (1974), 5866.9. R.J. Nichols, SPE ANTEC, Chicago, 1983, 130133.10. R.A. de Graaf, Thesis, University of Groningen, NL, 1996.40 Chapter 23Chemical KineticsI. INTRODUCTIONAs already stated in Chapter 1 there are various types of reactions that canbe performed in extruders, from which the most important are additionpolymerization, polycondensation, and grafting or functionalizing reac-tions. For the description of reactive extrusion it is important to know thekinetics in all stadia of the reactions, from diluted solutions to concentratedmelts. Unfortunately, most kinetic experiments reported in literature areperformed only in strongly diluted systems, whereas in extrusion polymer-ization the polymer concentration changes in time between 0 andapproximately 100%. This implies that for the rst stage of thepolymerization reaction where the polymer forms a diluted solution in itsmonomer, conventional kinetics can be used. The second stage of thereaction is much less documented. This stage is reached when the conversionpasses a certain level. During polymerization the reaction system becomesmore and more viscous. Above a critical value of the conversion, theviscosity becomes so high that this leads to a limitation in the mobility of thepolymer chains. In chain-growth radical polymerizations the consequenceis that the termination reaction is now controlled by diusion resulting ina reduced termination constant. On the other hand, because the diusionof the small monomer molecules is not yet restricted until very highconversions are reached, the propagation rate does not decrease signi-cantly. Due to the reduced termination velocity the amount of activepolymer radicals increases, resulting in an abrupt increase of thepropagation velocity and of the momentary degree of polymerization.This phenomenon is known as the Trommsdor eect or gel eect (1,2) andresults in a higher molecular weight and higher conversion than expectedfrom conventional kinetics.Another complication, generally not encountered in conventionalsolution polymerization, is the occurrence of a ceiling temperature. Many41polymerizations are equilibrium reactions that shift toward increasedmonomer concentrations at higher temperatures. Dainton and Irvin (3)rst established that above a certain temperature depropagation may occur.This may lead to an appreciable decrease in nal conversion. In traditional(solution) polymerizations the large amount of solvent acts as a heat sink,and temperature rise due to the reaction heat is limited. However, duringreactive extrusion the reaction heat can lead to a large temperatureincrease surpassing the ceiling temperature. In this case, the progress of thereaction is limited by the amount of heat that can be removed from theextruder.Whereas in chain-growth polymerizations a polymer molecule isformed in a very short time, after which it is terminated and excluded fromfurther growth, the molecules in a step-growth polymerization process keepgrowing during the entire reaction time. Bifunctional or multifunctionalmonomers or prepolymers react with each other by combination. Mono-mers with a functionality larger than 2 will form a polymeric network withthermo-set properties. Therefore, due to the requirement of thermoplasticityonly reactions with bifunctional molecules are interesting for reactiveextrusion. The step-growth polymerization processes can be divided intopolycondensation reactions and polyaddition reactions, depending onwhether a small molecular by-product is formed or not. For reactiveextrusion this implies, that in polycondensation reactions this by-producthas to be removed by devolatilization to keep the reaction going.The dierences between chain-growth polymerization and step-growthpolymerizations are generalized in Table 3.1II. CHAIN-GROWTH HOMOPOLYMERIZATIONSBulk polymerizations of monomers like acrylates, methacrylates, andstyrene belong to the class of free-radical chain-growth polymerizations(or addition polymerizations). With this type of reaction, each polymerchain is formed in a relatively short time and subsequently excluded fromfurther participation in the reaction process. As a consequence, at thebeginning of the reaction when the