Foam Extrusion Principles and Practice

TX68799 title 1/9/03 1:37 PM Page 1

Edited by S.-T. Lee, Ph.D.Sealed Air Corporation

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FOAMEXTRUSIONPrinciples and Practice

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To the Lord who gives us life, abundant life, and even eternal life.


Contents

ForewordPrefaceAcknowledgmentsList of Contributors

1. INTRODUCTIONSHAU-TARNG LEE

1.1 Thermoplastic Foam

1.2 Foam Extrusion

1.3 Recent Developments

1.4 Outline of the Book

1.5 References

2. STATISTICAL THERMODYNAMICS OF GAS SOLUBILITYIN POLYMERSROBERT SIMHA and PIERRE MOULINIÉ

2.1 Introduction

2.2 Thermodynamics

2.3 Statistical Thermodynamics

2.4 Methodology

2.5 Discussion

2.6 Outlook


2.7 Nomenclature

2.8 References

3. RHEOLOGY OF THERMOPLASTIC FOAM EXTRUSION PROCESSRICHARD GENDRON and LOUIS E. DAIGNEAULT

3.1 Introduction: The Importance of Rheology in Foaming Processes

3.2 Shear Rheology of Blowing Agent-Charged Polymeric Systems

3.3 Extensional Rheology for Extrusion Foaming of Polymers

3.4 Conclusion

3.5 References

4. FOAM NUCLEATION IN GAS-DISPERSED POLYMERIC SYSTEMSSHAU-TARNG LEE

4.1 Introduction

4.2 Equilibrium Considerations

4.3 Conventional Nucleation Theories

4.4 Cavitation

4.5 Foam Extrusion Nucleation

4.6 Summary

4.7 Nomenclature

4.8 References

5. FOAM GROWTH IN POLYMERS N. S. RAMESH

5.1 Introduction

5.2 Importance of this Study

5.3 Literature Review

5.4 Foam Growth Experiment

5.5 Foam Growth Modeling

5.6 Foam Growth Equations

5.7 Boundary Conditions

5.8 Comparison of Theory with Experiment

5.9 Conclusions

5.10 Nomenclature

5.11 References


6. POLYMERIC FOAMING SIMULATION: BATCH AND CONTINUOUSMASAHIRO OHSHIMA

6.1 Introduction

6.2 Batch Foaming

6.3 Continuous Foaming

6.4 Conclusions

6.5 Nomenclature

6.6 References

7. PROCESS DESIGN FOR THERMOPLASTIC FOAM EXTRUSIONLEONARD F. SANSONE

7.1 Introduction

7.2 High-Density Structural Foam Process

7.3 Low-Density Foam Process

7.4 Die Design Procedures for Foam Extrusion

7.5 References

8. FOAM EXTRUSION MACHINERY FEATURESWILLIAM C. THIELE

8.1 Preface Regarding Extruders for Foaming

8.2 Basic Properties of Extruders

8.3 Basic Unit Operations in Foam Processes

8.4 Extruder Types, Support Devices, and Where Subprocesses are Placed

8.5 General Extruder Observations

8.6 References

9. MIXING DESIGN FOR FOAM EXTRUSION: ANALYSIS AND PRACTICESCHI-TAI YANG and DAVID I. BIGIO

9.1 Introduction

9.2 Thermoplastic Foam Extrusion Processes

9.3 Mixing—Theories and Experiments

9.4 Mixing Practices in Single- and Twin-Screw Extruders

9.5 Process Challenges

9.6 Summary


9.7 Nomenclature

9.8 References

10. FOAMING AGENTS FOR FOAM EXTRUSIONTHOMAS PONTIFF

10.1 Introduction

10.2 Physical Foaming Agents

10.3 Chemical Foaming Agents

10.4 References

11. CONTINUOUS PRODUCTION OF HIGH-DENSITYAND LOW-DENSITY MICROCELLULAR PLASTICS IN EXTRUSTIONCHUL B. PARK

11.1 Introduction

11.2 Previous Studies on Batch and Semicontinuous Microcellular Processing

11.3 Background on Microcellular Plastics Processing

11.4 Formation of a Single-Phase Polymer/Gas Solution

11.5 Microcellular Nucleation Control

11.6 Suppression of Cell Coalescence

11.7 Promotion of Large Volume Expansion

11.8 Experimental Set-Up

11.9 Experiments and Discussion

11.10 Summary and Conclusions

11.11 Nomenclature

11.12 References

12. FOAM EXTRUSION OF POLYETHYLENE TEREPHTHALATE (PET)MARINO XANTHOS and SUBIR K. DEY

12.1 Introduction

12.2 Review of Pet Chemistry and Processing Characteristics

12.3 Foaming With Physical Blowing Agents

12.4 Foaming With Chemical Blowing Agents

12.5 Concluding Remarks

12.6 Acknowledgements

12.7 References


Foreword

IAM pleased to introduce this volume “Foam Extrusion: Principles andPractice” to the growing list of excellent technical monographs by the

Technomic Publishing Company. Dr S.T. Lee, the editor of and one of themain contributors to this volume is an acknowledged original researchcontributor in the area of Extrusion Foaming Mechanisms, as well as a leadingindustrial practitioner of Foam Extrusion.

We at the Polymer Processing Institute have, through our long and active in-volvement in this field, witnessed the impressive growth of foam extrusionboth as an engineering discipline and industrial practice. In our view thispresent book represents the maturing of Foam Extrusion as a significant pro-cessing technique.

The editorial approach and contents of this work place appropriate emphasison the fundamental phenomena of gas dissolution in polymers and its effectson melt rheology and on the complex and still not fully elucidated dynamicprocesses of foam nucleation and growth. With this background it attends toimportant aspects relating to the effects of the screw and the design as well asprocess variables on foam extrusion. The contributions under the heading of“Practices” are technologically both informative and significant, as they treatcomprehensively specific materials, process and products.

This volume will undoubtedly be used widely by and serve Foam Extrusionresearch, development and production practitioners. At the same time it willfind its way in the list of important reference texts for graduate courses inpolymer processing and structuring of polymeric materials and products.

Costas G. GogosPresident, Polymer Processing InstituteProfessor Emeritus, Stevens Institute of TechnologyResearch Professor, New Jersey Institute of Technology


Preface

THE texture of matter has been modified technologically since ancienttimes. Human survival depended on softening rice and other foods using

yeast, water, and heat, to make them compatible with digesting tissues. Theeffect of these techniques was to create expanded structure, which is widelyfound in many natural systems, ranging from tree pulp to marine organisms.With the emergence of plastics engineering, it was recognized that expandedstructure could be readily achieved in polymers, especially in thermomorphol-ogy reversible plastics. Since early in the twentieth century, polymer synthesiswas greatly upgraded to enhance polymer structure, and methods have beendeveloped to make broad ranges of polymeric products. Industrial foams weredeveloped near the middle of this century.

This book brings dissimilarly natured foaming and extrusion under onecover, in other words, it puts scientific principles and engineering practice to-gether. Starting with fundamentals, gas molecules in polymers, then moving toseparation, gaseous voids in polymers, scientific foundations are laid in such away that the microscopic transition from nuclei to a void (nucleation) and themacroscopic movement from a void to an object (formation) are plausibly ad-dressed. However, the detailed mechanism of converting from a dispersed to agrowth state is not fully explained, but the proposed path in this book bringsforth insights into this interesting area. Indeed, one of the underlying theoriesof gaseous inflation even engages the attention of cosmologists seeking to de-scribe the very early stage of the Big Bang.

Together with the science of foaming, this book continues into anotherpopular technology, extrusion. The art of processing to match the foaming re-quirements is addressed from the operation perspective: processing andshaping. The last section of this book presents interesting foam extrusion


developments, showing how scientific findings can be applied to the engineer-ing field, from principles to batch experimentation to continuous foaming.

An understanding of foaming principles and how to apply them to engineer-ing practice will benefit industrial and academic readers in building a coherentand solid confidence in foam extrusion so challenges can be approached proac-tively in the new millennium. This book can also be used as a supplementarytextbook for a graduate polymer, engineering, or science majors course.


Acknowledgments

Professor J. A Biesenberger of Stevens Institute of Technology, who passedaway in January, 1998, showed encouragement and offered valuable

advice even during his later stage of illness, and is particularly remembered.Professor C. B. Park of the University of Toronto, a chapter contributor, is ac-knowledged for his invaluable collaboration in critical decision making in1996. I would like to thank all the contributors and reviewers for their effortsin preparing the manuscripts, and providing useful comments to make thisbook the best possible. My special thanks go to Dr. David Todd of the Polymerprocessing Institute, Dr. Paul Handa of the Canadian Research Council, Dr. N. S. Ramesh of Sealed Air Corporation, and Dr. Marino Xanthous of the NewJersey Institute of Technology, for their help during the editing of this book. Iappreciate my employer, Sealed Air Corporation, and their support of this un-dertaking, especially Mr. Donald Tate. My secretary, Sandy Porporino, demon-strated superb in making faithful contacts throughout the editing of the book.To my wife, Mjau-Lin, her unconditional support is beyond what words canexpress.

I thank God for this precious opportunity to not only work with a group oftechnical experts who provided direct and indirect support to make this bookpossible, but also to learn to humble myself in acknowledging how much yetneeds to be explored.


List of Contributors

David I. BigioDepartment of Mechanical EngineeringUniversity of MarylandCollege Park, MD 20742

Louis E. DaigneaultIPEX, Inc.Port of Montreal BuildingWing 3, 1st Floor, Cité du HavreMontreal, Quebec H3C 3R5Canada

Subir K. DeyPolymer Processing InstituteGITC Building, Suite 3901New Jersey Institute of TechnologyNewark, NJ 07102-1982

Richard GendronNational Research Council for CanadaProcess Development75 de MortagneBoucherville, Quebec J4B 6Y4Canada

Shau-Tarng LeeSealed Air Corporation301 Mayhill St.Saddle Brook, NJ 07663

Pierre MouliniéBayer CorporationCorporate Polymer Research100 Bayer RoadPittsburgh, PA 15205-9741

Masahiro OhshimaDepartment of Chemical EngineeringKyoto UniversityKyoto 606-8501Japan

Chul B. ParkUniversity of TorontoDepartment of Mechanical Engineering5 King’s College Rd.Toronto, Ontario M5S 1A4Canada


Thomas PontiffTechmer PM299 Huntersridge RoadWinchester, VA 22602

N. S. RameshSealed Air Corporation10 Old Sherman Tpk.Danbury, CT 06810

Leonard F. SansoneSussex Plastics EngineeringP.O. Box 152Andover, NJ 07821

Robert SimhaDept. of Macromolecular ScienceCase Western Reserve UniversityCleveland, OH 44106

William ThieleAmerican Leistritz Extruder Corp.169 Meister AvenueSommerville, NJ 08876

Marino XanthosPolymer Processing InstituteGITC Building, Suite 3901New Jersey Institute of TechnologyNewark, NJ 07102-1982

Chi-Tai YangSealed Air Corporation301 Mayhill St.Saddle Brook, NJ 07663


CHAPTER 1

Introduction

SHAU-TARNG LEE

1.1 THERMOPLASTIC FOAM

FOAM can be defined as a gaseous void surrounded by a much denser con-tinuum matrix, which is usually in a liquid or solid phase. It exists widely

in nature, in cellulositic wood, marine organisms, and other phenomena, and itcan be made using synthetic processes (i.e., foamed plastics). The presence ofgas voids can be outside, encapsulation, or inside, irreversible volume expan-sion. In most cases, a gas phase possesses dramatically different properties andstructures (or states) than the surrounding solid phase, as opposed to differentproperty and similar structure (or state) blends, to make a lighter hetero-geneous composite structure [1].

A material property and density chart is shown in Figure 1.1 [2, 3]. It seemsto follow a linear band in the log–log scale. Foamed material evidentlyextends the solid property lower limit. When very tiny voids are evenly dis-persed in the solid matrix without seriously disrupting its continuity, theparent property hardly varies, even with less weight. As cell size, quantity, andits distribution varies, a much different composite property spectrum can thusbe established. In other words, foamed material’s performance/weight ratiocan markedly vary from foam-free material. Polymer synthesis and process-ing have shown dramatic improvements since the mid twentieth century.Foaming methods started to be transferred from lab scale to industrial scale.Foamed plastics have thus been used in many applications. Table 1.1 showssome established markets and foamed plastic attributes. Although the foamedplastic industry is highly fragmented, its demands continue to grow as indi-cated in Table 1.2, quoted from the 1997 Freedonia market report [4, 5]. In1996, over six billion pounds (three metric tons) of synthetic foamed plastics


were consumed in the United States alone. Apart from urethane foam, it wasslightly over three billion pounds. A constant growth between 3 to 4% inquantity and over 6% in sales has been projected for the U. S. and the globalmarket into the twenty-first century. Nowadays, it is almost unlikely to livewithout encountering foamed plastics directly or indirectly on a daily basis.Although it is a small portion of the market compared with the nonfoamedplastics industry, as illustrated in Table 1.3 [6], it may have a great future if itspotential is fully tapped.

Foamed plastics can be classified in different ways, for instance, by natureas flexible and rigid, by dimension as sheet and board, by weight as lowdensity and high density, by structure as open cell and closed cell, and by cellsize as foam and microcellular. In essence, standard nomenclature for foam in-cluding cell structure, density, and materials, such as from IUPAC, is ex-tremely desirable to minimize communication confusions. In any event, itsbulky nature limits it from being used for extensive transportation to makelocal produce more economical. It certainly develops specific niches geo-graphically to make effective communication more critical for this alreadydiversified industry. In this respect, technicality appears to be a commonground and, thus, a good starting point for creating a strong foundation fromwhich the foam industry can grow toward a more prosperous future.

Moving to technical domain, the type of polymer, the type of blowing agent,the expansion technique, and the post-foaming curing dictate foam formationand its morphology, and, thereof, the properties. It is not surprising to find that

FIGURE 1.1 Log-log of thermal conductivity and Young’s modulus vs. material density. (Datacollected from Cellular Solids, Gibson & Ashby, Pergamon Press, 1988, and Properties of Poly-mers, Van Krevelen, Elsevier, 1990.)


TABLE 1.1 Markets for Foamed Plastics.

Functions Markets Attributes Polymers

Cushioning Furniture Energy absorption Flexible PUTransportation PE, ABSConstruction

Insulations Construction Low thermal Rigid PU, PS, PEAutomotive conductivity Rigid vinyl

Sound absorptionProtection Packaging Soft and flat RIM PU, PS bead,

surface PE and PP sheetCushioning

Strength/weight Athletic Strength and RIM PU, x-linked Construction softness PE, PS, PVC, Marine, Medical flexible PUDecoration Phenolics, AcrylicsHousehold

Impact Absorption Automotive Sharp energy bead PP, x-linked Athletic absorption PE

Thermal/Chemical Thermoforming Thermal strength PS, X-linked PEElectrical Packaging Chem. and Flexible vinyl

Electrical electrical Epoxy, Siliconesinertness Rubber

Source: The Freedonia Group, Inc. (1997) [3].Note: Global consumption of foamed PS was 3.8 billion lbs (1.9 million tons) in 1996 [4].

TABLE 1.2 U.S. Foamed Plastics Demand: Past and Future (in Millions).

% Annual Growth

Item 1987 1996 2001 96/87 01/96

Total Foamed Plastics 4,558 6,325 7,420 3.7 3.2Demand (lbs)

Urethanes 2,363 3,325 3,910 3.9 3.3Polystyrene 1,316 1,676 1,900 2.7 2.5Other Polymers 879 1,324 1,610 4.7 3.6

Foamed Plastics 6,850 12,100 16,200 6.5 6.0Demand ($)

Source: Plastics Age, 40, Dec. (1994) [5].

TABLE 1.3 1993 Foamed Resin Consumption Ratio in Japan (Tons).

Unformed Formed Formed/Total

PE 954,780 50,006 5.0%PS 600,245 270,037 31.0%PP 866,782 14,429 1.6%PVC 1,313,514 8,713 0.7%PF 28,302 64 0.2%Others 843,636 41,782 4.7%Total 4,607,259 385,031 7.7%


foaming method and foaming formula are closely related. Even with a fixedpolymer/gas system and the same foaming method, the amount of voids(blowing agent percentage), their dispersion and distribution, and void inter-connection have profound impact upon its properties and thereby applications.While focusing on foaming, the independent variables are gas type, gascontent, processing conditions, and foaming dynamics, and the dependent pa-rameters are foam structure, morphology, and properties. Although deepfoaming understanding is still not readily available, some earlier publicationslaid down a good foundation. For instance, a solid technical perspective wasattempted by C. J. Benning in Plastic Foams, published in 1969 [1]. An exten-sive collection of thermoplastic foaming technology can be found in Poly-meric Foams [7] and Thermoplastic Foams [8]. Both are handbooks in nature.The former covers the existing foaming technologies classified by materials,the latter is based on general foaming processes and provides good coverage ofmechanical and chemical details of conventional foam processing.

The major weight of foamed plastics is polymer. Its long chain structureand, in certain cases, functional groups, display unique viscoelastic propertyversus temperature characteristics as illustrated in Figure 1.2 for polystyrene

FIGURE 1.2 Er(10), stress measured at 10 seconds after constant strain, vs. temperature forcrystalline polystyrene, for amorphous atactic polystyrene samples A (Mn � 140,000) and C (Mn � 217,000), and for lightly cross-linked atactic polystyrene. Shaded area is ideal for foamprocessing. (Adapted from A. V. Tobolsky, Properties and Structure of Polymers, John Wiley andSons, New York, 1960)


[9], in which application and processing ranges are determined. Regardingpolymer’s thermal response, it is categorized as thermoplastic and thermosetas listed in Table 1.4. Due to its thermal reversible structure, thermoplastic ma-terials became quite favorable in making common goods through various plas-ticating processes. By considering polymer’s chemical nature, including reac-tive functional groups and solvent compatibility, a reactor or a processor canbe selected and set to accommodate the necessary reaction or processing re-

TABLE 1.4 Thermoplastic and Thermoset General Comparison.

X-links Morphology Melt Viscosity Structure

Thermoplastic No Thermally reversible Arrhenius Amorphous dependency to Crystalline

Thermoset Yes Thermally irreversible Independent Amorphousof temp

TABLE 1.5 Common Foaming Technologies and Relevant Polymers.

Technologies Applicable Thermoplastics

Extrusion PS, PVC, PE, PP, PVOHMolded Beads PS, PP, PEInjection Molding ABS, PC, PPOReactive Injection PU, UFMechanical Blending PU, UF, Elastomer

TABLE 1.6 History of Foam Extrusion [9–17].

Time Authors or Companies Contents Reference

1931 Munters, G. and Foamed Polystyrene US patent 2,023,Tandberg, J. G. 204

1941 Johnson, F. L. Foamed Polyethylene US patent 2,256,483

1944 Dow Chemical Extruded Styrene [8]Foam

1948 Colombo, R. (L. M. P.) Twin-Screw [9]Processing

1962 Rubens, L. C., et al Extruded Ethylene US patent 3,067,Foam 147

1966 Boutillier, P. E. PVC Foam Extrusion Fr. patent 75594(Celuka Process) BP 1,184,688

1967 L. M. P. Twin-Screw Foaming It. patent 795,793 BP 1,152,306

1972 Parrish, R. G. (DuPont) Extruded Propylene US patent 3,637,Foam 458

1990 Shell/Petlite PET Foam Extrusion [17]


quirements so that adequate reactive processing can be accomplished. In thepast decades, material and machinery evolution showed amazing mutual ben-efits for fostering polymer processing industries. Table 1.5 summarizes avail-able foaming methods. In styrene, olefin, and vinyl foam produce, extrusionappears to be the primary technology, due not only to its continuous nature, butalso to its capability of handling thermoplastic material’s thermal reversiblecharacteristics. It thus became a common practice to implement gas phase intopolymeric melt for foaming. A brief foam extrusion history is presented inTable 1.6 [10–18]. It appears that the major foundation was laid in the 1960s inthe U.S. and Europe.

1.2 FOAM EXTRUSION

Foaming plastics has been developed as an extension of the extrusion appli-cation while extruder evolution is primarily based on its function optimization.Figure 1.3 shows the foamed ethylene setup prepared in 1941 [12]. Since the1950s, the extruder has been recognized not only as inherently effective inconverting thermal energy and mechanical power into processing heat forpolymer phase change, but also as being efficient in generating adequate posi-tive pumping force for fast material transport. Considering thermoplastic’smelting, molding and forming nature, the plastic extruder turned out to be anexcellent processing unit for converting thermoplastics into simple geometryproducts. Mixing and cooling were well implemented in the extruder, and itstarted to meet the critical processing conditions for foaming and has beenwidely adopted for production since the 1970s. History shows a solid synergyfrom thermoplastic foaming and extrusion.

Extrusion can be designed in such a way that various functions become pos-sible in a single processor, including reactive extrusion, devolatilization, x-linking, etc. Furthermore, screw design can be tailored to match polymerprocessing characteristics (shear and thermal sensitivities) to make the ex-truder a very useful processing unit. From a physical chemistry viewpoint,foam extrusion is simply a change of states and mass transfer as illustrated inTable 1.7. However, considering kinetics, degree of state change and residencetime for adequate mixing make extruder design and processing intriguingareas for scientists and engineers of various disciplines.

As for foaming, gas phase injection, mixing, and dispersion undoubtedlyadd complexity to thermoplastic extrusion. Figure 1.4 shows the relevantmechanisms for thermoplastic foam extrusion, in which both thermal activa-tion (chemical blowing agent) foaming and gas dissolution (physical blowingagent) foaming are included. Since polymeric melt is heavily dependent onprocessing history, downstream foaming cannot be viewed without payingclose attention to upstream kinetics. Also pointed out in Figure 1.4 are thepolymer processing and foam stabilization issues [19]. When low-density


FIGURE 1.3 Foamed polyethylene process (U. S. Patent 2,256,483).


foam and/or high-speed operation are imminent, the operation windownarrows. The balance of mechanical energy input and thermal energy transferand the balance of heating and cooling are critical concerns for an effectiveand efficient low-density foam extrusion. In other words, developing amelt/gas solution in the right foaming range as illustrated in Figure 1.5 is a key

TABLE 1.7 States and Conditions in Foam Extrusion Process.

Location Prior Extrusion In Extrusion At Die Tip Post-Extrusion

Materials Resin, Blowing Gas/Melt Gas/Polymer Air/PolymerAgent

Mechanisms Feeding Melting, Mixing, Foaming AgingCooling

State Solid, Liquefied Molten Gas/Melt Gas/SolidConditions Low Pressure High Pressure Low Pressure Low Pressure

Low High High Low Temperature Temperature Temperature Temperature

FIGURE 1.4 Thermoplastic foam extrusion characteristics for amorphous, semicrystalline, andcrystalline structures.


FIGURE 1.5 Foam extrusion units and their mechanisms.


subject in foam extrusion [20]. A desirable morphology can thus be developedfor applications.

Plastic properties, system parameters, processing setup, foaming, and post-handling consist of the necessary elements of a professional foam extrusiontechnology. They should be viewed in a balanced way to avoid erroneousanalysis. Nonetheless, as plastic synthesis and processing techniques continueto grow, so does the foaming technology and, thereof, the number of applica-tions of thermoplastic foams.

Table 1.8 shows common extrusion processes for foaming. Each extrusionprocess, of course, has its strengths that benefit certain operations and itsweaknesses that heighten business and technical concerns. Basically, theoptimal extruder/polymer combination remains a challenge in some existingindustries and is definitely a challenge in developing new foaming technology.A proper understanding of polymers, including concepts such as melting,flow, foaming, and forming, facilitates machinery design optimization andproduct property evaluation. On the other hand, an adequate knowledge of ex-truders can minimize unnecessary errors in selecting the right type and size ofmachinery during lab-to-plant or batch-to-continuous scale-up.

1.3 RECENT DEVELOPMENTS

A chemical blowing agent or a physical blowing agent or both are neededto generate gas phase for expansion at a lower pressure in foam extrusion. Aphysical blowing agent is generally preferred for foam under 0.2 g/cm3,termed low-density foam. Before the 1980s, CFC was preferred, mainlybecause of its soluble, volatile, and nontoxic nature. However, its stability andreactivity with ozone raised substantial concern about ozone depletion. The

* L/D: Screw length/Barrel diameter from [19]

TABLE 1.8 Common Extrusion Processes.

Type Advantages Disadvantages

Long Single Extruder • Less leaking point • Narrow melting/coolingL/D*: 38–42 • Less investment control

• Precise screw design• Long screw length

Tandem Extruders • Independent melting/ • More leaking pointsL/D*: 24–32 and 28–30 cooling control • High investment

• Can process high-melt • More power consumptionpolymers

Twin-Screw Extruder • Easy to control • Cooling limitedL/D: around 25 • Good mixing • Narrow melting/cooling

• Good heat transfer range


Montreal Protocol was signed in 1987 and became effective in 1989. It es-sentially called for global cooperation to phase out halogenated hydrocarbonsmanufacturing to minimize the continued ozone layer damage. According toAFEAS (Alternative Fluorocarbons Environmental Acceptability Study), themajor producers reduced CFC production from 980 metric tons in 1986 to 95metric tons in 1996 [21]. There was no doubt that a variety of gas operationtechnologies were affected. Foaming involved product exposure to the atmo-sphere and was classified as an open system, as opposed to refrigeration andair-conditioning that are closed systems, and it is definitely one of mostconcern. Besides, since the early 1990s, global warming known as the green-house effect, became another major issue. The Intergovernmental Panel onClimate Change (IPCC) reported scientific assessment on warming potentialsof halogenated hydrocarbons relative to carbon dioxide. Moreover, regula-tions were proposed to reduce the emission of not only fluorine-based, butalso carbon dioxide and methane volatile chemicals at the Kyoto conferencein 1997.

Since the late 1980s, foam producers in the developed countries began con-centrated research and development efforts to switch to friendly alternatives insupport of protecting the ozone layer. Most of them found substitutes for halo-genated blowing agents in the early 1990s. As a result, the foam industry notonly survived the challenge but continues to constantly grow, and enhance thefoaming knowledge basis. However, considering warming potentials, volatilecarbon dioxide faces not only technical hurdles but also legislation concerns.For general foam industries, other than ozone and warming issues, legislationand revisions from environmental agencies and safety and health agenciesremain viable issues in almost every country. Disposal, waste stream control,and usage of recycled plastics still require a deep understanding of foamingtechnology in order to continue to enjoy the status of being user and publicfriendly.

Since the mid 1980s, the Massachusetts Institute of Technology (MIT) haspresented a series of papers on the microcellular foaming concept, stemmingfrom the industrial challenge on improved performance/weight to enhancepolymer value. Although early works focused on batch process, it demon-strated nice foam structure under 5 �m cell with supercritical carbon dioxideblowing agent [22], which created a deep interest from industry and academia.Foaming method, cell structure, and morphology have been intensively inves-tigated by several institutes, and lately, Trexel reported success in commercialscale tests for polystyrene foam sheet. For the first time in foam history, it at-tracted a wide and deep dedicated effort from academia and industry. Up to1998, over twenty Ph.D. dissertations directly related to microcellular foaminghave been published worldwide. The number continues to increase. As a result,some interesting insights into the mysterious foaming, fine cell and flat sheetwith volatile blowing agent, have been shed. Continued commitment is still


necessary to assure more success in commercializing developed foam technol-ogy and in developing new foam technology.

As polyolefin resin producers successfully made liner low-density polyethyl-ene via metallocene catalyst to claim better control on monomer distribution andmolecular weight distribution [23], another opportunity to enhance foamingtechnology has arisen by tailoring resin structure to fit extrusion processes foroptimal foaming. Improved foam properties can thus be envisioned by eliminat-ing the “slack” portion of semicrystallines. Moreover, ethylene-styrene inter-penetrating (ESI) polymers were made with the same catalyst technology topose the possibility of making foam with “combined” benefits from eachmonomer to widen its application window by using one polymer [24].

Penetrating into the existing market becomes a real test for this developmen-tal project. Concerted efforts are necessary to succeed in this fast-paced society.High melt strength polypropylene is another example for foaming. It was firstpresented by Himont [25], in which, by chain extension, semicrystallinepolypropylene demonstrates a wider processing window and a much betterfoaming structure over the nonextended conventional PP. As a result, morepolypropylene research and development has been initiated. It is anticipated tohave more grades of better structured PP in the market for foaming. Recently, apolyethylene terephethalate (PET) resin supplier reported solid state polymer-ization technology enhancement to allow improved polymer strength PET forfoaming [26]. In brief, resin structure development opens interesting possibili-ties to further enhance foamed plastic strength/weight performance.

Extruder manufacturers have attempted to make bigger and better extruders.Bigger tandem lines and twins with improved screw design to minimize heatgeneration without sacrificing mixing and pumping capabilities are expectedto enhance the foaming window by enlarging exit dimension to make morepressure drop with less shear heat generation possible. As a result, bulkierfoamed product can be made for bulky and advanced applications. In essence,material and machine need close association to make useful synergies forfoaming.

1.4 OUTLINE OF THE BOOK

This book is divided in four parts, starting with the fundamentals: Chapters2 and 3 on thermodynamics and rheology of the gas/polymer system. The nextsection, Chapters 4 to 6, is focused on foaming including nucleation, growth,and their correlation with experimental and operational observations. Machin-ery issues are covered in Chapters 7 through 9, in which process and diedesign, mixing design and practice, and twin-screw foam extrusion are ade-quately addressed. Finally, applications are stressed in Chapters 10 through 12.A blowing agent overview is given and microcellular foam extrusion and poly-


ester foam extrusion are well discussed. Hopefully, this comprehensive cover-age will generate further insights on the complex foam extrusion subject toallow engineers to move into extensive applications with confidence and toallow scientists to view a wider horizon.

When we get to fundamentals, we have to confess that a sizable gap existsin understanding the detailed mechanisms at the molecular level and applyingthem properly in foam extrusion for a friendly production with business sense.Thermoplastics’ viscoelastic properties vary depending upon the amount ofblowing agent dissolved and the surrounding temperature and pressure. Phaseseparation occurs when surrounding conditions change to a point where gasphase starts to appear and continues to grow until it is balanced by polymerictension and adjacent cells. The latent heat, bubble expansion work, and meltelasticity [27] are involved in a nonisothermal condition. Moreover, extrusionmakes the already complex and dynamic foaming, nucleation, growth, andcoalescence, even more complex. It is my sincere hope that this book willserve as a valuable step in advancing the understanding of true foaming prob-lems for experienced foam experts and of how to apply the fundamentals infoaming for newcomers.

1.5 REFERENCES

1. C. J. Benning, Introduction in Polymeric Foams, Wiley-Interscience of John Wiley and Sons,New York, 1969.

2. L. J. Gibson and M. F. Ashby, of Cellular Solids: Structure & Properties, Pergamon Press,Elmsford, New York, 1988.

3. D. W. Van Krevelen, p. 533 of Properties of Polymers, Elsevier, New York, 1990.

4. “Foamed Plastics,” pub. Freedonia Group, Inc., Cleveland, Ohio, 1997.

5. W. D. Back, “Foamable Polystyrol-EPS,” Kunststoffe, 86, 10, 1996.

6. Plastics Age, 40, Dec. 1994, presented by Y. Kitamori, “Foamed Polyolefin Process Develop-ment,” in Thermoplastic Foam Conference sponsored by Ind. Tech. Res. Ins., Taipei, Taiwan,1995

7. D. Klempner and K. C. Frisch, editors of Polymeric Foams, Hanser, New York, 1991.

8. J. L. Throne, Thermoplastic Foams, Sherwood, Hinckley, Ohio, 1996.

9. A. V. Tobolsky, Properties and Structure of Polymers, John Wiley and Sons, New York, 1960.

10. G. Munters and J. G. Tandberg, “Heat Insulation,” U.S. patent 2,023,204, 1935.

11. F. L. Johnson, “Synthetic Spongy Material,” U.S. patent 2,256,483, 1941.

12. R. N. Kennedy, “Extruded Expanded Polystyrene,” Section XII of Handbook of FoamedPlastics, ed. by R. J. Bender, Lake, Libertyville, IL, 1965.

13. M. Martelli, “Twin Screw Extruders—A Separate Breed,” SPE Journal, 27, 25–30, 1971.

14. L. C. Rubens, J. D. Griffin and D. Urchick, “Process of Foaming and Extruding PolyethyleneUsing 1,2-dichlorotetrafluoroethane as the Foaming Agent,” U.S. patent 3,067,147.

15. P. E. Boutillier, “Extrusion of Plastics Material,” French patent 75594, appl. in 1966, Britishpatent 1 184 688, 1970.


16. L. M. P. “Process and Apparatus for Manufacturing Foamed Articles of Thermoplastic Mate-rials,” Italian patent 795,793, appl. in 1967 and British patent 1,152,306, 1969.

17. R. G. Parrish, “Microcellular Foam Sheet,” U.S. patent 3,637,458, 1972.

18. Y. Kitamori, “PET Foams and Applications,” Proc. of Thermoplastic Foams Technical Con-ference, spon. by Industrial Technology Research Institute, Taipei, Taiwan, 1995.

19. S. T. Lee, “A Fundamental Study of Thermoplastic Foam Extrusion with Physical BlowingAgents,” Ch. 13 of Polymeric Foams: Science and Technology, ed. by K. C. Khemani, Amer.Chem. Soc. Symposium Series 669, 1997.

20. K. D. Kolossow, Chap. 13: Extrusion of Foamed Intermediate Products with Single-ScrewExtruders in Plastics Extrusion Technology, ed. by F. Hensen, Hanser, New York, 1988.

21. AFEAS, “Production, Sales and Atmospheric Release of Fluorocarbons through 1996,”AFEAS Program Office, Washington, D. C., 1998.

22. J. E. Martini-Vvedensky, N. P. Suh and F. A. Waldman, “Microcellular Closed Cell Foams andTheir Method of Manufacture,” U.S. patent 4,473,665.

23. S. Lai and G. W. Knight, “Dow Constrained Geometry Catalyst Technology (CGCT): NewRules for Ethylene (a-olefins Interpolymers-Controlled Rheology Polyolefins,” 51st Ann.Tech. Conf. sponsored by Soc. Plas. Eng. Preprint 1188–1192, 1993.

24. S. V. Karande and B. I. Chaudhary, “INSITE Technology Based Ethylene Styrene Interpoly-mers for Foams Applications,” 1–5, FoamPlas ’98, sponsored by Schotland Business Re-search, Inc., New Jersey.

25. M. B. Bradley and E. M. Phillips, “Novel Foamable Polypropylene Polymers,” 48th Ann.Tech. Conf. sponsored by Soc. Plas. Eng. Preprint 717–720, 1990.

26. H. Al Ghatta, “Process for the Production of High Molecular Weight Polyester Resins,” U. S.patent 5,376,734, Dec. 1994.

27. C. Sagui, L. Piche, A. Sahnoune and M. Grant, “Elastic Effects in the Foaming of Thermo-plastics,” Physics Review E, 58, 4, 4654–4657, 1998.


CHAPTER 2

Statistical Thermodynamics of Gas Solubility in Polymers

ROBERT SIMHAPIERRE MOULINIÉ

2.1 INTRODUCTION

LEGISLATION against the use of blowing agents with ozone depletion poten-tial has forced many foam producers to change their processes. Because

gas solubility influences the nucleation and growth of cells in foams, it is oneof the primary concerns when changing physical blowing agents. To that end,recent experimental efforts have focused on the measurement of solubility ofgases in molten polymers at high temperatures and pressures often encoun-tered during foam extrusion. As a complement to experimental data being re-ported for solubility at these conditions, efforts have also been made to makeuse of equations of state (EOS) to model gas solubility. This work reports onthe use of the Simha-Somcynsky theory to model gas solubility. Much likeFlory-Huggins or Sanchez-Lacombe theories, the Simha-Somcynsky theorystems from treating molecules as segments on a lattice. In the case of amixture, the lattice contains both species, which are divided into nearlyequally sized segments, as illustrated in Figure 2.1 [1]. Unlike the other theo-ries, however, the Simha-Somcynsky theory allows for a pressure- and temperature-dependent fraction of vacancies or holes that are to express free-volume within the lattice, which account for molecular disorder in the latticemodel. Moreover, the equations derived from the Simha-Somcynsky theoryinclude temperature- and pressure-independent parameters that account forintra- and intermolecular interactions within the mixture’s components. TheSimha-Somcynsky theory has been successfully applied to model variousfluids and fluid mixtures [2]. Recently, the theory was applied to treat the sol-ubility of gases in molten polymers [3, 4]. In this work, the application of the


theory to gas solubility in molten polymers is illustrated. Various trends ob-served theoretically and experimentally are also discussed.

2.2 THERMODYNAMICS

The equilibrium between two phases 1 and 2 at a specified temperature andpressure is determined by the equality of the chemical potentials �i1 and �i2

for all constituents i in the two phases, in the presence of other constituents j,defined as follows [5]:

(1)�ik � ( �Gk>�nik)P,T, nik; j � i, k � 1, 2

FIGURE 2.1 Mixture of two molecules placed on a lattice. Both have been decomposed intosegments (black circles: four segments, white circles: three segments). Unoccupied sites are alsoplaced on the lattice in Simha-Somcynsky theory.


where Gk is the Gibbs free energy of phase k, and nik is the number of moles ofconstituent i in phase k. In our case, the vapor phase 1 contains the single com-ponent 1, and �11 is simply the Gibbs free energy of the vapor. This quantity isto be balanced by �12, the chemical potential of the condensed vapor dissolvedin the polymer. The functional dependence of both potentials on T and P and of�12 additionally on composition then determines the equilibrium composition,i.e., the solubility of the vapor. For �12 we have the following relation [5]:

(2)

with x1 the mole fraction of component 1 and Gm the free energy of themixture. Conventionally, other composition units are employed in the presentcontext. For example, employing the volume of gas over the volume of sub-strate, referring to STP conditions, we have the following:

(3)

where M2 and Vs2 are the molar mass and the specific volume, respectively, ofthe polymer. Our task, therefore, is to develop explicit expressions for theGibbs free energies of the vapor and the mixture. This is what statistical ther-modynamics is expected to accomplish.

2.3 STATISTICAL THERMODYNAMICS

2.3.1 THE VAPOR

The following equation is convenient for obtaining the chemical potentialusing equations of state:

(4)

Where �o is the chemical potential of gas when treated ideally. Many equations ofstate for gases allow the evaluation of the integral in Equation (4) to obtain �� fora gas using an equation of state. Once the chemical potential difference has beenobtained, the actual chemical potential of the gas can be calculated by adding theideal state contribution, �o. For a molecule with three volume-dependent degreesof freedom and mass m, the chemical potential �11 can be determined from:

(5)�11 � RT�n e p(Nah)3

kT(2�mRT)3/2 f � ��

�� o � ��

V

(p � RT/V)dV � (pV � RT)

S � x1/(1 � x1)(22,400/p)(M2VS2)�1

�12 � Gm � (1 � x1)�Gm/�x1


The logarithm term, containing Planck’s constant h and Avogadro’s numberNa, clearly represents the chemical potential of an ideal gas [6]. We note theunderlying assumption that rotational and vibrational degrees of freedom in apolyatomic vapor molecule are not perturbed by intermolecular interactions.We pursue this point in the next section.

2.3.2 THE CONDENSED PHASE: SINGLE CONSTITUENT

To model the structure of a melt, consider a lattice. Flexible polymer chains are assumed to meander through this lattice such that each of their segments executes thermal motions in a cell formed by its neighbors andlocated in average positions that are defined by the lattice sites. These motionsare subject to the restraints of intersegmental attractions and repulsions. Thisis the cell model originally devised by Lennard-Jones and Devonshire for rare gas-type liquids and extended by Prigogine [7] to fluids of chain mol-ecular constituents. This model, one will argue, possesses too much order fordisordered fluids. On the other hand, a lattice description offers mathemati-cal advantages in connection with the intrinsically difficult problem of thedense, disordered state. In an attempt to retain the lattice picture as far as possible, Simha and Somcynsky [1] formulated the lattice-hole model. Thatis, a volume (or pressure) and temperature-dependent fraction of lattice sites is unoccupied in order to simulate disorder. Thus, additionalentropy arises from the mixing of occupied sites and holes. The characteristicelements of the model include the intersegmental or intermolecular interac-tions and chain flexibility, where appropriate. This latter feature is to ac-knowledge the fact that a flexible chain is capable of “soft” (low frequency)internal motions in addition to “stiff” bond and bond angle deformations. Suchsoft motions are subject to intermolecular, and thus, volume-dependent per-turbations. These elements are accounted for by an assumed 6–12 Lennard-Jones pair potential involving a maximum attraction energy �* and a repul-sion volume * defined by the location of the maximum. Chain flexibility isto be characterized by a constant factor 3c, which represents the number ofvolume-dependent degrees of freedom [7]. For a linear C-C backbone “s-mer”with unrestricted internal bond rotation, , which includes thesix translational and rotational motions of the chain as a whole. For a realchain with more or less complex substituents, c becomes a disposable param-eter, expected to be of the order of s [see Equation (6)]. In terms of these quantities, we can define a characteristic temperature T*, volume V*, andpressure P* as follows:

(6)P* � qze*/s�*T* � qze*/(ck); V* � Na�*/m;

3c � s � 3 � 6

h � 1 � y


with , V* a specific volume for a molar segmental mass m, k the Boltzmann constant, and the lattice coordination number. In terms of these quantities, reduced variables of state can be defined.

The partition function formalism of statistical mechanics evaluates themodel to yield a free energy and an EOS. We refer to Reference [1] for detailsand state the result, expressed in reduced variables, viz:

(7)

with .Equation (7) is incomplete as a relation, since it contains the quan-

tity y. This quantity is expressed as a function of and by the physical con-dition that in thermodynamic equilibrium, y must minimize the Helmholtz freeenergy for a specified volume and temperature. This results in the followingequation:

(8)

The solution of Equation (8) yields y as a function of and . We observe thatfor large s and provided s/3c is constant, the coupled Equations (7) and (8)contain only scaled variables of state. That is, a universal surfaceensures; a principle of corresponding states is satisfied.

Equations (4) and (5) illustrate the significance of the EOS for the chemicalpotential and, ultimately, the solubility of the vapor. The same applies to thecondensed phase. Clearly, here the scaling parameters defined in Equation (6)must be known for the particular polymer and condensed vapor pair in order toproceed. These are to be obtained by the superposition of the theoretical scaled

onto the experimental PVT surface. The numerical accuracy of the theoryand the values of T*, P*, and V* have been discussed in detail for some 50polymers by Rodgers [8]. Over a pressure range of maximally 2,000 bar, theoverall average deviation is found to be and only

for a range of 500 bar. However, before these evaluations could be performed, something had to be done about the factor 3c/s appearing inEquation (8). We observe from Equation (6) the connecting relation as fol-lows:

(6)

There are three “intrinsic” quantities, i.e., the number s of segments in thechain, the molar segmental mass m, and the flexibility factor c, where isthe molar mass of the molecule. This leaves a freedom of choice. If the

s � m

(P*V*/T*)m � (c/s)R, with R � Nak

�4 10�4�7 10�4 cm3/g�V

T�V�P�

T�V�P�

T�V�

� yQ2(2.409 � 3.033Q2)/(6T�)s/3c[(s � 1)/s � y�1ln(1 � y)] � (1 � �)�1(� � 1/3)

T�V�P��V��T�

Q � (yV�)�1; � � 2�1/6yQ1/3

P�V�/T� � (1 � �)�1 � 2yQ2(1.011Q2 � 1.2945)/T�

z � 12qz � s (z � 2) � 2


segment is identified with the chemical repeat unit, then s is given for a speci-fied molar mass, and c becomes an adjustable parameter, to be determined to-gether with the scaling constants to yield the best fit, consistent with Equation(6). As an alternative, we may adopt a priori a value for c/s, e.g., 1/3 for a longchain. Both procedures have been applied in the past and, it should be noted,will not affect the quantitative success of the theory. In the present context, thesecond and more convenient method will be employed. The molar mass m inEquation (6) then indicates the size of the segment yielding one volume-dependent degree of freedom. For a complex structure, such as a polycarbon-ate, this will be but a fraction of the monomer unit.

As for the small species, the balance of chemical potentials requires theinput of the c-value used in the vapor phase. For a rare gas, we have

. In a polyatomic species, there are additional rotational and vibra-tional degrees of freedom. These would require a consideration of intermolec-ular, volume-dependent perturbations and thus a detailed consideration of themolecular structure. The inherent difficulties make this impracticable andbeyond the scope of the present theory. We assume instead that the molecule isa unit with three external degrees of freedom. It is characterized then for ourpurposes by the intermolecular parameters �* and *, see Equation (6). Thekinetic term then becomes identical with the first temperature factor inEquation (5).

2.3.3 THE CONDENSED PHASE: MULTICONSTITUENT

The generalization of the foregoing results has been obtained making the as-sumption of random mixing [2]. The scaled EOS, Equation (7), and theminimum condition, Equation (8), in scaled coordinates retain their validity,and the parameters become averages over the composition. The new elementsare the cross interactions between unlike species to be added to the self inter-actions. Specifically, for a binary system we obtain [2] the following:

The repulsion volume ⟨*⟩ and the maximum attraction ⟨�*⟩ of the mixture aregiven in terms of the self, 11 and 22, and cross interactions, 12, are given bythe equations

and

(9)B2,4 � X12e*11�

*2,412 � 2X1(1 � X1)e*12�

*2,412 � (1 � X1)2e*22�

*2,422

� �* �2 � B4/B2; � e* � � B22/B4

�s� � x1s1 � x2s2; �c� � x1c1 � x2c2

s � c � 1


with . The quantity ⟨qz⟩ is the average of qz, defined by Equa-tion (7) and the average ⟨s⟩. Equation (9), combined with the definitions, Equa-tion (6), applied to constituents and to the mixture averages, determines theEOS of the mixture.

Equation (9) can be read in two ways. Provided the EOS of the mixture andconstituents has been measured, all interactions can be extracted. On the otherhand, if information about the cross-interaction parameters is available orassumed, the EOS of the mixture can be computed. It is the latter route wemust take here. The theory of intermolecular forces suggests the geometricmean proposition

(10)

with �e close to unity. Moreover, we set

(11)

This represents an arithmetic average of lengths, when �v is unity. Thus, whenthe EOS data for the polymer and the small component in the vapor and con-densed phases have been evaluated, �e and �v are the only disposable parame-ters. We recall the extensive amount of polymer data at hand [8]. Also, for anumber of gases, the virial coefficients over ranges of temperature have beenmeasured.

2.3.4 THE FREE ENERGY OF THE MIXTURE

For the free energy Gm, we have the following expression [3, 9]:

(12)

For simplicity, we have omitted the average symbol in s and ms and note that

�s� �m�→s � m � x1s1m1 � x2s2m2

� c[(1 � �)�1 � 2yQ2(1.011Q2 � 1.2045)/T�/s � m

� 3

2c1x1ln[2�m1RT/(Nah)2]�

3

2c2(1 � x1)ln[2�m2RT/(Nah)2]

� (1 � �)3/Q] � cyQ2(1.011Q2 � 2.409)/2T�� s(1 � y)ln(1 � y)/y � (s � 1)ln [e/(z � 1)] � c[ln(v*/Na)

Gm/RT � x1ln x1 � (1 � x1)ln(1 � x1) � ln(y/s)

�*12 � v(�*1/3

11 � �*1/322 )3/8

e*12 � e(e*11e

*22)1/2

X1 � x1q1z/8 qz 9


We recognize in Equation (12) in the first two lines the contributions from theentropy of mixing holes and sites occupied by the two constituents, followedby equation of state terms, and finally, kinetic energy contributions. The ther-modynamic prescription , with Equations (5), (2), and (12), thenyields the equilibrium mole fraction x1 and finally the solubility S, Equation(3). The lengthy expression for �12 has been derived [10]. However, it is moreconvenient to proceed by numerical differentiation of Equation (12).

2.4 METHODOLOGY

It is initially necessary to obtain the scaling parameters (i.e., T*, P*, V*) forthe gases and the polymers, since SS equations of state are required for eachcomponent of a given mixture. The scaling parameters were determined byfitting Equations (8) and (9) to experimental liquid densities, with T* and V*as dependent variables. Nonlinear least squares fitting can be done with com-mercially available software packages. Saturated vapor-liquid density datawere used for determining the scaling parameters for CO2[11]. Scaling pa-rameters for the polymers were adapted from literature values reported byRodgers [8] or determined with experimental p-V-T data. As required by thetheory, the polymer segment sizes were adjusted such that the molar repulsionvolumes of the segments (v*) matched those of the gas molecules:

(13)

This often leads to segment sizes that are smaller than the polymer repeat unit.The chemical potentials of the gaseous phase can be determined with equa-tions of state. An example of such a calculation is described for HFC 134a inresearch by McLinden et al. [12] The chemical potential of the gas and thescaling parameters were then entered into computer programs developed tosolve Equation (12) for a given pressure and temperature. Thus, solubilitycurves can be generated by performing such calculations for several tempera-tures and pressures.

2.5 DISCUSSION

2.5.1 COMPARISON BETWEEN EXPERIMENT AND THEORY

Once the equations of state for the mixture were developed, the disposableparameters �e and �v were adjusted to reconcile the theoretical equations withexperimental data. Experimental data reported by Sato et al. were used to fitthe mixture equations for CO2 [13]. Values of 1.065 were both obtained for �e

m1v*1 � m2v*

2

�11 � �12


and �v. Figure 2.2 illustrates the computed CO2 solubilities along with experi-mental data. Except for a difference observed at higher pressures for solubili-ties at 373°K, the agreement between the experimental solubilities and theo-retical predictions is very good. Furthemore, a decrease in CO2 solubilitieswith increasing temperatures is correctly predicted by the SS equations.

The difference observed at higher pressures is due to the concavity of thecomputed solubility curve. At 453°K, however, the solubility curve is linearover the same pressure range. Figure 2.3 shows calculations for the solubilityof HFC 134a in PS, previously reported by Simha and Xie along with exper-imental data reported by Daigneault et al. [4,14]. Interestingly, the solubilitycurves show similar behaviour to those for CO2, where the solubility curvesbecome more linear as temperature increases. In the case of 134a, it was believed that this was due to the pressure approaching the saturated vapor condition. [4] Solubility predictions at 373°K for CO2, however, show that this is not the case, since it is well above its critical temperature( ). As will be shown later, it is believed that this is theresult of competing temperature and pressure effects on computed solubility,which will be discussed later.

Tc for CO2 � 304.2°K

FIGURE 2.2 Solubilities of carbon dioxide in polystyrene. Lines: theoretical calculations;Symbols: data reported by Sato et al. [13].


Figure 2.4 illustrates solubilities predicted for N2, CH4, CO2, and Ar inpolybutadiene (PBD) at different temperatures, previously reported by Xie andSimha [3]. With respect to the critical temperatures of the gases, solubility de-creases with decreasing critical temperature. Except for N2, a decrease in solu-bility is predicted with increasing temperature. This positive temperature de-pendence is also observed experimentally for N2 in natural rubber [15] andpolystyrene [13]. These temperature dependences reflect competing efforts ofreduction in polymer-solvent attractions and enhancement of free-volumeavailable with increasing temperature.

At this stage, a discussion as to the behavior of the mixture with changes intemperature and pressure is useful. Solubility does not only depend on thefree-volume available, but also on the interaction between the gas and thepolymer and interactions within the gas molecules. As the vapor pressures of aliquid increase with temperature, the tendency to reside in the condensedphase (polymer) decreases. Also, as greater pressures are exerted on the con-densed phase, the free-volume tends to decrease. Ultimately, the dominantfactor accounts for the temperature-pressure behavior. Hence, for N2, inter-

FIGURE 2.3 Solubilities determined for HFC 134a in polystyrene at three different tempera-tures. Lines: Theoretical calculations; Symbols: Data reported by Daigneault et al. [14]. Figureadapted from Reference [4].


molecular interactions are low enough that solubility is sensitive to changes inthe polymer. The temperature dependence of solubility has been noted to showpositive and negative behavior for noble gases, with solubility decreasing athigher temperatures for Ar and Xe. Thus, molecular size also influences thepressure-temperature behavior of solubility [16]. Figures 2.2 and 2.3 show thatat lower temperatures, the theory predicts an eventual decrease in free-volumedue to the pressures exerted on the polymer liquid. In light of the solubilitymeasurements for CO2 and HFC 134a, experimental data have yet to demon-strate the existence of a maximum in the solubility-pressure curves.

2.5.2 INFLUENCE OF EQUATION OF STATE PARAMETERS FOR CO2

The scaling parameters P*, T* and V* previously reported by Xie andSimha [3] were extracted from low pressure data between 5 and 7.5 bar, and anequation that allows for simplifications for low pressures (i.e., ) [4]:

(14)ln V� � A(s, c) � B(s, c)T�3/2

P� � 0

FIGURE 2.4 Dependence of theoretical solubility (symbols) on temperature at 1 bar for carbondioxide (CO2), methane (CH4), argon (Ar), and nitrogen (N2) in polybutadiene. Data obtainedfrom Reference [3].


Thus, linear regression of low-pressure V-T data yielded the scaling parametersfor CO2. In this work, however, the scaling parameters obtained for CO2 madeuse of liquid p-V-T data between 217–304°K. The scaling parameters obtainedby each procedure are compared in Table 2.1.

Figure 2.5 compares the fit of predicted volumes to actual volumes at differ-ent temperatures and pressures. In both cases, the standard error of predictionfor V is within 0.5%. The Xie-Simha parameters give a better fit in the lowtemperature region, but result in divergences above 290°K. Thus, the scalingparameters are sensitive to the data used to determine them. The solubilities

1. Derived using all p-V-T data. 2. Derived from limited low T data.

TABLE 2.1. Scaling Parameters Determined for CO2.

m V* T* P*(g/mol) (cc/g) (K) (bar)

CO21 44.01 0.586 2960 9542

CO22 44.01 0.623 3043 9227

FIGURE 2.5 Specific volume of carbon dioxide as a function of temperature along the saturatedvapor curve. Line: actual data [11]; Open symbols: using parameters reported by Xie and Simha[3]; Closed symbols: derived using complete saturated vapor curve.


computed at 373°K and 453°K from the two sets of scaling parameters areshown in Figure 2.6. Although differences are observed with respect to thecalculated solubilities, the shapes of the diagrams are unaffected.

The segment size for PS was set such that the molar volumes, v*, of the gasand effective polymer repeat units were identical. In this case, CO2 is roughlyhalf the size of the chemical PS repeat unit. Because 3c/s has been kept fixedin the computations, segment sizes are decreased at the expense of flexibiity ofthe segments. Although the number of segment(s) depends on the total molec-ular weight of the polymer, Xie and Simha demonstrated that this effectbecomes negligible at high molecular weights. In this work, the molecularweight was set to 124,800.

The disposable parameters �e and �v are supposed to reflect specific interac-tions that may occur between the gas and polymer. In the case of �e, added at-tractions between the gas and the polymer are incorporated into the equationswhen �e is greater than one. Figure 2.7 illustrates solubility calculations withsystematic changes in �e. A significant increase in solubility is observed as �e

is increased. As expected, solubility increases with �e, indicating that attractiveforces can increase the solubility of a gas agent in a polymer. Nevertheless, a

FIGURE 2.6 Solubilities for carbon dioxide in polystyrene determined with scaling parametersshown in Table 2.1; Open symbols: determined with parameters reported by Xie and Simha [3];Closed symbols: this work.


15% increase in �e increases solubility at least sixfold, showing that the EOSare very sensitive to changes in these scaling parameters. We note that twomeasurements suffice to determine �e and �v. Allowance for T or p depen-dences of these parameters merely introduces empiricism into the theory. Amore thorough understanding of the siginificance of these parameters will bepossible as more experimental solubility data becomes available.

2.5.3 SOLUBILITY COMPUTATIONS WITH OTHER STATISTICAL-THERMODYNAMIC MODELS

There are other statistical thermodynamic models available for modelingpolymer liquids. A review by Rodgers [8] compares the predictions of severalequations of state applicable to polymer melts. Several theories have been ex-tensively used for mixtures, such as Sanchez-Lacombe. As with Simha-Somcynsky theory for gas solubility in polymers, the polymer-gas system istreated as a liquid mixture, whose EOS is derived by applying mixing rules tothe scaling parameters of the pure constituents. A detailed discussion on theSanchez-Lacombe EOS and the mixing rules for each scaling parameter when

FIGURE 2.7 Effect of �e parameter on computed solubilities of carbon dioxide in polystyreneat 373°K.


modeling gas solubility can be found elsewhere [17–19]. Among the mixingrules, a binary interaction parameter �ij is also included to reconcile computa-tions with experimental data. Finally, solubility predictions are computed byequating the composition-dependent chemical potentials of the mixture and ofthe gaseous phase [17–19]. Good quantitative predictions of gas solubilityhave been demonstrated by Sanchez-Lacombe and Panayiotou-Vera theoriesfor CO2 in PDMS or 1,1-difluoroethane in PS [17]. Good correlations werealso obtained with Sanchez-Lacombe theory for N2 and CO2 in PS [13,20].

An important consideration when making use of the Sanchez-Lacombemodel, however, is that the binary interaction parameter �ij is temperature de-pendent. Figure 2.8 shows solubility predictions using the Sanchez-Lacombetheory for CO2 in PS at different temperatures. These predictions are based oncorrelations found by Sato et al. with their experimental solubility data [13].The correlations show that the binary parameter �ij must be determined foreach solubility isotherm. Computations using Simha-Somcynsky theoryshown in Figures 2.2 and 2.3, however, showed reasonable agreement with ex-

FIGURE 2.8 Solubilities computed with Sanchez-Lacombe theory for carbon dioxide in poly-styrene at 373, 413, and 453°K, using parameters reported by Sato et al. [13].


perimental data using single values for �� and �v. This is in the spirit of a self-consistent theory.

As shown earlier, vapor-liquid equilibria are often used for obtainingscaling parameters for the gas. Calculations using Simha-Somcynsky theorydemonstrated that the data range used for determining scaling parameters has

TABLE 2.2 Scaling Parameters Reported by Sato et al. (I) [13] and Kwag et al. (II) [20] for Solubility Computations with S-L Theory.

P* �* T*Substance (bar) (g/cc) (K)

CO2(I) 72.03 1.580 269.5CO2(II) 45.80 1.430 330.0PS(I) 38.70 1.108 739.9PS(II) 35.70 1.105 735.0

FIGURE 2.9 Solubilities for carbon dioxide in polystyrene at 150°C computed with Sanchez-Lacombe theory. Computations with scaling parameters listed in Table 2.2: parameter set I (solidline) and parameter set II (dashed line).


an important influence on solubility computations. Table 2.2 compares twosets of scaling parameters reported for pure CO2 and PS, determined indepen-dently [13,17]. In the case of CO2, the difference in the scaling parameters issignificant. The values for CO2(I) were determined with only a portion of thesaturated vapor curve, below 269°K. As mentioned previously, it is desirableto maximize the data range of pure component data since it minimizes varia-tions when extrapolating the pure component EOS to higher T and p condi-tions used for solubility computations.

Figure 2.9 illustrates Sanchez-Lacombe computations for CO2 in PS at150°C, using both sets of parameters listed in Table 2.2. The predictions withparameter set (I) are based on a �ij value of , calculated with an empir-ical temperature dependence from the �ij values reported in Figure 2.8; predic-tions with parameter set (II) were done with a �ij value of 0.0855, reported inthe literature [20]. These computations show that very different solubilitieswere obtained by each, demonstrating that there is still a need for developingaccurate and consistent techniques for gas solubility measurements.

2.6 OUTLOOK

The quantitative success of Simha-Somcynsky theory toward gas solubilityin polymer melts suggests further experimental and theoretical directions. Themost obvious issue facing the theory is the existence of the maxima predictedin the solubility isotherms. Several extensions of the theory are currently beingexplored. Among those of interest to foam process scientists are the treatmentof blowing agent mixtures as well as foam aging properties. The issue of foamaging raises the issue of solubility in the glass-transition region (Tg) and in theglassy state, as well as the shift of the glass-transition temperature by the dis-solved gas. Glassy-state solubilities are important when considering the per-meation of gases into and out of a finished foam. Furthermore, the glassy statealso exhibits the well-known features of formation history-dependent proper-ties and time-dependent properties of the glassy state. Although conceptuallymore involved for glassy polymers, the Lattice-Hole theory has been appliedto a polymer equation of state [21]. The nonequilibrium character is acknowl-edged in this treatment by the elimination of the equilibrium condition,Equation (8).

2.7 NOMENCLATURE

�ik Chemical potential of component i dissolved in matrix k�o Chemical potential of an ideal gasNa Avogadro’s numberc Volume-dependent degrees of freedom

�0.118


s Number of segments dividing a moleculez Coordination number for a given atom ( in this work)h Planck’s constantk Boltzmann’s constant�* Maximum attraction energyG Gibb’s free energyn Molar quantityp PressureP* Scaling pressure

Reduced pressurey Occupied volume fractionh Free-volume fractionV VolumeV* Scaling volume (cc/g)v* Scaling volume (cc/mol)* Measure of the segmental repulsion volume

Reduced volumeR Gas constantT TemperatureT* Scaling temperature

Reduced temperaturexi Mole fraction of component iS Solubility (expressed in grams of gas per gram of polymer)�e Correction constant for geometric mean averaging [see Equation (10)]�v Correction constant for arithmetic mean averaging assumption for

length scales [see Equation (11)]

2.8 REFERENCES

1. Simha, R. and T. Somcynsky. Macromolecules, 2 (1969) 342.

2. Jain, R. K. and R. Simha. Macromolecules, 17 (1984) 2663.

3. Xie, H. and R. Simha. Polymer Int., 44 (1997) 348.

4. Simha, R. and H. Xie. Polymer Bull., 40 (1998) 329.

5. Guggenheim, E. A. Thermodynamics. Amsterdam: 1959, North Holland Publishing Co., pp. 215–216.

6. Kestin, J. and J. D. Dorfman. A course in Statistical Thermodynamics. New York: 1971, Aca-demic Press, pp. 313.

7. Prigogine, I. The Molecular Theory of Solutions. Amsterdam: 1957, North Holland PublishingCo.

8. Rodgers, P. A. J. Appl. Polym. Sci., 48 (1993) 1061.

9. Jain, R. K. and R. Simha. Macromolecules, 13 (1980) 1501.

10. Nies, E., A. Stroeks, R. Simha, and R. K. Jain. Colloid Polym. Sci., 268 (1990) 731.

T�

V�

P�

z � 12


11. Angus, S., B. Armstrong, and K. M. de Reuck, eds. International Thermodynamic Tables ofthe Fluid State:Carbon Dioxide. New York: 1976, Pergamon.

12. McLinden, M. O., J. S. Gallagher, L. A. Weber, G. Morrison, D. Ward, A. R. H. Goodwin, M. R. Moldover, J. W. Schmidt, H. B. Chae, T. J. Bruno, J. F. Ely, and M. L. Huber. ASHRAE J.,3282 (RP-588), p. 263

13. Sato, Y., M. Yurugi, K. Fujiwara, S. Takishima, and H. Masuoka, Fluid Phase Equilibria, 125(1996) 129.

14. Daigneault, L. E., Y. P. Handa, B. Wong, and L.-M. Caron. Proc. SPE ANTEC ‘97 (1997)1983.

15. Van Amerogen, G. J., Rubber Chem. & Tech., 37 (1964) 1065.

16. Curro, J. G., K. G. Honnell, and J. D. McCoy. Macromolecules, 30 (1997) 145.

17. Garg, A., E. Gulari, and C. W. Manke. Macromolecules, 27 (1994) 5643.

18. Sanchez, I. C. and P. A. Rodgers. Pure and Appl. Chem., 62 (1990) 2107.

19. Sanchez, I. C. and R. H. Lacombe. Macromolecules, 11 (1978) 1145.

20. Kwag, C., L. J. Gerhardt, V. Khan, E. Gulari, and C. W. Manke. ACS PMSE Preprints, 74(1996) 183.

21. McKinney, J. E. and R. Simha. Macromolecules, 9 (1976) 430.


CHAPTER 3

Rheology of Thermoplastic Foam Extrusion Process

RICHARD GENDRONLOUIS E. DAIGNEAULT

3.1 INTRODUCTION: THE IMPORTANCE OF RHEOLOGYIN FOAMING PROCESSES

BECAUSE the production of extruded thermoplastic foams, such as foamsheets or boards, is largely linked to the rheology of the mixture of a poly-

meric matrix with a physical blowing agent that is kept dissolved until the meltis allowed to foam at the die exit, then Section 3.2 will deal mostly with therheological behavior, in a shear field, of this one-phase system.

The knowledge of the rheology of such polymer/dissolved blowing agentmixtures is critical because of the following:

(1) It improves our fundamental understanding of the process, and it is a valu-able information source for the optimization of the processing conditions.Not all blowing agent/polymer pairs behave the same way with regard totheir plasticization effect. The extent of the viscosity reduction can be re-flected through the temperature at which the mixture can be processed, thelowering of the torque exerted on the machine, or the increase of themaximum throughput at which the extrusion line can be run.

(2) It is a must for computer-assisted die design, since it is the key element forthe numerical simulation of the flow. Viscosity results first should be trans-lated into a rheological model compatible with the flow simulation soft-ware package. This model should take into account the effect of the manyvariables on the viscosity levels, such as type and concentration of theblowing agent, temperature, pressure, and shear-thinning behavior.

(3) Since the foam plastic industry will be facing new HCFC regulations thatwill force it to look for replacements for the present ozone-depleting


chemicals, the knowledge of the rheology of polymer/blowing agentsystems is a key parameter in the development of new foam compounds.Not only should the blowing agent replacements yield adequate foamproperties, but the new systems should typically exhibit the same proces-sibility as their predecessors to limit the extent of equipment modifica-tions. For example, it is not surprising to find an increased interest forcarbon dioxide, CO2, as a potential replacement blowing agent because ofsafety and cost considerations.

For this tailoring of foam product properties by new combinations of poly-mers and blowing agents, the extensional rheology of the polymer in the two-phase system is critical as discussed in Section 3.3. A better understanding ofthe role that extensional rheology plays during the foaming process is a mustbecause of the following:

(1) Not all polymer resins are suitable for foaming, and a clear understandingof the prerequisites for foaming in terms of the rheological behaviorshould help in the design of alternative resins and optimization of existingones.

(2) Foam properties are largely linked to cellular morphology. Besides the nucleation stage, the following steps, cell growth and stabilization, whichare governed largely by the extensional rheology, should dictate the finalfoam structure.

3.2 SHEAR RHEOLOGY OF BLOWING AGENT-CHARGEDPOLYMERIC SYSTEMS

3.2.1 RHEOMETRICAL CONSIDERATIONS

Unfortunately, the rheology of mixtures of a polymeric matrix and a physi-cal blowing agent cannot be directly measured on standard laboratory rheolog-ical equipment such as cone and plate or capillary rheometers. A closed pres-surized rheometer is necessary because the system must be kept under pressureat all times in order to prevent degassing.

Even so, capillary and slit die viscometers are the most frequently used ap-paratuses for the study of such systems of polymers and blowing agents.During the extrusion of the foam, the measurements can be conducted in-line(directly in the process stream) or on-line (a sampling stream is diverted fromthe process flow line and transferred to the measuring apparatus) using therheometer attached at the end of the extruder. In some other cases where themeasurements are conducted off-line, standard capillary viscometers can bemodified to accommodate the pressure requirements.


For either slit or capillary rheometers, herein also referred to as dies, the vis-cosity measurements are derived from the pressure drop observed through thechannel of a known geometry, at a given volumetric flow rate (see Table 3.1). Ithas been observed that, under given conditions of pressure and temperature,bubble nucleation may start inside the die as a result of insufficient blowingagent solubility at the concentration of interest [1, 2]. The formation of gasbubbles strongly affects the shear stress and thus the pressure profile along thedie axis, and deviations from linearity are encountered (see Figure 3.1). Takingthis problem into account, the following alternative protocols have been pro-posed: measurements based only on the linear portion of the pressure profileusing several pressure transducers [3, 4], back pressure assembly such as avalve [5] or a gear pump [6, 7, 8] attached at the exit of the die and set to main-tain the pressure inside the die above the critical pressure required for bubblenucleation, and the use of very long length-to-diameter (L/D) capillaries to min-imize the relative contribution of the nonlinear portion of the pressure drop [9].

Off-line measurements require particular care to the sample preparation andto the loading of the sample into the apparatus, because the concentration ofthe blowing agent must be determined precisely and kept constant up to themeasuring cell or die, while the pressure is maintained above the criticaldegassing value to prevent phase separation [10, 11]. A much simpler experi-mental protocol can be followed when conducting the measurements on an ex-trusion line: the extruder is first used to form a single-phase system from thetwo components, polymer and blowing agent, and second to pump the mixture

TABLE 3.1 Viscosity Calculations for Capillary and Slit Die Rheometers.

Capillary(diameter Dc and Slitlength Lc; �Pc is (h is the height of the slit,

the pressure drop w its width, L the distance Geometry across the capillary) between P1 and P2)

Shear stress, j12(a)

Apparent shear (b)rate, (at volumetric flow rate Q)

Power-law (c)index, n

Actual shear rate (d)at the wall,

Viscosity, �(e)

� ��12

��

�� a2n � 1

3nb ��app

�� a3n � 14n

b ��app

n � �log �12>�log ��app

��app��app �

6Q

w h2��app �

32Q

�Dc3

�12 � c h2(1 � (h>w))

d c P1 � P2

Ld�12 �

�PcDc

4Lc


through the slit or capillary die, while maintaining the pressures at relativelyhigh levels [5, 12]. Both single- and twin-screw extruders can be used to thatpurpose, provided that a single-phase solution is formed upstream from themeasuring die; this will be a function of the mixing efficiency of the extruderas well as the residence or equilibrium time in the extruder.

Some on-line measurements have also been obtained using a commercialslit die rheometer [6, 7, 8, 13]. The material flows from the process up aconduit into a gear pump as shown in Figure 3.2. The material is pumped viathe inlet gear pump through the rheometer head and is returned to the processvia the exit gear pump and the return conduit. The output from the process ex-truder is not affected. The instrument head is fitted with a die that is rectangu-lar in cross section (a slit die). Three pressure transducers are mounted to beflush with the face of the die as shown in Figure 3.2. This instrument can bemade to function as a constant stress or a constant rate machine. The pressuredrop between the transducers P1 and P2 is measured, and the volume through-put to give a given stress or shear rate is calculated from the known rotational

FIGURE 3.1 Axial pressure profile along a die of constant cross section: beyond entranceeffects, a linear pressure drop is followed by a deviation from linearity as bubbles are nucleating.


speed of the inlet gear pump and its capacity. A third pressure transducer islocated near the exit of the slit die to control the absolute level of pressurewithin the slit channel. This happens through the manipulation of two inde-pendent gear pumps that control the flow in the measurement stream. With thiskind of on-line rheometer, one should be aware that sampling delays must beexpected, so a complete purge of the sampling conduits must be performedbefore any characterization test is conducted.

3.2.2 EFFECT OF THE BLOWING AGENTON THE SHEAR VISCOSITY

Literature is scarce on the rheological evaluation of mixtures of polymerresins with physical blowing agents. This may be attributed to the complexityof the experimental setup, as described in the previous section. Table 3.2 liststhe conditions under which the rheological evaluation of systems in the litera-ture has been made. This table includes only foamable systems based on a

FIGURE 3.2 Schema of a commercial on-line rheometer (Rheometric Scientific). P1, P2 and P3

are the pressure transducers, and T1 and T2 are the thermocouples.


physical blowing agent. Chemical blowing agents are not included becausemost decompose to water or carbon dioxide or nitrogen or combinations ofthese [1, 9, 19, 20, 21, 22, 23, 24]. They often yield other compounds con-tributing to the polymer plasticization. The extent of their influence on rheol-ogy also depends on the fraction of decomposition.

The key element of the viscosity response is that the dissolved gas or liquidinduces plasticization of the polymer, which can be translated in terms of theapparent decrease of the viscosity. Typical viscosity results are presented inFigure 3.3(a) and Figure 3.3(b): these examples relate to mixtures of PS with

*Methods: CD/E: capillary die mounted on the extruder; CD/PV: capillary die mounted on a pressurevessel; PCR: pressurized capillary rheometer; OLR: commercial on-line rheometer; MFI: melt flowindexer; NM: not mentioned.

TABLE 3.2 Physical Foaming Agent Rheology Studies.

Blowing Agent

ConcentrationPolymer Type (wt%) T (°C) Method References

LDPE R-12 5–20 110–160 CD/E 3, 12LDPE R-114 10–20 110–160 CD/E 3, 12LDPE R-114 0–20 120 NM 14LDPE R-12 � R-114 10–20 110–140 CD/E 3LDPE R-22 0–20 110 CD/E 15LDPE R-22 21 100 CD/PV 16LDPE n-butane 15 100 CD/PV 16LLDPE R-114 10–15 140–160 CD/E 12PP R-12 10 160–180 CD/E 12PP R-114 5–20 150–170 CD/E 12PP CO2 0–4.9 150–220 OLR 7PP Phenol 1–5 180–240 MFI 17

alcoholPB R-12 10–20 140–160 CD/E 12PB R-114 10–20 150–170 CD/E 12PDMS CO2 0–20.7 50–80 PCR 10, 18PS R-11 10–15 150–170 CD/E 4, 12PS R-12 5–15 140–170 CD/E 4, 12PS R-12 0–12 135–246 NM 14PS R-11 � R-12 5–15 140–170 CD/E 4PS R-134a 0–4.3 150 PCR 11PS R-134a 0–15 130–156 OLR 6PS R-142b 0–15 114–175 OLR 6PS R-152a 0–10 150 PCR 11PS CO2 0–5 150 PCR 11, 18PS CO2 0–4 220 CD/E 5PS CO2 0–3.7 150–200 OLR 7PS Phenol 1–5 180–240 MFI 17

alcohol


HCFC 142b, at different temperatures and compositions, as indicated on thegraphs. These results are representative of the plasticization behavior encoun-tered in all investigated systems. That range of shear rates is also typical ofsuch viscosity measurements using slit or capillary dies, spanning generallybetween 1 and . In this range of rates, most polymers’ viscosity be-havior falls in, or near, the power-law region.

Figure 3.3(a) illustrates the effect of composition on the viscosity level, atroughly constant temperatures (125°C and 150°C). The range of compositionsinvestigated is such that the viscosity readings fall within the operatingwindow of the rheological apparatus. For this reason, it is rare to find, for suchexperiments, results over a wide composition range at a constant temperature.Figure 3.3(b) illustrates this limitation by showing the plots of similar viscos-ity curves for different blowing agent concentrations (from 0 to 15 wt%)where the temperature was selected in order to maintain nearly identical vis-cosity levels. For these examples, the temperature varies from 187°C for thepure PS to 114°C when adding 15 wt% of HCFC 142b.

Simple observations can be made from these two figures:

• At high levels of shear, the slopes on the graphs are identical. All curvesthus exhibit the same power-law index. Globally, the shape of the curvesremains approximately the same for any temperature or composition.

• From Figure 3.3(a), one can roughly estimate the degree of plasticizationin terms of the viscosity reduction measured either at constant stress or at

1000 s�1

FIGURE 3.3 Viscosity of PS with HCFC 142b: (a) at two nominal temperatures, 125°C and150°C; (b) for different combinations of composition and temperature yielding similar viscosities.


constant rate. Adding 2.5 wt% of HCFC 142b to PS lowers the viscosityby a factor of 4.0 at constant stress or by a factor of 1.6 at constant rate.

• The curves of Figure 3.3(b) suggest the equivalence principle that theincorporation of 2.5% of HCFC 142b to PS is equivalent to an increaseof the temperature by roughly 10°C. This result may be linked to twointeresting concepts: first, running at a concentration of 10 wt% ofHCFC 142b, one would expect to be able to run the process at atemperature 40°C lower than that achievable with pure PS only; second,if we relate the viscosity reduction to the lowering of the mixture’s glasstransition temperature, Tg, as we will do in an upcoming section, then theaddition of HCFC 142b blowing agent can be translated into the changeof the glass transition temperature of PS by approximately perweight percent of HCFC 142b. An exact number is provided through afine numerical analysis, a procedure detailed in the following pages.

These examples, and most of the results shown in the references listed in Table 3.2, raise the question of how the viscosity reduction resulting from theaddition of a physical blowing agent should be presented and analyzed. Em-pirical evaluation of the viscosity reduction, as a function of the blowing agentconcentration, could be reported in terms of apparent plasticization effect.Nevertheless, such reporting would not help our fundamental understanding ofthe plasticization behavior. In addition, it would not be possible to generalizethese results with a formalism helpful in predicting the viscosity for new mix-tures of polymers and blowing agents.

Details regarding the way of reporting the results, their limits, their uses,and the extent of applicability, are given in the following sections.

3.2.2.1 Apparent Plasticizing Effect Evaluated at Constant Rate

Rate-controlled viscosity measurements have been conducted by Han andcoworkers on numerous systems of polymers and blowing agents (see Table 3.2). They chose to translate the degree of plasticization observed into aviscosity reduction factor (VRF) defined as follows:

(1)

This factor was calculated under set temperature and shear rate. Han et al. havereported the following [3, 4, 12]:

(1) The value of VRF, for a given system of polymer and blowing agent, withset blowing agent concentration, was practically independent of the shearrate and temperature, within the range of measurements.

VRF �Viscosity of the mixture of molten polymer and blowing agent

Viscosity of the molten polymer

�4°C


(2) For a given system of polymer and blowing agent, the value of VRFdecreases as the blowing agent concentration increases.

(3) The VRF values differ for different polymers or blowing agents used.Figure 3.4 illustrates these empirical findings.

One should be cautious about conclusions drawn from such constant rate ex-periments. Even though these results are very attractive due to their relativesimplicity, and even if such experiments are seemingly conducted with easewhile reflecting a production concern of constant throughput, attention shouldbe paid to the conditions under which the data were obtained before making

FIGURE 3.4 Viscosity reduction factors, at constant rate, as a function of the concentration ofblowing agent for various polymers. These results were obtained at temperatures of 150°C and160°C [12].


generalizations. Empirical findings based on larger experimental ranges maybe more insightful in developing a global understanding of the rheological be-havior of mixtures of polymers and blowing agents.

First, the measurements should be made under the same conditions underwhich the foam will be produced: for instance, in the case of polystyrene, theaddition of the physical blowing agent may yield viscosity reductions that canaccommodate extrusion temperatures typically as low as 120°C. In this case,useful results should cover a broader temperature range to suit the conditionsencountered throughout the process. This is particularly true for amorphouspolymers. Then, at very low temperatures, the viscosity of the amorphouspolymer phase alone, used as the reference, may be experimentally difficult toobtain, which precludes the general use of a VRF parameter. The lower limitfor processing semicrystalline polymers is, however, still dictated by the tem-perature of crystallization, which is only slightly influenced by the presence ofthe blowing agent [25].

Second, most of the results obtained by Han et al. are limited to the power-law region, where the viscosity functions, straight lines on a log-log plot, areparallel. For this particular range of shear rates, where all the results belong tothis power-law dependency, one can expect to find a constant ratio between theviscosity of the mixture and that of the pure polymer, irrespective to the shearrate. However, it can be anticipated that extrapolation to low shear rates, priorto the power-law regime but still within a pertinent rate range for foam appli-cations, would yield erroneous estimates. Viscosity curves covering a broaderrange in shear rates should exhibit low-shear-rate Newtonian plateau regions,or at least some curvature in the viscosity curves that would tend to level off atlow rate values. Classical viscosity scaling principles apply a double shift toboth � and axes and do not reduce the scaling on a constant rate basis.Scaling at constant stress is thus the better procedure.

3.2.2.2 Apparent Plasticizing Effect Evaluated at Constant Stress

The results shown in Figure 3.5(a) for the PDMS/CO2 system at 50°C [10]are a good illustration of the concentration-dependent viscosity curves en-countered for physically foamable polymeric systems. The viscosity curves fordifferent gas concentrations exhibit similar slopes in the power-law regions,and Newtonian plateau regions can be observed at low shear rates for mixturescontaining a high level of the blowing agent. Because of the pronounced simi-larity between these curves, classical viscoelastic scaling principles are envis-aged, with curve shifting performed at constant stress. Analogous to the time-temperature superposition shift factor aT, the concentration-dependentviscosity curves can be shifted according to a shift factor aC that will dependon the concentration of the blowing agent, while the temperature is maintainedconstant. This results in the master curve illustrated in Figure 3.5(b). Again,

��


this procedure necessitates sets of data obtained at a constant temperature overthe range of interest of the blowing agent concentration.

Mixtures of PS with various blowing agents at 150°C are compared inFigure 3.6(a). Results shown in Section 3.2.2.1, previously expressed on thebasis of constant rate, have been translated here using the power-law index toconform to the constant stress criterion.

Several observations can be made from this figure:

• There is an excellent agreement between the results obtained fromdifferent laboratories [6, 7, 11] using different techniques for the fewsystems reported by more than one author: notably, HFC 134a and CO2.

• The viscosity ratios reported on a constant stress basis span over a muchlarger scale than when reported on a constant rate basis. We might saythat this represents the true nature and amplitude of the plasticizationeffect.

• The plasticization effect, reported as a function of the percent by weightof blowing agent, is more drastic for BA of low molecular weights: thelargest variation in the viscosity is encountered for the carbon dioxide

, while the least pronounced effects are observed for fluorocarbons R-11 and R-12 (MW respectively of 137.4 and 120.9g/mol). HCFC 142b and HFC 134a behave similarly, and they have close molecular weights (100.5 and 102.0 g/mol, respectively).

(MW � 44.0 g/mol)

FIGURE 3.5 Viscosity curves for PDMS/CO2 at 50°C for different compositions: (a) viscosityversus shear rate; (b) same curves reduced to a master curve, using a composition-dependent shiftfactor aC [10].


However, it can be anticipated that the plasticization at one particular temper-ature may not be applicable at a different temperature, especially for amor-phous polymers like PS where the viscosity dependency to the temperaturefollows an exponential fit. This is illustrated in Figure 3.6(b), where the vis-cosity reduction of the mixture of PS with CO2 is given for different tempera-tures [5, 7, 11]. As the temperature is increased, the plasticization effect is lesspronounced, thus indicating a significant effect of the temperature on viscosityreduction. A proper way of reporting the plasticization effect should be toisolate the contributions of the blowing agent and of the temperature in orderto generalize at any condition.

3.2.3 FREE VOLUME AND GLASS TRANSITION TEMPERATURE

3.2.3.1 Theory for Concentrated Polymer Solutions

A strong correspondence exists between the rheology of a concentratedpolymer solution and that of a pure polymer melt. The influences of molecularmass, temperature, and shear rate on the viscosity are quite analogous. Thenature and the concentration of the diluent are the key characteristics that shiftthe behavior of the concentrated polymer solutions.

In thermoplastic foam processing, the polymer is often chosen to exhibithigh viscous properties, which are beneficial during the bubble nucleation and

FIGURE 3.6 Plasticization of PS expressed on a constant stress basis in terms of reduced vis-cosity : (a) for various blowing agents, at 150°C [6, 7 ,11, 12]; (b) with CO2 asthe blowing agent, at different temperatures [5, 7, 11].

(�mixture/�PS � aC)


growth phases: the molecular weights of such polymers are quite high. On theother hand, the concentration of the blowing agent, which acts as the diluent, iskept to relatively low levels of usually less than 20 wt%. For these reasons, theconcentration of polymer beyond which the slope of log � against log MWchanges abruptly is normally not a preoccupation because it is exceeded. Thisparticular case for mixtures of polymers and blowing agents will simplify therheological picture.

It is generally accepted that the addition of a solvent decreases the viscosityof a polymer due to the following two causes [26]:

(1) A decrease of the viscosity of the pure polymer due to an increase of its freevolume, which translates into a decrease of the glass transition temperature.

(2) A real dilution effect, with the resulting solution viscosity falling betweenthat of the pure polymer and that of the pure solvent.

Each contribution will be examined separately.

3.2.3.1.1 Increase of the Free Volume and Decrease of the Glass Transition Temperature

The viscosity of molten polymers at different temperatures can be related tothe free volume fraction f, which is set equal to , with v being thetotal volume and v0 the occupied volume:

(2)

In the liquid state, that is, above the glass transition temperature, the depen-dence of the free volume can be defined as follows:

(3)

where fg is the free volume fraction at Tg, and �f is the thermal expansion co-efficient of the free volume. The combination of the above two equationsyields the well-known Williams-Landel-Ferry (WLF) equation [27]:

(4)

c1 and c2 are constants reflecting the temperature-dependent free-volume frac-tion. This equation relates the variation of the viscosity to the temperature inreference to the glass transition temperature of the polymer system.

Equation (4) is valid for a mixture of a polymer and a solvent. c1 and c2 arereported to be independent of the solvent fraction [26]. Tg is the sole parame-

log �/�g � �c1(T � Tg)

c2 � T � Tg

f � fg � �f (T � Tg)

ln � � ln A � B/f

(v � v0)/v


ter that will reflect the composition of the mixture. The glass transition tem-perature of a polymer is lowered when a liquid or a gas of low molecularweight is dissolved into the polymer. The measurements of the depression ofthe glass transition temperature based on traditional laboratory methods suchas for Differential Scanning Calorimetry (DSC) are fraught with uncertaintybecause polymer samples containing the dissolved blowing agent are difficultto prepare and prone to foam at usual low test pressures.

A number of methods are proposed in the literature to calculate the mixtureTg of two components. Unfortunately, most are based on the respective com-ponent Tg [26, 28], whereas, more often than not, the glass transition tempera-ture of the blowing agent is not known. As a quick approximation, the blowingagent Tg can be set to 2/3 of the melting temperature on an absolute scale [29].

An estimate of Tg can also be obtained by the following theoretical relationdeveloped by Chow [30]. It should be noted that this relation is particularlyuseful since it does not require knowledge of the Tg of the diluent.

(5)

where

(6)

(7)

Tg0 is the glass transition temperature for the pure polymer and Tg for thesolution whose weight fraction of diluent is �. Md and Mp are, respectively,the molecular weight of the diluent and that of the polymer repeat unit. �Cp

is the change in specific heat of the polymer at its glass transition. z is a co-ordination number, and R is the gas constant. A value of was found tobe appropriate for mixtures of polystyrene with diluents of molecular weightsin the order of 100 g/mol [30]. For the mixture of PS with CO2, a value of is preferred [31]. Other properties for polystyrene are

and [30, 31].

3.2.3.1.2 Dilution Effects

The description of the dilution effects is often reported as �s, the viscosity ofthe solution, being proportional to the �th power of �p, the volume fraction of

�Cp � 0.3209 J/(g � K)Mp � 104.15 g/molz � 1

z � 2

and �zR

Mp �Cp

��/Md

z(l � �)/Mp

lnTg

Tg0� [(l � ) ln(1 � ) � ln]


the polymer, with � varying between values of 3.5 and 5 [26]. Setting �p as theviscosity of the polymer, the dilution effect can be written as follows:

(8)

High fractions of the diluent are also expected to have some effects on theshear-thinning behavior usually observed for the polymers of interest. Follow-ing are definitions of the three different regions of viscosity dependency withthe shear rate:

(1) At low shear rates, the viscosity is independent of the rate of deformation,and the polymer behaves as a Newtonian fluid (Newtonian plateau region)with a viscosity expressed as the zero-shear viscosity, �0.

(2) At high shear rates, � is a decreasing function of the rate, and this de-pendency can be expressed as a power-law dependency (power-lawregion):

(9)

with n defined as the power-law exponent.

(3) For intermediate shear rates, a transition zone is observed that links theNewtonian plateau region to the power-law region. The width of the tran-sition zone is a function of the polydispersity of the polymer.

Shear-thinning is then observed in the last two regions, and the onset of vis-cosity dependence on shear rate could be specified by a characteristic shearrate , or its counterpart, a characteristic shear stress 0. It can also be ex-pressed as a characteristic time �, that is equal to the reciprocal of :

(10)

Typically, one can define such a characteristic value at the point where � hasbeen reduced to some arbitrary fraction of �0.

For polymer solutions, the shear-thinning behavior can be modified in twoways [32]:

(1) If the polymer is sufficiently diluted, the power-law exponent will cease tobe the one observed for the pure polymer melt and will become a functionof the diluent concentration due to the severe modifications in the polymercoil entanglements. This was observed for moderate polymer concentra-tions, but concentrations usually found in foam applications do not fallinto this category. For this reason, the power-law exponent for mixtures of

�0 � �0 ��0 � �0/��

��0

��0

� � k ��n�1

log �s � log �p � � log �p


polymer with a physical blowing agent should remain that of the purepolymer melt.

(2) The onset of the shear-thinning behavior, as defined previously usingeither 0, �, or , will vary with the modification in the level of entan-glement due to the presence of the diluent. The shear-thinning behavior forpolymer solutions will start at higher shear rate values than that of purepolymer melt, and 0 should be found proportional to �p.

In summary, with a practical concentration limit of 20 wt% physical blowingagent for foam applications, expandable mixtures could be interpreted as con-centrated polymer solutions given that the blowing agent acts as a low molecularweight solvent and that the blowing agent is dispersed on a molecular scale, sothat the limit of solubility of the blowing agent, under the given pressure andtemperature conditions, has not been reached. Furthermore, in addition to theglobal lowering of the viscosity with the addition of the blowing agent, and sincefoams rely on polymers of high molecular weights, we should also consider theeffect of the diluent on the entanglement network that may be translated intosome modifications of the shear-thinning zone, notably in the transition zonelocated between the Newtonian plateau region and the power-law region. Essen-tially, the presence of the diluent molecules close to the polymeric chains will actas a lubricant, easing the flow displacement of polymer macromolecules.

3.2.3.2 Case for Amorphous Polymers

A simple model based on the previous theory is herewith presented. Theresults are from various studies conducted with polystyrene, in turn mixed withseveral blowing agents, using a commercial on-line slit die rheometer [6, 7, 8].The link is made between the rheological behavior and the key processing vari-ables such as the type of blowing agent, its concentration, the processing condi-tions of pressure and temperature, and the rate prevailing in the flow.

3.2.3.2.1 Computation of the Glass Transition Temperature

The rate dependency of the viscosity can be modeled using a modifiedCarreau equation [33]:

(11)

where �0 is the zero-shear viscosity, 0 is the characteristic shear stress, andm1 and m2 are parameters related to the curvature of the viscosity curve and theslope in the power-law region.

� ��0

(1 � ((�0/�0)��)m1)m2

��0


The procedure to numerically determine the temperature and compositiondependency of the viscosity was the following. Since the curves can be super-imposed by shifting, parameters m1 and m2 are constant for a given polymer.They were evaluated quite accurately off-line for the polymer without blowingagent. By fitting the data to the above modified Carreau equation, the �0 and0 values were obtained for each specific set of experiments obtained undergiven conditions of temperature and composition. For the several examplespreviously presented in Figure 3.3(a) and Figure 3.3(b), a master curve couldbe constructed using reduced variables. Shifting vertically and horizontally the

FIGURE 3.7 Viscosity curves of Figure 3.3 for mixtures of PS with HCFC 142b, expressed asa master curve using reduced axes.


viscosity curves shown in Figure 3.3(a) and Figure 3.3(b) translates intomaster curve reduced axes, �/�0 and (�0/0) � (see Figure 3.7).

The zero-shear viscosity values, �0, were first corrected for the dilutioneffect that is reported to be proportional to the 3.5 power of the polymer con-centration. For amorphous polymers such as PS, at temperatures less than100°C above their glass transition temperature, the WLF equation [Equation(4)] is used. For PS, the parameters of the WLF equation are and

. The resulting �0 values were then fitted through this WLFequation. As stated before, this equation is governed by two variables: T andTg. T is the experimental temperature, and Tg was used as a fitting parameter

c2 � 50.0 [26]c1 � 13.7

��

FIGURE 3.8 Zero-shear viscosity values for mixtures of PS and HCFC 142b at different com-positions and temperatures and fitted to the WLF equation [Equation (4)].


function of the concentration of the blowing agent. WLF fits are graphically il-lustrated in Figure 3.8 for the different compositions of HCFC 142b that wereinvestigated.

The above procedure has been applied to mixtures of PS with variousblowing agents. The resulting values of Tg are plotted in Figure 3.9 as a func-tion of the blowing agent concentration. The lowering of Tg with the presenceof the blowing agent was anticipated because it acts as a plasticizer. The Tg es-timates obtained from the predictive model developed by Chow [30] are alsoplotted in Figure 3.9. Agreement is quite good between estimates and experi-mental results for most of the cases, especially at low concentrations. These

FIGURE 3.9 Glass transition temperatures of PS as a function of the blowing agent type andconcentration. Symbols are for experimental results and lines are for estimates using the Chowequation [Equation (5)].


results can also be reported in terms of the lowering of the Tg per blowingagent unit (see Table 3.3).

The resulting 0 obtained for the example using a mixture of PS with HCFC142b are plotted in Figure 3.10 as a function of the blowing agent concentra-tion. Despite the significant scatter in data, results shown in that figure exhibita trend in accordance with the theory stating that 0 decreases as the level ofentanglement is slightly reduced by the diluent.

3.2.3.2.2 Effect of the Pressure on the Viscosity

It is a well-known fact that the viscosity of polymers is pressure sensitive.This was also verified for the case of mixture of polymer with blowing agents.

FIGURE 3.10 Characteristic stress, 0, as a function of the composition, for PS/HCFC 142bmixtures.


The effect of pressure on the viscosity can be translated into a shift in the Tg

value in the WLF equation:

(12)

where P is the pressure of measurement, Tg is the glass transition temperatureof the mixture at , is the glass transition temperature at P, and D3 is apressure coefficient.

Viscosity measurements are shown in Figure 3.11(a) for a mixture of 7.5wt% of HFC 134a with PS at 140°C, expressed as shear stress versus apparentshear rate. Each curve corresponds to a different level of pressure set in therheometer slit through the variation of the exit pressure P3. The levels of pres-sure chosen are high enough to satisfy the condition of bubble-free flow.

T�gP � 0

T�g � Tg � D3P

TABLE 3.3 Depression of the Glass Transition Temperature of Polystyrene.

�Tg/Unit BABlowing Agent (°C/wt%)

HCFC 142bHFC 134aCO2

Pentane [34] �8.0�6.8�4.1�4.5

FIGURE 3.11 Shear response of a mixture of 7.5 wt% of HFC 134a with PS at 140°C, at differ-ent levels of pressures: (a) expressed in terms of shear stress versus shear rate; (b) same resultsgrouped on the basis of constant-stress measurements, as a function of the average pressure.


The stress-rate curve is shifted to the left as the pressure is increased insidethe measuring cell, which corresponds to the expected increase of viscositywith pressure. This variation is rather small but is still significant. Analyzed onthe basis of constant-stress measurements, as in Figure 3.11(b), results show asteady but constant decrease of the shear rate as the pressure is increased, forall stress levels. This behavior can be modeled through the variation of theglass transition temperature, Tg, with pressure [Equation (12)]. The coefficientfor the pressure dependency D3 was found to be a decreasing function of theblowing agent concentration, as displayed in Figure 3.12, with values rangingbetween for PS with no blowing agent to for PScontaining 15 wt% of HCFC 142b.

0.3 K � MPa�10.8 K � MPa�1

FIGURE 3.12 Coefficient for the pressure dependency, D3, as a function of the blowing agentconcentration, for PS/HCFC 142b mixture.


3.2.3.2.3 Vapor-Liquid Equilibrium

The solubility of a blowing agent into a given polymer is a function of thepressure and the temperature. Experiments conducted at a given temperatureshould be made above a critical pressure at which bubble nucleation occurs inorder to make measurements on a single-phase system.

The pressure conditions in the measuring cell, externally controlled throughthe use of a valve or a gear pump, affect the rheological response by modifyingthe amount of gas dissolved. This is illustrated in Figure 3.13 for a mixture of10% 134a with PS at 130.5°C. This figure exhibits an unusual response com-

FIGURE 3.13 Shear rate response with pressure at constant shear stress, for a mixture of PSwith 10 wt% of 134a at 130.5°C, undergoing phase separation.


pared to results shown in Figure 3.11(b). Viscosity is no longer increased bystepping up the pressure. On the contrary, it is reduced as the pressure is in-creased, and this translates into an increase of the apparent rate at constantstress level. This behavior can be explained by the extra amount of blowingagent dissolved with a further increase of the pressure that accordingly plasti-cizes the melt to a lower viscosity value. The plasticization behavior is pre-ponderant over that of the pressure dependency of the viscosity.

The plasticization behavior is illustrated in Figure 3.14 for mixtures of PSwith HFC 134a, at 180°C with a mean pressure inside the die of ,where the apparent decrease of the viscosity measured at a constant stress level

P � 10.8 MPa

FIGURE 3.14 Plasticization behavior of mixtures of PS with HFC 134a at 180°C and meanpressure of 10.8 MPa.


of is displayed. The decrease of the viscosity can be fittedthrough an exponential relationship with the blowing agent content. On thissemi-log plot, the linear trend can be extended to a certain critical composition,at which point the viscosity tends to level off. Under such temperature and pres-sure conditions, the maximum concentration of HFC 134a that can be dissolvedin PS was found to be approximately 7.6 wt%. Conducting experiments over awide composition range can thus provide information on the vapor-liquid equi-librium for a given combination of polymer and blowing agent under controlledprocessing conditions of pressure and temperature.

3.2.3.3 Case for Semicrystalline Polymers

The above proposed equations are not applicable to semicrystalline poly-mers, such as PE and PP, processed at temperatures well above .For example, the glass transition temperature of PP is .

A generalized modified Arrhenius-WLF equation has been successfullyused to fit the viscosity data obtained at different pressures and temperaturesfor various amorphous and semicrystalline polymers [35]:

(13)

in which A , B [K], and Tr [K] are constants. In the case ofamorphous polymers, the above equation may be rearranged under the classi-cal form of the WLF equation [Equation (4)]. For semicrystalline polymer, Tr

should be set to zero, and Equation (13) reduces to a classical Arrhenius form:

(14)

The viscosity is again related to the glass transition temperature, with pressureeffects also taken into account through the pressure coefficient D3. The knowl-

�0 � D�exp e E�

Ra1

T�

1

(Tg � D3P)bf

� [K � Pa�1][Pa � s]

�0 � A exp e B

T � Tr�

�P

T � Trf

�20°CTg � 100°C

�12 � 39.8 kPa

TABLE 3.4 Properties to Calculate Viscosity Dependence on Temperature for Semicrystalline Polymers [28, 36].

Polymer E� (kJ/mol) Tg (K)

Polyethylene (LDPE) 25 195Polypropylene 40 253


edge of the energy of activation, E�, is required, and selected values are listedin Table 3.4 for the two most frequently used thermoplastic semicrystallinepolymers in foam applications.

Using Equation (14) and applying a similar procedure to that described inSection 3.2.3.2, Tg values were calculated from the experimental data forsystems PP/HCFC 142b and PP/CO2. The results are reported in Figure 3.15.For similar blowing agents, the plasticization behavior expressed in term ofthe decrease of Tg is less drastic for PP when compared to the results obtainedfor PS, previously shown in Figure 3.9.

FIGURE 3.15 Glass transition temperatures for PP as a function of the blowing agent composi-tion for HCFC 142b and CO2.


The temperature of crystallization is a very important constraint for the pro-cessing of semicrystalline polymers. The presence of a blowing agent maylower the melting point. Figure 3.16 illustrates this fact through experimentalresults on LDPE with various physical blowing agents [25]. The magnitude ofthe depression of the crystallization temperature was reported to be a functionof the molecular weight of the blowing agent and its solubility. However, itcannot be anticipated from these results that the processing window of suchpolymers is greatly widened compared to the enormous changes encounteredwith amorphous polymers.

FIGURE 3.16 Lowering of the temperature of crystallization of LDPE due to the presence ofvarious blowing agents [25].


3.2.4 TWO-PHASE SYSTEMS: BUBBLE NUCLEATION AND FOAMING

3.2.4.1 Effect of Shear on the Cell Nucleation

The bubble point in vapor-liquid equilibria studies is a first-order equilib-rium transition. In theory, nucleation occurs at the point at which the pressuredrops to the thermodynamic vapor pressure. In practice, however, it has beenfound that supersaturation is not a sufficient condition for observing bubblenucleation. Bubble formation takes place more readily when a mixture ofpolymer and blowing agent is exposed to a shear field.

Experimental evidence of the influence of shear stress on the conditions ofbubble nucleation was given by Sahnoune et al. [37]. A nonintrusive ultrasonictechnique detected the onset of bubble formation for mixtures of PS andHCFC 142b. Bubble growth induces a strong increase in ultrasonic signal at-tenuation caused by the scattering of the ultrasonic wave. In-line experimentswere conducted on a flowing polymer submitted to shear. Off-line experimentswere conducted on a confined sample for which pressure and temperature werecontrolled. A comparison of flow conditions in Figure 3.17 at the same tem-perature shows that a shear-free field yields much lower degassing pressuresthan those obtained under given shear stress.

Using a light-scattering technique, Han and Han observed the same phe-nomenon for mixtures of PS with R-11 [38]. Bubble nucleation occurred in thecenter of a slit flow channel at a total normal stress level greater than the ther-modynamic equilibrium pressure. They have also observed that the onset ofbubble nucleation changed with the position in the direction perpendicular tothe flow direction and this can be explained by the velocity profile and stressdistributions in the slit channel. They suggested that the bubble nucleationmay be induced by flow, which would be the primary mechanism near thecenter of the flow, and by shear stress, for positions near the die wall.

Nucleation behavior was also investigated by Lee for mixtures of LDPEwith CFC 12 and CFC 114, using talc as nucleating agent [39, 40]. It was ob-served during experiments conducted at constant talc concentration that agreater number of cells were formed at higher levels of shear rates, as shownin Figure 3.18. It has been proposed that the presence of shear stress can helpto pull the gas phase out of the solid cavities provided by the nucleating agent.The shear force should act as a “catalyst” to lower the energy barrier betweenthe stable gas cavity and the unstable bubble phase. The capillary number, Ca,which is the ratio of shear force to surface tension force, is pivotal in charac-terizing the foam nucleation behavior. It is defined as follows:

(15)Ca � r2 � �� / 4 R �


with r the curvature of the interface between the gas and the polymer melt, �the viscosity of the polymer, the shear rate, R the cavity mouth radius and �the surface tension. It can be assumed that is required to initiate nucle-ation. Under given circumstances, for example, , the stress term givenby the product � would overcome the surface tension.

3.2.4.2 Shear Viscosity of the Foam Phase

Most of the literature that deals with the rheology of cellular materials isbased on aqueous foams made from surfactant solutions and air [41]. Studies

��Ca � 1

r � R

��

FIGURE 3.17 Comparison of the bubble nucleation process for flowing versus static mixturesof PS with 12.6 wt% of HCFC 142b at 135°C, measured using an ultrasonic technique [37]. Theflow condition shear stress was . Take note that the x-axis is reversed.�12 � 25 kPa


performed on cellular plastics, though scarcely mentioned in the literature, aremore within the scope of this work. It is, however, worthwhile to mention thatthe complexity of such studies on the viscosity of a cellular structure dependson the many factors that influence the flow behavior of the foams, includingratio of the bubble size to that of the channel, size distribution of the bubbles,bubble aspect ratio due to flow-induced anisotropy, pressure, and interactionbetween the wall and the fluid.

Fortunately, in order to achieve good quality foam of low density, processesbased on thermoplastics must be controlled so that bubble nucleation occurs

FIGURE 3.18 Cell count as a function of shear rate for mixture of LDPE/CFC-12 using a talccontent of 0.275 wt% [39].


close to the exit of the die, if not outside the die. This infers that the extrusionprocess, from the point where the physical blowing agent is dissolved withinthe molten polymer up to the die lips, sees only a single-phase polymer systemwhose rheology was covered in the previous sections.

The shear rheology of the two-phase cellular materials is thus of minor im-portance in most polymer applications. There are rheological properties moresignificant in the last process step of bubble growth and stabilization.

3.3 EXTENSIONAL RHEOLOGY FOR EXTRUSION FOAMING OF POLYMERS

3.3.1 DEFINITIONS

During the foam extrusion process, bubble growth takes place outside theforming die and involves extensional, or elongational, flow. Nucleation gener-ates a two-phase structure, where gas bubbles are surrounded by polymerwalls. As the bubbles grow during foaming, these walls are stretched. Thisstretching is similar to that which occurs during film blowing or blow molding.A common feature of these processes is that they are controlled by the exten-sional rheology.

This two-phase system implies that the polymer being stretched has lostsome of the blowing agent diluent, the gas now within the cells. Although thegas depletion process is time dependent, we may assume that the gas concen-tration within the polymer has rapidly dropped to zero. Thus, the extensionaldeformation is applied to the neat polymer. The extensional rheology thatshould concern us at this point during the bubble growth and cell stabilizationis, therefore, that of the pure polymer.

Even if extensional rheology has enjoyed increasing popularity over theyears, the amount of scientific literature still lies well behind that devoted toshear rheology. It is now recognized that this rheological behavior is the key tounderstanding and controlling processes such as film blowing and blowmolding. Most publications on this topic are, in fact, motivated by the require-ments of these major processes. The importance of the extensional rheology tofoam processing is, unfortunately, still not fully appreciated.

Three types of extensional flow are known: uniaxial, planar, and biaxial ex-tension. Even though biaxial stretching is the main mode of deformation inprocesses like film blowing and polymer foaming, the relatively few rheologi-cal studies presented in the literature have been primarily devoted to the uni-axial extensional viscosity, �E. The reason for that lies in the availability ofreliable techniques and the experimental difficulties associated with thesemethods.


Extensional rheology is analogous to shear rheology: a uniform rate of de-formation (strain rate for extensional deformation) is applied to the polymer,and a resulting stress (elongational stress �E) is measured. Definitions of thevarious parameters are summarized in Table 3.5.

Experiments have shown that when material is subjected to deformation at aconstant strain rate, the stress evolves with time [and thus, with strain; seeEquation (d) in Table 3.5] until either the specimen breaks or the stress reachesa steady-state value. This behavior, where the stress is a function of time,

, is known as “transient,” and it provides valuable information of thepolymer behavior. It is usually presented in the form of a “stress growth func-tion,” as illustrated in Figure 3.19 for LDPE. This information is of industrialrelevance, because in many processes, the polymer melt is exposed to exten-sional flow fields over a limited period of time. For these applications, the tran-sient elongational flow properties are more relevant than the steady-state be-havior.

Figure 3.19 shows that for LDPE at high extensional strains, the extensionalviscosity tends to increase well above the linear viscoelastic curve. This be-havior is known as “strain hardening” (SH), and it is associated with a rapid in-crease of the elongational viscosity at large strain. It can be quantitatively ex-pressed as the ratio of the measured value of the stress growth function to thatcalculated from viscoelastic principles [see Equation (f) in Table 3.5). SH isgenerally related to the inability of the macromolecules to disentangle quicklyenough to follow the exponential deformation. Long chain branching, as inLDPE or modified PP, is the molecular structure parameter that would explainthe occurrence of SH. Other sources of SH have been identified, such as poly-dispersity (or molecular weight distribution, MWD) and bimodality of themolecular weight distribution, with the presence of a high molecular weightpolymer (HMW) component. In this latter case, the presence of long times inthe relaxation spectrum may be part of the explanation for the observed in-crease in the transient extensional viscosity with time [42].

� � �(t)

�e

TABLE 3.5 Definitions for Uniaxial Extensional Rheometry.

Velocity of extensional deformation U (a)

Hencky rate of strain (b)

Elongational stress �E (c)Hencky strain (d)

Stress growth function (e)Strain hardening SH (f)Steady state, Trouton, viscosity �T (g)lim

�e→0 �T ( �e) � 3�0

SH(�e,t) � ��E,obs./�

�E, linear

��E (�e0,t) � ��

E (t)/ �e0��E

e � ln(L/L0) � �e t�E � F / A

�e �1L

dLdt

�UL

�e

U � �e L


The SH deviation from the linear-viscoelastic growth curve generallyoccurs at a given value of strain that is nearly independent of the extensionalstrain rate [43]. This implies that if SH should be part of the rheological be-havior to make a polymer foamable, then the stretching process associatedwith bubble growth must exceed that particular strain level. Also, the strainhardening effect is usually amplified as the strain rate is increased. Thus, forhigh enough extensional strain rates, the polymer melt may behave like a per-fectly elastic solid [43]. At low strain rates, SH tends to diminish and, accord-

�e

�e

FIGURE 3.19 Typical stress growth functions at 200°C for a branched polyethylene, LDPE.The strain rates are indicated. These measurements were performed on a Rheometrics ExtensionalRheometer, Model RER-9000.


ing to the Trouton rule [Equation (g) in Table 3.5], it should vanish at lowenough deformation rates.

The total amount of deformation experienced by the polymer melt duringfoaming may be approximated as a Hencky strain of 3 to 4. Also, the biaxialextensional flow that takes place during the bubble growth occurs over alimited period of time, typically only a few seconds, which yields strain ratesin the range of 1 to .

The magnitude of strain hardening has also been reported in terms of thetype of deformation. Uniaxial deformation yields the highest SH, while SH isbarely visible for biaxial stretching [44, 45, 46]. This observation, combinedwith the fact that polymer foaming is based on biaxial deformation, raises the following question: should the magnitude of SH be excessively large inuniaxial deformation to be significant in biaxial deformation in order to meetthe prerequisites for polymer foaming, or is the magnitude of the SH in uniaxial deformation a false indicator for polymer performance? In the lattercase, it has been suggested that the indicator be changed for some other rheological value, such as yield strain, and measured under biaxial defor-mation [46].

At low rates of elongation and long deformation times, the extensionalstress should reach a steady-state value. Under these conditions, the ex-tensional, “Trouton” viscosity �T is obtained that can be related to the Newtonian shear viscosity through a factor of 3 [see Equation (g) in Table 3.5]. Such relation between shear and extensional viscosity can also bestated in the two other types of deformation, namely for planar (�P) andbiaxial (�B) viscosities:

�p / �s � 4; �B / �s � 6 (16, 17)

“Melt strength” is a fashionable term in the foam business vocabulary. Themelt strength refers to the maximum tensile strength (stress at break) measuredduring the continuous drawing of an extrudate from a die. This index yieldsonly qualitative estimates of the extensional rheology, and it can be comparedon many aspects to its shear rheology counterpart, melt index (MI). Becausemelt strength is relatively easy to measure, it has often been used for qualitycontrol of resins used for film blowing or blow molding. Even though mea-surement of the melt strength may appear attractive because it is easy toperform and it implies large deformations and high strain rates, it also hasseveral drawbacks. The melt strength does not yield consistent quantitativeresults in terms of the extensional viscosity as stated previously, and it suffersfrom lack of uniformity for the temperature and the stress involved. Moreover,the viscous and elastic components are both compounded in the rate of strainand no information on the transitional behavior can be obtained.

lim�e, ��→0

lim�e, ��→0

5 s�1


3.3.2 METHODS AND RHEOMETERS

Contrary to the shear rheology that is well documented for a very broadrange of polymers, the extensional rheology has suffered from the complexityrequired in the experimental setup to generate valuable information for thistype of deformation under well-controlled conditions.

Since the extensional viscosity is defined as the ratio of stress �E and rate ofstrain , the experiments should be conducted with one of these variables heldconstant. In either case, the measured elongational viscosity depends on time,temperature, and the deformation rate. The constant stress method impliesshorter experimental times and is, therefore, more convenient to use forsteady-state measurements. The constant rate of strain method, however, pro-vides more information about the transitional behavior.

Very few commercially available instruments provide extensional viscositymeasurements. In the past, the Rheometrics Extensional Rheometer (RER,commercialized by Rheometric Scientific [47], and originally developed byMünstedt [48]) was based on experiments conducted through variation of the specimen length by separating the two ends of the specimen. Typically, a constant extensional strain rate was obtained by exponentially varying the velocity of the ends with time. The polymer sample was held in an oil bath and maintained at constant temperature. The Hencky strain was limitedto 3.1.

This instrument has been replaced recently by the Elongation Rheometer forMelts RME (developed by Meissner [49], and commercialized by RheometricScientific). It is based on the following approach: the constant gauge lengthrheometers draw the specimen between rotary clamps at fixed points in space,maintaining the specimen length but changing its volume. The rotary clampsrotate with constant angular velocity. The samples of rectangular cross section,prepared from compression-molded plaques, float on a cushion of inert gas.Hencky elongation of up to seven can be achieved.

The measurements of the extensional viscosity associated with convergentflow, often reported as the Cogswell method, can be easily obtained from rhe-ological capillary experiments [50, 51]. The Cogswell method extracts infor-mation related to the extensional viscosity from the Bagley correction, P0,usually computed to correct shear viscosity data obtained by capillary rheom-etry. This parameter can also be obtained from the pressure measurementsusing the so-called orifice flow . Thus, the elongational stress �E isrelated to the pressure drop in the orifice die P0, or to the Bagley correction,through:

(18)�E �3

8(n � 1) �P0

(L/D � 0)

�e


The strain rate is given by:

(19)

where n is the power-law slope of shear stress vs. shear rate in capillary flow,is the shear rate in a capillary of equivalent diameter, �12 is the shear stress

and � and �E, the shear and extensional viscosity, respectively.At higher rates of deformation (e.g., above ), this method was found to

be quite accurate. At lower strain rates, however, converging flow measure-ments tend to underestimate the steady-state response of the extensional vis-cosity because of the transient nature of stress growth and the uncontrollabletime scale of the convergent flow measurements. Improvements of this methodhave been achieved through the lubrication of the flow using a low viscosityfluid near the die wall and through the use of a hyperbolic-shaped die thatimposes a constant elongational strain rate [52].

Several other methods have been developed to measure extensional viscos-ity [53, 54], such as the bubble inflation rheometer in which the polymer isbiaxially deformed as a bubble through the displacement of hot silicone oil[55], and the lubricated squeeze flow method that is applicable to planar andbiaxial deformations. Such an instrument, developed by Macosko et al. [56],was commercialized as the Multifunction Axial Rheometer System, Mars III,by Polymics [57].

Many instruments that provide melt strength measurements are available onthe market. For example, most modern capillary rheometer manufacturersoffer melt strength measurement accessories. This test is often referred to as aRheotens experiment, named after the tensile testing apparatus developed byMeissner [43, 58, 59] and commercialized by Goettfert [60]. A typical testconsists of a continuous increase of the haul-off speed of the extrudate whilemonitoring the tension. At the breaking of the melt, the maximum values of therotation speed of the clamp and its force are linked to the extensibility andtensile strength (melt strength) of the polymer.

3.3.3 ELONGATIONAL RHEOLOGY OF POLYMERS

Even though reliable experimental methods have been developed, literatureis still scarce on rheological responses under extensional deformation. Severalattempts have been made to correlate molecular structure to elongational vis-cosity. On the other hand, information that explicitly links the elongationalviscosity behavior of polymers to their foamability is still in its infancy. Somekey elements, notably the strain hardening phenomenon observed mainly forbranched polymers and identified as a critical property for foamability, will bereviewed in the following pages.

1 s�1

��

�e �4�12

��

3(n � 1)�P0 or � �� 2�E �e

�e


3.3.3.1 Polyolefins

The initial growth of the bubbles initially requires a low viscosity. Subse-quently, a high extensional viscosity is advantageous such that the cell walls—the melt membranes between the bubbles—may withstand the stretching forceexperienced during the later stages of bubble growth. Linear polyolefins do notpossess such characteristics, and attempts to produce foams with these poly-mers generally yield cell collapsing. The resulting high open-cell content pre-vents their use in many applications.

Polyolefins that have long chain branchings (LCB), such as LDPE which ispreferred for polyolefin foams, behave differently. Their stress growth func-tions, illustrated in Figure 3.19, exhibit strain hardening that helps with the sta-bilization of the cellular structure. Comparison of the elongational responsesbetween polymers that yield opposite foam qualities, for example LDPEversus LLDPE (Figures 3.19 and 3.20, respectively), highlights the prerequi-sites for good foam production. A linear polyethylene such as LLDPE gener-ally does not show any SH behavior, which makes it a very poor candidate forfoam extrusion. This underlines the importance of the elongational viscosity infoam processing.

Synthesis technology applied to the production of LDPE makes it possibleto produce macromolecules with different chain structures. Tubular technol-ogy yields a “comb” type branching, while vessel or autoclave technologyleads to a more complex, “tree” type of structure for the side branching (seeFigure 3.21). More recently, the introduction of the metallocene technologyyields new pathways for the synthesis of macromolecules with precisely con-trolled composition, molecular weight distribution, and structure. Anotherexample is that linear resins such as LLDPE and HDPE, designed to show bi-modality in their MWD, exhibit elongational rheological behaviors that maybe suitable for foam applications [61].

The impact of the degree of branching on melt strength for LDPE hasreceived some attention [62, 63, 64, 65], and the results yield unambiguousconclusions: an increase in the LCB content translates directly into an increaseof the melt strength, with the molecular weight or the melt flow rate maintained constant. Typically, for resins having the same MI, the meltstrength will follow that order: linear HDPE or LLDPE �tubular LDPE(“comb” type) �vessel (“tree” type), as shown in Figure 3.22(a). Figure3.22(b) illustrates the unique relation between melt strength and maximumstretching ratio, irrespective of the structure of the polyethylene resin.

Linear polypropylene (PP) was known as a resin that was difficult to foam due to its narrow temperature processing window, the lower end con-trolled by the melting point of the polymer, and the upper bound linked to thelow viscosity that causes cell collapse [66]. This poor performance, whichmakes cell growth unstable during the foaming process, is linked to the


absence of strain hardening, as shown in Figure 3.23(a) for a conventionallinear PP.

Recent developments of resins applicable for foam processing put the em-phasis on the molecular structure prone to improve their melt strength with thesame shear viscosity or melt index. For example, at Montell, the developmentof a technology that induces long chain branching in polypropylene [66] was abreakthrough in the mid 1980s. As shown in Figure 3.23(b), the “High MeltStrength” PP (HMS-PP) has SH behavior, comparable to LDPE, shown in

FIGURE 3.20 Typical stress growth functions at 200°C for a linear polyethylene, LLDPE. Thestrain rates are indicated. These measurements were performed on a Rheometrics ExtensionalRheometer, Model RER-9000.


FIGURE 3.21 Schematic drawings of branching in macromolecules of LDPE produced by dif-ferent technologies: (top) tubular technology yields “comb” type of branching; (bottom) vesseltechnology yields “tree” type of branching.

Figure 3.19. Another example can be given for a polypropylene-polystyrenegraft copolymer that has been developed by melt reaction, to overcome theweakness of the strain hardening of the linear polypropylene [67]. The graftcopolymer showed SH and high foamability, with density reduction factor ashigh as 30. Increasing the melt strength then became the name of the game,and innovative resins dedicated for foam applications are more likely to maketheir emergence on the market. Such resin developments have been presentedfor HDPE [68] and PET [69, 70, 71].

Blending of polymers is another method of incorporating SH effects into theextensional rheological behavior. Studies on LLDPE/LDPE blends haveshown that these immiscible blends can yield systems having an intermediatemelt index (which can be related to the shear flow behavior), and synergisti-cally higher melt strength (which should be derived from higher strain harden-ing responses) than predicted from the additivity rule. In contrast withbranched/linear PE blends, the blends of either linear/linear or branched/branched PE type did not show the same effects. For melt strength synergism,


FIGURE 3.22 (a) Melt strength as a function of melt index, for polyethylenes having differentdegrees of long chain branching: linear PE (HDPE, LLDPE), LDPE by tubular technology(“comb” type), and LDPE by vessel technology (“tree” type) [65]. (b) Melt strength as a functionof the maximum stretch ratio; all polyethylenes (HDPE, LDPE, LLDPE) are confounded into thesame relationship [63].

FIGURE 3.23 Typical stress growth functions at 180°C for different polypropylenes: (a) con-ventional linear PP and (b) Montell high-melt-strength (branched) PP, HMS-PF-814. The strainrates are indicated. These measurements were performed on a Rheometrics Extensional Rheome-ter, Model RER-9000.


a mixture of linear and branched species of similar molecular weights maytherefore be required [72].

A similar study on LLDPE/LDPE blends, whose objective was to proposenew and easier-to-process blend formulations for the film blowing process, hasshown that addition of as little as 2 wt% of LDPE to LLDPE already generatedsome SH and improvement of the bubble stability during film blowing [73, 74].

3.3.3.2 Polystyrene

Strain hardening is commonly observed for PS, although it disappears atlow strain rates [44]. By contrast, branched polyolefins show SH regardless ofthe strain rate. This suggests that different mechanisms of entanglement are re-sponsible for SH in these two polymers. In LDPE, it originates from physicalentanglement of macromolecules (enhanced by their side branching), while inPS, it comes from the interactions between the aromatic rings.

The relation between the Trouton viscosity �T and the zero-shear viscosity�0 holds in both uniaxial and biaxial deformation for polystyrene melts [44].Since it is well known that �0 can be correlated to the molecular weight, thesame type of relationship was consequently found for �T [75, 76]. The time-temperature superposition was found applicable despite the nonlinear elonga-tional flow properties of polystyrene; it was not clear, however, to what extentthe temperature dependence was still valid over the entire range of strain [77].

Presence of a high molecular weight component in a bimodal MWD hasbeen reported to increase the strain hardening behavior, with HMW fraction aslow as 0.8 wt% [42]. For bimodal MWD resin, the rheological responsemimics that of branched polyolefins in terms of the SH behavior. It was con-cluded that the existence of relaxation times above 1,000 s, provided by theHMW fraction, should govern the SH in uniaxial elongational flow [42].Bimodal MWD or broadening the MWD should then be beneficial for increas-ing the SH behavior.

Contrary to the case of polyolefins, where SH was found essential for theirfoamability, the role of strain hardening has not yet been clearly defined forPS. Polystyrene resins are easy-to-foam materials. Their processability may beexplained in terms of the high degree of plasticization due to the presence ofthe blowing agent, and their high energy of activation, which should contributeto the rapid solidification of the polymer matrix and, therefore, to the cell sta-bilization.

3.3.4 ELONGATIONAL RHEOLOGY OF BLOWING AGENT-CHARGED POLYMERIC SYSTEMS

Before closing this section on extensional rheology, it should be pointed outthat this type of flow prevails within the forming die, where the polymer/

��


blowing agent mixture still exists under a single-phase system. The pressuredrop experienced by the polymeric mixture near the die exit has two contribu-tions, shear and extensional. The shear rheology of a blowing agent-chargedpolymeric system was extensively covered in the first part of this chapter.Several experimental setup concerns were also underlined. It has also been re-ported that measurement of the extensional viscosity is rather complex and isassociated with several experimental difficulties. For these reasons, practicallyno study of polymer/physical blowing agent mixtures under extensional defor-mation has been reported. One exception is the experiment conducted usingthe extrudate haul-off measurement method on a mixture of LDPE and physi-cal blowing agent (11 wt% isopentane) [78, 79]. The results indicated a reduc-tion of over 75% in the extensional viscosity, accompanied with a twofold in-crease in the stretch ratio at break.

In general, it might be expected that the plasticizing effect observed forshear rheology should also be encountered in extensional rheology, on thebasis of their relationship in the linear viscoelatic domain (Trouton rule).However, it is not clear if this translation from shear to extensional still pre-vails for deviations from linear behavior, such as the strain hardening effect.More studies would be required to elucidate this aspect.

3.4 CONCLUSION

The main rheological characteristic of single-phase mixtures of polymersand blowing agents is the plasticization phenomenon. It is quantified mostlyby the lowering of the Tg that is well documented for amorphous polymers.

Predictions of semicrystalline polymer/blowing agent mixture viscositiesare also calculable above Tm. The degree of plasticization is, however, less sig-nificant than that of amorphous polymers.

The need for understanding the rheological behavior of broader ranges andtypes of polymers and blowing agents can only be filled by a wider prolifera-tion of viscosity measuring apparatuses such as the pressurized rheometers inpresent use.

We need not close the door on new model developments such as those basedon free volume theory. These may provide a further link between measurablemacroscopic properties such as viscosity or solubility and inherent micro-scopic phenomena such as molecular packing.

Insofar as rheology is only one of many variables influencing the foamingprocess beyond the single-phase portion, two-phase systems discussed in thischapter dealt mostly with bubble nucleation and cell stabilization. Experimen-tal evidence shows that a shear field enhances nucleation. Work is still underway to quantify this observation.

In the bubble growth and stabilization regime, low viscosity for bubble nu-cleation but increasing elongational viscosities during cell formation are desir-


able traits of foaming resins. The elongational viscosity, especially its nonlin-ear response at high strain, has been identified as one of the critical propertiesthat semicrystalline polymers should possess to be foamable. The extensionalviscosity behavior, through this strain hardening effect, appeared to be moresensitive to high molecular weight components than the shear viscosity.

The goal that follows is to increase our understanding of the phenomenonand its incidence on the morphology of the foam, that is, the cell size anddensity. This will lead to better modeling, allowing the tailoring of polymerelongational viscosities to optimize the foam density and morphology.However, it must be pointed out that extensional flow is only part of thecomplex process. The final strategy must encompass the other elements, viz.,solubility of the foaming agent, shear flow behavior inside the extruder, nucle-ation, shaping and cooling, etc. Unfortunately, there is still informationmissing on several aspects of the foaming process that prevent direct incorpo-ration of the extensional flow measurements into a process model.

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CHAPTER 4

Foam Nucleation in Gas-Dispersed Polymeric Systems

SHAU-TARNG LEE

4.1 INTRODUCTION

NEW phase formation is a common physical and/or chemical phenomenaand includes actions such as boiling, foaming, solidification, decomposi-

tion, etc. [1–3]. It is a key element in quite a few phase separation processes,for instance, evaporation, crystallization, devolatilization [4], and foam extru-sion [5,6]. Focusing on physical phenomena, new phase formation, alsoknown as nucleation, can originate from self-structural adjustment or fromforeign “seeds” as a way to release an outside change-induced load. Its unsta-ble nature easily lends itself to unstable phase separation. Foaming basicallyinvolves bubble nucleation and bubble growth (phase separation) to make afoamed product that can be defined as visible gas cells dispersed in a densercontinuum matrix.

Foaming can occur with denser medium in a dynamic state or a static state,ranging from boiling to wave foaming to plastic foam. Bubble formation canbe caused by a variety of sources including heat, vacuum, motion, reaction,and cavitation. Table 4.1 lists the common phenomena and possible mecha-nisms. Boiling is a common phenomenon in which micro vapor bubbles inliquid are formed through a homogeneous and/or heterogeneous mechanism.In principle, gas molecules disperse in the liquid phase and become energeticenough to overcome surrounding confinement to expand into a visible size.Superheat is a typical example, in which the vapor pressure exceeds theambient pressure to a point where bubble formation becomes the effective wayto minimize the chemical potential difference. Crystallization is another well-known subject; under supersaturation, a tiny nucleus forms and expands insize to join with a nearby developing nucleus to cause phase transformation.


Both phenomena are induced by energy variation, yet kinetics are greatly af-fected by heterogeneity. Similarly, a pressure-induced superheat, often in aliquid/gas or melt/gas system, requires an expanded view on energy sources.To be precise, a clean and smooth surface simply provides surface energy toreduce the foaming superheat threshold. As for a porous surface, it not onlyoffers surface energy but also provides residence for gas molecules in the cav-ities. The former is heterogeneous nucleation, and the latter is cavitation. Bothwill be further discussed from the thermoplastic foam extrusion perspective in

TABLE 4.1 Phase Separation Phenomena and Its Mechanisms.

Phenomena Mechanisms

Boiling HeatPlastic Foaming Heat and/or Reaction or Pressure ReductionCavitation Pressure VariationDevolatilization Vacuum, Inert Gas SeedingWave Foaming Hydrodynamic Pressure

FIGURE 4.1 Schematics of various gas bubble formations; homogeneous, heterogeneous, andcavitation.


the following sections. Figure 4.1 presents a schematic drawing to differentiatehomogeneous, heterogeneous, and cavitation nucleation.

It should be pointed out that there is a difference between nucleation and nu-cleation rate. The former is a thermodynamic phenomenon focusing on thefirst bubble formation, and the latter is a kinetic mechanism indicating thespeed of the bubble formation. If a sharp thermodynamic instability can be im-plemented to make impulse nucleation, a swarm of bubbles will come into ex-istence within a very brief period. Nucleation, #/cm3, and nucleation rate,#/cm3/s, are, therefore, very similar in quantity. A sharp pressure drop is a verycommon practice in foam extrusion in making multibirths out of one nucleat-ing site unlikely.

Although quality foam products can be routinely and consistently produced,how the invisible gas clusters get together to overcome the surroundingtension to evolve into visible bubbles remains unsettled inmany aspects [7]. It is conceivable to start this chapter with equilibrium con-siderations, then proceed to conventional nucleation theories, and concludewith modifications made when applied to actual foaming processes. We willthen cover flow- and thermal-induced cavitation from thermo- and hydrody-namic viewpoints. This chapter ends with applications to thermoplastic foamextrusion.

4.2 EQUILIBRIUM CONSIDERATIONS

The gas solubility in liquid has been addressed by splitting the solutionenergy and entropy into two parts: the formation of cavities and the diffusionof the gas molecules into them [8]. The activity of the gas cavity depends onthe nature of the gas/liquid system and the surrounding temperature and pres-sure. An equilibrium state is established when the gas diffusion rates, in andout of the cavity, are equal.

When gas dissolves in a polymeric melt, a vapor pressure is established. Ac-cording to the Flory-Huggins equation:

(1)

where a is activity, defined as the partial pressure over the vapor pressure, p/Po,and � is the interaction parameter. Assuming a dominant polymer phase, Equa-tion (1) becomes:

(2)

and Henry’s law constant, Kw, can be expressed as follows:

(3)Kw � p/Wg � �p/�g Po exp(1 � �)

p/Po � Vs exp(1 � �)

ln(a) � ln(Vg) � Vp � � Vp2

(i.e., � 0.1 mm)


where W and � represent the weight fraction and density, respectively. Table 4.2[4, 7, 9–12] lists several common gas/polymer Henry’s law constants. The tem-perature dependence of Henry’s law constant can be presented as follows [13]:

(4)

where �Hs represents the heat of solution, R represents the gas constant, andsubscript o is the reference state. By knowing the equilibrium constants at twodifferent temperatures, the constants of Equation (4) can be determined inorder to calculate the Henry’s law constant at other temperatures.

In foam extrusion, the loading of the blowing agent can be calculated via de-composition or preset injection. In general, foam extrusion in nature has asharp pressure release at the die end, that, from the processing viewpoint, iscontinuous foaming; however, from the nucleation perspective, it is a typicalone-point (impulse) nucleation that is confirmed by uniform cell structure inextruded foam products. In other words, as mentioned earlier, nucleation rate(#/cm3/sec.) and total nucleation (#/cm3) are interchangeable for foam extru-sion with a sharp pressure drop at the die tip, assuming nucleation is completedin fraction of second.

At a given die flow geometry, with known Kw and Wg, one can easily figureout the vapor pressure to determine the pressure ratio (PR) that is defined asfollows:

(5)

Referring to Figure 4.2, as PR is greater than one, the bubble nucleus tends toexpand into visible foams. When PR is equal to one, it is a good referencepoint for nucleation. A general guideline in die design is to keep the nucleationpoint as close to the die end as possible to not only prevent premature foaming,

PR � Vapor Pressure / Die Flow Pressure

Kw � Kwo exp(�Hs/R(1/To � 1/T))

TABLE 4.2 Selected Henry’s Law Constants at 177°C.

System Kw, atm Reference

Polystyrene/Styrene 30 Werner, 1981 [9]50 Biesenberger and Todd, 1983 [4]

LDPE/I-butane 280 Chaudhary and Johns, 1998 @ 160°C [10]LDPE/CHCIF2 595 Durill and Griskey, 1966 [11]

600 Lee, 1996 [7]LDPE/CC12F2 118 Gorski et al., 1983 [12]LDPE/C2H3CIF2 190 Lee, 1996 [7]LDPE/C2H4F2 504 Lee, 1996 @ 187.8°C [7]PMMA/MMA 85 Werner, 1981 [9]HDPE/Hexane 115 Biesenberger and Todd, 1983 [4]


but also to allow optimal free expansion. However, when tiny gas bubblesform inside the die, due to its high pressure nature, the die design becomes ex-tremely critical in allowing controlled expansion without disrupting flow in-tegrity prior to exit. It is also noted that the overall die pressure can help cal-culate pressure-induced slippery flow in the extruder to determine its netpumping capacity. Although extrusion is a dynamic state and surrounding con-ditions are not constant, equilibrium considerations, at least, allow us to estab-lish a general idea of nucleation that can easily extend into real design.

It is essential to view the dynamic nucleation process from the equilibriumviewpoint. Considering a static state, mechanical equilibrium can be written asfollows:

(6)

P represents external pressure, and � and Rb represent surface tension andbubble radius, respectively. The critical radius can be calculated while reduc-ing P to generate superheat. Knowing the number of cells in a unit volumeformed, Nb/V, a mass balance equation, or chemical equilibrium, can easily beestablished:

(7)Pce � Po � 4/3� Rbcr3 (Nb/V) Pb Kw

Pme � P � 2�/Rb

FIGURE 4.2 Pressure profiles in parallel and tapered plates’ gas/melt flow with temperatures asan ordinate. The dotted line represents vapor pressure, and PR � Flow Pressure/Vapor Pressure.


where, , and R and T denote ideal gas law constant and tem-perature, respectively. Subscript o represents initial state. In equilibrium

, we obtain a radius quadratic equation:

(8)

in which, , and P is the surrounding pressure. It waspointed out [14, 15] that a perturbation is needed to make unstable growth pos-

X � (Nb/V)4/3�Kw

Rbcr4 XP � Rbcr

3 X2� � Rbcr (Po � P) � 2� � 0

Pb � Pme � Pce

Kw � Kw/RT

FIGURE 4.3 Computational results of critical bubble radius for 4,880 ppm styrene in poly-styrene under 5 mmHg. represents a small perturbation to move equilibrium from unstable A tostable B.


sible, as illustrated in Figure 4.3. Shafi and Flumerfelt [16] proposed a Taylorexpansion based on the Peclect number to figure out perturbation quantity.Since foam extrusion involves dynamic variables to make automatic perturba-tions, bubble growth appears to be a natural consequence. However, viewingthe stable equilibrium radius, the corresponding volume expansion becomesunrealistic. That means spherical shape and equal bubble volume, common as-sumptions for bubble growth, cannot coexist. In fact, with respect to packingtheory, 75% gas void, approximately three times expansion, is the limit for theaforementioned assumptions, over which contact with neighboring bubble andsubsequent distortion become inevitable. In any event, this dynamic processinvolves other real parameters, such as bubble interaction and diffusion loss, tomake it impossible for the stable bubble radius to exist. Also noted in the equi-librium equation is the critical role played by bubble number density, Nb/V,which is as important in foam nucleation and growth.

4.3 CONVENTIONAL NUCLEATION THEORIES

When variation of internal or external conditions occurs, the system itselfautomatically starts to adjust to the “disturbances.” Sometimes it simplyreestablishes a stable state. Other times, a sharp change is necessary, such asbubbling. Since gas molecules tend to adjust themselves faster than liquidmolecules, foaming becomes a way to alleviate the thermodynamic “load.”This thermodynamic phenomenon is demonstrated in Figure 4.4, the pressure-volume diagram. It shows that enough superheat is needed to make phasechange possible, as indicated, from a stable state to an unstable state. Atmodest superheat, metastable state appears. Cahn [17] postulates a wave func-tion to describe “new phase” molecule distribution, when the wavelength in-creases to a point where a new phase automatically appears. Nucleation itselfappears to be a “process” rather than a “point.” In quenching and crystalliza-tion [18], lengthy phase separation appears to correlate well with the spinodaldecomposition concept. Moreover, Keller [19] noted in the polyethylene mor-phology experiments that two crystallization mechanisms, stable chain foldinggrowth and metastable spontaneous thickening growth, compete with eachother depending upon the temperature drop rate. In a relatively brief bubblingprocess, impulse nucleation, thermodynamics, and kinetics in a metastablestate are not separable. Here, we would like to proceed with the conventionalnucleation theories, followed by modifications and cavitation, and ending withextrusion nucleation.

4.3.1 HOMOGENEOUS NUCLEATION

In the classical theory of nucleation, the nucleation rate is governed by therate at which invisible gas clusters are energized by effective diffusion as a


result of supersaturation to exceed the critical radius [1, 20–22]. According toGibbs [2], a gas cluster containing n molecules can be expressed as follows:

(9)

where W(n) is the minimum work to sustain a bubble, N is the number of mol-ecules per unit volume of the metastable state, and k and T are the Boltzmannconstant and absolute temperature, respectively. By multiplying a frequencyfactor, B, the rate of nucleation can be expressed as follows:

(10)J � B N exp (�W(n)/kT)

C (n) � N exp(�W(n)/kT)

FIGURE 4.4 Phase diagram: bimodal and spinodal. The shaded areas represent a metastableregion.


In the metastable region, the total work includes surface area generation, sizeexpansion, and evaporation.

(11)

where �, A, V, P, and �, denote the surface tension, bubble surface area,volume, pressure, and gas molecules’ chemical potential, respectively. Thesubscripts l and g represent liquid and gas, respectively. Assuming it is in aspherical shape, Figure 4.5 illustrates that a minimum work must be obtainedto make size expansion irreversible. It corresponds to the critical bubble size.However, under critical size, it is hardly possible to get sufficient work to resistthe surrounding surface tension force that in theory, can compress the gascluster out of existence. If the cluster can be sustained in a nonspherical shape(i.e., string), where the surface tension force is not at a maximum, the clustercould survive.

At equilibrium, the chemical potentials, �g and �l, are equal, and Wbecomes:

(12)

for the critical condition, or considering the Laplace equation formechanical equilibrium, one obtains:

(13)

Minimum work becomes the following:

(14)

Blander and Katz [3] obtained the following equation for the rate of nucle-ation:

(15)

where m represents the mass of a gas molecule. In polymer processing, it isreasonable to assume Pl equal to P, representing the surrounding pressurewhile the gas/melt resides in the barrel. Then, the difference between Pb and Pbecomes superheat.

(16)

At a slight superheat (i.e., Pb barely over P), diffusion is able to reestablishequilibrium before reaching the corresponding Rbcr; in other words, the nucle-

SH � Pb � P

J � N (2�/(�m))1/2 exp (�16��3/(3kT(Pb � Pl)2)

Wmin � 16��3/(3(Pg � Pl)2)

Rbcr � 2�/(Pg � Pl)

�W/�r � 0

W � 4�r2� � (4/3) �r3(Pg � Pb)

W � �A � (Pg � Pl) Vb � n (�g � �l)


ation rate becomes negligible. Equation (16) suggests at least two ways toinduce enough thermodynamic instability for nucleation, pressure release, andtemperature increase. Since thermoplastic polymer is a poor thermal conductorand will decompose at a high temperature, the former appears favorable.

Knowing Kw and Wg, we are also able to calculate SH and then the nucle-ation rate. As indicated in Table 4.3, a modest superheat is not sufficient tobring forth gas bubble formation. It is noted in Figure 4.6 by Tadmor et al. [23]that nucleation shows too strong a sensitivity toward temperature increase to

FIGURE 4.5 Works for bubble expansion from Vo to pass Vc for continual expansion.


(Reprinted with permission from Lee, Polym. Eng. Sci., 33, 1993.)1Henry’s law constant [7].2Reference [3].3 .J � A exp(2B)

TABLE 4.3 Homogeneous Nucleation Rate Calculation; LDPE/CFC-12.

Temp. Temp. Kw1 �P � �2 J3

(°c) (°k) (atm) (atm) (g/ml) (erg/cm2) B

60 333 64.6 12.9 0.91 5.12 7.07 286 070 343 68 13.6 0.91 4.0 6.25 119 080 353 78 14.6 0.91 2.9 5.32 38.2

100 373 102 19.4 0.91 0.7 2.61 0.3100 373 126 12.6 0.91 0.7 2.61 0.69100 373 136 1.1 0.91 0.7 2.61 90 0120 393 109 20.8 0.905 — — — —

1.31 10321.95 10321.4 1016

(#/ml � s)(#/ml � s)A 1032


realistically correlate with actual foaming. SH can be established by dissolvinggas in the polymer and then applying pressure drop or temperature rise. Nor-mally, SH can be precisely controlled in a batch process.

Since polymer always contains residual catalyst or unreacted monomers orcontaminants, from the thermodynamic perspective, it is hardly possible tojustify homogeneous nucleation in polymeric melt foaming. However, whenthe pressure gradient and the surface tension dominate, it is not surprising tofind good agreement with homogeneous predictions. Table 4.4 presents PS/N2

nucleation results that suggest that SH is a viable homogeneous nucleation pa-rameter.

The homogeneous equation was tested by batch microcellular experimentsduring which an inert-gas-saturated amorphous polymer was exposed to a

FIGURE 4.6 Nucleation rate calculations vs. foaming temperature for 5,000 ppm styrene inpolystyrene under 10 mmGg and 760 mmHg, respectively. (Plot based on results given by Tadmoret al. in their presentation at the first PPS at Akron, 1985 [22].)


lower pressure and a higher temperature (above Tg) to induce fine cell forma-tion. Figure 4.7 presents the comparison. It is not surprising to find orders ofmagnitude difference from predictions. First, an amorphous polymer canhardly be structurally characterized by the homogeneous approach. Second,pressure reduction and temperature increase generally happened simultane-ously in actual processing and affected gas activity and polymer chain mobil-ity effects. The thermodynamic-based model especially cannot cover the latter.Modification becomes necessary to improve agreement with batch foamingexperimental results [24].

(Data collected with permission from Kumar and Suh, Polym. Eng. Sci. 30, 1990.)

TABLE 4.4 Superheat Effects on Nucleation for PS/N2.

Saturation Pressure Foaming Pressure Superheat Cell DensityMpa Mpa Mpa #/cm3

4.0 0.1 3.9 107

7.0 0.1 6.9 2 107

10.5 0.1 10.4 8 107

14.0 0.1 13.9 8 108

FIGURE 4.7 Homogeneous nucleation comparison between theory and experiment; cell densityvs. external pressure for PS/N2. (Replot from V. Kumar’s Ph.D. Dissertation, MIT, 1998 [23].)


4.3.2 MODIFIED NUCLEATION THEORIES

In the conventional nucleation theories, the rate of nucleation is governedby the rate of diffusion (or vaporization) of gas molecules from the surround-ing liquid through the interphase. For general liquids, Kagan [25], in 1960, in-cluded the hydrodynamic and heat transfer effects for vaporization to obtainthe corrected formula:

(17)

Blander and Katz [3] and Blander [26] developed a similar correction toaccount for diffusion and viscosity-controlled nucleation rate:

(18)

(19)

Ruengphrathuengsuka [27] developed a general nucleation expression for anon-Newtonian fluid, including the hydrodynamic, heat, diffusion, andviscous effects.

(20)

in which . The parameters, �g, �g, and Mg represent the gasdensity, gas chemical potential in liquid phase, and gas molecular weight, re-spectively. The surface tension and the cluster pressure (or bubble pressure),Pb, appear to show strong influences on the nucleation rate calculation. Withrespect to a higher saturation pressure, the cluster pressure becomes higher; inother words, a higher solubility is obtained. Moreover, as suggested in Figure4.8, a higher pressure tends to lower the gas/melt surface tension that was obtained through Wihelmy technique (net force divided by contact area) byRuengphrathuengsuka [27]. Figure 4.9 shows a higher cell density at increasedsaturation pressure or foaming temperature, and the temperature has a similarimpact in the batch design LDPE/nitrogen experiments. Similar results werereported by microcellular HIPS/CO2 extrusion experiments by Park et al. [28].At increased temperature, the solubility becomes lower, and this helps nucle-ation by leaving less residual gas in the polymer. Combined with highervolatility, a higher diffusion coefficient, and lower surface tension, it is notsurprising to find the temperature increase a primary parameter for foaming.Nucleation density could affect thin foam sheet density. As pointed out by Leeand Ramesh [29], the foaming efficiency, defined as the actual foam density

Y � �g�g�l/Mg

exp(�16��3/(3kT((Pb � Pl)2 � Y))

J � N/(1 � �D � ��)(2�/�/m(1 � YRbcr/�))1/2

J� � N�/�(�/kT)1/2(Pb/(Pb � Pl)) exp(�16��3/(3kT(Pb � Pl)2)

JD � ND(Cb � Cl)(kT/�)1/2 exp(�16��3/(3kT (Pb � Pl)2)

J � N�/�(�/(kT))1/2(1 � Pl/Pb) exp (�16��3/(3kT(Pb � Pl)2)


over the theoretical density, becomes higher at a higher saturation pressure ora higher cell density because gas loss from the sheet is reduced.

Unlike semicrystalline LDPE, Goel and Beckman [30] experimented amor-phous polymethylmethacrylate (PMMA) with carbon dioxide, in which a lesssensitive thermal dependency of cell density was observed. At increased tem-peratures, the reduced surface tension and solubility are obvious factors formore nucleation. However, increased diffusion can cause significant surfaceevaporation when the surface-to-volume ratio is high, for example, thin sheet.In PET microcellular experiments, Baldwin et al. [31] noted that the skin hasless cell density than the center, and when foaming temperature was above100°C, thermal dependency became insensitive. Kumar et al.’s PVC foam ex-periments employed 2 mm thick sheet rather than 0.4 mm [32]; the tempera-

FIGURE 4.8 Surface tension variation vs. saturation pressure for LDPE/N2. (Reprint from Ruengphrathuengsuka’s Ph.D. Dissertation, Texas A&M, 1992 [26].)


ture showed a greater impact as illustrated in Figure 4.10. Temperature appearsto draw different, and sometimes, competing mechanisms into the nucleationphenomena. Considering semicrystalline polymer, the temperature effects oncrystallinity formation make it a critical nucleation parameter. A brief thermalcause and effect summary is presented in Table 4.5.

In the polystyrene/toluene nucleation analysis, Han and Han [33] proposedthe free energy change:

(21)

where �F represents the free energy change required for single-componentphase transformation, and subscripts s and t represent supersaturation andpolymer-solvent interaction. Considering an empirical equation for the fre-

�Fp � �F � �Fs � �Ft

FIGURE 4.9 Pressure and temperature effects on LDPE/N2 nucleation. (Replot from Rueng-phrathuengsuka’s Ph.D. Dissertation, Texas A&M, 1992 [26].)


quency factor, the semiempirical nucleation rate for polystyrene and toluene isproposed as follows:

(22)

where D represents the diffusion coefficient. With viscosity and surfacetension dependent on the temperature and the diffusion coefficient dependent

J � 4.71 1034MD/(4�Rbcr)exp(�(42,344/T � �Fp/(nkT))

*Enhance bubble growth.

TABLE 4.5 Foaming Temperature Effects on Nucleation.

High Temperature Nucleation

Surface Tension Decrease IncreaseShear Viscosity Decrease *DecreaseElastic Viscosity Decrease No EffectCritical Superheat, SHc Decrease IncreaseDiffusion Increase No EffectSolubility Decrease IncreaseVolatility Higher More

FIGURE 4.10 Cell density vs. foaming temperature for PVC/CO2 nucleation. (Plot based ondata from V. Kumar et al., ANTEC, 1992 [31].)


on the free volume and temperature, J was calculated, and its comparison withexperimental results is shown in Table 4.6 [33]. Although a reasonably goodagreement was observed, Han and Han claimed a more satisfactory model todescribe pre-nucleation pockets and a model for coalescence is still needed.

Patel et al. [34] used small-angle X-ray analysis to detect the nitrogen solu-bility in LDPE melt by correlating cluster distribution to report a good agree-ment with Henry’s law constant. In hydrocarbon homogeneous nucleation,Kwak et al. [35, 36] postulated cluster formation in the supersaturated stateand investigated its stability by assuming face center packing and constant dis-persion force. Either one needs justification for concentrated polymer. Furtherinsight on cluster formation and transformation into a critical pocket will beextremely important in comprehending the complex nucleation dynamics.

Instead of using the Sugden expression for the surface tension [33] or theEotvos expression [23], Ruengphrathuengsuka [27] performed experiments toinvestigate its variation with temperature and pressure for the LDPE/nitrogensystem as presented in Figure 4.11, in which the surface tension decreasedover 50% after loading with a gas blowing agent. Shafi et al. [37] presented an“influence” volume approach to account for growth-induced gas diffusion inthe rate nucleation process, in which nucleation continued until all melt wasinfluenced to a point below the prescribed threshold. The modified homoge-neous nucleation equation is as follows:

(23)

Where, I, �, and Z denote elasticity number, activity coefficient of dissolvedgas, and compressibility factor of gas in the melt, respectively. Further experi-ments are necessary to verify the postulation. Because gas molecule is in therange of Angstrom, thousands of gas molecules without compression are re-quired to make up a micro-sized hole. Fast diffusion into a gas pocket or acombination of gas pockets at a pressure drop are plausible routes for homo-

J � N(2�/�mB)1/2exp(�16��3/(3kT(Pb � Pl � I � Pbln/Z)2)

(Reprinted with permission from Han and Han, J. Polym. Sci. B: Polym. Phys., 1990.)

TABLE 4.6 Nucleation Comparison for PS/Toluene; Experiments and Predictions.

Concentration Temperature of polystyrene (number/m3) (number/m3)

(°C) (wt%) (Experimental) (Theoretical)

150 60 17.33 40.00150 50 4.374 16.76150 40 1.481 2.531170 50 7.480 16.76180 50 12.29 14.05

N 10�19N 10�15


geneous nucleation and more and precise experiments are necessary for thegas/melt system.

In polymer/gas batch foaming, the discrepancies between prediction and ex-perimental results still exist. In fact, material impurities (residual catalyst, un-reacted monomers, dusts, etc.) and machinery contact in foam extrusion makeheterogeneous nucleation a more realistic mechanism to consider.

4.3.3 HETEROGENEOUS NUCLEATION

Heterogeneous nucleation accounts for the surface energy when nucleationoccurs at the interface of a liquid and a clean surface. Its interfacial phenomenais depicted in Figure 4.12, and Blander and Katz [3] proposed its work asfollows:

(24)W � �lgAlg � (�sg � �sl)Asg � �P Vb � n(�g � �l)

FIGURE 4.11 Surface tension variation vs. temperature for LDPE and LDPE/N2. (Reprint fromRuengphrathuengsuka’s Ph.D. Dissertation, Texas A&M, 1992 [26].)


Subscripts lg, sg, and sl represent liquid-gas, solid-gas, and solid-liquid inter-phases, respectively. Because of the presence of solid surface, a chemicalequilibrium between gas and melt is not useful for bubble formation. Consid-ering the interfacial contact, the nucleation rate J is obtained as follows:

(25)

where F, the geometry factor, is defined as . Compu-tational results of PS/S are tabulated in Table 4.7, in which differences fromreality are hardly justifiable. Attaim [38] noted the presence of a critical upperlimit determined by thermodynamic parameters and greatly affected by kineticfactors. Modification became necessary to improve agreement with experi-mental observations.

In addition to the chemical potential, the surface energy and deformationenergy [39], Colton and Suh [40] proposed to correct chemical potential bysubtracting L-J energy to describe Polystyrene/Zinc stearate and carbondioxide nucleation. As indicated in Figure 4.13, orders of magnitudes differ-ence from experimental results are difficult to justify. Colton [41] applied thelinear mixing rule to calculate the surface tension of semicrystallinepolypropylene for a mixed-mode nucleation. Nucleated polypropylene andcopolymer had better agreement with experimental data than non-nucleatedand talc-filled polypropylene.

Ramesh et al. [42] reported a better cell density correlation by adding rubberparticles in the amorphous polymer and in polystyrene, and they postulatedthat preexisting cavities are the main sources for nucleation. It was found thatthe size of the rubber particles in the polystyrene phase follow the log-normaldistribution. By applying proper empirical constants, good nucleation agree-

(2 � 3cos � (cos)3)/4

J � N2/3(1 � cos)/2(2�/(�mF))1/2 exp(�16��3/(3kT(Pb � Pl)2)

FIGURE 4.12 Heterogeneous nucleation schematics.


aKw(T) are from Werner, 1981 [9].b�(T) are found using Watson’s expansion method.c�(l) are calculated using Eötvös’ equation.d M: molecular weight of styrene.J � A exp(�B), A � 3.1 1035(�2�/M)1/2, B � 1.2 105�3/(T � SH2)

TABLE 4.7 Heterogeneous Calculations for PS/S.

Temp. Temp. Kwa SH �b �c Jd

(°C) (K) (atm) (atm) (g/cm3) (erg/cm2 B

150 423 5.0 0.012 0.79 18.1 9.66 0171 444 7.9 0.026 0.76 15.6 8.62 0190 463 10.5 0.039 0.74 13.9 7.91 0210 483 15.0 0.062 0.72 12.1 7.18 0230 503 21.5 0.095 0.70 10.4 6.47 0250 523 34.8 0.161 0.67 8.6 5.64 0280 553 52.6 0.25 0.64 6.2 4.58 0300 573 109.9 0.54 0.62 4.7 3.86 0325 598 181.3 0.89 0.59 2.9 2.88 0350 623 403.4 2.00 0.55 1.2 1.70 2.27.4 101

6.0 1037.4 1048.2 1055.5 1062.9 1071.1 1084.5 1081.5 1091.2 1010

(#/cm3 � sec)(#/cm3 � sec)A 1032


ment was observed as illustrated in Figure 4.14. Also noted is the submicronparticle size for effective nucleation.

Lee [43] reported that even for low-level gas dissolution in a polymeric meltsystem, neither homogeneous nor heterogeneous nucleation theories were ableto describe foam nucleation. Table 4.7 contains polystyrene and styrene het-erogeneous nucleation calculations. When gas dissolution increases, intra- andintermolecular forces become important. Nucleation modeling will be morecomplicated. Nonetheless, Jemison et al. [44], based on the heterogeneousresults on methanol and water, concluded that the favorable conditions for sat-isfying nucleation kinetics were not realistic. Therefore, these theories werenot able to offer a solid ground for plastic foam formation in foam extrusion orin foam devolatilization.

4.4 CAVITATION

Cavitation is a physical phenomenon that most often occurs in the areas ofdiscontinuity in the fluid due to external disturbance-induced pressure varia-tion. Bubble formation occurs when the pressure reduction is greater than thecritical value or its difference overcomes surrounding confinement. As pointed

FIGURE 4.13 Microcellular nucleation comparison between theory and experiment forPS/CO2. (Replot with permission from Colton and Suh, Poly. Eng. Sci., 27, 7, 1987 [39].)


out by Rayleigh in 1917 [45], this phenomenon involves physical and flowproperties and sometimes the chemical properties of the fluid. It is a verycomplex research topic, and a clear understanding has not yet been reached.

For simple liquids, Knapp et al. [46] ascribe bubble formation to vibrations,vortices, or local pressure variations that accompany flow acceleration at highflow velocities, for instance, upon pouring or shaking a just-opened soda can orwine bottle, pressure variations induce more superheats to already supersatu-rated solution to cause vigorous foaming. In fact, long-chain polymer is knownfor its viscoelastic and creeping nature, and it tends to maintain flow continuity[47]. In other words, flow-induced significant acceleration is not anticipated forviscous polymeric melt. It is not, however, unusual to observe quench-inducedcavitation in melt solidification, as reported on LDPE by Ainslie [48].

FIGURE 4.14 Cell density vs. particle size effects for HIPS/CO2 Nucleation: computation andexperiment. The solid line represents computational results. (Replot with permission from Poly.Eng. Sci., 1944 [42].)


Besides, a hydrophobic solid surface surrounded by liquid can provide resi-dence for undissolved gas as illustrated in Figure 4.15, which becomes a nucleusfor bubbling when favorable thermodynamic conditions occur. Chin [49] postu-lated that existing cavities appeared to be a plausible mechanism for nucleationin foam devolatilization. It should be pointed out that cavitation is different fromclassical heterogeneous nucleation that has no preexisting “gas seeds” in the in-terface. It is also different from gas entrainment during motion when hydrody-namic force exceeds the surface tension force to cause forced nucleation [50].

Microvoids and “holes” are postulated to exist in statistical equilibriumthroughout the liquid as a result of random thermal fluctuations [51, 52]. Theradius of these holes is around , and the probability of spontaneousformation of holes capable of expanding is negligible. Free volume is a well-established concept in polymers. It successfully characterizes the polymermelt viscosity by applying “holes” theories. Lee [43], by applying the Turnbulland Cohen probability model [53], pointed out the improbability of formingholes with a radius close to the critical bubble radius. One can argue that, in adynamic state, it is not impossible to observe free volume distribution shiftingto extremes to generate nucleable holes. However, foam extrusion is too farabove the glass transition temperature to cause significant variation of freevolume distribution. As illustrated in Figure 4.16 from devolatilization experi-ments [54], very low deformation is sufficient to enhance nucleation. In the vi-sualization experiments, as vacuum was established in a staged manner, new

10�8 cm

FIGURE 4.15 Stabilization of gas-solid pocket in hydrophobic crevice: (a) liquid saturated withgas, interface with an equilibrium contact angle ; (b) liquid undersaturated with gas,liquid advances when , gas solution proceeds to establish �e; (c) liquidsupersaturated with gas, liquid recedes when , gas phase expands till

.�R � �e

�R (recede angle) � �e

�A (advance angle) � �e

�e � �/2 � �


bubbles came into existence when a new lower vacuum was applied. That sug-gests that a given superheat can induce new bubbles into formation.

In the rubber industry, Gent and Tompkins [55] presented theoretical resultsof expanding a small hole in a highly elastic solid. Considering surface andelastic energy, the inflation pressure is as follows:

(26)

where R and G represent cavity radius and elastic constant of the polymer, re-spectively, and subscript 0 denotes initial state. Inflation pressure can be over50 atm for a submicron hole (i.e., 100 A radius), which appears to be reason-able for foam extrusion. In making high-impact polystyrene (HIPS), polybuta-diene is mixed in the PS. The former has a higher thermal expansion co-efficient. It can be conceived that after cooling to room temperature, athermal-induced stress may exceed interfacial cohesion to cause microvoids.This was confirmed by Kekkula et al. [56] by using a Transmission ElectronMicroscope (TEM) to investigate rubber particle morphology as shown inFigure 4.17. Noteworthy is the void dimension in the submicron domain.Ramesh et al. [57] used the microvoids in the HIPS to control cell nucleation

P � 2�/R � G(2.5 � 0.5 (R/R0)�4 � 2(R/R0)�1)

FIGURE 4.16 Nucleation visualization experiment (Methyl Chloride in PDMS—photographstaken through glass tube: (a) vacuum applied at 21 sec, (b) low RPM commenced at 50 sec, (c) pool volume increase, (d) bubble disappearance. (Reprinted with permission from Biesen-berger and Lee, Polym. Eng. Sci., 27, 1, 1987 [53].)


when saturated with carbon dioxide gas and then exposed to an elevated tem-perature. They reported that particle size of minimum submicron (0.2 micron)is necessary to function as an effective nucleator as indicated in Figure 4.14.Lately, in the simulation of cavity growth in polymer-rubber blend, Steenbrinkand Giessen [58] reported that there is a threshold value for rubber modulus atwhich the cavity would grow.

Harvey et al. [59], in their foam formation in organisms study, proposed thatthe undissolved gas nuclei could exist in submicroscopic, hydrophobic cracksand interstices in microscopic solid surface cavities. Various possible states ofcavity are presented in Figure 4.15. This mechanism offers two great advan-tages: first, it explains the pre-nuclei state, and second, it provides a physicallyconceivable way of distributing nuclei throughout liquids. Also noted was thesubmicron size of crevice, . Atmospheric and industrial dustmay provide such particles. In devolatilization experiments, Biesenberger andLee [60] found that in the absence of a nucleating agent, polydimethylsiloxanemelt showed minimum foaming after vacuum was applied, however, a slightdeformation drove out swarms of bubbles immediately. They combined themetastable state and cavity concept to ascribe shear as a detaching mechanismfor gas bubble from solid cavity. However, one can argue that shear-induced

10�5 to 10�4 cm

FIGURE 4.17 Transmission electron micrograph (TEM) of high-impact polystyrene (HIPS);rubber particles in polystyrene (Reprint from Keskkula et al., Polymer, 27, 1986 [55].)


FIGURE 4.18 Cavity model—five successive stages for gas bubble formation: (a) stable gascavity, (b) at pressure reduction, (c) metastable cavity, (d) under shear and (e) unstable gas bubble.(Reprinted with permission from Lee and Biesenberger, Polym Eng. Sci, 29, 1989.)


viscosity reduction is favorable for gas cluster expansion. It was pointed outby Lee [7] that a slight deformation appears to be sufficient to drive out vigor-ous foaming. Deagneault et al. [61] reported solubility drop under high shearfor polystyrene. Solubility reduction evidently contributes to bubble forma-tion. Again, for low shear and combined with an almost instant foaming re-sponse, the solubility reduction does not appear to be a plausible mechanism.

The proposed five successive steps for bubble formation are illustrated inFigure 4.18, in which stable gas cavity evolves into metastable cavity when thesurrounding condition changes. The pressure drop rate is evidently a key factorin developing metastable cavities. In theory, a successive gradual pressuredrop can release the whole pressure for a long time without generating anybubbles. On the contrary, at a sharp pressure drop, it is easier to have themeniscus fall outside the static contact region to form metastable cavities. Atstep (d), a shear force simply distorts the gas cavity into a lower interfacialtension state that favors cavity expansion. When it exceeds the critical state, itgrows into a spherical bubble. This model offers a reasonable and qualitativedescription for correlating shear effects with foaming in a melt flow.

Another hypothesis is worth mentioning before we move to foam extrusion.That is the “string” theory. It assumes that gas molecules form strings dis-persed in the melt, and sufficient diffusion time is lapsed for homogeneity. Theshape of the string is determined by total pressure and the surrounding poly-meric molecular structure. When the pressure drop rate gets higher, it has lesstime for the string to group together, and it is easier to form nucleating sites atvarious locations of strings as long as the critical condition is met. Althoughthis model needs further work to correlate with observations, it, at least,explains the pressure drop rate effects on cell density.

4.5 FOAM EXTRUSION NUCLEATION

Han and Han [62] studied nucleation of polystyrene and trichlorofluo-romethane (CFC-11) extrusion, in which a slit die with side glass windowswas established for laser detection of bubble images. They reported two kindsof nucleation: flow induced at the center and shear induced at the die wall. Athigher CFC-11 loading, as shown in Figure 4.19, the nucleation point is closeto the theoretical prediction, PR (pressure ratio) equal to one. Center cells wereshown to be larger in size than those of the side. Earlier nucleation appeared tobe a reasonable explanation.

Lee [7] investigated foam nucleation on an extruder with a specially de-signed die to allow die gap adjustment externally. In the LDPE dichlorodiflu-oromethane (CFC-12) extrusion experiments, a physical nucleator was addedto control cell size and its distribution. It can form a conglomerate as a po-tential nucleating site [63]. Shear-enhanced foam formation was qualitativelywell correlated with preexisting cavity theories. Force balance on metastable


cavity as presented in Figure 4.20, a replot of Figure 14.8(d), demonstratesdominant shear force and surface tension force, which gives the followingcapillary number:

(27)

where � and � represent the melt viscosity and the average shear rate, respec-tively. Figure 4.21 suggests a critical radius, around 0.3 micron, by extrapolat-ing laser experimental results. Also noted in Table 4.8, it is relatively insensi-tive to the temperature and the weight of solvent. When plotted, the celldensity vs. Ca in a semi-logarithmic scale, a straight-line mode in Figure 4.22,instead of concave curve in the linear-linear cell density vs. � chart, under-scores the important role played by shear force in the metastable state. Its log-linear ordinates are similar to the general form of the rate equation:

(28)

where K1 and K2 are, generally, material parameter with frequency factor andsystem parameter, respectively. Evidently, the straight-line mode suggests that

J � K1 exp(�K2)

Ca � Rbcr��/(4�)

FIGURE 4.19 Nucleation experiments: (a) pressure profile and (b) nucleation sites in the slitflow channel for PS/CFC-11 (4 wt%) at 180°C. (Reprinted with permission from Han and Han,Polym. Eng. Sci., 24, 28, 1988 [61].)


FIGURE 4.20 Metastable cavity under shear: capillary number (Ca) defined as shear force overtension force, , (b) after distortion, R2��/(4).Ca � (a) R1��/(4�)

FIGURE 4.21 Bubble radius vs. time for PS/Toluene nucleation at an equilibrium pressure of2,859 Kpa and at three temperatures (0°): (O) 150, () 170 and (□) 180. (Reprinted with permis-sion from John Wiley & Sons, Inc., Figure 16 of Han and Han, J. Poly. Sci. B: Poly Phys., 28,1990a [68].)


the shear force is an energy source for nucleation. The use of a chemicalblowing agent is a common practice for nucleation without adding a physicalnucleator. This becomes an interesting comparison; as illustrated in Figure4.23, shear enhancement increases dramatically by adding a physical nucleator[63]. How to incorporate the shear energy into the free energy change termbecomes another interesting subject for foam nucleation.

Dey and Todd [64] conducted visual experiments by implementing a sap-phire window to videotape gas/melt flow. They reported that a two-phase flowis detrimental for consistent foaming, and when the extrusion melt temperatureis reduced to close to the melting point, a cloudiness appeared prior to swarmsof nucleation. Sites of crystallization become potential nucleation sites forfoaming, however, the actual processing temperature has to be kept muchhigher than the melting point of the polymer to facilitate viscous flow in theextruder. It is a common practice to add a nucleating agent to assist cell sizeformation and its distribution.

The extrusion process generally provides adequate thermal and mechanicalenergies to polymers to form a homogeneous melt to evenly disperse in anarrow flow region to build up enough pressure for optimal free expansion. Infoam extrusion, a higher temperature seems to be a favorable factor in generat-ing bubbles. However, the melt strength needed to sustain bubbles becomes alimiting parameter. Thermal effects on morphology are presented in Figure 4.24[65]. The cell structure, or cell integrity, appears to be better when the process-ing temperature is decreased. This also suggests that the nozzle temperature andthe melt temperature can independently control the surface cell structure andcore cell structure, especially when a large die flow region is used.

Park et al. [28] designed various die nozzles for HIPS/CO2 extrusion exper-iments in which the nucleation phenomena at similar total pressure drop anddifferent pressure drop rates were studied. As illustrated in Figure 4.25, finercells were associated with a sharp pressure gradient rate that was attributed tothe gas diffusion and its characteristic length. However, considering the preex-isting cavities, a near straight line could be obtained in the log-linear plot of

(Reprinted with permission from Han and Han, J. Polym. Sci., B: Polym. Phys., 1990.)

TABLE 4.8 Critical Radius Results.

Polymer Temperature Critical Pressure Critical Time CriticalConc. (wt %) (°C) (kPa) (s) Radius (�m)

60 150 271.0 0.302 0.2460 170 303.0 0.273 0.2850 150 315.1 0.277 0.2950 170 381.4 0.248 0.3150 180 408.5 0.238 0.3240 150 486.3 0.214 0.33


cell density vs. capillary number. In the conventional nucleation theory, thedegree of superheat defined in Equation (16), the difference between systempressure and surrounding pressure, is a more critical parameter than the pres-sure drop rate. However, as illustrated in Figure 4.26 [66, 67], after gas disso-lution is completed, surrounding pressure increase can make fugacity increaseto suggest that superheat is no longer solely dependent on the amount of gas

FIGURE 4.22 Nucleation Results for LDPE/CFC-12; log (cell density) vs. Capillary number atdifferent talc nucleating agent levels. (Reprinted with permission from Lee, Polym, Eng. Sci., 33,1993.)


dissolution. In foam extrusion, after a given amount of gas is injected to dis-solve in the molten polymer, extruder pressure can be easily built up muchhigher than the system vapor pressure. The additional hydrostatic pressure willnot improve solubility. However, it establishes additional “mechanical” super-heat, which can be expressed as follows:

(29)

A higher operation pressure can certainly make a higher total superheat at thecost of more power consumption. The resulting higher pressure drop rate canincrease the number of metastable sites by promoting gas activity under thecavity membrane. In general, a high pressure drop inherently causes high shearin the processing. The shear energy can virtually develop more heat for theflow system to, in turn, increase gas volatility. Shear force can, thus, enhancethe transfer from the metastable to the unstable state. In addition, a sharp pres-sure drop rate and high shear tend to make a viscoelastic polymer “swell,” in

SH � SHce � SHme

FIGURE 4.23 Shear effects for various nucleators with and without fluoropolymer (400 ppmFP) at different nucleating agent levels—FPN is an endothermic chemical blowing agent fromReedy International. (Reprinted from Lee, ASME, Cell. Micro. Mat., 53, 1994 [62].)


FIGURE 4.24 Thermal effects on cell morphology for HIPS/CO2 foams; microstructures atvarious melt (Tc) and nozzle temperatures (Tn). (Reprinted with permission from Behravesh et al.,ANTEC, 1998.)


FIGURE 4.25 Cell density vs. pressure drop rate for HIPS/CO2. (Replot with permission fromPark et al., ASME, Plas. And Plas. Comp., Vol. 46, 1993.)

FIGURE 4.26 Hydrostatic pressure effect on polymer/gas fugacity. (Reprinted from Handa,NRC lecture notes, 1998.)


other words, to bring forth its expansion potential, which is another favorablecondition for nucleation.

In the laser detection and visual experiments with polystyrene/CFC-11, Hanand Han [62] observed early nucleation in the center of a slit die. Center cellsappeared larger than side cells at the die exit. To prevent early center forma-tion, Lee and Kim [68] designed a sharp tapered end attached to a pipe die forLDPE/HCFC-142b experiments. It provided a sharp pressure drop at die endto minimize premature foaming for over 25 times expansion. Center nucle-ation was examined against skin nucleation for pressure-controlled and shear-controlled comparison. In Figure 4.27, the skin shows more nucleation thanthe center. The latter is pressure drop rate controlled, and the former experi-ences high shear. Again, the cavity model appeared fitting in describing thedifferences.

4.6 SUMMARY

Although foam extrusion involves efficient energy transfer and effectivematerial transport, it adds more complexity to the already complex dynamicnucleation. This chapter adopts a realistic approach, starting with fundamental

FIGURE 4.27 Rod nucleation results for LDPE/HCFC-142b; skin vs. core. (Reprinted with per-mission from Lee and Kim, ANTEC preprint, 1998 [67].)


principles to evolve to correlate with extrusion parameters. Nucleation is thebeginning of a process to stabilize a supersaturated state en route to a stablestate. Applying equilibrium theories, one can calculate the chemical superheat,SHce, that is determined by the amount of gas dissolution and the subsequentpressure drop and/or temperature rise. The nucleation rate equations devel-oped previously account for chemical superheat and surface tension confine-ment. They fail to explain parameter variation and surrounding phase-inducedtransport issues. It is virtually not surprising to find that orders of magnitudediffer between the experimental results and predictions in batch foaming.Modifications were made to include the transport, rheological, thermal, andphysical properties, and to cover the gas dissolution and its interaction withpolymeric melt. However, differences from observations still exist. The cavitymodel and mechanical contribution to superheat were proposed to underscorethe importance of metastable state in foam nucleation. The stable-metastable-unstable process appears to be plausible for foam nucleation. Although quali-tative agreement was observed, quantitative agreement should be explored onthe existing theoretical and experimental bases.

In polymer/gas analysis, it is worthwhile to establish a useful phase diagramcovering a gas-enriched phase to a polymer-concentrated phase. The former israrely available for a gas/melt foaming system. It will offer a logical “path”from the formation of gas clusters and its transformation from a stable to ametastable and, ultimately, to an unstable state. Energy terms involved in thisseparation kinetics can be identified and, hopefully, quantified for modificationand implementation in the nucleation equations to make them more realistic.

Based upon superheat (SH) and phase separation, Figure 4.28 illustrates asimplified sketch in which SHc denotes critical superheat for nucleation,whereas SHT denotes the total superheat determined by gas dissolution andpressure reduction. Phase separation and spinodal decomposition concepts, asindicated in Figure 4.4, strongly suggest that a modest superheat, or SHc, benecessary for nucleation. In actual foam extrusion, SH is a function of posi-tion, or time, in the pressure-controlled die flow region. Knowing the criticalbubble size, submicron, as reported by Han and Han [69], critical superheatcan be calculated as follows:

(30)

Assuming a negligible hydrostatic pressure contribution, the nucleation pointcan be determined inside the die. From that point on, positive SH continues toincrease until SHT at the die end, during which growth starts and continues toprogress outside the die into free expansion. However, it is desirable to figureout the effects of hydrostatic pressure not only in its contribution to superheat,but also in its drop rate to convert into energy terms for an analytical expres-sion. When surface tension variation with temperature, gas concentration, and

SHc � 2 � / Rcr


pressure is available [70], Equation (29) can become a more realistic founda-tion for rate equation development. A further issue is the secondary nucleationout of surface stretch as observed by Albalak et al. [71]. It is more mechanicalthan chemical-induced nucleation. An overall view is necessary to coverchemical and mechanical contribution to superheat.

A narrow die flow is necessary to build up high enough pressure to over-come critical superheat to the die end for free expansion, in other words, tokeep PR (pressure ratio) above one until the die end is reached. On the otherhand, the corresponding shear heat generally makes the heat-sensitive nucle-

FIGURE 4.28 Nucleation in nonparallel plate pressure flow; flow pressure and vapor pressure(or fugacity) variation in flow direction.


ation even more sensitive. That means that temperature variation in flow direc-tion and its distribution in cross-flow direction can make nucleation deviatefrom impulse (or one-point) nucleation. For maximum expansion, melt/gasneeds to be cooled to enhance melt strength before entering the die. The inter-facial phenomenon, melt/die surface, becomes another interesting processingissue. As the nucleation experimental technique continues to be upgraded, cur-rently, ultrasonic techniques have been used to enhance foaming [72] and havebeen applied to monitor foaming [73]. Combined with a high-speed camera onthe side window for dynamic nucleation experiments, insight into the precriti-cal state can be established.

Total pressure, pressure drop rate, and shear energy appear to qualitativelycorrelate with nucleation via cavity model. Nucleation potential (superheat)increases as total pressure, dissolved gas partial pressure, or processing pres-sure increases. The nucleation barrier seems to be reduced by pressure droprate and shear energy to make more bubbles come into existence from ametastable state. A detailed development including cluster formation andtransformation and interfacial contact variation under nonisothermal heattransfer is necessary for comprehending the dynamic foam nucleation. The“string” concept may play a role in cluster formation. Nonetheless, the funda-mental foaming principles, engineered parameters, and visualization tech-niques presented in this chapter are useful tools in correlation with observa-tions and actual machine design for better nucleation control.

4.7 NOMENCLATURE

A Surface area, cm2

a ActivityB Frequency factor for nucleation equationC(n) Gas cluster containing n moleculesCa Capillary number, R��/(4)D Diffusion coefficient, cm2/sec.F Geometry factorF Free energy changeG Elastic constantJ Nucleation rate, #/cm3/sec.Kw Henry’s law constant, atmKw� Dimensionless Henry’s law constantK1 Material constant for simplified nucleation equationK2 System constant for simplified nucleation equationk Boltzmann constantM Molecular weight, gm Mass of a gas molecule


N Number of molecules per unit volumeNb/V Cell density, #/cm3

n Number of moleculesP Pressure or external pressure, Pa or psiPR Pressure ratio; flow pressure/vapor pressureP0 Vapor pressure, Pa or psiP Pressure difference, Pa or psip Partial pressure, PaR Radius, cavity or bubble, cmSH Superheat, PaT Temperature, °KV Volume, cm3

Wg Weight fraction of gas phaseW(n) Work to sustain a pocket with n moleculesX Constant, (Nb/V)3/4 Kw�Y Constant

Greek letters:� Interaction parameter for Flory-Huggins equation� A small perturbation� Shear rate, 1/sec.� Viscosity, poise or Pa-sec.� Chemical potential� Contact angle, degree� Density, g/cm3

Surface tension, dyne/cm

Subscriptsb Bubble phasec Critical statebcr Critical bubble radiusce Chemical equilibriumD Diffusion controlledg Gas phasel Liquid phaselg Liquid-gas interfaceme Mechanical equilibriummin Minimump Polymer phasesg Solid-gas phasesl solid-liquid phaset Polymer-solvent interactionT Total� Viscosity controlled


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71. Albalak, R. J., Tadmor, Z. and Talmon, Y., “Polymer Melt Devolatilization Mechanisms,”AIChE J., 36, 9, 1313–1320, 1990.

72. Tukachinsky, A., Tadmor, Z. and Talmon, Y., “Ultrasound-enhanced Devolatilization ofPolymer Melt,” AIChE J., 39, 359, 1993.

73. Sahnoune, A., Piche, L., Hamel, A., Gendron, R., Daigneault, L. E. and Caron, L. M., “Ultra-sonic Monitoring of Foaming in Polymers,” Soc. Plas. Eng. Ann. Conf. (ANTEC), preprint2259–2263, 1997.


CHAPTER 5

Foam Growth in Polymers

N. S. RAMESH

5.1 INTRODUCTION

THERMOPLASTIC foams have diverse applications in everyday life. Insula-tion, surface protection, sports, recreation, and cushioning are some of the

major applications of olefinic and styrenic foam products. Extrusion has beenconventionally used for producing low-density foam sheet and rods with phys-ical blowing agents in the last decades.

Foam nucleation, foam growth, and cell coalescence are the three majorevents in the foaming process. The dynamic nature of thermoplastic foam for-mation introduces extra variables, greatly increasing the analysis complexityof this extrusion process.

This chapter covers a condensed review of papers dealing with foam growthmodels and experiments. The latest approach to model foam extrusion is alsopresented. A fundamental study focusing on the influence of blowing agent onbubble growth during thermoplastic foam extrusion is presented. The extrudedmolten mixture expands and cools simultaneously when exposed to ambientconditions. The bubble growth is influenced by the concentration-dependentblowing agent diffusion coefficient, the transient cooling of the expandingfoam, the influence of blowing agent on polymer viscosity, and the escape ofblowing agent from the surface of the foam. Previous models in the literaturedo not consider these significant influences. A modified model is presented ac-counting for those more subtle effects. In addition, a new experimental tech-nique is described to collect experimental bubble growth data.


5.2 IMPORTANCE OF THIS STUDY

In general, the foaming process involves three important steps: nucleation,bubble growth, and bubble coalescence. Another chapter in this book dealtwith the phenomenon of nucleation. This chapter deals with foam growth inpolymers. Bubble collapse and coalescence in polymers are not desirable, andthe foaming process is tuned to avoid that phenomenon. It is well known thatthe cell size, cell size distribution, cell geometry, type of cells, and foamdensity play major roles in controlling the mechanical properties of a foam.The fundamentals of a bubble growth study are important because the proper-ties of cellular materials directly depend on the shape and structure of the cells.Hence, it is necessary to be able to predict and control the cell size during thefoam growth of bubbles in the mold or in a free foam sheet expansion toachieve the desired mechanical properties.

5.3 LITERATURE REVIEW

Several investigations addressing the theoretical and experimental analysesof bubble growth and collapse in fluids and polymers have been available inthe literature since 1917. The historical development of important models islisted in Table 5.1. Most of the models can be classified into two groups: singlebubble growth model and cell model (swarm of bubbles growing without in-teraction). The references [1–29, 36] are given at the end of this chapter.

5.3.1 SINGLE BUBBLE GROWTH MODELS (1917–1984)

Between 1917 and 1984 [1–17], the published models focused on thegrowth or collapse of a single bubble surrounded by an infinite sea of fluidwith an infinite amount of gas available for growth. Although these modelsgave several insights into bubble growth phenomena, their practical applica-tion in industry was severely limited, because in real life, the foaming processinvolves the growth of numerous bubbles expanding in close proximity to oneanother with a limited supply of gas. This led to the development of a newmodel called the “Cell Model” that will be discussed in the next section.

5.3.2 CELL MODEL (1984–1998)

The cell model has been widely used to describe devolatilization and batchmicrocellular and foam extrusion processes. Gross motion, no bubble motion,and motion without shear have different implications on the cell model.


The concept of a cell model was first introduced by Amon and Denson [18]in 1984. The study involved the growth of a group of gas bubbles separated bya thin film of polymer and dissolved gas during the injection molding process.The foam was divided into spherical microscopic unit cells of equal and con-stant mass, each consisting of a liquid envelope surrounding a single bubble,and the gas available for growth is thus limited. Because of this more realisticassumption, the cell model yielded a final radius, while other single bubblegrowth models showed growth of bubble radius with time, infinitely. This fun-damental improvement caused more interest in this area of research, andseveral studies have emerged since then. However, the Newtonian viscosityequation was used to describe the rheology of the polymer due to the com-plexity of the problem. Later, it was modified to account for the non-Newton-ian viscoelastic effects to make it more suitable for polymeric systems [19].

Cell models [18–29, 34] can be broadly classified into two groups: cellmodel for closed system with no blowing agent and gas loss effects and modi-fied cell model for foam extrusion with blowing agent and gas loss effects.They are described in the next section. Recently, Shafi, Joshi, and Flumerfelt[32] did good work and proposed a model by combining nucleation and foamgrowth processes to study the effects of operating conditions on bubble growthdynamics in polymeric foams. The final bubble size distribution dependedupon nucleation rate and bubble growth dynamics. However, that modelassumed Newtonian behavior for the polymer and neglected important fea-tures of the “Cell Model” that limits its application to real-life processes. Forexample, the previous studies [21–23] show that viscoelastic phenomena areimportant in changing bubble growth characteristics. The gas loss and blowingagents are important in matching typical foam extrusion processes for manu-facturing thin sheets.

5.3.2.1 Viscoelastic Cell Model for the Injection Molding Process

5.3.2.1.1 Arefmanesh and Advani Model

The validity of the cell model was initially tested by experimental work byAmon and Denson [18], Arefmanesh et al. [20–21], Ramesh and Malwitz [25],and Lee and Ramesh [24]. The first two research groups concentrated on ex-periments to verify prediction of the cell model during the injection moldingprocess, where the bubble growth occurs in a closed system. Amon andDenson [18] used low-density polyethylene with a chemical blowing agent,whereas Arefmanesh et al. used [20] polycarbonate with a chemical blowingagent. The assumption of no gas loss from the mold was adequate, since thefoam growth occurred in a closed mold. These studies showed a qualitative


TABLE 5.1 Historical Development of Bubble Growth Models.

Transport Phenomena in BubbleGrowth Process

Momentum Mass RheologicalAuthor(s) Year Transfer Heat Transfer Transfer Model

Rayleigh, Lord 1917 inertial isothermal — —Epstein and Plesset 1950 — isothermal yes —Scriven 1959 yes nonisothermal yes Newtonian

Barslow and 1962 viscous isothermal bubble NewtonianLanglois surface

diffusionDarby 1964 — yes — NewtonianYang and Yeh 1966 viscous conduction — Ostwald

ModelStreet 1968 viscoelastic isothermal — OldroydGent and Tomkins 1969 elastic isothermal yes Neo-

HookeanStewart 1970 elastic isothermal bubble Neo-

surface Hookeandiffusion

Street, Fricke, and 1971 viscous conduction yes Power LawReissRosner and Epstein 1972 — yes —Zana and Leal 1975 viscoelastic conduction yes Newtonian,

Oldroyd BVillamizar and Han 1978 — — — —

Patel 1980 viscous isothermal yes NewtonianHan and Yoo 1981 yes isothermal yes Viscoelastic

DewittPapanastasiou, 1984 viscoelastic — — BKZ typeScriven, and viscoelasticMacosko

Upadhyay 1985 viscoelastic nonisothermal yes Lenov,viscoelastic

Amon and Denson 1984, viscous conduction yes Newtonian1986

Arefmanesh and 1991 viscoelastic conduction diffusion at viscoelasticAdvani bubble Maxwell

interface

Ramesh 1991, viscoelastic conduction yes Maxwell,1992 power law

Lee, Ramesh, and 1993 viscoelastic conduction yes convectedCampbell MaxwellRamesh and 1995 viscoelastic nonisothermal MaxwellMalwitzLee and Ramesh 1995, viscoelastic nonisothermal Maxwell

1996 from sheetsurface

Ramesh and 1997 viscoelastic nonisothermal MaxwellMalwitz from sheet

surfaceRamesh and 1998 viscoelastic nonisothermal MaxwellMalwitz evaporation

�surface

�gas loss

�gas loss

�gas loss


Influence of BlowingAgent on

Bubble Blowing BubbleTheoretical (T) Growth Agent Polymer Diffusion Count ReferenceExperimental (E) Medium (B/A) Viscosity Coefficient Study No.

T — — — single 1T water air — — single 2T water- vapor — — single 3

ethyleneglycol

T vinylidene nitrogen — — single 4copolymer

E — — — — single 5T — — — — single 6

T — — — — single 7T — air — — single 8

T rubber air — — single 9

T rubber — yes — single 10

T iron melts nitrogen — — single 11T — — — — single 12

E polystyrene chemical — Constant single 13HDPE, PC B/A

T — — — Constant single 14T and E polystyrene chemical — Constant single 15

B/AT hydroxyl — — constant single, 16

propyl cellate bubblein water growth

collapseT and E polystyrene, physical — constant single 17

polycarbonate blowingagent

T and E LDPE chemical — constant swarm 18, 19blowingagent

T and E polycarbonate chemical — constant swarm 20, 21blowingagentFLC-95

T and E polystyrene physical — constant swarm 22, 23N2, CO2

T and E LDPE HCFC — constant swarm 24

T and E PVOH water, yes constant swarm 25methanol

T and E LDPE HCFC-22 yes constant swarm 26, 27, 34HCFC-142b

T LDPE n-butane yes concentration- Swarm 28dependentdiffusion

T and E LDPE butane yes concentration- swarm 29dependentdiffusion


agreement between experimental data and theoretical results and have led to abetter understanding of the processing of polymeric foam materials.

Ramesh et al. [22–23] have tested the validity of the cell model by conduct-ing a cell growth experiment during microcellular foaming process using ascanning electron microscope as shown in Figure 5.1(a). Polystyrene was usedwith physical blowing agents such as nitrogen and carbon dioxide. In all of theabove cases, the blowing agent loss was considered to be negligible, and,therefore, the no gas loss boundary condition was adequate to predict the foam

FIGURE 5.1 (a) Comparison of theory with the experiment for the foam growth in polystyreneat 378 K when carbon dioxide was used as a blowing agent; (b) comparison between experimen-tal foam density data and simulation results at various final cell density, #/cm3; and (c) comparisonbetween experimental foam density data and simulation results for HCFC-22 and HCFC 142b attwo different levels.

(a)


(b)

(c)


growth kinetics reasonably well. However, in the polymeric foam extrusionprocess of interest here, the foam sheet or rod is allowed to expand freelyunder atmospheric conditions. The assumption of no gas loss to surroundingsno longer applies for the actual processing. Therefore, such gas escape must beaccounted for, especially with thin foam shapes. Furthermore, the previousmodels do not include further complicating effects such as the influence ofblowing agent on polymer viscosity and the concentration dependence of the

TABLE 5.2 Comparison of Bubble Growth in Batch and Continuous Processes.

Bubble Growth Study In

Process Microcellular Batch Conventional FoamParameters/Properties Foaming Process Extrusion

1. Process Batch Continuous2. Key steps Gas saturation and Direct gas injection into the

heating the polymer in extrudera constant temperaturebath

3. Polymer studied Polystyrene LDPE4. Polymer type Amorphous Semicrystalline5. Blowing agent Nitrogen, Carbon

dioxide n-butane6. Foaming temperature Isothermal Nonisothermal7. Blowing agent surface No Yes

evaporation8. Diffusivity of blowing Concentration Concentration dependent

agent independent9. System Pellet expansion Rod expansion

10. Polymer Viscosity Plasticized due to Plasticized due to blowingblowing agent agent

11. Bubble size, �m12. Cell count/cm3 of foam 108 20013. Foam density range, 200–300 30

Kg/m3

14. Foam expansion time, 60–120 seconds 1–2 secondssecond

15. Experimental study on Microscopic Study Measurement using thefoam growth video technique, cell

growth study via video techniques

16. Model used Cell model with Modified cell model withisothermal, no gas loss blowing agent and gas effect and blowing loss effects (Figure 5.7). agent effect on Modified boundary diffusion (Figure 5.1) condition.

17. Comparison—Theory Reasonable Goodvs. Experiment

18. Figure/(Reference) Figure 5.1/[22] Figure 5.7

�1,000�20


blowing agent on diffusion during the bubble growth process. Table 5.2 showsthe comparison of bubble growth studies done by Ramesh [22] for a batch mi-crocellular process and a continuous extrusion process. This chapter showsimprovement on the former models to more closely reflect thermoplasticfoaming dynamics including the author’s ongoing research [22–25] for thepast eleven years on modeling foam growth in the extrusion process.

5.3.2.2 Modified Viscoelastic Cell Model for the Foam ExtrusionProcess

5.3.2.2.1 Ramesh, Lee, Malwitz Model

Recently, Lee and Ramesh [34] studied the effects of foam sheet thicknessand nucleation cell density on thermoplastic foam sheet extrusion. Low-density polyethylene was used with HCFC-22 and HCFC-142b to producefoam sheets of various thicknesses and nucleation characteristics. They used a70 mm counterrotating twin-screw extruder to produce foams. The results areshown in Figures 5.1(b) and 5.1(c). It was concluded that solubility, rheology,and gas loss transport mechanisms play an important role in determining thefoaming efficiency during foam sheet extrusion. While predicting the foamdensity as a function of final cell density (or number of cells/unit volume) andfoam sheet thickness, they used mathematical equations from packing theoryto calculate the ratio of bubbles present closer to the surface to the bubblespresent in the core portion of the foam sheet where there is no gas loss. Thevalue of this ratio, of course, strongly depends on the nucleation density(which is defined as the number of bubbles nucleated per unit volume of thepolymer) and the thickness of the foam sheet. With this theoretical back-ground, an attempt was made to check the validity of the modified model bycomparing it with the experimental data. Although the improved cell modelpredicts the experimental data very well, between 919 kg/m3 to 60 kg/m3, itwas observed that the agreement decreases for increased expansion ratios andvolatility of blowing agent, where the nonspherical nature of the bubble andbubble-bubble interaction phenomena become pronounced. Higher nucleationrates and extrusion of thicker foam sheets seem to enhance foam efficiency.Correlation with cell geometry and nonspherical bubble dynamics and consid-eration of interaction between bubbles during the growth process wouldgreatly benefit in understanding the low-density foam process and would assistin product design.

In this chapter, a new approach has been taken to model bubble growthduring the foam extrusion process. The objective is to present a new model de-scribing the thermoplastic foam formation process, where the foam is ex-panded unrestricted nonisothermally and the blowing agent plays an importantrole in changing the rheological and other physical properties.


The following major changes have been made to historical models toaccount for blowing agent effects on foam dynamics:

(1) Gas loss to surroundings from a foam sheet or rod from the cells that areadjacent to the surface. Mathematically, the gas loss boundary condition isdifferent.

(2) Blowing agent plasticizes the polymer. Therefore, the reduced viscosityvariations as a function of concentration during foam expansion are usedfor simulation based on experimental rheological data.

(3) The concentration-dependent diffusion coefficient is included to modelmore accurately the actual nature of the blowing agent-polymer binarysystem.

(4) Transient cooling of the foam is accounted for as a nonisothermal foamexpansion problem under ambient process conditions. Temperature effectson viscosity, diffusivity, and blowing agent pressure are considered, forexample.

The non-Newtonian nature of the polymer/blowing agent mixture was pre-dicted using the upper convected Maxwell Model. The convected Maxwell issimple and, therefore, it is widely used to study the influence of viscoelasticityon flow calculations. More details are listed in the literature [35]. Experimen-tal data were gathered to describe the rheology of the polymer/blowing agentmixture and its influence on foam development.

5.4 FOAM GROWTH EXPERIMENT

The experimental objective was to establish the bubble growth data duringfoam processing. Since bubbles tend to grow quickly, typically within 2 to 3seconds, to the final radius for low-density foams below about 30 kg/m3, it isvery difficult to measure their growth with real time. On the other hand, it isrelatively easy to measure the diameter of the expanding rod of foam when itexits the die and grows until it reaches the final equilibrium diameter. Hence, itwas decided to conduct a foaming experiment to produce a cylindrical rod offoam so that its expansion can be easily measured. To accomplish this task, theexperimental procedure described below was followed.

Figure 5.2 shows the experimental setup for collecting the bubble growthdata. A low-density 2MI polyethylene resin having a specific gravity of 0.919was blended with 0.25% talc and metered into a Haake twin-screw corotatingextruder. The use of talc yields fine and uniform cellular structure. Theblowing agent was added at the midsection of the barrel to allow completemixing with the molten polymer. Then, the plasticized melt was cooled beforebeing extruded through a rod capillary nozzle. When the gas-charged polymer


exited the die, nucleation of bubbles occurred due to thermodynamic instabil-ity, and the strand expanded due to the growth of bubbles assisted by diffusionof gas into the cells. The cylindrical rod continued to expand until it reachedthe final steady diameter. The bubble growth (rod expansion) stopped due todepletion of gas in the polymer and stiffening of the cell walls. A digital caliperwas used to measure the rod diameter as it expanded with traveling distancefrom die exit. The local velocity of the strand was determined using a videocamera system to interpret the rod expansion data in terms of time. An ink dotwas introduced on the strand at the die exit as a video marker. The time it tookfor the dot to move along the travel distance was monitored to determine localvelocity. The obtained experimental data are plotted in Figure 5.7.

5.5 FOAM GROWTH MODELING

As foam rod exits from a die, one-dimensional heat transfer is assumed.Heat conduction becomes the dominant heat transfer mechanism. The heatloss effects on foam growth are found to be less important when the diameterof the foam rod exceeds 10 mm. The average temperature of the thin foam asit is exposed to ambient conditions can be found from the standard heat trans-fer equation in the literature [30].

The foam rod formation is pictured in Figure 5.2. The schematic diagram ofthe cell model is shown in Figure 5.3. The appropriate bubble growth model-ing equations are listed here.

FIGURE 5.2 Experimental setup for measuring rod expansion data.


5.6 FOAM GROWTH EQUATIONS

To define gas pressure inside the bubble, the integrated momentum equationreduces to the following:

(1)

Rheological Equations:

(2)

(3)

where:

(4)

Growth of Radius:

(5)d

dt (�gR3) � 3�DR2 c �c

�rd

r�R

f(c) � viscosity reduction factor �

Polymer viscositywith blowing agent

Viscosity of polymerat same temperature

�*0 � �0 exp c Ev

Rg a 1

T�

1

T0b d *f(c)

� ��*

0

G �(1) � ��*

0�

Pg � P� �2�

R� �R

Rf (�� )drr

� 0

FIGURE 5.3 Gas loss boundary condition in the cell model.


Concentration-Dependent Diffusion Equation:

(6)

where diffusivity is a function of blowing agent concentration, and it changeswithin the polymer envelope during the gas-diffusion process. The diffusivityalso depends strongly on the temperature. Mathematically,

(7)

Where A, B, and C are constants fitted to the experimental data that depend onthe nature of the blowing agent. The values of A, B, and C need to be obtainedexperimentally. For this work, the values used based on our experimental dataand the data provided by the resin supplier are listed in Table 5.3.

5.7 BOUNDARY CONDITIONS

The initial and boundary conditions are as follows:

(8)

(9)c(R,t) � KwPg

c(r,o) � co � KwPgo

D(c,T) � [1 � Ac]10�7e(B�c/T)

�c

�t� Vr

�c

�r�

1

r2 �

�r aDr2�c

�rb

TABLE 5.3 Experimental Parameters for Bubble Growth Calculations(from our Own Experiment and the Resin Data from the Supplier).

Process Variables Values

1. Surface tension of low-density polyethylene (LDPE)

2. Molecular weight of butane (blowing agent) 58 kg/kg mole3. Initial blowing agent concentration 6.0% by weight4. Foaming temperature, To 383 K5. Ambient temperature, Ts 293 K6. Henry’s law constant, Kw

7. Density of LDPE 920 kg/m3

8. No. of bubbles per 1 cm3 of foam (from experiment) 1369. No. of bubbles across strand diameter 5

10. Diffusion constant parameter, A 0.533411. Diffusion constant parameter, B 21.9312. Diffusion constant parameter, C 7,090 K

2.235 � 108Pa

30 mNm


For bubbles situated in the core of thick sheet expansion,

(10)

For bubbles on the surface of foam sheet that undergoes gas loss:

(11)

where

(12)

km is defined as the mass transfer coefficient derived from the penetrationtheory [30] and “t” is the foam growth time. The surface evaporation or gasloss condition can be mathematically expressed in Equation (11).

(13)

The boundary condition, Equation (10), represents a closed-cell systemwhere there is no gas loss or escape to its surroundings. This is true in the in-jection molding process because the foam expansion occurs inside the mold.

But, in the practice of producing foams with unrestricted rise, gas loss is en-countered from the bubbles that are adjacent to the top and bottom surfaces ofthe foam. The influence of gas loss on foaming efficiency is especially pro-found when the extruded shape is thin. Some of the gas close to the surface,instead of diffusing into the cell, diffuses to the surface and transpires into theatmosphere. As a result, the final surface cell size is smaller than that of thecore cell. As the final foam density is lower, or the shape is thinner, more gasescape is anticipated. In other words, high concentration of blowing agentsand/or high surface-to-volume foam sheets accelerate gas loss from a sheetsurface, thereby lowering the blowing agent effectiveness. This phenomenonis compounded at lower atmospheric temperatures that decrease the foamgrowth rate. A similar situation is encountered when a small diameter foam rodis extruded.

The above system of equations was solved numerically by an iterative nu-merical scheme. In order to facilitate the numerical simulation, a definite valueof initial radius, Ro, is required. Bubble growth originates from thermody-namic and mechanical instability in the system with perturbed initial radius[18, 32, 33, 36]. Hence, the selection of initial radius is important to achieve

R(t � 0) � R0

km � 2 B D

t

D �c

�r� km(cs � c�)

�c

�r� 0


great accuracy in the predicted results. Great care is needed to model success-fully. This principle is not clearly emphasized in the literature so far. Thebubble growth seems to be a strong function of the value of the perturbedinitial radius during the induction period that is less than 8% of the total ex-pansion time. Beyond this initial growth time, i.e., greater than 8% of the total growth time, the foam growth rate is found to be independent of thegrowth radius according to Denson [18], Upadhyay [17], Ramesh [22], and Arefmanesh [20]. For all practical reasons, it is better to calculate the initialradius from fundamentals of mechanical equilibrium principles that are in-volved with the calculation of a critical bubble radius. The value of the criticalbubble radius, Rc, can be easily calculated from the force balance at the bubble

wall that can be written as , where � is the surface tension and P is

the pressure difference between the liquid polymer phase and the dissolved gasphase. For example, in the case of Figure 5.1, the critical radius for the poly-styrene-CO2 system ranged from 0.1�m to 1�m depending on the variousfoaming conditions. Hence, for the entire simulation, the value 1�m waschosen for the initial radius, Ro. Solving the model yields the bubble radius asa function of time. However, to achieve accurate results, a careful evaluationof rheological and diffusion properties is needed. Rheological properties forLDPE with butane were obtained using Haake capillary rheometer. An experi-mental setup is shown in Figure 5.4. Dissolution of blowing agent tends toplasticize the molten polymer and decrease the polymer viscosity. Rheologicalresults for LDPE/butane system are shown in Figure 5.5, from which a viscos-ity reduction factor, f(c), for appropriate blowing agent concentration was de-termined for the bubble growth simulation. The concentration and temperatureeffects on diffusion of butane in LDPE are shown in Figure 5.6. These resultsare obtained by fitting data presented by Coonahan [31]. The diffusion coeffi-

Rc �2�

P

FIGURE 5.4 Schematic diagram of the capillary rheometer.


cient of butane in LDPE as a function of temperature and concentration can beexpressed in the following form:

(14)

where A, B, and C are constants fitted to the experimental diffusion datashown in Figure 5.6. Although the modeling equations are the same whether aphysical or a chemical blowing agent system is used, the appropriate blowingagent gas properties must be used to run the simulation.

D (c, T) � ([1 � Ac] 10�7) e[B�C/T]

FIGURE 5.5 Influence of blowing agent on viscosity (the dotted line corresponds to 15%butane data).

FIGURE 5.6 Concentration effect on gas diffusivity [31].


The other simulation parameters used for all cases in this study are listed in Table 5.3. The model yields the result in terms of bubble radius as a func-tion of time. The growing bubble reaches an equilibrium bubble radius oncethe gas is depleted. Finally, the bubble diameter was multiplied by the num-ber of cells that are simultaneously growing across the diameter of the ex-panding rod to calculate the rod diameter. The simulated results are plotted inFigure 5.7.

5.8 COMPARISON OF THEORY WITH EXPERIMENT

Figure 5.7 shows the comparison of Ramesh et al.’s model with Arefmaneshet al.’s model [20–21] and the experimental data. The solid line denotes thecurrent model, dashed line denotes a previous model. The prediction of thefoam strand diameter by the new model seems to agree well with the experi-mental data when the concentration and surface gas loss effects are included.The previous model predicts longer growth time due to neglecting concentra-

FIGURE 5.7 Comparison of experiment versus theory.


tion effects. Furthermore, the predicted induction time is longer and the shapeof the curve does not seem to match the characteristics exhibited by the exper-imental data. The previous model also predicts a higher strand diameter thanexperimentally observed because it assumes no gas loss from the bubbles thatare close to the surface. A significant difference in strand diameter leads toserious discrepancies in predicting the final foam density, as it depends on thesquare of the rod diameter. Therefore, analysis including blowing agent con-centration and surface escape effects in the thermoplastic foam expansionmodel is essential to accurately predict foam growth rate and density.

5.9 CONCLUSIONS

An overview of bubble growth models and experiments is presented in thischapter; Ramesh et al.’s modified model presents a new approach for modelingbubble growth during extrusion processing of foams that for the first time in-cludes blowing agent concentration and temperature effects on physical prop-erties during foam formation and gas loss. Gas loss, blowing agent, and tran-sient cooling effects are found to be important. Predictions by this new modelagree well with experimental data. A simple but useful experimental techniqueis presented to collect the foam growth data. The predictions of previous foamgrowth models lacking the influence of blowing agent concentration effects inthese binary systems differ significantly from experimental observations in ex-truded thermoplastic foam formation in an open system. This is another steptoward arriving at a more thorough understanding of the concentration and gasloss interactions of the free-form foam process. Although the bubble growthdiscussion dates back to 1917 in the literature, still more modeling and exper-imental skills are required to describe polymeric foam systems.

5.10 NOMENCLATURE

c Gas concentrationcs Surface gas concentrationco Initial gas concentrationc∞ Surrounding gas concentrationD Diffusion coefficient, cm2/secEv Activation energy for viscosity equationf(c) Viscosity reduction factorG Elastic modulusKw Henry’s law constantPg Gas pressure at time tPgo Initial gas pressure inside the bubble


P∞ Surrounding pressureRo Initial bubble radiusRg Gas constantR Gas-polymer interfacial radiusr Radial coordinateRf Cell outer radiusRo Initial bubble radiusT Foaming temperature, °KTo Initial sheet temperature, °KTs Surrounding room temperature, °Kt Foam growth timeVr Radial component of velocity

Modified zero shear viscosity according to equation�rr, �∞ Stress in radial and circumferential directions�(1) Convected time derive of stress tensor� Rate of strain tensor� Density of polymer�g Density of blowing agent� Surface tension of the polymer, N/m

5.11 REFERENCES

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�*0


20. A. Arefmanesh, Ph. D. Thesis, Dept. of Mech. Eng., Univ of Delaware (1991).

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25. N. S. Ramesh and Nelson Malwitz, SPE ANTEC J., 2171 (1995).

26. S. T. Lee and N. S. Ramesh, Adv. Polym. Tech., Vol. 15, 297 (1996).

27. S. T. Lee, N. S. Ramesh and G. A. Campbell, Polym. Eng. Sci., Vol. 36, 2477 (1996).

28. N. S. Ramesh and N. Malwitz, Polymeric Foams, ACS Ser. 669, Chapter 14, 206 (1997).

29. N. S. Ramesh and N. Malwitz, SPE ANTEC J., 1907 (1998).

30. J. R. Welty, C. E. Wicks and R. E. Wilson, Fundamentals of Heat and Mass Transfer, JohnWiley and Sons, NY, 556–557 (1969).

31. V. C. Coonahan, Ph.D. Thesis, Dept of Chem. Eng., Univ. of Maryland (1971).

32. M. A. Shafi, K. Joshi and R. W. Flumerfert, Chem. Eng. Sci., Vol. 52, 635 (1997).

33. S. T. Lee, PhD. Thesis, Stevens Institute of Techology, ChE Dept (1986).

34. S. T. Lee, N. S. Ramesh, “Cellular and Microcellular Materials,” ASME ‘96, 71–80 (1996).

35. R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids, SecondEdition, Vol. 1: Fluide Mechanics, pp. 345–346, John Wiley & Sons (1987).

36. M. A. Shafi and Flumerfelt, Chem. Eng. Sci., 628–643 (1996).


CHAPTER 6

Polymeric Foaming Simulation: Batchand Continuous

MASAHIRO OHSHIMA

6.1 INTRODUCTION

THE use of polymeric foams is rapidly expanding due to their excellentproperties including light weight, high strength/weight ratio, and superior

insulating abilities. The foaming methods can be divided into two categories:physical and chemical. In the former, dissolving a gas (such as nitrogen orcarbon dioxide) into polymer at a specified temperature and pressure createsfoams. Once the dissolution is completed, either the pressure is reduced (as inextrusion foaming) or the temperature is increased in order to supersaturate thegas (as in compression foaming). In chemical foaming, foams are created bydecomposing a chemical blowing agent that has been incorporated into apolymer. At a certain temperature and pressure, a chemical reaction (usually amolecular decomposition) releases the foaming gas. In either method, the nu-cleation and subsequent bubble growth create the cellular structure in thepolymer.

A basic understanding of the cause-and-effect relationships between theprocessing conditions and bubble size and foam density are important tocontrol the cellular structure and to produce foamed product of high quality.Many researchers have been studying nucleation and bubble growth in poly-mers and developing several models. Two chapters of this book, 4 and 5, havealready been dedicated to the modeling of foaming. One deals with the model-ing of the nucleation phenomena, and another describes the modeling ofbubble growth dynamics. In order to simulate bubble size distribution anddensity, simultaneous consideration of nucleation and bubble growth dynam-ics is indispensable. This chapter deals with foaming simulation that combinesnucleation and bubble growth models to estimate the effects of different pa-


rameters such as viscosity, dissolved gas concentration, and pressure releaserate. The chapter is roughly divided into two sections: one is for the simulationof batch foaming, and the other is for continuous foaming, i.e., foaming in theflow. In each section, basic models of nucleation and bubble growth dynamicsare described together with a total mass balance equation for all bubbles thatplays a role of jointing nucleation models together with bubble growth models,followed by some results of parametric computations to illustrate the relativeimportance of the parameters.

6.2 BATCH FOAMING

The classical work on bubble nucleation and growth goes back to Zeldovich[1]. The pioneering modeling of the growth of a single gas bubble in a polymermatrix was carried out by Street et al. [2]. The latter authors introduced theconcept of a finite influence volume around each bubble. They also consideredthe effects of heat, mass, and mass transfer on bubble growth. During the in-tervening years, numerous models have been published [3–5, 12–19]. Re-cently, extending the influence volume approach, Shafi et al. developed amodel for free expansion polymer foaming that includes simultaneous nucle-ation and bubble growth [6–9]. In this section, employing their models as thebasis, modeling as well as simulation of simultaneous nucleation and bubblegrowth for batch physical foaming is described.

The physical foaming processes can be divided into four basic steps:

(1) Dissolution of gas into polymer at elevated pressure

(2) Nucleation of bubbles in a supersaturated solution of gas in a moltenpolymer matrix, by releasing the pressure or increasing the temperature

(3) Growth of bubbles in molten polymer to an equilibrium size

(4) Stabilization of the foam structure by lowering the temperature below themelting point or the glass transition temperature

6.2.1 NUCLEATION MODEL

Shafi et al. proposed models for steps (2) and (3), above [6]. It was assumedthat, initially, the equilibrium dissolved gas concentration is co at pressure PD0.To describe bubble nucleation, the models of heterogeneous and homogeneousnucleation rates were given by the following [6, 8, 9]:

(1)Jhet (t) � fhet exp a �16��3F

3kBT{PD0 � PC � I{Gk,�} � PD0 ln�/Z2L}2b NS


(2)

where Jhet and Jhom represent the rates of heterogeneous and homogeneous nu-cleation, respectively, NS denotes the number of heterogeneous nucleationsites, fhet and fhom are frequency factors for the heterogeneous and homoge-neous nucleation, respectively, kB is Boltzmann’s constant, T denotes temper-ature, co is concentration of the dissolved gas, t is the time since the beginningof foaming, is the average concentration of gas dissolved in the polymerand Pc is the ambient pressure, I{Gk,�}, �, Z2L, and L denote the elasticitynumber, activity coefficient of dissolved gas, the compressibility factor andAvogadro’s number, respectively, and � and denote surface tensionand the wetting factor for the heterogeneous nucleation that depends only onthe wetting angle �.The total nucleation rate at time t was given by the following:

(3)

The derivation is based on the classical approach that predicts the criticalradius for bubble nucleation: , where �bp is the interfacialtension coefficient between the bubble and polymer matrix and �P is the pres-sure differential between the inside bubble pressure and the ambient pressure:

. Since the free energy of nucleation is proportional to thebubble volume, the theory predicts high sensitivity: .However, in the newer theory, the classical pressure drop, �P, is reduced by in-corporating the effects of viscoelasticity and nonideal solution effects [6].

Additional details and the history of nucleation models can be found in thenucleation modeling chapter of this book (Chap. 4).

It is important to recognize that at the moment of phase separation, asdefined by the spinodal conditions, �bp might be equal to 0. As the concentra-tion of gas molecules in the polymeric matrix decreases, the interfacial tensioncoefficient is expected to increase toward its equilibrium value. However, it isdifficult to assess the dynamic concentration at the nucleating bubble wall and,consequently, the value of the parameter �bp [10] is also difficult to assess.

6.2.2 BUBBLE GROWTH MODELS

The main difference between the old foaming simulation models and therecent one is the careful analysis of the bubble growth kinetics that start im-mediately after the bubble is nucleated. The motivation for inclusion of the

�G*het � �bp3 /�P2

�P � PD � Pc

r* � 2�bp/�P

Jtotal(t) � Jhom(t) � Jhet(t)

F � F(�)

C(t)

� fhom exp a �16��3

3kBT{PD0 � PC � I{Gk,�} � PD0 (ln�)/Z2L}2b LC(t)

Jhom(t)


growth kinetics is the presence of the well-known exclusion volume—thevolume of the material around each bubble wherein the concentration of thedissolved gas is below the equilibrium concentration, co.

The bubble growth mechanism was described using the equations ofmotion, mass balance over the bubble, and gas diffusion in the surroundingpolymer phase [11]:

(4)

(5)

(6)

The initial conditions are as follows:

(7)

The boundary conditions are as follows:

(8)

(9)

where r is the coordinate and � is the time since the bubble was born, D and �,respectively, denote the diffusion and viscosity coefficients, PD(�) is pressureinside the bubble at time �, and R and represent the radius of the bubble andits growth rate, respectively.

By Equation (6), the polymer surrounding the bubble is dealt with as a Newtonian fluid. This might severely limit practical use, especially for situa-tions in which the Deborah number is not negligible [2]. One could take non-Newtonian behavior of polymer into account as is done by the cell model [5,12, 13, 14]. However, for the sake of computational simplicity, Equation (6)was employed for all simulation calculations illustrated in this chapter. In thesimulation, it was also assumed that the dissolved gas concentration c(r, �)around a bubble depends on the radial position, r, and time, �, and that the gasconcentration, c(R, �), at the surface is determined by the gas pressure insidethe bubble according to Henry’s law: .

Basically, simultaneous nucleation and bubble growth simulation is carriedout in the following way (Figure 6.1): every moment, the number of bubbles

PD(t) � k�1H c(r, �)

R#

c(R,�) � cR (�) � kHPD(�)

c(,�) � co

c(r,0) � c0 � kHPD0

�c

�t�

R#R2

r2 �c

�r�

D

r2 �

�r ar2

�c

�rb

d

dt a4�

3 PDR3

RgTb � 4�R 2D

�c

�r `

r�R

4� R#

R� PD � PC �

2�

R


nucleated is calculated using Equations (1) and/or (2) as a function of averagegas concentration in the polymer matrix, , ambient pressure, Pc(t), andtemperature. Then, for each bubble born at time t, the bubble size growth iscalculated by Equations (4)–(6) with the boundary conditions, Equations(7)–(9) [Figure 6.1(a)]. By taking the total mass balance between residual gasin polymer and gas consumed in the growth of all bubbles, the average gasconcentration in the polymer is recalculated and used for nucleation calcula-tion at the next moment, [Figure 6.1(b): �t is the simulation time step].At the next moment, retaining the bubble growth calculation for all bubblesalready born, the nucleation and bubble growth calculation for newly nucle-ated bubbles is carried out in a similar way to that carried out in the previoustime step.

In Shafi’s study as well as in the simulations performed in this chapter, it isassumed that whenever the bubble is born, i.e., whatever value average gasconcentration takes, the pressure in the newly born bubble, PD0, is always de-termined by the initial gas concentration, i.e., . However, the as-sumption can be modified so that PD0 becomes with modifications ofgas concentration profile calculation.

The average dissolved gas concentration, , in polymer was calculatedfollowing the influence volume approach.

6.2.3 INFLUENCE VOLUME

Assuming that a bubble is born at time t�, and the operating trajectory ofpressure release is given, one can calculate the radius, the pressure inside thebubble, and the gas concentration profile in the polymer surrounding thebubble at time t by solving Equations (4) to (6) with . Consequently,� � t � t�

C(t)

k�1H C(t)

PD0 � k�1H co

t � �t

C(t)

(a) (b)

FIGURE 6.1 Simultaneous nucleation and bubble growth calculation.


one can assign an “influence volume” to the bubble, inside which no nucle-ation can take place. This is schematically presented in Figure 6.2.

In Figure 6.2, the volume defined as , with, is called the influence volume at time t for the bubble born at time

t�. S(�) is the radial position at which the dissolved gas concentration is equalto the nucleation threshold, cs. As the bubble grows, the concentration gradientpropagates radially in the surrounding polymer, thus, the influence volumealso grows. Instead of solving the partial differential equation with a movingboundary, the gas concentration profile in the surrounding polymer can be ob-tained using a moment (integral) method, i.e., the weighted residual methodproposed in the literature [15].

The integral method assumes that the gas concentration profile can be ap-proximated by a polynomial function:

When , the relation between the volume Vs ( ) and Vcb ( )of the bubble born at the time t� can be given by:

(10)Vs(t � t�) � e1 � a co � cs

co � cR (t � t�)b1/4 f Vcb(t � t�)

r � rcbr � rsNd � 3

c(r) � cR

co � cR� 1 � (1 � x)Nd�1 where x �

r3 � R3

r3cb � R3

� � t � t�Vs(�) � 4�[S3(�) � R3(�)]/3

FIGURE 6.2 Influence volume of a bubble.


Vcb is the volume enclosed by the radial position outside of which the dis-solved gas concentration is equal to co. Its value is calculated by using the fol-lowing equation:

(11)

where .Equation (11) is derived directly from the mass balance of gas between the

bubble and surrounding polymer:

(12)

In the simulation, the nucleation threshold of the dissolved gas concentrationis assumed to be equal to co, where co is the initial dissolved gasconcentration. Every bubble has an influence region; therefore, subtraction ofthe total influence volume of every bubble from the initial polymer volumegives the total volume of the noninfluence region, VL(t), where the new bubblecan generate:

(13)

where the initial value of VL, VL(0), is equal to the polymer volume.The average dissolved gas concentration in the noninfluence region, , is

then expressed by the following:

(14)

The first term on the right-hand side denotes the initial amount of dissolvedgas, and the second expresses the total amount of gas existing in all bubbles,while the third represents that dissolved in the influence volume. To solve

��t

0

VL(t�)Jtotal(t�) • �S(t�t�)

R(t�t�)

4�r2c(r,t � t�)dr¶ dt�

C(t)VL(t) � coVL(0) � �t

0

VL(t�)Jtotal(t�) 4�

3 PD(t � t�)R(t � t�)3

RgT dt�

C(t)

VL(t) � VL(0) � �t

0

VL(t�)Jtotal(t�)Vs(t � t�)dt�

cs � 0.95

4

3 �

PD(t � t�)R(t � t�)3

RgT�

4

3 �

PD(0)R(0)3

RgT� �

rcb

R

{co � c(r,t)}4�r2dr

R(0) � 2�/(PDo � Pc)

Vcb(t � t�) �20�{PD(t � t�)R(t � t�)3 � PDoR(0)3}

3RgT(co � cR(t � t�))


Equation (14), S(�), which is the radius of influence volume, is defined asfollows:

(15)

6.2.4 BUBBLE SIZE AND DENSITY AT THE FINAL EQUILIBRIUM

One of the assumptions made by Shafi et al. is that bubbles are spherical, notmutually interacting, and not coalescing. Thus, at time tf, when the total influ-ence volume becomes equal to the polymer volume [i.e., VL(t) becomes zero],the nucleation stops and the number of bubble becomes constant. However,the bubbles keep growing by consuming the gas dissolved in Vs(t) until anequilibrium is reached.

After the nucleation stops, for , the bubbles and the influence volumeshare the total amount of gas initially dissolved in Vs( ), which is the in-fluence volume at time t for the bubbles born at time ti. From the mass balanceof the gas, the final size of the bubbles born at time ti can be calculated asfollows:

(16)

Substituting the force balance at equilibrium and ,

(17)

into the above equation, the resulting equation is given by

(18)

Solving the nonlinear algebraic equation provides the final size of bubblesborn at time ti, .

6.2.5 SIMULATION RESULTS AND DISCUSSIONS

Using the relations presented in the previous sections, several numericalsimulations can be performed using Equations (1)–(18). The parameter valuesused for the simulation are listed in Table 6.1. These were mostly taken from

R( � ti)

� aPc() �2�

R( � ti)b akHVs(tf � ti) �

4

3 �

R( � ti)3

RgTb

coVs(tf � ti)

PD( � ti) � Pc () �2�

R( � ti)

C() � kHPD( � ti)

coVs(tf � ti) � C()Vs(tf � ti) �4

3 �

PD( � ti)R( � ti)3

RgT

tf � tit � tf

S(t � t�) � e a4

3 �R(t � t�)3 � Vs(t � t�)b

3

4�f 1/3


Reference [6]. The parameter values of viscosity and diffusion coefficientswere obtained from the author’s experiments. In the author’s experience, thesimulation results were very sensitive to the parameter values in the nucleationrate equations, such as the surface tension, �, and the wetting factor F.

6.2.5.1 Effect of Pressure Releasing Rate on the Bubble Size andDensity

Figure 6.3 shows a simulation result for a LDPE and nitrogen system. It isassumed that at a pressure of 12.7 MPa, nitrogen dissolves into a molten LDPE

FIGURE 6.3 Effect of pressure release rate on bubble size.

TABLE 6.1 List of Parameter Values.

T(°C) 188� (Pa.s) 6,542 [measured]

[estimated by experiments]Reference [6]

fhom

fhet Reference [6]F 0.1

References [6], [25]I(Gka) (Pa) Reference [6]Z2L 4.46 Reference [6]�x 0.497 Reference [6]

3.96 � 1051.12 � 10�2�(N m�1)

3.97 � 10112.0 � 10203.61 � 10�5kH(mol.N�1.m�1)2.0 � 10�9D(m2.s�1)


and the system reaches equilibrium. Physical foaming is conducted isother-mally by pressure release. For the simulation, it was also assumed that thepressure is released as a function of time, such that it is linearly decreased at aconstant rate, kp:

By changing the value of kp, the effect of pressure release rate on bubble sizeand density was simulated.

The simulation result illustrates that the average bubble size becomessmaller and the number of bubbles becomes larger as the rate of pressurerelease increases. These simulation results could qualitatively explain the ex-perimental results that are shown in Figure 6.3 by open squares.

6.2.5.2 Effect of Dissolved Gas Concentration on the Bubble Sizeand Density

Assuming the dissolved N2 gas concentration profile established in themolten LDPE, the simulation is performed for the case in which the pressure isreleased from 10.1 to 0.1 MPa at the rate of . Figure 6.4 shows thesimulation result. In this simulation, concentration dependence of the surface

kp � 10.1

R

Pc(t) � ePc(0) � kpt: for Pc(0) � kpt � Pc()Pc(): for Pc(0) � kpt � Pc()

FIGURE 6.4 Effect of dissolved gas concentration.


tension was not taken into account. The simulation shows that the averagebubble size becomes smaller and the number of bubbles becomes larger as theinitial concentration is increased. This is what we call a “pizza-sharing situa-tion”: when one has to share a pizza with friends, your piece becomes smalleras the number of the friends you have to share with increases.

To perform a more precise simulation, one has to consider concentration,pressure, and temperature dependencies of physical parameters such as shearviscosity [20], surface tension [10], solubility constant, and diffusion coeffi-cient [5, 18].

6.2.5.3 Interaction between Homogeneously Nucleated andHeterogeneously Nucleated Bubbles [24]

During industrial foaming processes, a nucleating agent such as talc is oftenused to increase bubble density. The presence of the nucleating agent providesheterogeneous nucleation sites for foaming but does not preclude homoge-neous nucleation. Homogeneous nucleation may still occur in the regionswhere local density of the heterogeneous nuclei is low. However, homoge-neous nucleation affects heterogeneous nucleation by reducing gas concentra-tion in the polymeric matrix. Due to the competition between these two nucle-ation mechanisms, the bubble density might be reduced as the concentration ofheterogeneous nucleation sites increases. Colton and Suh [3] reported this phe-nomenon for autoclave-prepared polystyrene microcellular foams. They de-scribed the phenomenon by employing the following heterogeneous and ho-mogeneous nucleation rate equations:

(19)

(20)

where nb is the number of gas molecules in a bubble, and � is the time since thefirst heterogeneous nucleation occurred.

The term of in the homogeneous nucleation rate equation,Equation (20), expresses the concentration of gas molecules left after the con-sumption of dissolved gas by the heterogeneous nucleation. However, theirtheory, i.e., Equations (19) and (20), could not describe the bubble size andfoam density under the conditions of coexistence of the two nucleation mech-anisms.

Using the nucleation and bubble growth models mentioned above, the inter-action between the two types of nucleation mechanisms could be simulated.Figure 6.5 illustrates the computational results. Change of the bubble density,Nb, is shown in the figure as a function of the number of the heterogeneous nu-cleating sites, Ns, for four rates of the pressure release. The models could

(co � Jhet � nb)

Jhom � (co � Jhet�nb)fhom exp(��G*hom/kBT)

Jhet � Nsfhet exp(��G*het /kBT)


predict that the increasing number of heterogeneous nucleation sites reducesbubble density locally. As the rate of pressure release increases, this reductionof bubble density diminishes and eventually disappears for high rates of pres-sure release, .

The temporary drop of Nb versus Ns can be better comprehended by consid-ering the pressure release diagram of Figures 6.6 (a, b, c), for a system with arelatively low concentration of nucleating agent. When pressure is releasedgradually, the heterogeneous nucleation precedes the homogeneous onebecause of the free energy difference. Until the homogeneous nucleationstarts, the heterogeneously nucleated bubbles alone consume the dissolved gasin the polymer. As the pressure release rate, kp, decreases, the time differencebetween onsets of the two nucleation mechanisms becomes larger and, conse-quently, gas consumption before the onset of the homogeneous nucleation in-creases. In consequence, the density drop becomes more evident as the pres-sure release rate is reduced.

Figure 6.7 (a, b, c) shows the volume occupied by each size of bubble(4�R3Nb/3) for three levels of the heterogeneous nucleation concentration,viz., , 107, and 1012. At lower concentrations of the heterogeneouslynucleated sites [see Figure 6.7(a)], the size of the heterogeneously nucleatedbubble is larger than that of the homogeneously nucleated ones, and this indi-cates the possibility that when two nucleation mechanisms occur simultane-ously, the bubble size distribution may have two peaks. On the other hand,when Ns is large [see Figure 6.7(c)], the population of the heterogeneously nu-

Ns � 103

kp � 150 MPa/s

FIGURE 6.5 Mixed modes of nucleation.


FIGURE 6.6 Dynamics of bubble density in mixed modes of nucleation: (a) , (b) �

, and (c) .kp � 40.4 Mpa.s�120.2kpkp � 10.1

FIGURE 6.7 Volume of bubbles in mixed modes of nucleation.


cleated bubbles dominates the system. These phenomena could be observed aslong as the heterogeneous nucleation rate had lower free energy than the ho-mogeneous one and increased monotonically by the number of heterogeneousnucleation sites.

6.3 CONTINUOUS FOAMING

6.3.1 VISUAL OBSERVATION

Compared with the modeling of batch foaming, relatively few publicationsfeature models and simulation of continuous foaming processes such as extru-sion foaming and injection foaming. One of the difficulties in simulating con-tinuous foaming results from the fact that flow induces many changes in thenucleation mechanism and physical properties. As described in the nucleationmodel chapter of this book, Han and Villamizar [17] observed the bubble for-mation in a shear field by using a light scattering technique and reportedseveral kinds of nucleation mechanisms: flow-induced and shear-induced nu-cleation, nucleation by thermal fluctuations, and nucleation by cavitation. Re-cently, Tujimura et al. conducted a visualization observation of bubble nucle-ation in foam extrusion die for a PP-isobutane with talc system [21]. Using along-distance microscope and high-speed video, they observed the dynamicbehavior of bubble nucleation in a shear field of a slit-die equipped with aquart glass window and obtained the pictures illustrated in Figures 6.8 and 6.9.Figure 6.8 shows the pictures of foaming at three different inlet pressures. The

FIGURE 6.8 Visual observation of foaming behavior in the die at various extrusion pressures(inlet flow pressure): (a) 3, (b) 5, and (c) 7 Mpa. Courtesy of Kanegafuchi Chemical.


white part indicates the foam, and it starts at a distance of 5–15 mm from thedie exit. By increasing the inlet pressure of polymer flow, the onset position offoaming is shifted toward the die exit as can be seen in Figure 6.8. Figure 6.9shows the magnified pictures of the onset position of foaming. Those weretaken under the three different talc concentrations. They reported two charac-teristics of bubble formation: formation of a wedge-shaped bubble film, wherenucleation of one bubble seems to induce other nucleation and forms a wedge-shaped gas film; and formation of a single, bullet-shaped bubble that seems tobe induced by the talc and runs in the gas film.

6.3.2 FOAM MODELS IN THE SHEAR FIELD

No perfect model is available to quantitatively simulate the foaming phe-nomena observed in Figures 6.8 and 6.9. However, several attempts have beenmade to simulate the bubble growth in a shear field [12, 13, 17, 19]. As aresult, the current models could qualitatively predict the onset location ofbubble formation, average bubble sizes, and density. Murayama et al. pro-posed a scheme for estimating the onset position of foam formation in the ex-trusion die of the PP-isobutane system, which was the identical system fromwhich Figures 6.8 and 6.9 were taken [22]. They used models composed of aclassical nucleation model, Patel’s bubble growth model, which is a singlebubble growth model in the finite polymer sea, and Baldwin’s fluid model[19]. The basic idea behind their modeling is the integration of macroscopicflow models with the models of microscopic behavior of the bubble as de-scribed by Equations (1)–(18). Baldwin et al. modified the non-Newtonianfluid model of the flow running through a constant cross-sectional slit of height

FIGURE 6.9 The magnified fields of bubble nucleating behavior at various talc concentrations:(a) 0%, (b) 0.1%, and (c) 1%.


2B and width W [23] so that the model could consider the change in bulk vis-cosity and flow against the volume fraction of bubble (Figure 6.10).

(21)

where is the pressure drop along the flow of the z-direction. mf and n,respectively, are the power law coefficient and index of the bulk viscosity ofthe foamed polymer fluid:

(22)

m is the constant. Vg and Vp are the total volume rate of the gas phase(bubbles) and that of polymer, respectively. Q denotes the volumetric flow rateof foamed polymer fluid and is given by the following:

(23)

Using Equations (21)–(23) with Equations (1)–(18), foaming in the flow canbe simulated in the following manner: Using Figure 6.10 as a reference, the slitflow can be divided into N elements of length �z. The polymer pressure andpolymer volume flow rate at the first element are given as a boundary condi-tion. When the pressure Pc(i �z) and volumetric flow rate Q(i�z) at the up-

Q � (Vg � Vp)

� � mf�# n�1 � m c1 �

Vg

Vp � Vgd �# n�1

�dPc/dz

�dPc

dz� c 2 � 1/n

2WB2 Q d n 1

B mf

FIGURE 6.10 Flow through a slit.


stream of the i-th element are given, the time period �ti needed for flow to runthrough the i-element can be calculated by dividing 2 B W �z by the volumet-ric flow rate Q(i�z). Then, the number and growth of bubbles nucleated duringthe period is calculated using Equations (1)–(18). Substituting these calcula-tion results into Equations (21)–(23) gives the local gas phase volume, Vg, vol-umetric flow rate, Q, and pressure drop, �P(i �z). These values are used as

and for the next calcula-tion at the neighbor element.

6.3.3 SIMULATION AND EXPERIMENTAL RESULTS

Figure 6.11 is a result given by Murayama et al. [22]. The dots represent theexperimental data. The average bubble sizes are measured from the picture andare plotted along the location from the die exit. In the simulation, the locationwhere the nucleation rate exceeds a threshold value, Js, is regarded as the onsetpoint of nucleation. The dotted line represents the simulation results by themodels of Equations (1)–(12), which are nucleation rate plus single bubblegrowth models in an infinite polymer matrix (an infinite amount of gas). The

Pc((i � 1) �z) � Pc(i �z) � �P(i �z)Q((i � 1) �z)

FIGURE 6.11 A simulation result of foaming in a shear field. Courtesy of Kanegafuchi Chemical.


solid line represents the results by their models, Equations (1)–(12), with amass balance equation [i.e., simplified Equation (14)]:

(24)

Apparently, the simulation results conducted under the assumption of an infi-nite amount of gas show larger bubble size and greater bubble density than theexperimental data. By introducing the mass balance equation, Equation (24),the models could simulate a situation in which the gas available for bubble nu-cleation and growth runs out in the middle of the die, and, therefore, the bubblesize reaches a plateau value. Because the total volume of the region where nu-cleation could take place is always equivalent to polymer volume, Vp, theirsimulation overestimates the number of bubbles that could nucleate by thetime gas runs out. As a result, the calculated position where the gas runs outand reaches the plateau value is different from that observed in the experi-ments. It might be interesting to simulate these results using the influenceregion models, i.e., Equations (1)–(18) and Equations (21)–(23) mentioned inthe previous section.

Even though a discrepancy existed between the experimental data and sim-ulated values, the onset position of bubble foaming as illustrated in Figure 6.8could be successfully predicted by introducing the threshold value, Js, for thenucleation rate.

6.4 CONCLUSIONS

Simulation schemes for batch and continuous foaming are described, basedon Shafi and Flumerfelt’s recent work. The models used in batch foaming thesimulation can take into account nucleation and bubble growth simultane-ously. These models were combined with the macroscopic fluid model whencontinuous foaming was simulated. The foaming models described in thissection can deal with only two steps of foaming processes (nucleation andbubble growth). To perform at consistent foaming simulation, the models forthe remaining two steps (i.e., gas dissolution and foam structure stabilizationprocesses) are also indispensable.

C(t)VP � co VP � VP �t

0

4�

3 J(�)PD(t � �)R(t � �)3

RgT d�


6.5 NOMENCLATURE

B Half of the slit height (m)Average dissolved gas concentration (mol )

c0 Initial dissolved gas concentration (mol )cR Dissolved gas concentration at a bubble surface (mol )cs Threshold of dissolved gas concentration (mol )D Diffusivity of gas in polymer melt ( )fhom Frequency factor of homogeneous nucleation rate ( )fhet Frequency factor of heterogeneous nucleation rate ( )�G* Critical free energy of nucleation (J)I(Gk,a) Elasticity number of nucleation (Pa)Jhom Homogeneous nucleation rate ( )Jhet Heterogeneous nucleation rate ( )Jtotal Total nucleation rate ( )kB Boltzmann constant ( )kH Solubility coefficient ( )kp Rate of pressure release ( )Nb Bubble density ( )Ns Number of heterogeneous nucleation sites ( )Pc Pressure in continuous phase or ambient pressure (Pa)PD Pressure in the bubble (Pa)PD0 Initial bubble pressure (Pa)Q Volumetric flow rate of fluid ( )r Radial coordinate (m)R Radius of a bubble (m)Rg Gas constant

Average bubble radiusBubble radius growth rate ( )

tf Time nucleation stops (s)t� Time at which a bubble is nucleated (s)T Temperature (K)Vcb Volume of concentration boundary (m3)Vs Influence volume (m3)VL Noninfluence volume (m3)Vp Volumetric flow rate of polymer ( )Vg Volumetric flow rate of gas ( )W Slit width (m)z Distance (m)Z2L Compressibility factor of dissolved gas solute in polymer melt ( )� Viscosity (Pa s)� Surface tension ( )J m�2

�

m3 s�1m3 s�1

m s�1R#R

m3 s�1

m�3m�3

Pa s�1mol m�3 Pa�1

J K�1m�3 s�1

m�3 s�1m�3 s�1

s�1s�1

m2 s�1m�3

m�3m�3

m�3C


t Time (s)� Activity coefficient of dissolved gas solute in polymer melt ( )

6.6 REFERENCES

1. Zeldovich, Ya. B., Zh. Eksp. Theor. Fiz., 12, 525 (1942); Acta Physico-chim. USSR, 18, 1(1943).

2. Street, J. R., Arthur, L. F. and Reiss, L. P., Ind. Eng. Chem. Fundam., 10, 54–64 (1971).

3. Colton, J. S. and Suh, N. P., Polym. Eng. Sci., 27, 7, pp. 500–503 (1987).

4. Ramesh, N., Rasmunssen, S. and Campbell, G. A., Polym. Eng. Sci., 34, pp. 1685–1698(1994).

5. Goel, S. K. and Beckman, E. J., AIChE J., 41, pp. 357–367 (1995).

6. Shafi, M. A., Lee, J. G. and Flumerfelt, R. W., Polym. Eng. Sci., 36, 14, pp. 1950–1959(1996).

7. Lee, J. G. and Flumerfelt, R. W., J. Appl. Polym. Sci., 58, pp. 2213–2219 (1995); J. Colloid In-terface Sci., 184, 335 (1996).

8. Shafi, M. A., Joshi, K. and Flumerfelt, R. W., Chem. Eng. Sci., 52, 4, pp. 635–644 (1997).

9. Joshi, K., Lee, J. G., Shafi, M. A. and Flumerfelt, R. W., J. Appl. Polym. Sci., 67, 1353 (1998).

10. Utracki, L. A., private communication (1998).

11. Barlow, E. J. and Langlois, W. E., IBM J. Res. Develop., 6, pp. 329–337 (1962).

12. Amon, M. and Denson, C. D., Polym. Eng. Sci., Sept, 24, 13, pp. 1026–1034 (1984).

13. Afefmanesh, A., Advani, S. G. and Michalelides, E. E., Polym. Eng. Sci., Oct. 30, 20,1330–1656 (1990).

14. Ramesh, N. S., Rasmussen, D. H. and Campbell, G. A., Polym. Eng. Sci., Mid-Dec, 31, 23,pp. 1657–1664 (1991).

15. Rosner, D. E. and Epstein, M., Chem. Eng. Sci., 27, pp. 69–88 (1972).

16. Patel, R. D., Chem. Eng. Sci., 35, pp. 2352–2356 (1980).

17. Han, C. D. and Villamizar, C. A., Polym. Eng. Sci., July, 18, 9, pp. 687–698, pp. 699–710(1978).

18. Ramesh, N. S. and Malwitz, N., ANTEC ‘95, pp. 2171–2174 (1995).

19. Baldwin, D. F., Park, C. B. and Suh, N. P., MD-Vol. 53, Cellular and Microcellular Materials,ASME, pp. 85–107 (1994).

20. Park, C. B., Lee, M. and Tzoganakis, C., PPS-14, Yokoyama, pp. 277–282 (1998).

21. Tujimura, I., Zenki, T. and Ishida, M., PPS-14, Yokoyama, pp. 113–114 (1998).

22. Murayama, T., Ikeda, J. and Ishida, M., JSPP ‘98, Osaka, pp. 169–170 (1998).

23. Bird, R. B., Armstrong, R. C. and Hassager, O., Dynamics of Polymeric Liquid, John Wiley &Sons, New York (1987).

24. Ohshima, M., Inamori, K., Takada, M. and Tanigaki, M., PPS-NA, Toronto, pp. 36–37 (1998).

25. Ruengphrathuengsuka, W., Texas A & M, Ph.D. Thesis (1992).

�


CHAPTER 7

Process Design for Thermoplastic FoamExtrusion

LEONARD F. SANSONE

7.1 INTRODUCTION

DEPENDING on the polymer used and the end-use application, thermoplasticfoams are produced with densities ranging from 3% to 50% of the

polymer density. Higher density foams utilize chemical blowing agents (CBA)that decompose to release gas that is dissolved in the melt. As the pressure isreduced in passing through the die, the gas is released to form the foam. Lowerdensity foams utilize liquid or gaseous blowing agents injected into a plasti-cating extruder. These blowing agents dissolve in the melt and have a strongplasticizing action causing a large reduction in melt viscosity. An attempt toform a foam under these conditions results in excessive expansion, cellrupture, and collapse of the structure. This effect necessitates the reduction ofmelt temperature to avoid overblowing and cell rupture. Although heat can beextracted by cooling the downstream zones of the extruder barrel, the conflict-ing requirements for design of a plasticating extruder versus the design forheat extraction limit the production rate. Higher production rates can be ob-tained by using a second extruder operating in tandem with the plasticating ex-truder. The primary function of the second extruder is to cool the melt to a tem-perature range where good quality foam may be formed.

Good instrumentation is necessary to provide adequate control needed forextrusion of foam products. Modern self-tuning temperature controllersprovide stable operating temperature. A retractable melt thermocouplemounted in the die adaptor allows measurement of the temperature distributionin the melt stream. The device allows positioning of the thermocouple tipduring operation to obtain the melt temperature profile. Use of a high-speedrecorder or computer data acquisition can reveal time-dependent temperature


fluctuations caused by poor mixing or surging. Fixed melt thermocouples canprovide misleading information because they cannot indicate the temperatureextremes in the melt stream.

A pressure transducer located near the screw tip provides vital informationto confirm proper design of the die and operation of the extruder. An extruderscrew is a pressure-sensitive pump. At low pressures, work input will be inad-equate to provide proper mixing, while at high pressures, excessive melt tem-perature may require reduction of output rate.

7.2 HIGH-DENSITY STRUCTURAL FOAM PROCESS

High-density structural foams find applications competing with productstraditionally made from wood. PVC is the leading plastic used in these appli-cations due to its favorable physical properties and cost. The CBA can be dis-persed in the compound during the pelletizing process, but care must be takento avoid excessive melt temperature that will cause the CBA to decomposeprematurely. The utilization of PVC dryblend powder circumvents thisproblem and, in addition, eliminates the cost of pelletizing. Both single- andtwin-screw extruders are successfully used in forming PVC foams from dry-blend powder.

High-density foams can also be formed from PE, ABS, PS, PP, and otherpolymers. These materials are generally not available in powder form and arebest handled by using blowing agent concentrates or pellets that have beencompounded with the blowing agent incorporated during the pelletizingprocess. Selection of the CBA depends on the processing temperature of thepolymer. If the decomposition temperature of the blowing agent is too low, itwill decompose prematurely in the extruder, and the gas will be ventedthrough the feed throat. Conversely, if the decomposition temperature is toohigh, the decomposition temperature will not be reached, and gas will not beevolved. The decomposition temperature can be adjusted by using an activatorthat induces decomposition at a lower temperature. It should be noted thatmany common additives used in polymer formulation act as activators so thatformulation changes may affect the decomposition temperature. Suppliers ofCBA compounds have developed materials suited to various polymers and canprovide recommendations for required concentration and operating condi-tions.

When using polymers in powder form, air entrapment can cause large blis-ters in the extrudate. This can be avoided by using a metered feed to allow airto escape in the feed throat or by using a two-stage screw with vacuumventing. Another approach is to use a small-diameter tube inserted in the feedthroat to act as an air vent. Residual moisture will also cause large blisters andshould be removed by vacuum venting or hopper drying.


Experience in extruding solid, unfoamed products with the particularpolymer chosen for foam extrusion is helpful in setting up operating condi-tions for foam extrusion. However, additional constraints needed to form goodquality foam may require alteration of operating conditions typically used forextrusion of solid products.

7.2.1 SCREW DESIGN FOR SINGLE-SCREW EXTRUDERS

A screw that provides good mixing and control of melt temperature for agiven polymer will provide good results for structural foam extrusion. Someadjustment of barrel zone temperatures may be required to initiate blowingagent decomposition at the right time and to provide the optimum melt tem-perature as the polymer enters the die. As indicated by Rauwendaal [1], barrierscrews fitted with a mixing section give excellent results. Extruder manufac-turers have developed screw designs specific to various polymers and canprovide recommendations for foam extrusion.

7.2.1.1 Setting Operating Conditions on Single-Screw Extruders

7.2.1.1.1 Feed Throat

The feed throat is typically cored to provide cooling of this section. Coolingis beneficial for low-melt-point polymers that may stick to the inside surface ifthe feed throat is allowed to reach a high temperature by conduction from zone1 of the extruder barrel. It should be recognized that typically, two to threescrew flights are within the feed throat section, and they comprise part of thescrew feed section. Screw and barrel temperatures, bulk density, and pellettemperature affect feeding of solids. Feeding is optimized with low friction onthe screw and high friction on the barrel. High-melting-point polymers maynot require feed throat cooling and may actually show improved feeding by al-lowing the feed throat section to come to a higher temperature. Cold pellets,caused by storage in an outside silo during winter, may cause erratic feedingdue to the reduction of the friction coefficient on the barrel surface. This maybe alleviated by preheating the pellets using a hopper dryer or by heating thefeed throat by circulating a hot fluid under controlled temperature conditions.

7.2.1.1.2 Barrel Zone 1

Care must be taken in setting zone 1 barrel temperature to avoid prematuredecomposition of the blowing agent that will result in loss of density reduc-tion. However, excessively low zone 1 temperature may result in poor mixingand poor extrudate quality. In addition, some polymers show a very sensitiverelationship between zone 1 temperature and feed efficiency. Studies relating


friction coefficients to metal surface temperature and material temperaturehave been described by Gregory [2]. Other studies have included the effects ofpressure and surface speed. Darnell and Mol [3] showed that minimizing fric-tion on the screw and maximizing friction on the barrel surface optimizessolids feeding. Polymers typically show an increase in friction coefficient asthe surface temperature is increased, reaching a peak and then diminishing asthe temperature is increased further. Some polymers such as polystyrene (PS)have a very sharp peak, making control of zone temperature critical. Others,such as high-density polyethylene (HDPE) have a very broad peak, allowing abroad temperature range to be utilized while maintaining good feeding effi-ciency. Materials such as polypropylene (PP) have a very flat response to tem-perature and exhibit low feed efficiency. It should be noted that compound ad-ditives such as slip agents and lubricants often alter the frictionalcharacteristics drastically. Although most polymers show adequate feed effi-ciency, those with poor feeding characteristics can be improved by cooling thefeed section of the screw.

Improper zone 1 temperature can result in surging due to erratic feeding.The best approach is to start with a low zone 1 temperature, observe extrudatequality, pressure stability, and foam density, and then adjust zone 1 tempera-ture as required. If limits on zone 1 temperature are found to be narrow, zone 2temperature can be raised to promote melting and mixing. It is important toreach the decomposition temperature prior to the metering section of the screwin order to allow the released gas to be solvated and dispersed uniformly.

7.2.1.1.3 Downstream Barrel Zones

A reverse temperature profile on the barrel promotes early melting that im-proves mixing and reduces the temperature gradient in the melt stream as itenters the die. As indicated above, excessive temperature in zone 1 may causethe blowing agent to decompose prematurely with loss of gas through the feedthroat. When high temperatures are employed in either zone 1 or 2, it is usuallynecessary to set the downstream zone temperatures below the desired melttemperature to avoid excessive melt temperature as the polymer enters the die.Extraction of heat in the downstream zones raises the melt viscosity, impartingmore shear work to the polymer resulting in improved mixing and melt homo-geneity.

A retractable melt thermocouple is useful in measuring the temperature gra-dient in the melt stream as it passes through the adaptor section. It is not un-common to find temperature gradients as large as 40°F in the melt stream dueto improper operating conditions or a worn screw and barrel. Large tempera-ture gradients will result in underblown or overblown portions of the extru-date. Excessive melt temperature will result in overblowing, subsequent cellrupture, and collapse of the structure. Low melt temperature causes the foam


density to be too high. Temperature gradients can be reduced by good screwdesign, proper barrel zone temperatures, or the use of a static mixer. The staticmixer provides a uniform temperature distribution as well as a more uniformdistribution of the dissolved gas. Care must be taken in selecting a static mixerwhen processing materials with poor thermal stability as some designs utilizegeometries resulting in excessive residence time.

7.2.2 SCREW DESIGN FOR TWIN-SCREW EXTRUDERS

Although twin-screw extruders can be employed in the processing of a widevariety of polymers, their main application in foam extrusion is in the produc-tion of PVC products utilizing dryblend powders. The elimination of the costof pelletizing and the ability to maintain controlled melt temperature at a highproduction rate provides manufacturing cost reductions that offset the higherequipment capital cost compared to a single-screw extruder. Intermeshing,counterrotating twin-screw machines for powder extrusion of PVC com-pounds are available with conical or parallel screw geometries, and they typi-cally employ metered feeding. To accommodate the need to compress thepowder material and extract trapped air and moisture, the screws are designedwith feed, compression, first metering, venting, compression, and a secondmetering section. As with single-screw extruders, barrel heat is arranged inzones in order to optimize the temperature for each section of the extruder. Inaddition, the temperature of the screws is controlled over the entire length bycirculating a heat transfer fluid though the bores of the screws.

Compression is obtained by reducing the available volume in the screwchannels by changing the pitch and number of thread starts. In the case ofconical screws, the reduction of diameter also contributes to the compressionas the material is conveyed forward. After the first metering section, thevolume is increased so that this section runs partially empty to allow ventingof air and moisture. The volume is then reduced and conveyed into the secondmetering section that builds pressure to pump the material through the die. Thescrew flights are designed to have clearances between the crown of the flightand the root of the opposing screw and adjacent flanks, typically in the rangeof 0.040 to 0.120 inches.

7.2.2.1 Setting Operating Conditions for Twin-Screw Extruders

Since there are substantial gaps between the screw flights, counterrotatingtwin-screw extruders are not positive displacement pumps, but they achieve60% to 85% volumetric pumping efficiency in the feed section under floodfeed conditions. Metering the feed so that the screw flights are just visible willreduce the output slightly but will allow entrapped air in the powder to escapethrough the feed throat.


The CBA can be incorporated in the dryblend powder or added at the feedthroat using a screw feeder. A CBA concentrate will provide good dispersionwhen added with a feeder but will also increase material costs.

Employing metered feeding allows start-up of the extruder in a starved con-dition to initially operate at low power input. After observing melt temperatureand product quality, feed rate can be increased as required. As the filled lengthis increased, power input, shear work, and mixing are increased. In addition,increasing screw temperature and zone 1 barrel temperature will move thefusion point back in the extruder, thus increasing mixing length and melt tem-perature.

The first metering section acts as a dynamic throttle, causing a pressurebuildup that in turn drives more material through the flank and crown/rootgaps in the compression and metering sections where high shear rates areimposed. Depending on the design of the screws and feed rate, the flow rate ofthe first metering section may be 25% above the theoretical drag flow rate.Shear rates in the gaps are typically in the range of 200 to 600 reciprocalseconds, while the rates in the screw channel may be only 5 to 10 reciprocalseconds. The intermittent high shear rate, followed by conveying at low shearrate provides good dispersion of compound additives without causing exces-sive melt temperature. In addition, the large surface area of the screws allowssubstantial extraction of heat through screw cooling. Heat transfer fluid tem-peratures are typically in the range of 275°F to 325°F for PVC powder com-pounds. Depending on the lubricity of the compound, higher temperaturesmay cause it to stick to the screw surface and may also cause subsequentthermal degradation.

As with single-screw extrusion, care must be taken to avoid premature risein the melt temperature, resulting in decomposition of the CBA and loss of gasthrough the feed throat or the vent section. The preferred condition at the ventis a semi-fused crumb. If the material is still in powder form at the vent, airleaking from the feed section will cause blow-over when vacuum is applied. Ifa well-fused ribbon is formed, blow-over is avoided, but the melt temperaturemay be high enough to cause premature CBA decomposition. Depending onscrew design and compound characteristics, this may be alleviated by operat-ing with an open vent or at reduced vacuum levels in the range of 2 to 5 inHg.Starve feeding to the extent that the crowns of the screw flights are just visibleallows release of much of the air before the material is conveyed to the ventsection.

The melt temperature should reach the decomposition temperature of theCBA in the compression section prior to the second metering section. This pro-vides time for the released gas to be dissolved and dispersed in the melt underhigh pressure. Failure to reach the decomposition temperature just prior to thesecond metering section will result in inadequate density reduction. Attemptsto correct this by increasing the die temperature will result in density reduction


on the surface of the extrudate and a higher density core due to the poorthermal conductivity of the polymer. This approach can also cause overblow-ing of the surface material, causing cell rupture and a very rough appearance.

As with single-screw extrusion, a retractable melt thermocouple installed inthe die adaptor and a pressure transducer mounted near the screw tips are vitalinstruments needed to control operating conditions. The best operating condi-tions are obtained by operating at a sufficient high pressure to raise the melttemperature in the second metering section by shear work. Normally, thebarrel zone temperature for the metering section will be set at 10°F to 30°Fbelow the desired melt temperature for extrusion of PVC. The variation in melttemperature through the melt stream as measured by incrementally moving thethermocouple position provides information useful in setting barrel zone andscrew temperatures. High temperature at the centerline of the adaptor flowchannel can be corrected by reducing screw temperature and/or raising the me-tering barrel zone temperature.

Excessively low operating pressure will result in poor mixing, large temper-ature gradients in the melt stream, and large density gradients in the product.Conversely, excessively high pressure will cause high melt temperature result-ing in overblowing and cell collapse. Due to the substantial gaps in the inter-meshing region of the screws, the metering section of the extruder performs asa pressure-sensitive pump. As pressure is increased, the fill point of the screwsmoves back toward the vent section. Additional increase in the pressure willeventually cause vent flooding.

7.3 LOW-DENSITY FOAM PROCESS

Foams with densities as low as 1.5 lb/cu ft can be produced by utilizingliquid or gaseous blowing agents commonly termed physical blowing agents.These blowing agents must be soluble in the polymer at high pressure and tem-perature and must be at least partially insoluble when pressure is reduced.When the applied pressure falls below the level of the partial pressure of theblowing agent, bubble nucleation is initiated. Commonly used physicalblowing agents include HCFC 141b and 142b, hydrocarbons propane, butane,and pentane, and argon or carbon dioxide gas. Cell nucleators such as fine-par-ticle calcium carbonate or talc are used at 1 to 2% concentration in order toprovide a fine cell structure. Physical blowing agents are metered into the ex-truder under high pressure and are dissolved in the melt. Studies by Han [4, 5]indicate that at the concentrations used to obtain low-density products, physi-cal blowing agents have a strong plasticizing action on the melt, greatly reduc-ing the viscosity. The high melt temperature and intensive shear required toproperly disperse the blowing agent prevents direct extrusion into a die as thehigh partial pressure of the blowing agent and the low viscosity will cause


overblowing, cell rupture, and collapse of the extrudate. Although a screw canbe designed to minimize work input in the downstream region, conflicting re-quirements for cooling versus intensive mixing and limited surface area forheat extraction severely limit the production rate capability. For this reason,commercial systems often employ a second extruder in tandem with the plasti-cating extruder. The second extruder is typically one size larger than the plas-ticating extruder and functions as a heat exchanger designed to optimize ex-traction of heat in order to reduce the melt temperature into a range where asatisfactory foam can be formed.

7.3.1 SINGLE-SCREW DESIGN FOR LOW-DENSITY FOAMPLASTICATING EXTRUDER

A barrier type screw with an intensive mixing section downstream of theblowing agent injection point is recommended. An L/D ratio of at least 32:1 isrecommended in order to provide sufficient time and shear to obtain good dis-persion of the blowing agent and cell nucleator. A screw design found toprovide good performance with the polymer used for solid extrusions will besatisfactory for use in the plasticating extruder in a tandem foam extrusionsystem.

7.3.2 SETTING OPERATING CONDITIONS FOR THEPLASTICATING EXTRUDER

The recommendations for operation of the feed throat as described for high-density structural foams apply here as well. The setting of zone 1 barrel tem-perature differs in that we are not concerned with premature decomposition ofa CBA and thus have considerably more latitude in setting zone 1 barrel tem-perature. The first concern is to utilize a temperature that provides steadysolids feeding. Second, a reverse temperature profile with zone 1 set higherthan the required melt temperature provides early melting that enhancesmixing. It is important to assure that melting is completed before reaching theinjection port. If the solid bed extends to the injection port, the blowing agentwill flow through the bed and escape through the feed throat. A gas detector inthe feed hopper is useful to assure that there is no backflow of the blowingagent, especially if combustible blowing agents are used. If zone 1 temperatureis limited by feeding performance, melting can be accelerated by using a hightemperature in zone 2 to assure that a melt seal has been formed.

The blowing agent is injected downstream of the barrier section and prior tothe mixing section. Blowing agents in the liquid state can be metered by usinga variable speed multiplex piston pump. The metering pump capacity shouldbe selected to provide multiple small volumes in order to approach continuousflow. Calculating the number of screw revolutions per injection pulse will in-


dicate if the injection rate has approached continuous flow. The injection pumpshould only be started after assuring that the screw is filled and pressure at thescrew tip has reached the normal operating level in order to avoid forward orbackward flow of the blowing agent.

The injection nozzle should be fitted with a check valve to avoid cloggingbefore the injection pump is started. Metering of gaseous blowing agents re-quires instrumentation to measure pressure, temperature, and volume flow ratein order to control the mass flow rate.

In order to minimize the amount of heat that must be extracted in thecooling extruder, the downstream zones should be held at a temperature belowthe melt temperature. In addition, the melt pipe connecting the plasticating ex-truder to the cooling extruder should be designed to minimize the pressuredrop. Higher pressure requires higher screw speed to maintain the same outputrate. This, in turn, causes a larger temperature rise in the melt stream. In addi-tion, there is a melt temperature rise in the feed pipe which is as follows:

(1)

where: temperature rise, °F; drop, psi; density , lb/in3; and heat capacity, BTU/lb °F.

7.3.4 COOLING EXTRUDER SCREW DESIGN FOR LOW-DENSITY FOAM

Since the polymer has been melted and mixed prior to entering the coolingextruder, the cooling extruder screw design is significantly different from thatof a plasticating extruder screw. There is no need to have a feed section such asthat required for a plasticating screw. Since the pumping characteristics of amelt are determined by its viscous properties, we are not concerned with theeffects of bulk density and frictional characteristics as with the case for solidsfeeding. In order to effectively reduce the melt temperature, we must minimizethe energy input to the melt due to mechanical work. By examining the equa-tions for work input and output rate for a single-flighted, single-screw extruderpumping a polymer melt, we can develop a design and operating mode thatprovides the highest throughput with the minimum energy expended.

Considering a small element along the screw axis, the net output rate is asfollows:

(2)

where , in3/sec; flow correction factor;diameter, inch; speed, revolutions/sec; h � channelN � screwD � screw

Fd � dragQnet � volumetric flow rate

Qnet�Fd �2 D2 N h (1 � e/ t) sin� cos�

2 �Fp � D h3 (1 � e/ t) sin2�

12 � dP

dL

CP � specific� � melt�P � pressure�T � average

�T � �P/� Cp (under adiabatic conditions)


depth, inch; flight width parallel to screw axis, inch; pitch, inch; helix angle, degrees; flow correction

factor; viscosity, lbf sec/in2; and gradient along

screw, psi/inch.If the pressure rise along the screw is zero, the output rate, termed the drag

flow rate, is as follows:

(3)

This condition is obtained by adjusting the screw speed of the plasticating ex-truder to maintain the pressure at the inlet to the cooling extruder equal to thepressure at the exit. The power input over a small segment where conditionscan be considered isothermal is as follows:

(4)

where input, in lbf/sec; viscosity over flight land, lbfsec/in2; and screw/barrel clearance, inch. Since there is no pressuregradient along the screw, the term Q�P is zero under drag flow conditions. Thepower input is:

term 1 term 2

(5)

Term 1 is the power expended by shear work in the downstream and cross-stream directions. Term 2 is the power expended by shear work in the leakageflow over the flight land. With a new screw and barrel, this term is small incomparison to term 1. However, as the radial screw/barrel clearance, �,becomes large, the power expended at the flight land increases, causing largetemperature gradients in the melt. In addition, the metering performance of thescrew deteriorates causing poor tolerance control.

At a given flow rate, we can minimize term 1 by optimizing the helix angle,�. The power input per unit volume is calculated by dividing power input byQd, the drag flow rate. By increasing the pumping efficiency, the screw speed

� �2 D2 N2 �L e

� tan �d �L

�E � c�3 D3 N2 � ( 1 � e/t ) ( cos2 � � 4 sin2 � )

h

� � radial�L � melt�E � power

� �2 D2 N2 �L e]

� tan � dL � Q�P

�E � [ �3 D3 N2 � ( 1 � e / t ) (cos2 � � 4 sin2 �)

h

Qd �Fd �2 D2 N h (1 � e/ t) sin� cos�

2

dP

dL� Pressure� � melt

Fp � pressure� � screwt � screwe � screw


can be reduced while maintaining the same output rate. It is necessary to take into account the effect of screw speed on the viscosity of the polymer.This can be accomplished by employing the power law relationship,

in Equations (2) and (4). When the energy input per unitvolume is compared for a screw using the customary “square pitch” (helixangle of 17.66 degrees) with a screw using a helix angle of 30 degrees, a 20%reduction in energy input per unit volume can be attained while running thescrew at 64% of the speed needed to provide the same output using a squarepitch screw.

In order to extract sufficient heat from the melt in order to drop the temper-ature to a range where quality foam can be formed, the barrel temperature mustbe well below the melt temperature. From the standpoint of extracting heat, ashallow channel depth would be beneficial because polymers have poorthermal conductivity. However, it can be seen from Equation (4) that reducingthe channel depth, h, causes additional power input. We have two conflictingvariables and find that there is an optimum channel depth depending on thescrew design, operating conditions, and polymer properties. In addition, thereis an optimum barrel temperature. If the barrel temperature is set too low, thepolymer viscosity is increased excessively, causing more current draw on theextruder motor and resulting in increased melt temperature.

Due to mechanical work input, heat is generated in the small elementstudied at the rate of:

(6)

where c is a factor converting mechanical power to heat flow rate. In order toreduce the melt temperature, this heat must be extracted. The total heat flowrate required is:

(7)

where: temperature entering the cooling extruder and temperature leaving the cooling extruder.

To effectively remove the heat at a high rate, it is important to optimize thedesign of the barrel cooling system. Older extruders have used copper tubeswrapped into grooves in the barrel surface. This limits heat transfer due to poorcontact with the barrel caused by differential thermal expansion, low contactarea, and eventual corrosion. The best design utilizes split aluminum blockscontaining resistance heater elements and stainless steel tubing for circulationof cooling water. They must be closely fitted and tightly clamped to the barrelsurface.

As the melt temperature is reduced, the viscosity is increased and mechani-cal heat generation is increased making it more difficult to extract additional

T2 � meltT1 � melt

q � qm � � Qd Cp ( T1 � T2 )

qm � c �E

�0 (N/N0)(n�1)� �


heat as the exit end of the extruder is approached. Good instrumentation anddata recording allow the operator to evaluate various operating strategies toarrive at optimum operating conditions. Recommended instruments includepressure transducers at the screw tips of both extruders. In addition, a pressuretransducer should be located at the entry port of the cooling extruder to allowthe operator to equalize the entry pressure with the exit pressure. Retractablemelt thermocouples should be mounted in the adaptors of both extruders toallow adjustments to minimize temperature gradients in the melt stream andrecord any fluctuations with time. In order to optimize cooling performance,both extruders should be equipped with wattmeters. The cooling system zonesshould be equipped with flow meters and thermocouples to measure the heatextraction rate at each zone. A computer control system can acquire this infor-mation, process it, and provide a basis for adjusting operating conditions. Op-erating conditions can be stored for various products, and startup procedurescan be set to coordinate the operation of the two extruders and the blowingagent injection pump.

7.4 DIE DESIGN PROCEDURES FOR FOAM EXTRUSION

The primary function of an extrusion die is to form a product from moltenpolymer on a continuous basis while meeting property and dimensional re-quirements. A secondary function is to provide the optimum pressure at thescrew tip to assure that the extruder properly mixes the polymer and delivers itto the die at a uniform rate. Since both single- and twin-screw extruders arepressure-sensitive pumps, excessive pressure will result in high melt tempera-ture, frequently requiring a reduction of output rate to bring the process intocontrol. If the pressure is too low, mixing may be inadequate, resulting in poorappearance or inadequate physical properties. A die system includes the itemsdownstream of the screw tip. Sections include an adaptor, a transition or distri-bution section where the flow channel is altered from the circular bore of theadaptor, and an orifice where the shape of the product is formed. If filtering isrequired for the product, the effects of the screen pack and breaker plate mustbe considered.

Not only must the total pressure drop across the die system be controlled,the distribution of the pressure drops within the die must also be considered inorder to provide the best control of the shape and dimensions of the product.This involves calculating the pressure drops in each region of the die, takinginto account the geometry of each section and applying the appropriate flowanalysis. The design is optimized by maximizing the pressure drop in theorifice region and minimizing the pressure drops in the other regions. Theregion having the highest pressure drop has the greatest influence on the flowdistribution. The pressure drop in the orifice region is controlled by setting the


land length in order to provide a sufficient pressure drop. The viscous proper-ties of the polymer must be considered as well as the production rate and themelt temperature required.

Foam extrusion adds another requirement in that the pressure gradient andflow rate through the die must be great enough to prevent premature foam for-mation within the die. Foam formation is a nucleation and growth process.When the pressure within the die drops below the partial pressure of theblowing agent, the nucleation process is started. Nucleation is initiated at sitesformed by additives such as talc, calcium carbonate, or other additives. Initia-tion of nucleation takes time as evidenced by extrudates issuing from the die athigh speed with no visual evidence of foam formation for 1 or 2 inches. Afternucleation, bubbles grow in size, increasing the product volume and reducingthe density. The concentration of blowing agent and melt temperature deter-mine the amount of density reduction. The expansion is limited by cooling ofthe gas as it expands and subsequent extraction of heat from the polymer. Thereduction in gas pressure and increase in the viscosity of the polymer termi-nates the expansion process. Thin-gauge products can be reheated in order toachieve post-expansion to provide additional density reduction.

If the extrusion rate is too low or the melt temperature is too high, foam willform within the die, cells will be ruptured by the shearing action, and the struc-ture will collapse. To avoid this, it is necessary to maintain good control of themelt temperature and the temperature gradient within the melt stream. Ex-tremes of melt temperature will result in voids due to insufficient blowing,high-density regions, or collapsed regions due to overblowing,

The capillary rheometer is the instrument most commonly used to obtainrheology data for polymers. It utilizes a cylindrical chamber and piston todrive the polymer at a controlled rate though a small bore capillary. By mea-suring the force on the piston and computing the volumetric flow rate, theshear stress and apparent shear rate can be determined. Due to the geometry ofthe instrument, the Bagley [6] correction procedure must be used to deduct theentry pressure loss from the shear stress calculation. The Rabinowitsch [7] cor-rection factor is applied to account for the pseudoplastic nature of polymermelts.

Since the polymer is melted by conduction in this instrument, typically re-quiring 6 to 8 minutes, polymers containing blowing agent will start to releasegas prior to the start of the test. The dissolved gas has a strong plasticizingaction resulting in the reduction of viscosity. Variable amounts of gas lossprovide erratic and misleading viscosity data. In addition, data obtained at lowshear rates will exhibit extrudates issuing from the capillary that have ex-panded within the capillary and collapsed, again giving misleading data.

The problems associated with the capillary rheometer can be avoided byusing a slot rheometer as shown in Figure 7.1. The device employs a slot diefitted with a melt thermocouple and three pressure transducers to measure the


pressure gradient. The first transducer is typically placed 1/3 of the land lengthof the slot downstream of the entry to avoid measuring pressure in the entryregion. The use of three transducers allows comparison of the local pressuregradients to assure that the first transducer is downstream of the entry region.If a structural foam compound utilizing CBA is evaluated, a conventional 3⁄4�or 1� laboratory extruder may be used to melt and mix the material and drive itthrough the slot die at various conditions of melt temperature and flow rate.The melt temperature, mass flow rate, and appearance of the extrudate arerecorded. Sample densities are measured for correlation with operating condi-tions to provide information useful in die design and developing full-scale op-erating conditions.

Because it is difficult to maintain the same melt temperature over a widerange of throughput rates, it is necessary to use multivariate statistical analysisto determine the rheological parameters. Shear stress and shear rate are calcu-lated from the slot rheometer data using the following equations:

(8)

(9)�#

�2Q(a � bn)

RhAn

�Rh�P

�L

FIGURE 7.1 Slot rheometer for foam compound rheology.


where: stress, psi; radius, area/perimeter; drop between pressure taps, psi; beween pressure taps, inch; rate, 1/sec; flow rate,in3/sec; a, factors using aspect ratio obtained from Figure 7.2,Equations (10) and (11) using coefficients in Table 7.1 and Table 7.2;

law exponent; and flow area, in2.A � cross-sectionaln � power

b � shapeQ � volumetric�

#� shear

�L � distance�P � pressureinch � flowRh � hydraulic � shear

FIGURE 7.2 Flow channel geometries and nomenclature.

TABLE 7.1 Coefficients for Equation (10).

SLOT ANNULUS

A0 0.50 0.250A1 �1.321099 3.525716A2 4.339961 �20.943061A3 �11.399043 61.164339A4 17.873964 �92.305040A5 �14.120467 69.031394A6 4.338235 �20.224675

TABLE 7.2 Coefficients for Equation (11).

SLOT ANNULUS

B0 1.00 0.750B1 �0.840096 3.590286B2 1.73808E-03 �21.350268B3 3.810358 62.083357B4 �8.594332 �93.253366B5 8.127828 69.480584B6 �2.826797 �20.302289


Equations for calculating shape factors a and b:

(10)

(11)

Using the power law relationship, the following equation correlates shearstress with shear rate and temperature:

(12)

Where stress, psi; , lbf secn/in2; rate,1/sec; law exponent; activation energy, BTU/lb mol;

constant, 1.9872 BTU/°R lb mol; and temperature,Deg. Rankine. The equation is linearized by taking logarithms in order tomake a linear multivariate regression:

(13)

The values of m, n, and �E are then determined from the data set.

7.4.1 DIE DESIGN FOR HIGH-DENSITY STRUCTURALFOAM PRODUCTS

High-density structural foam products having density of about 50% of thepolymer density find applications as a wood replacement. These productsutilize a CBA to provide release of gas upon reaching a decomposition tem-perature. An alternate approach is to inject a gas such as carbon dioxide intothe extruder. In either case, the gas must be dissolved in the melt and thor-oughly mixed before the melt enters the die. Examples of two approaches fordie design are given for rigid PVC foamed to a density of 40 pcf.

7.4.1.1 Free-Foaming Method

The free-foaming method employs a die orifice smaller than the product sizeand a vacuum calibrator to form the shape of the product and to hold dimen-sional tolerances. Design for a simple rectangular shape is provided as anexample.Product: rectangular profile with 1/64� radius corners.Density: Material: Rigid PVCMelt density at 400 F: 0.045 lb/in3

Consistency at 400 F: 3.86 lbf secn/in2

Power law exponent: 0.433

40 pcf �/� 3 pcf0.25� � 2.00�

ln � ln m � n ln �#

� �E/R T

T � absoluteR � gas�E � flown � power

�#

� shearm � consistency � shear

� m �# n exp(�E/R T)

b � B0 � B1e � B2e2 � B3e3 � B4e4 � B5e5 � B6e6

a � A0 � A1e � A2e2 � A3e3 � A4e4 � A5e5 � A6e6


Production rate: 80 lb/hr at 2300 psiAdaptor: The adaptor has a included angle cone sectionand 0.50 inch bore, 4 .000 inches longVolume expansion ratio:Width expansion ratio: Die orifice width: Thickness expansion ratio: Die orifice gap: Orifice aspect ratio:

The pressure drops across the adaptor cone and bore are found using theKozicki [8] relationship:

(14)

where drop across section, psi; of section, inch;, lbf secn/in2; of

section, inch; rate, lb/hr; a, factors from Figure7.2 and Equations (10) and (11); law exponent; density,lb/in3; and flow area, in2.

For an aspect ratio of 0.125 from Equations (10) and (11), and.

The die orifice with a 1.000 inch land is evaluated: .This pressure drop is insufficient to provide good flow distribution and is inad-equate to prevent premature foam nucleation. By utilizing a 1.25 inch prelandwith a 0.100 inch gap, the pressure distribution becomes:

The transition between the adaptor bore and the preland has been ne-glected as it will make only a small contribution to the total pressure drop.Similarly, the cone portion of the pressure drop is not seen to be significant.A properly designed extruder screw will typically operate well within arange of of the optimum pressure so that the total pressure drop of 2,194 psi is adequate. The steep pressure gradient in the preland and landsections and the small cross-sectional flow area assures that premature nucle-ation will not occur.

On issuing from the die orifice, we like to observe foaming starting 1⁄8 to 1⁄4inch from the die face. The partially foamed extrudate is fed into a water-

�/� 15%

Total � 2,194 psi �P (1.250 land) � 324 psi

�P (0.100 preland) � 1130 psi �P (0.50 bore) � 692 psi

�P (cone) � 48 psi

�P(1.000 land) � 259 psib � 0.901

a � 0.384�P (0.50 bore) � 692 psi�P (cone) � 48 psi

A � cross-sectional� � meltn � power

b � shapeW � throughputRh � hydraulic radius � area/perimeterm � consistency

L � length�P � pressure

�P �mL

Rh c W(a � bn)

1,800�RhAnd n

0.200/1.600 � 0.125.25/1.248 � 0.200

(1.944)1/3 � 1.2482.0 / 1.248 � 1.600

(1.944)1/3 � 1.248(1728 � 0.045 lb/in3 )/40 pcf � 1.944

2.000 inch � 60°


cooled vacuum calibrator where foam expansion is completed. A dense skincan be formed by blowing air on the surface of the extrudate as it enters thecalibrator. However, excessive cooling will restrain expansion, resulting infailure to fill the calibrator. The calibrator dimensions are typically about 1%larger than the finished product size to allow for thermal shrinkage. Very goodtolerances can be held on the part as the calibrator does the final forming ofthe extrudate. Excessive discrepancies in the flow distribution will not affectthe dimensions but will cause density variation in the product that may bedetrimental.

7.4.1.2 Constrained Foaming Method

The rectangular slat described above can also be produced using a processdesignated Celuka® developed by Ugine Kuhlmann, S. A. Paris, France. Thetechnique involves using a die with a core plate. The vacuum calibrator ismated to the die face plate with 0.010 to 0.015 inch standoff. For PVC foam,the internal dimensions of the calibrator are about 1% larger than the finishedproduct to allow for thermal shrinkage. The die orifice is designed with di-mensions 0.020 inch less than the calibrator to assure that the extrudate entersthe calibrator freely. The following analysis demonstrates the design proce-dure.Product: rectangular profile with 1/64 inch radius cornersDensity: Material: Rigid PVCMelt density at 400 F: 0.045 lb/in3

Consistency at 400 F: 3.86 lbf sec/in2

Power law exponent: 0.433Production rate: 80 lb/hr at 2300 psiAdaptor: The adaptor has a included angle cone sectionand 0.50 inch bore, 4 .000 inches longVolume expansion ratio: Calibrator size: Die orifice dimensions: Orifice flow area:

Core plate size:Orifice perimeter:

Orifice hydraulic radius: Shape factors: The pressure drops across the adaptor cone and bore are found using theKozicki relationship, Equation (14).�P (cone) � 48 psi

a � 0.5, b � 1.00.3275/8.299 � 0.03946 inch

2 � (0.2325 � 2.000 ) � 2 � (0.075 � 1.842) � 8.299 inch

0.075 � 1.842Calibrator area/1.9442/3 � 0.2525 � 2.020/1.9442/3 � 0.3275 in2

0.2325 � 2.0000.2525 � 2.020

(1728 � 0.045 lb/in2 )/40 pcf � 1.944

2.000 inch � 60°

40 pcf �/� 3 pcf0.25� � 2.00�


The die orifice with a 1.000 inch land is evaluated: Total �P with or 668 psi less than 2,300 psi requiredoperating pressure.If the land is increased to 1.75 inch: Total

As the extrudate enters the calibrator, the outer skin can be quickly cooled toform a dense, tough surface. Since foam is a poor conductor, the inside willcontinue to foam inward to fill the cavity formed by the core.

7.4.2 DIE DESIGN FOR LOW-DENSITY FOAM PRODUCTS

Low-density foam products typically utilize the tandem extruder processwhere the second extruder is used to cool the melt to avoid excessive blowingand cell rupture. The die must be designed to minimize total pressure drop inorder to minimize the work input to the melt in the cooling extruder. However,if the pressure is too low, the foam will be formed inside the die, resulting incell rupture and collapse of the foam structure. The melt must be maintained ata pressure above the partial pressure of the blowing agent at the operating tem-perature for as long as possible. Since there is a pressure gradient in the die, atsome point, the pressure inside the die will fall below the partial pressure ofthe blowing agent. Since foam formation is a nucleation and growth process, itis possible to avoid premature expansion if a steep pressure gradient is main-tained and sufficient flow rate exists in order that the polymer exits the dieorifice before cell nucleation starts. With unpigmented material, a clear meltcan be observed issuing from the die. In processes where a high exit velocitycan be achieved, a clear melt can be observed extending for an inch or morefrom the die face.

The following information is needed to design the die:

a. Product dimensions and foam density

b. Production rate, melt temperature, and pressure at the screw tip

c. Number and mesh sizes of screens and breaker plate dimensions

d. Extruder adaptor dimensions

e. Consistency and melt density of the polymer at the operating melt temper-ature

f. Partial pressure of the blowing agent and the nucleation time at the operat-ing temperature

The mean nucleation time can be determined by experiment using an instru-mented slot die. By adjusting the flow rate until foaming appears just at the dieexit and knowing the pressure gradient in the land, the mean velocity and meannucleation time can be calculated.

�P � 2,301 psi�P(1.75� land) � 1,561 psi

1 inch land � 1,632 psi�P(1� land) � 892 psi.

�P (0.50 bore) � 692 psi


The following example illustrates the design process.Product: , 2.0 pcf density125 lb/hr, 250F melt temperature, 900 psi maximum at screw tip.Screen pack and breaker plate not used.Adaptor bore is .Die orifice:Melt density: 0.02818 lb/in3

where:Consistency, Power law exponent, Blowing agent partial pressure at Mean nucleation time,

The geometry of each section of the die must be determined, and the appro-priate flow relationship must be applied to compute the local pressure drop.The following relationship uses shape factors related to the geometry of thesection in Equation (14) in order to compute the pressure drop.

(15)

Evaluate the pressure drop across the adaptor: ; ; ;

; for a circular cross section; and .

In order to distribute the flow uniformly to the full width of the orifice, acoat-hanger manifold design is used. Since some pressure loss is experiencedin flowing down the manifold, it is necessary to compensate for this pressurereduction by cutting each half of the manifold at an angle forming a coat-hanger shape. The pressure at the centerline of the die is highest, and thepreland length and gap at the center must be designed to provide a pressuredrop equal to that experienced in flowing to the end of the manifold. In addi-tion, the pressure gradient down the manifold should be linear. This can beclosely approximated by tapering the manifold cross section. This is necessaryto achieve a linear pressure gradient because the flow rate down the manifolddiminishes in a linear fashion due to material leaking out of the manifold andflowing out of the die orifice.

The flow equation can be written in differential form:

(16)

The flow rate down each side of the manifold at the centerline is W/2. Thelocal flow rate is ). The local hydraulic radius and cross-WX � W/2(1�x/Lm

dP �m

Rh c W(a � bn)

1,800�RhAnd n dL

204 psi (adaptor)�P �a � 0.5, b � 0.75A / p � 0.1249 inch

Rh � hydraulic radius �� perimeter � � D � 1.5708 inch0.1963 in2A � � D2/4 �L � 3.0 inches

�P �mL

Rh c W(a � bn)

1,800�RhAnd n

tm � 6.7 sec250°F � 120 psi

n � 0.2834m � 2.0 lbf secn / in2 at 250°F

7.5� � 0.200.50� � 3� long

10� � 1� foam slab


sectional area must also be expressed as a function of the distance down themanifold. Figure 7.3 illustrates the geometry used for the manifold. Since themanifold is symmetrical, only one side must be evaluated. The pressure gradi-ent down the manifold is then determined by making a numerical integration.The pressure drop and the linearity of the pressure gradient are adjusted bychoosing proper values of the manifold dimensions. Performance of a numeri-cal integration yields the valves shown in Table 7.3.

Evaluate the pressure drop across one inch of land at the die orifice: land length, 1.0 inch; width, 7.5 inches; gap, 0.20 inch; ;

; inch; and . The aspect ratio approximates an infinitely wide slot

so the shape factors are for a rectangular cross section. pressure drop, psi and (1� land).

Since the pressure at the entry to die land is well below the partial pressureof the blowing agent, nucleation and cell growth may take place within the diewith resultant cell rupture. By increasing the land length to 2.5 inches, thepressure at the land entry is raised to 150 psi or 30 psi above the partial pres-sure of the blowing agent. The distance from the die orifice where the pressurereaches 120 psi is . The mean residence timewithin the die after reaching 120 psi is ;

. The total pressure droptm � 2 � 3600 � 1.5 � 0.02818/125 � 2.4 sectm � LN � 3600 � A � �/W

LN � 120/150 � 2.5 � 2 inches

�P � 60 psi�P �a � 0.5, b � 1.0

ratio � h/w � 0.02667e � aspectradius � A / p � 0.0974Rh � hydraulic15.4 inch

p � perimeter � 2(w�h) �A � flow area, � w � h � 1.50 in2h � orificew � orifice

L �

FIGURE 7.3 Geometry of tapered manifold for slot die.


across the die is the sum of the pressure drops across the adaptor, preland, andland: Total .

Note that it was necessary to reduce the gap in the preland to 0.080 inch toobtain a higher pressure in this region. The pressure drop of 310 psi in theregion where the product shape is formed contributes to improved thicknessdistribution. Since the mean residence time is below 3.7 sec, and the total pres-sure drop is below 900 psi, the design is satisfactory.

Since foaming is a three-dimensional expansion process, we might expectexpansion of width and height to be in direct proportion to the orifice size.However, it is found that the edges of the die orifice tend to restrain the widthexpansion, causing corrugation of the extrudate. In addition, residual elasticstresses and molecular orientation can cause further distortion. Corrugationcan be prevented by using rolls to level the surface of the foam extrudate as de-scribed in the Carlson [9] or Aykanian [10] patents. Other techniques includeforming between parallel flat plates while allowing the edges to form freely orextruding into a rectangular jacket where all four sides are formed. Due to thedifficulty in predicting the effects caused by edge restraint and elastic stresses,it may be necessary to make modifications to the die orifice to obtain the spec-ified product dimensions.

�P � 204 � 160 � 150 � 514 psi

TABLE 7.3 Tapered Manifold Analysis Obtained by Numerical Integration.

Tapered Manifold for Slot Die

Temp m n Density RateProject Material F psi s lb/cu in lb/hr

lowdens1 LDfoam 250 2.0000 0.2834 0.02818 125.0

Die Width Preland Gap Manifold Angle Center Depth Channel Radius7.500 in .080 in 12.7500 Degrees .625 in .200 in

ShearRelative Pressure Deviation Rate To minimize deviation, adjustDistance psi psi 1/sec center depth and channel radius.

0.0 160 0.0 37.00.1 145 0.9 36.4 To minimize manifold-preland0.2 129 1.1 35.5 pressure difference, adjust manifold0.3 113 0.9 34.3 angle and/or preland gap.0.4 96 0.4 32.5 Manifold Preland0.5 80 �0.3 30.0 Delta P Delta P Difference0.6 63 �1.2 26.8 psi psi psi0.7 46 �2.1 22.4 160 160 00.8 29 �2.6 16.60.9 14 �2.1 9.0 Angle U Angle S Preland Lc1.0 0 0.0 0.0 Deg. Deg. Length in in

1.7704 9./6856 0.640 0.532


7.5 REFERENCES

1. Rauwendaal, C., Screw Design for Foam Processing, Plastics World, 38, (May 1997).

2. Gregory, R. G., Friction Coefficients of Plastics and Steel, Proc. SPE ANTEC, (1969).

3. Darnell, W. H. and Mol, E. A. J., Solids Conveying in Extruders, SPE Journal, 20, (April1954).

4. Han, C. D. and Ma, C. Y., J. Appl. Polym. Sci., 28, 831 (1979).

5. Han, C. D. and Ma, C. Y., J. Appl. Polym. Sci., 28, 851 (1983).

6. Bagley, E. B., End Corrections in the Capillary Flow of Polyethylene, J. Appl. Phys., 28, 624(1957).

7. Rabinowitsch, B., The Viscosity and Elasticity of Sols, Z. Physik Chem., A115, 1 (1929).

8. Kozicki, W., Chou, C. H. and Tiu, C. Non-Newtonian Flow in Ducts of Arbitrary Cross-sectional Shape, Chem. Eng. Sci., 21, 665 (1966).

9. Carlson, F. A., U.S. Patent 2,857,265.

10. Aykanian, A. A., U. S. Patent 2,945,261.


CHAPTER 8

Foam Extrusion Machinery Features

WILLIAM C. THIELE

8.1 PREFACE REGARDING EXTRUDERS FOR FOAMING

BOTH single-screw and twin-screw extruders are used to make foamedproducts. Many processing schemes and materials are employed, which

means that there is really no standard device or process method. A “think-through” machinery approach follows to help define a processing system thatis most likely to work for a specific foamed product.

It may be somewhat generalized that high-density foams are easier to makethan low-density foams. Sometimes, using blowing agents is easier than in-jecting gas, although the growing foam bubble is unlikely to realize fromwhich source its gas has come. Polymers that strain harden best support foammanufacturing.

Such easy generalizations do not really apply to machine systems. If,however, the process is reduced to its subprocesses (unit operations), rationalchoices can become apparent. These choices might include whether to use atwin-screw or single-screw extruder, whether these should be in single or cas-caded format, or whether chemical blowing agent or gas injection is best.Many foaming applications can be satisfied quite well by single-screw ex-truder devices. An objective of this chapter is for you to sort out the fewest andsimplest devices required to do your job.

This chapter will first describe the capabilities and limitations of screw ex-truders (single-screw and twin-screw) as foam-making tools. The next sectionwill discuss the candidate subprocesses or unit operations in foaming thatrelate to extruders. The final sections will comment on primary and supportmachinery properties and choices.


8.2 BASIC PROPERTIES OF EXTRUDERS

Somewhere, the extruder is charged with fineness of mixing an injected gasor a blowing agent into the polymer. It may also be required to compoundother ingredients into the recipe. These might include regrinds, colorants, sta-bilizers, nucleating agents, or modifiers (such as to make the polymer bettersupport bubble growth). In addition to melting, pumping, and forming jobs ofprofile extruders, foam systems also bear mixing responsibilities of com-pounding extruders while delivering melt in a process window that is right foruniform bubble nucleation and growth.

The properties of extruders are balanced against the basic demands of sub-processes in foaming operations. Comparing the mixing of compounding extrud-ers versus traditional internal mixers can be a helpful part of understanding this.

8.2.1 SIMILARITIES TO CONTINUOUS MIXERS

Twin-screw extruders transfer mechanical energy somewhat like internalmixers, through turning two screws or rotors. Internal mixers have intensecooling provisions to remove heat from the viscous mixing powered by themotor. Surrounding the rotors, it is possible to assign five basic activityregions. These are as follows:

(1) Screw or rotor channels with relatively mild strain rates

(2) Lobal capture region where material confronts an advancing mixer “wall”

(3) Tip acceleration region fed from lobal pools

(4) Apex regions where the twin chambers of the device meet

(5) Intermesh/proximity region where the two screws or rotors most closelymeet

These exist in both internal mixers and extruders (Figure 8.1). The latter fourcan apply extensional and shear forces to accomplish dispersive mixing.Screws or rotors may be designed to capture or minimize these forces (Figure8.2). Much of the mixing in foam processes is distributive, and mixers that candivide and recombine melts at high rates and at low energy per division arepreferred (Figure 8.3). Again, channel shear and extensional strain rates arelow, due to the deep flighted nature of twin-screw extruders and internalmixers and also due to a characteristically lower screws’ or rotors’ speeds offoam processes.

While single-screw extruders cannot participate in the last two regions (forlack of a second screw), lobal capture and tip acceleration to some degree ispossible. The most familiar single-screw lobal capture and tip accelerator is ina Maddoc mixing section. Pin, vane, and other types of distributive mixers canbe made to work in single-screw extruders.


FIGURE 8.1 Mass transfer regions.

FIGURE 8.2 Wide and narrow kneader elements.


8.2.2 OTHER BASIC PROPERTIES OF SINGLE-SCREW ANDTWIN-SCREW EXTRUDERS AND DIFFERENCES FROMINTERNAL MIXERS

Three other properties make extruders more suitable than internal mixers for foam processes. They are continuous, “small-mass,” and “longitudinal”(Figure 8.4).

The need for continuous, steady output is the main reason internal mixersare not common in foam processes. Batch operations in the melt parts of theprocess promote inconsistencies in the product.

Extruders being “small-mass” relates to the localized material volume,which is bounded by barrels and screws. It is tiny when compared to thebounded large mass in an internal mixer or even in a continuous internal mixer.Extruders have approximately five to seven times the surface-to-volume ratioas compared with internal mixers. This is very important for temperaturecontrol with foams that can have fairly narrow process windows.

The small mass property also relates to tiny transport distances for mixingblowing agents (and additives). Short transport distances within screw flightsor screw mixing elements promote speed and accuracy for incorporating mate-rials into polymers. For example, nucleating agents, which may be added atbelow 1%, are more quickly and accurately distributed within small volumeswith their short transport distances than they would within large melt domains.

FIGURE 8.3 High division rate mixers.


Longitudinality is also a critical property. That refers to the extruder’s ca-pability to sequentially perform subprocesses or unit operations along itslength. These unit operations are mechanically powered through the mainmotor and gearbox driving the screw(s). The heat transfer requirements ofthese unit operations are satisfied by the reaction-grade heating and coolingprovisions in the extruder’s barrel(s), whether the barrels are one-piece orsegmented.

Gearboxes can and should be supplied strong enough that the power trans-mission limitation lies with the screw(s), whether the machine is a single-screw or twin-screw type. Segmented screws are highly desirable because thebest screw pieces (elements) can be strung onto screw shafts to optimize unitoperations to be conducted along their length. The torque limitation becomesthe strength of the cross section of the shafts onto which the elements arestrung to power a given process volume. As single-screw extruders power

FIGURE 8.4 Localized mass and length of mixing devices.


processes with only one shaft, and because their screws are deepened in thefeed area, fully segmented screws are generally not practical for them.

Segmented screws are practical for twin extruders (Figure 8.5). Commercialsegmented twin-screw machines are generally built with screws that have anoutside-to-inside diameter ratio of 1.43/1 to 1.56/1. This balances availableprocess volume to the strength of the screw shafts.

Most pipe and profile type twin-screw extruders have one-piece screws.Having no screw shafts, they can transmit high torque. Screws made to targetfunctionality and longitudinality may not be available for the uncommon re-quirements of your foam process.

While single-screw extruder screws are generally one piece, they can betorque limited for reasons that include transmitting power with only one screwinstead of two and having a deep-cut feed section that leaves a smaller root di-ameter cross section available.

Various unit operations in foam processes will be discussed that involvefeeding, mixing, cooling, and pumping. It is important to run unit operationsefficiently. That will maximize the number of jobs that can be sequenced alongthe screws, the quality of performing those tasks, and even the practical lengthof the extruder to house them.

8.2.3 SINGLE-SCREW VERSUS TWIN-SCREW EXTRUDERS INFOAM PROCESSES

Single-screw extruders can be preferred over twin-screw types usually fortwo reasons.

(1) For a given screw diameter, a single-screw is usually half the price of atwin.

(2) Single-screws are simpler to understand and maintain than twin-screws,although they are not necessarily easier to operate.

FIGURE 8.5 Construction of modular twin-screw extruder screws.


Twin-screw extruders would be opted for performance reasons. Some of thespecial capabilities demonstrated by twin-screw extruders as compared withtheir single-screw counterparts include the following:

(1) Greater and more steady solids feeding

(2) Twin-shaft drive to power more sequenced unit operations

(3) Better dispersive mixing of nucleating agents and polymer systems

(4) Fast, even incorporation of blowing agents

(5) Better cooling and temperature control capability

(6) More thorough mass temperature homogenization

(7) Relatively strong and stable dynamic seals before gas injection points

These statements do not apply to every foaming processes. Foam-relatedprocesses in general have tighter specific requirements than do basic com-pounding or profile extrusion processes. It can be further generalized that thefussiness of the process is inversely proportional to the density of the foam.Specific requirements to make foamed products vary.

8.2.4 LIMITATIONS OF TWIN-SCREW FOAM EXTRUDERS

Thus far, only a few limitations to using twin-screw extruders have been ex-pressed: twin-screws are expensive and their shafts in the case of segmentedscrews tailored to your process restrict the torque, even with recent industryadvances. There are other limitations, such as not being able to feed a solidparticle that is much bigger than the flight depth. If you wish to perform an insitu reaction that requires twenty minutes, you might expect only a tenth or atwentieth of the output rate as compared with roughly a half-minute dwell-time typical of compounding processes. Substantial costs may be incurred toarmor a machine against corrosive, abrasive, or adhesive wear. Fortunately,foaming processes are not generally subject to any of these additional prob-lems.

Heat transfer is an important limitation. It can also affect shaft torquedemands. For example, when foaming gases are injected (whether in liquid orgas phase) and become dissolved in the polymer system, the viscosity plunges,as does usually the softening point. It is necessary to cool the material to alower and uniform temperature to achieve an output process window (ofmaybe only a few degrees). The ability to do this total heat transfer, and also toavoid frictional hot spots on the screws, places constraints upon screw speed,the screws’ geometry, and the barrels’ design. Hopefully, cooling will be com-pleted before the shafts’ torque is exhausted.

Torque and heat transfer are serious boundaries. Getting enough torque tothe right kinds of special screw shapes to power the subprocesses within the


extruder’s volume is most often the more serious problem of the two. This isgenerally true for single-screw and twin-screw devices alike, with exceptions.

8.2.5 SOME DISCUSSIONS ABOUT FREE VOLUME ANDSCREWS’ TORQUE

Today’s single-screw and twin-screw gear technology supports very hightorque possibilities. Unfortunately, the shafts onto which the screw elementsare strung are torque limiting. The screw shafts at the middle of the extruderonly need to carry the combined torque contributions from the screw elementsof the output half of the extruder. The shafts under the feed throat screw ele-ments carry the sum of the torque load contributions of all of the elements forthe entire screw set (Figure 8.6). That position is the torque limiting point inextruder design (or should be). This is also the weak point for single-screwone-piece screws, a fact particularly illustrated for smaller machines (3.5 inchOD and under) with various “shank collections” from broken screws.

It is unfortunate that the most productive foaming screw designs are prohib-itively complicated and too nonstandard to be machined in one piece. One-piece screws would avoid the torque limitations imposed by screw shafts.

FIGURE 8.6 Screw shafts’ loading.


However, segmented screws are very maintenance friendly and may be recon-figured in response to new developments of the art and the need to be changedto make different products. However, at least one manufacturer, Leistritz (NewJersey, U.S.), in October, 1998, announced the ability to machine complicatedone-piece shaftless custom screws, primarily for sanitary reasons, for the phar-maceutical industry.

The common term, “free volume,” means the space available for processingin an extruder of a given screw diameter for a given length. It could be ex-pressed as cc/D, where D is a length of barrels with screws equal to the diam-eter of a screw. It has also been expressed as liters per meter. The idea is thatgreater volume produces more product. That is only true, however, if the shafts(and gearbox) can transfer the needed power to the volume of the screw ele-ments.

Today, it is common for twin-screw extruders to have a flight depth basedupon a compromise between mechanical energy transfer (from torque) and theavailable process volume. If the relationship of shaft cross section to usefulvolume is high, then the machine would be very strong (fat shafts and insidediameter with respect to screws’ outside diameter) but would have little pro-ducing capacity. If the volume compared to shaft area is high (skinny shaftsand small inside screws’ diameter with respect to screws’ outside diameter),then there will be a large volume for doing processes but little strength topower them.

The outside diameter divided by the inside diameter (“OD/ID ratio”) seemsto fall between 1.43/1 and 1.56/1 as a balance between the two above ex-tremes. High-strength splined screw shafts are required. Sometimes theseshafts are produced by strain hardening/“hammering” processes. Such shaftsare over 20% stronger than those produced by cutting. These issues hold truefor both corotating and counterrotating extruder types. Corotating and coun-terrotating machines share the same OD/ID depth compromise and, therefore,the same basic extruder barrels sections for a given gearbox centerline spacing(Figure 8.7).

A similar tradeoff exists in the feed section of a single-screw extruder.Making the feed depth great, and, therefore, making the metering depth aftercompression residually large, is a tradeoff against mechanical strength of thescrew in the main feed root cross section. (Parallel twin-screw extruders haveapproximately the same flight depth along their entire length.)

It is interesting that the OD/ID compromise between free volume and torqueis reasonable for other aspects of foam processes. The viscous heating whencompared with shallow devices is less. Volume output per rotation is reason-able, as are mixing and heat transfer. These are subjective statements withoutapology. The relationship of OD/ID describes twin-screws as inherently“deep-flighted” devices when compared with single screws. In the meteringsections of plasticating single-screw foam extruders, OD/ID ratios can range


from 1.1/1 to 1.3/1. A nonplasticating and noncompressing single-screwdevice used for melt cooling, however, can be as deep as OD/ID of 1.8/1 oreven more.

Substantial efforts have been undertaken to make shafts of a given sizestronger. This has been done through stress-relieved spline designs, spe-cial metals, and new treatments of metals. Some manufacturers (Werner &Pfleiderer, Leistritz, and perhaps others) are strain-hardening shafts through ahammering or rolling process. Better torque safety and management tech-niques are also used. For long, segmented twin-screws, these combined effortshave raised state-of-the-art mechanical energy availability from about 2.3watts/rpm/cc to approximately 3 watts/rpm/cc. This is the maximum motorpower in watts at full torque scaled to one rpm over the standard free volumeof one diameter of screws length. This represents a total torque improvementof about 30%! This is an interesting testimony to engineering and urgency.

8.2.6 OVERVIEW OF USING THE EXTRUDER

First, some nonmachinery basic rules are important. They include that thepolymer system, blowing agent, and nucleating agent should work right to-gether. For example, the gas must be sufficiently soluble in the polymer systemto achieve the target foam density and the polymer system must support thegrowth of bubbles.

Second, there are machinery rules. The pieces must perform the unit opera-tions you elect to perform to make the product. Extruders, therefore, are not in-troduced as the historic appliances that have been used, but as a platforms ontowhich functions of your process can be operated.

Extruders are continuous, small-mass, and longitudinal. Unit operations orsubprocesses may be sequenced along the length of their screw(s). These unitoperations are mechanically powered by sections of the screw(s). The barrel(s)should have reaction-grade heat transfer, including liquid cooling and electri-cal heating. The screws have a weak strain-rate region, their channels. Twin-screws (like internal mixers) can employ lobal capture, barrels apexes, mixertips, and intermesh (proximity) regions are made available for intensive

FIGURE 8.7 Classical corotating and counterrotating screws.


mixing, while single-screws can achieve still substantial performance fromscrew designs of the art not involving a second screw. Screw shapes exist to dolow-energy distributive mixing.

Extruders are versatile, but special attention is required for torque and heattransfer boundaries in foam processes. All of these generalizations are equallyvalid for intermeshing corotating and counterrotating machines as well assingle-screw extruders.

8.3 BASIC UNIT OPERATIONS IN FOAM PROCESSES

Foam processes differ, depending upon target density, polymers, gas injec-tion versus blowing agent, finished product shape and form (including whetherpart of a coextrusion), special performance properties, and the like. Noexample describes all of them. However, the following may help to provide ageneral understanding of likely subprocess issues involved with makingfoamed products.

The example is in-line manufacturing of a sheet or a shape, inclusive ofcompounding a polymer system with additives and a nucleating agent in atwin-screw extruder with modular barrels and screws. The gas (or blend ofgases) for foaming is injected. Variations could be envisioned for coextrusions,high-density foams, gas supply through chemical blowing agents, and the like.

Downstream cooling and calibrating processes are not part of the example.Nearly all of the unit operations listed can be done by the extruder. Ques-

tions arise concerning whether they can or should all be done together in theextruder. Some of them may need to be transferred to other devices to relieveloads from the screw shafts or for other reasons. Sometimes, a subprocessmight just work better in an external device. The choices will depend upon thematerials’ system, the product form, the capabilities of equipment, and yourown preferences.

Basic common unit operations, from materials’ feeding through dieforming, may include:

(1) Polymer system feeding—premix or multiple streams

(2) Melting/compounding—blend polymers, disperse nucleating agents, color

(3) Dynamic sealing—prevent gas blow-back

(4) Gas injection—steady, regulating, non-ponding

(5) Distribution—high-distribution rate rapid incorporation

(6) Cooling—bring temperature and viscosity to process window

(7) Pumping—pumping power for final die flow

(8) End homogenization—create mass and thermal homogeneity

(9) Die forming—exit homogenous morphology for right bubble growth


A few of these could be split or resequenced in some process trains (Fig-ure 8.8).

8.3.1 POLYMER SYSTEM FEEDING

For this example, it is assumed to feed one polymer, a stabilizer, a colorant,and a nucleating agent. The gas is sufficiently soluble in the polymer toachieve the desired foam density. Conflicts about the stabilizer and colorant af-fecting the nucleation and bubble growth processes have been already re-solved. The nucleating agent is not soluble in the polymer, which is a generalqualification to perform its function. (It is possible for a little well-dispersednonsoluble gas to act as a nucleating agent.)

Twin-screw extruders are starve-fed. The screws’ design and screws’ speeddetermine the mass-transfer rates. The rate of feeding sets the output rate andamount of remastication. These two parameters are part of balancing theprocess. In general, starved screws turning fast constitute harsh processing,while fuller screws turning slowly constitute gentle processing. The energyrate to the screws is proportional to the product of screws’ speed and the torqueapplied to them.

FIGURE 8.8 Gas-injected foam screws.


Foam processes tend to be moderately gentle. This is in spite of the need todisperse nucleating agents, colorants, and additives, as well as possibly blend-ing polymers. Twin-screws are generally not flood-fed like most single-screwextruders. One or more powder or pellet feeders are part of rate and formula-tion control.

The feeder(s) should be gravimetric to maintain your recipe with the gas,which is injected later. Metering a premix to the main port needs just onefeeder. However, the mix must not segregate. Using powdered resin is onetrick used to keep premixes stable. Very small amounts of powders can some-times be made to cling onto pellets. Small amounts of pellets can sometimes bemade to remain static within powders, if the powders do not frequently move.These are some techniques to stabilize premixes. If premixes are unstable, thenusing additional gravimetric feeders may be necessary.

Separate gravimetrically fed streams may not deliver accurately at lowrates. The output of foam lines can be cooling rate limited, and the componentfeed streams can be small. For 100 kg/hr of product, perhaps only 1⁄2 kg of talcnucleating agent might be needed. Gravimetric feeders at 1⁄2 kg/hr and similarrates need to be chosen and operated carefully, as normal units and installa-tions may perform in an unstable manner.

Additive streams may sometimes be combined to achieve a rate at which afeeder becomes stable. Some of the main polymer may also be made intopowder that can then be used for establishing premixes with additives for de-livery at a rate more acceptable to production gravimetric feeders. Otherschemes can also be devised, but operating gravimetric feeders at least 3–5kg/hr, and preferably, 12 kg/hr or faster, is a good policy.

The main solids’ stream(s) should not be delivered from high on a servicedeck but rather from close to the screws to ensure reliable delivery withoutclinging to and releasing from a drop tube wall, “clouding away,” or fluidiz-ing excessively. This is particularly important if the materials are powders. Acompact system can also be designed to promote rapid product changeovers.

It is not likely that the feed throat will appear overfilled, unless the feedstockis fluffy, fluidized, or otherwise difficult. It is important to remember that theextruder does not see “bulk density.” It sees “feed density.” The relation ofbulk density to feed density follows:

Where effective feeding density the extruder sees; mea-sured bulk density of the material not moving; bulk density changefrom turbulation dropping from the feeder to the screws; change inbulk density from back gassing turbulation from the screws; changein bulk density by screw flight movement turbulation of the feed stock;

in bulk density from electrostatic dispersion; and increase in bulk density provided from mechanical stuffing pressures.

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Df � Db � ddt � dbg � dft � ded � dec


By means of lowering feeders, opening relief vents, installing back-gassingbaffles, neutralizing electrical charges, and possibly even mechanically cram-ming, feeding properties may be improved in twin-screw and single-screw ex-truders. Twin-screws are deep flighted, and they are normally not feed limitedin foam applications unless there are major fluffy components, such as foamedregrind.

Normal screw types may be used in the feed throats of the various types oftwin-screw extruders. Ones causing excessive friction at the feed throat shouldbe avoided.

The melting/compounding subprocess follows feeding. However, someprocess trains can benefit from an external melter/mixer feeding the twin-screw extruder. That device could sometimes be a single-screw extruder.

8.3.2 MELTING AND COMPOUNDING

If only melting and light mixing are needed, a single-screw extruder wouldbe adequate. However, it may be important to deagglomerate and disperse thenucleating agent. It could also be necessary to disperse a colorant and controlits effects upon cell nucleation and bubble growth. Blending two polymersmight be required. These and similar situations can justify the twin-screw ex-truder for melting and mixing.

In these cases, dispersive mixing may be required in this region, as inintense compounding extruders. Some stress rate may be required to fractureagglomerates or to reduce polymer/additive phase domains. That stress rate isthe product of some controlling material modulus (influenced by viscositiesand the presence of particles) and a strain rate (from the shear and elongationalmovement of the material in the screws).

The screw design to do this unit operation can include proven classical disper-sive mixers and/or newer generation geometries. The design, however, needsto compensate for the lower 30–200 rpm speeds of many foam machines asopposed to 200–1,200 rpm and higher speeds of compounding-only machinesdoing similar mixing.

The materials should be mixed to be ready to see gas. This relates to mor-phology and temperature. Ideally, the temperature should be raised some tocompensate for the freeze-off effects when the gas is introduced. Unfortu-nately, that cannot always be done, since high viscosities may be needed tomake the dynamic seals hold gas pressure and prevent blow-back. High injec-tion pressures, even those below 100 bar, place special requirements on themixers, which may be part of the dynamic seal system.

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8.3.3 DYNAMIC SEALING

At low gas injection pressures, 5–20 bar, this operation can usually be builtinto the melting and compounding subprocess. For high pressures, dedicatedseals are advised.

Using an external, side arm, melter/compounder is a special case. In thatconfiguration, a dynamic seal might be needed upstream of the melt inputpoint to the extruder. Alternately, some pumping and mixing must be carriedover to the twin-screw extruder to drive normal seals. Seals operating at highpressures upstream and before the melt input might require the sealingmedium for their elements to be externally supplied from a separate source.

The normal case, however, should be a designated screw element groupthat’s job is to allow the compounded polymer system to pass but to preventblow-back of any gas. These elements may be cascaded discs, special flights,or other appropriate barriers as needed. They are executed similarly for coun-terrotating and corotating machines (Figure 8.9).

FIGURE 8.9 Dynamic seals and mixing elements for gas injection.


The energy requirements to seal gas pressures over 200 bar, such as with su-percritical carbon dioxide, will be very substantial.

8.3.4 GAS INJECTION

The gas may be in liquid phase or in gas phase. In either case, the foamingagent pumping mechanism should provide good volumetric control. (Somereasonably good results have been achieved regulating gas flow by pressuresensing at the injector and in the extruder barrel. These have tended to betricky or fortunate. Load cell mounting of the gas tank can be linked to controlthe injection accuracy in some cases. How to keep liquid pumping systemsfrom gas locking or gas phasing and how to get volumetric control at a criticalpoint in gas phase and maintain it seem to be regarded as proprietary practiceby some processors.

Pressure and temperature monitoring in the extruder barrel near the injectoris important at least for process verification. That information is a good indica-tion of whether the exit rate of melt from the dynamic seals and the gas fromthe injector are constant. For dual injection of two complementary gases, theinjector pressures should be compared to help control the mixture.

Concentration variances can occur even if the metering of the gases fromthe metering device is positive. This variation would be seen in the barrel’spressure measurement near the injectors and perhaps in the lines themselves.The line from the metering device to the injector should be short, rigid, andsmall.

A worse-case example will illustrate these factors. A bad delivery linewould be long, elastic, and big. A momentary melt impingement upon the in-jector would require a pressure rise to blow it out. The line has considerablevolume, and it will stretch, so that the time to raise the pressure will be long.Meanwhile, the melt is flowing further up the injector, which in turn requireseven more pressure. When the pressure finally rises to blow out the injector, asurge of gas will occur that was preceded by a period of gas-less extrusion, ofcourse.

Delivery from small, short, rigid lines tends to be constant. Momentary meltplugging is almost instantly blown out without disturbing the process.

Short, steel tubing small enough to have a measurable pressure drop alongits length at the target rate is ideal. These issues are important for constant de-livery of liquid-phase gases. They are much more important for gas-phasegases that are more compressible.

8.3.5 HIGH-RATE DISTRIBUTIVE MIXING

The gas is soluble in the polymer system to the amount necessary to achievethe target foam density. Once the gas is dissolved, the rheology of the material


is uniform. Before that has been achieved, a liquid or gas phase exists concur-rently with a polymer melt phase. It is critical to prevent mass ponding of thegas or liquid.

To minimize ponding, the injection should occur over very high divisionrate distributive mixers, with substantial pressure under the injector. As the gasexits the injectors, it is greeted by rapid passages of mixer protrusions that pre-clude pond forming and accelerate dissolution. The absolute worst, oppositecase would be to inject at low pressure over flighted low mass transfer rate el-ements. Liquid ponds or large gas bag domains would be formed that wouldgreatly retard the dissolution process and could result in dissolved gas concen-tration variances.

The speed of dissolution may, therefore, be inversely proportional to thepresence of ponded gas domains. Speed is important to get the job done accu-rately with minimum energy. Using minimum energy for this and other unitoperations on the twin-screw extruder makes more shaft torque available foradditional unit operations or for increasing productivity and/or quality.

While some foam machines mix gases with simple kneaders and related el-ements, special elements targeted to the task can perform better. Rememberthat the earlier mixing zones used enough mixing stress to reduce phase andagglomerate sizes. That is not so true here. The gas, by definition, is soluble inthe polymer system. High-rate, low-energy distribution can be the dominanttool to speed the dissolution of gas into the polymer. When a nonsoluble gas isused in small amounts partly as a nucleating agent, bilobal mixing elementsare useful to reduce the domain sizes.

For process trains utilizing twin-screw extruders, the dynamic seals, injec-tion, and gas mixing are almost always within the twin-screw extruder, eventhough some unit operations may, or may not, have been shifted to outsidedevices.

8.3.6 COOLING

When gases are dissolved into the polymer system, they function as a plas-ticizer. The viscosity of the melt drops, as does its softening point. Theseeffects increase approximately as the foam density decreases.

The melt must be cooled to raise its viscosity in preparation to be formedthrough a die. There will be a temperature, pressure, and shear relationship inthe die that will hopefully cause nucleation and fine bubble growth to beginimmediately upon discharge. If the melt is too warm, nucleation and bubblegrowth in the die can disrupt the process, and the bubbles will be too large. Iftoo cool, nucleation and bubble growth will occur too late or bubbles may notgrow or grow fully.

After gas mixing, the screws should just cool and forward the melt. Unfor-tunately, the screws also provide something else, viscous heating. Therefore,


the heat being removed from the barrels is somewhat in competition withpumping heat being put in through the turning screws.

Tight intermesh tracking screws are prone to viscous heating, both in classi-cal corotation and in classical counterrotation. Open-meshing single-flightedelements are equally preferred for both of these extruder types. They are alsopolished to reduce friction (Figure 8.10).

The barrels’ sections are usually longitudinally cored for liquid cooling toaccomplish the total cooling in as short a length as possible. As the viscosityrises, a significant torque contribution will result for the screw shafts.

Some processes will fully cool the material in the extruder. Some will partlyor fully cool the material in a heat exchanger or in a slow-turning separatesingle-screw or twin-screw cascaded pumping extruder. In general, a processtrain should consist of a minimum number of devices.

8.3.7 PUMPING

Powering flow through the forming die would ideally be done from thetwin-screw extruder. It could alternately be done with a gear pump, a cascadedsingle-screw extruder, or a cascaded twin-screw extruder. At least the firstthree of the four options have been done in production.

The pumping unit operation in an extruder might be accomplished with the same loosely meshing elements that are used for cooling. For cases inwhich they would be too weak, single-flighted close-meshing elements would

FIGURE 8.10 Low shear cooling, mixing and pumping screws.


be used in either corotation or counterrotation. If classical bilobal corotatingelements are used, their recommended flight advance is approximately

diameters per turn.Like other unit operations on the extruder, pumping should be done as effi-

ciently as possible to place the least torque on the screw shafts. An exceptionto this rule would be elements sufficiently severe to cause frictionally heatedspots on the surface hot enough to cause premature foaming.

8.3.8 END HOMOGENIZATION

Besides achieving a target mass temperature into the forming die, it is nec-essary that the temperatures of small mass domains do not significantly differ.If they do, there may be tiny regions of foaming in the die and/or regions of re-tarded nucleation and large bubbles in the product.

Extruder pumping tends to leave hot “turtle track” domains in the melt.Near the end of the extruder, high distribution rate mixers can be used to ho-mogenize the melt at low energy. Some processes can tolerate these at theextreme end of the screws. Some prefer some weak forwarding elements (thatdo not generate hot domains) to follow them.

If a gear pump is used, its hot domain tracks may be blended out with astatic mixer. A cascaded pumping extruder will sometimes require the same. Ifa heat exchanger follows the pumping, the various temperature output streamsfrom its tubes may sometimes need to also be blended.

8.3.9 DIE FORMING

Dies vary greatly with specific prefoam rheologies and product type. Asfoam densities become greater, die systems more resemble their nonfoamcounterparts. Die forming is one of the foam unit operations that users usuallyconsider to be proprietary art. But, a few generalities can be mentioned.

The temperature control of the die must be very uniform. This helps to keepthe nucleation point even across a sheet or profile cross section. The conse-quences of failing to do that have been discussed previously. Liquid tempera-ture control may be needed and/or more heat zones should be used as com-pared with nonfoam dies.

Localized internal decompressions should be avoided or minimized thatcould cause premature localized nucleation and bubble growth.

The shear history of the material at each point exiting the die should besimilar. It is known that shear is a factor in promoting nucleation. Complicateddies may require localized temperature/shear compensations.

These generalities also relate to sandwich and single-sided coextrusion.

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8.4 EXTRUDER TYPES, SUPPORT DEVICES, AND WHERESUBPROCESSES ARE PLACED

In the example, or in your own process, the extruder will be assigned jobs tothe extruder according to possibilities and preferences. Preferences are valid.Making the extruder more efficient will allow more tasks to be placed on theextruder. When this cannot be done, tasks can be diverted to external devices.

8.4.1 CLASSICAL EXTRUDER TYPES AND EFFICIENCY

It is the intermeshing twin-screw, more than single-screw, extruders thatseem to power the most subprocesses and have the most modularity to supportefficiency improvements. There are several generic types of intermeshingtwin-screws. For all of them:

(1) Core patents or concepts were fully in place before 1950.

(2) The screws tracked each other during rotation to wipe and/or mix.

(3) Early screw shapes dominate the current machine offerings.

The classical forms of these twin-screws can be nonideal for making foamedproducts due to the following:

(1) Close-meshing elements cause unwanted viscous heating and difficultiesin cooling.

(2) Classical screws may demand excessive shaft torque in unit operations.

(3) Dynamic seals and gas mixing can be inefficient.

(4) The numbers of unit operations on a screw’s length can be small.

The main classical forms of intermeshing twin-screws include:

(1) Counterrotating, intermeshing• Slow speed; Profile heritage; Cincinnati-Milacron, Krauss-Maffei, etc.• High speed; Compounding heritage; Leistritz

(2) Counterrotating, nonintermeshing (not significantly used in foams)• High speed; Compounding heritage; Welding Engineers

(3) Corotating, intermeshing.• Low speed; Profile heritage; LMP (Columbo), Windsor• High speed; Compounding heritage; Werner & Pfleiderer, Leistritz, etc.

In practice, the classical screw shapes have worked reasonably well for theirpurposes, particularly when supported by the current higher mechanicalstrengths and heat transfer. Much work has been done to characterize the clas-sical screw shapes. Conclusions about them tend to be defended. New process


shapes are often logical modifications of classical ones. In short, twin-screws,and their single-screw counterparts, tend to be burdened with historicalbaggage when applied to sensitive foaming processes.

8.4.2 MAKING TWIN-SCREWS MORE EFFICIENT IN FOAMINGPROCESSES

Limits to the number of subprocesses and/or the quality of performing themoccur when a boundary condition is reached. Assuming the extruder torqueand heat transfer cannot be changed (and are hopefully state-of-the-art), manythings can be done to help the extruder’s capability. These include new screws’types and staging, formulation modifications, and operating conditions. Theunit operations of the example illustrate these.

While feeding requires little energy, melting and mixing does. Some pow-dered polymer to nucleate melt, additives, or a mixture of carriers can removesome shafts’ load. Minimizing feed throat cooling or preheating can also help.Mixing elements that quickly develop an acceptable morphology for gas intro-duction can be useful.

Dynamic sealing to prevent blow-back of injected gas is difficult at highpressures with forward flights and kneaders. Short disc stacks and special sealscan replace longer, torque-consuming sealing sections. The torque to sealagainst high injection pressures can be very substantial.

Mixing of injected “gas” must be very rapid to conserve energy. High divi-sion rate distributive mixers prevent “ponding” that would otherwise usuallyhappen in classical mixers. By definition, the gas is soluble in the polymer formaking foam. Therefore, no dispersive mixing is needed unless ponds wereformed with droplets that require reduction (Figure 8.11).

Classical forwarding elements are prone to viscous heating. Open-meshingforwarding elements are relatively low-energy forwarders. Therefore, thecooling rate, heat out less heat generated, with them is much greater. There isno danger of coalescence since the gas and carrier by definition in foaming aremutually soluble. Formula modification to reduce the torque load duringcooling and other extruder processes can be productive.

Open meshing elements are ideal for pumping as the pressure rise is distrib-uted over a larger length of barrel for heat transfer, and hot spots are less likelyto be formed with high domain temperature differentials.

Powering end thermal homogenization with active low-energy distributorson the screws consumes less energy than powering static mixers from axiallygenerated flow energy. The morphology results are similar. Foamed productshave tight condition windows in their dies for mass and thermal homogeniza-tion to maintain profile shape and constancy of cell morphology.


These examples are generally effective with any intermeshing twin-screwextruder. As more twins in foam processes must first blend polymers and coloror stabilize the formulation, the demands to operate at higher screws speedswhile still doing rapid cooling are increasing. These conflicting demands causedeviation from classical art.

8.4.3 WHICH TYPE OF TWIN-SCREW EXTRUDER?

All of the improvements to screw design and unit operations’ managementcan be applied to all of the commercial intermeshing twin-screw extruders.Applying foaming operations’ parameters to the extruder may be more impor-tant than the type of twin-screw extruder that is chosen.

Tailoring the extruder for foaming processes usually makes it more produc-tive than taking it as an off-the-shelf appliance. This is also true for single-screw machines.

People may favor an extruder type, such as counterrotation for its accom-modation of high-pressure dynamic seals. However, the issue is not usuallycourrotation or corotation. The factors of modularity and available compo-

FIGURE 8.11 Twin-screw research foam extruder.


nents plus torque adequate to power the unit operations are generally more im-portant.

8.4.4 WHERE TO PUT SUBPROCESSES WHEN THE EXTRUDERCANNOT DO THEM

When shaft torque, heat transfer, or other boundaries do not permit all ofthe desired unit operations to be placed on the extruder, then some sub-processes must be designated to external devices. It is assumed that the clas-sical twin-screw (or single-screw) device has been upgraded as fully as possi-

FIGURE 8.12 Twin-screw foamed sheet extrusion. Courtesy of American Leistritz ExtruderCorp.


ble. If that has been done, then there is no choice but to relocate some of the work of the total process (Figure 8.12). Some possibilities include the following:

Action Device Issue

External melter Single-screw extruder System controlPowered dynamic Seal block and driver Shafts’ positioningsealsExternal cooler Single-screw extruder, Homogenizing, control

etc.External pumping Gear pump, extruder Homogenizing, controlExternal end mixing Static mixer Gear pump (alt.) to drive it

Cascade systems have favored downstream coolers. These may be slow-turning single-screw extruders or heat exchangers. They could also be twin-screw devices. Somewhere, mass and thermal homogenization has to be done.Static mixers need drivers. There are no standard solutions.

There is an argument to relieve the extruder of its melting work with an ex-ternal melter. This can be a single-screw extruder feeding the polymer systemto the twin-screw ahead of the gas injection. Advantages in dynamic sealingcan also be engineered.

Again, there seem to be no really standard foam processes. Differingprocess requirements, a small market, and tendencies toward confidentialitycontribute to explaining the general lack of standard foam equipment.

8.5 GENERAL EXTRUDER OBSERVATIONS

The extruder is a useful tool for foam manufacturing because it is continu-ous, small mass, and longitudinal. The intermeshing twin-screw classical ex-truder types were based upon steric tracking of their intermesh regions duringrotation to produce wiping and/or mixing. That basis presents positive andadverse properties for making foams.

By analyzing the needs of the step processes required to make the foamedproducts and not being subservient to the classical geometries and approachesof the extruders, it is possible to make foams with twin extruders with aminimum of support devices. While extruders, including single-screws, maynot satisfy all requirements, they can be optimized to excel beyond what couldbe done in their classical formats.


8.6 REFERENCES

1. Thiele, W. “Polymer Processing Advances in Counterrotating Intermeshing Twin-Screw Ex-truders,” Proceedings of the University of Akron, Akron, Ohio (May 24, 1994).

2. Erdmenger, R. German Patents 815,641 and 813154 filed (Sept. 1949).

3. Thiele, W. “How Twin-Screw Extruders Work,” Continuous Compounding in the 90’sRETEC, Somerset, NJ, Dec. 1 (1993).

4. White, J. Twin-Screw Extrusion. Chapter 7, Hanser, New York (1991).

5. White, J. Twin-Screw Extrusion. Chapter 10, Hanser, New York (1991).

6. Utracki, L. A. and Abdellah, A. Compatibilization of Polymer Blends, Canadian National Re-search Council, Boucherville, PQ May (1995).

7. Gogos, Costas, G. “New Mixing Developments,” Proceedings of the Leistritz Twin ScrewWorkshop, Somerville, NJ (May 23, 1995).

8. White, J. L. and Lim, S. “An Experimental Study of Flow Mechanisms, Materials Distribu-tions and Morphology Development in a Modular Intermeshing Counterrotating Twin ScrewExtruder of Leistritz Design,” Inst. of Polymer Engineering, Univ. of Akron, Akron, Ohio(Jan., 1993).

9. White, J. Twin-Screw Extrusion. Chapters 7–12, Hanser, New York (1991).

10. Booy, M. L. “Geometry of Fully Wiped Twin-Screw Equipment,” Polymer Eng. Sci., 18, 973(1978).

11. Knights, M. and Thiele, W. “Which Twin-Screw Compounder is for You?” Plastics Technol-ogy, April (1995).

12. Thiele, W. “Introducing the Twin-Screw Extruder as a Continuous Reaction and Compatibi-lization Tool,” Proceedings of the National Research Council Reaction Course, NRC-CRNC,Boucherville, Quebec (December 4, 1995).

13. Thiele, William C. “Configuring Twin-Screw Extruders to Develop Target Morphologies,”Compounding ‘96 Conference, Philadelphia, Pennsylvania (August 26, 1996).

14. Thiele, William C. “Twin-Screw Extruders for Foam Processing,” Foam Conference, LCMCommunications, Somerset, New Jersey (December 10, 1996).

15. Thiele, William C. “Trends and Guidelines in Devolatilization and Reactive Extrusion,” Na-tional Plastics Exposition, Society of the Plastics Industry, Chicago, Illinois (June 18, 1997).

16. Thiele, William C. “Non-Classical Approaches for Blending Polymers,” PolyBlends ‘97RETEC, Canadian National Research Council, Boucherville, Quebec (October 10, 1997).

17. Thiele, William C. “Twin-Screw Technology for Making Pellets from Powdered Metal,” PIM98, International Conference on Powder Injection Molding of Metals and Ceramics, Univ. ofPennsylvania, State College, PA (April 28, 1998).

18. Todd, David B., Ed. Plastics Compounding Equipment and Processing, Hanser, New York(1998).


CHAPTER 9

Mixing Design for Foam Extrusion: Analysisand Practices

CHI-TAI YANGDAVID I. BIGIO

9.1 INTRODUCTION

EXTRUSION is known as a complex and dynamic plasticating process inconverting thermoplastic raw materials into more useful products. It is

capable of generating high temperature and high pressure without sacrificingpumping capacity. Foaming virtually became an interesting application of ex-trusion. Since other chapters focus on design and processing issues, thischapter begins with mixing theory followed by its applications to various typesof extruders. Typical thermoplastic foam extrusion processes will be describedbriefly as they dedicate the type of processes and machinery used and how thetheory of mixing is applied.

Mixing is very important in any polymer processing application. Manyother ingredients are added to the main polymer to meet finished product prop-erty requirements. These ingredients can be additives, modifiers, fillers, col-orants, or other polymers. To break up the large agglomerates or clumps intosmaller particles, dispersive mixing is achieved by generating proper levels ofshear and elongational stresses in the processing equipment. On the otherhand, distributive mixing relies on strain rates to spread out and homogenizeall ingredients uniformly throughout the spatial polymer mixture domain. Forboth types of mixing, the objective is to obtain uniform dispersion and distri-bution of the ingredients in the main polymer matrix.

Thermoplastic foam extrusion is a polymer processing application whereadditives, sometimes a nucleating agent and a foaming agent (chemicalfoaming agent or physical blowing agent) are mixed with a thermoplasticpolymer in an extrusion system. A foamed product is made by proper designand operating conditions in the downstream equipment and the die. A uniform


distribution and control of the foam cells are important to obtain the desiredfoamed product properties. The first step for achieving this is to have a goodmixing of the foaming agent in the polymer mass. Beyond the mixing require-ments of uniform dispersion and distribution, there is an added requirement forminimizing the energy input to the foaming agent.

From the processing point of view, the mixing process is critical in foam ex-trusion in the following aspects:

• gentle dispersive mixing of the nucleating agent and other additives withthe polymer system

• good distributive mixing of chemical foaming agents• fast incorporation and good distribution mixing of physical blowing

agents• good distributive mixing for homogenization of polymer/gas solution

system• good distributive mixing for uniform cooling of polymer/gas solution

system

To obtain the required type and level of mixing in the above, the extrudersfor making foamed products must be capable of performing the followingprocess functions:

• frequent flow division/splitting and reorientation• efficient heat transfer• streamlined flow path without hot spots• forward pumping

9.2 THERMOPLASTIC FOAM EXTRUSION PROCESSES

There are two distinct thermoplastic foam extrusion processes. One createsa higher density foam product and the other a lower density foam product. Thethermoplastic foam extrusion process and the cellular foam structure are af-fected by the type of foaming/blowing agents, the evolved gas and its solubil-ity, method of compounding, processing temperatures, and melt viscosity.Figure 9.1 shows the schematic process diagrams of these two foam extrusionprocesses. In cases where the polymers have weak melt strength, such as poly-olefins, the foam process may be modified by inducing cross-linking duringfoaming. The cross-linking may increase the melt strength, that can stabilizethe cell growth and obtain a better foam structure.

This section briefly describes these two foam extrusion processes. It pro-vides key information with regard to the important roles of mixing and how todesign proper mixing sections to meet the various mixing capability require-ments in each thermoplastic foam extrusion process.


9.2.1 HIGH-DENSITY FOAM PROCESS

For the higher density foam product, the thermoplastic foam extrusionprocess utilizes a chemical foaming agent (CFA) that decomposes at a pro-cessing temperature to evolve gas (e.g., nitrogen, carbon dioxide) to form thecellular foam structure. In some cases, such as foamed PVC products used asa wood replacement, physical blowing agents may be used in preference tochemical foaming agents. The chemical foaming agents are either endother-mic or exothermic when they release the gas. The heat or energy associatedwith the decomposition reaction affects the polymer melt temperature and theprocessing window. There are also chemical foaming compounds that containendothermic and exothermic CFAs. The exothermic component provides thegas volume and pressure needed for lower densities, while the endothermicpart produces a stable, fine, and uniform cell structure. Some available chem-ical foaming agents are listed in Modern Plastics Encyclopedia [1]. The listshows the types of chemical foaming agents, trade names and suppliers, pro-cessing temperature range, gas yield, and types of plastics recommended for use.

Special caution must be taken in temperature control to avoid prematuremelt temperature rise before the melt seal, resulting in decomposition of theCFAs and loss of gas through the feed throat or the vent section. The chemicalfoaming agents are available in different forms [2]. The powder forms can betumble-blended with resin pellets or dry-blended with resin powder. They arealso available in pellet concentrates that facilitate more precise feeding andbetter dispersion.

FIGURE 9.1 Schematic of thermoplastic foam extrusion processes.


9.2.2 LOW-DENSITY FOAM PROCESS

The lower density foam process employs physical blowing agents injectedinto the extruder by a high-pressure injection system. Physical blowing agentsare atmospheric gases or hydrocarbon-based volatile organic liquids. Atmo-spheric gases used as blowing agents include nitrogen and carbon dioxide, whichhave low solubilities and high volatilities in polymers. Common hydrocarbon-based blowing agents are isobutane and isopentane, which have high solubilitiesand high diffusivities in polymers. Chlorofluorocarbons (CFCs) have beenbanned for use due to environmental concern. Arecent development has been the“microcellular foam process,” which utilizes supercritical fluids of atmosphericgases as the blowing agents [3]. These blowing agents dissolve in the polymermelt and have a strong plasticizing effect causing a large reduction in melt vis-cosity. The polymer melt viscosity can be reduced by more than 50% after beingmixed with the blowing agent [4]. The reduced melt viscosity could causeoverblowing, cell rupture, and collapse of the extrudate. The melt viscosity has tobe raised by lowering subsequent extruder barrel zone temperatures in order tohave proper rheological properties to facilitate die forming and subsequentfoaming. However, reduction in barrel zone temperatures for cooling mayrequire a reduction in throughput rate to achieve the desired product temperature.

A longer extruder, or more commonly, a second extruder (e.g., anothersingle-screw extruder) in tandem, is used for the purpose of cooling the melttemperature to a range where satisfactory quality foam can be formed [5, 6].This is not economical since either a longer screw extruder or a second ex-truder involves equipment investment. Therefore, rapid and uniform coolingof the polymer system is one of the process challenges in foam extrusion.

Nucleating agents are normally used to provide initial nucleating sites andfine cell structure. Fine particle talc and calcium carbonate are commonly usedas nucleating agents at 0.2 to 2% concentration. Special nucleating agents areavailable to control the size and distribution of the foam cells produced. Theyare made to provide higher efficiency than pure particle nucleation created bytalc or calcium carbonate.

In light of the above foam process descriptions, the following is a list of re-quirements for designing the mixing sections to obtain desired foam extrudedproducts:

• pre-dynamic-seal mixing: dispersive mixing/melting• gas/liquid injection mixing: distributive mixing with low-energy/high-

division mixing elements• final homogenization mixing: distributive mixing with low-energy/high-

division mixing elements and good conveying capability• cooling: distributive mixing for rapid and uniform cooling


9.3 MIXING—THEORIES AND EXPERIMENTS

As mentioned earlier, mixing plays several important roles in the foam ex-trusion process. Some of the mixing processes that may be involved in suc-cessful foam processing include the following:

(1) Adding a low-viscosity liquid additive that must be included into thepolymer matrix—once it is included into the matrix, it must be stretchedout, broken up and distributed well enough throughout the polymer system

(2) Adding a solid additive so that the agglomerates are broken up to the fun-damental element or adding a high-viscosity liquid or melt so that it isbroken up into drops and then distributed evenly throughout the polymersystem

(3) Adding a solid, so that it is not broken up but rather is distributed evenlythroughout the polymer system for later action

(4) Mixing and dissolving physical blowing agents

Each one of these processes is achieved through some fundamental aspect ofmixing. They are related but are governed by different forces and equations.The first example of a low-viscosity liquid being stretched out through thematrix, especially in the case of no to low interfacial tension, is a case wherethe interfacial area is being stretched by the deformation of the interface.

The purpose of this section is to present the fundamentals of the mixingprocesses in the context of foam processing. For this discussion, “well-mixed”is defined as follows: Given a system with a global volume fraction of a minorcomponent into the major component, in our case a foaming or nucleatingagent into a polymer matrix, the system is well mixed if the same volume frac-tion is found in any subset of the overall system. For this definition of well-mixed, the mixing process has two functions. The first is to reduce the scaleof segregation from the initial, agglomerated scale to the final or desired scale.For example, if an immiscible liquid were being injected, the liquid would bestretched and broken to a final drop size or area scale. In the case of solids addition, this would describe the process of breaking up the agglomeratesdown to the fundamental kernel or particle size. For each of these processes,there is extensive literature on the fundamentals of the processes and applica-tions.

The second function, after reducing the scale, is to distribute the materialevenly throughout the medium. The classical methods to quantify the physicsand the process of mixing are insufficient to predict the quality of distribution.The distribution is something that can be quantified as a result of a calculation,but it is not something that comes directly from the physics. This will befurther discussed.


9.3.1 DISTRIBUTIVE MIXING

The first example for foam processing, given above, is for a liquid additivewhere the interfacial tension between it and the polymer is negligible. Themotion of the major fluid component, the polymer, causes the dispersed phaseto deform. The act of deformation causes the interface to deform and stretch.Distributive laminar mixing refers to the physical process of two fluids beingblended such that the physical separation distances are reduced to a scalewhere diffusion or chemical reaction can occur. The mathematics and nature ofdistributive mixing have been expressed in terms of the kinematics of the flow[7–11] and by the continuum mechanics [12–14]. Each approach describes“mixing” as the growth of an interfacial line or interface, though each offers aunique viewpoint.

The kinematic approach provides an overall view to the mixing process andan understanding as to the nature of mixing. This approach allows one to seedirectly whether a mixer is “linear” (i.e., the growth of interfacial area is linearwith the applied shear strain) or whether it is “exponential.” In spite of the lim-itations of the two-dimensional assumptions required in the theoretical devel-opment, this approach enables the practitioner to have insight into the natureof the flow, even for complex three-dimensional flows. By contrast, the advan-tage of continuum mechanics is that it provides the mathematics necessary toexamine the details of the flow. Given the current computational power readilyavailable and given the current requirements for very tight product properties,knowledge of every aspect of the flow provides the information to relate theflow dynamics with the product properties. For example, the 1–5% of productthat is not acceptable in an industrial process can make the entire batch unac-ceptable to the customer. Continuum mechanics can determine the aspects ofthe flow that could be causing that result, which can lead to appropriatechanges in the flow geometry or operating conditions.

9.3.1.1 Laminar Mixing

Numerous measures and indices have been proposed to characterize amixture’s state of “mixedness.” Many of these are indirect measures, such asthe mixture’s bulk electrical conductivity, the resistance of cured material tosolvent or ultraviolet penetration, or some other gross property of the mixture.These measures are often directly applicable to the performance of a particularproduct, but while they may have direct technological application, they offerlittle insight into the mechanisms of mixing.

Mixing in polymer melt processing is primarily the reduction of scales ofsegregation between immiscible fluids. The scale of a polymer mixture is typ-ically described by either an average striation thickness or the amount of inter-


facial area. Interfacial area generation was recognized by Brothman [15] as aprimary mechanism for mixing. Mohr et al. [16] introduced the striation thick-ness (proportional to the inverse of the interfacial area), to characterize mixingdue to laminar shear flow. The interfacial area, now accomplished by deter-ministic considerations, appeared later in the work of Spencer and Wiley [7].Many indices have been proposed in recent years to quantify the mixed state.Most of these are simply related to interfacial area or striation thickness distri-butions.

9.3.1.2 Theoretical Approach

9.3.1.2.1 Interfacial Area Growth in Simple Shear

The first fundamental study of mixing in laminar flow was based on interfa-cial area growth in a simple shear flow field. Spencer and Wiley [7] consideredthe deformation of an arbitrary oriented element of interface within a fluid un-dergoing simple shear. They found the growth of interfacial area to be a func-tion of the magnitude of the shear and the initial orientation of the element:

(1)

where Ai and Af are the initial and final interfacial areas, s is the magnitude ofshear strain, and � and � are the angles defining the initial orientation of theelement. This relation applies only to simple shear that has a constant velocitygradient everywhere in the flow field. This fact makes the calculation of thedeformation tensor trivial or even unnecessary. Calculation of deformationtensor in complex flow fields requires a procedure for calculation of velocitygradient as well as integration of this tensor to obtain deformation tensor.

Erwin [9] derived an upper bound for the increase of the length of an inter-face in shear flow for very large deformation. He discussed the importance ofthe direction of interface with respect to the principal directions of strain andderived the following relation for the growth of an element of area subject toan arbitrary three-dimensional strain of finite magnitude:

(2)

in which the direction cosines describe a unit vector perpendicular to theelement of area in its initial orientation, and �’s are the principal elongationratios.

Af

Ai� c cos �2

�2x

�cos �2

�2y

�cos �2

�2z

d 1/2

Af

Ai� [1 � 2s cos � cos � � s2 cos �2]1/2


9.3.1.2.2 Reorientation in Changing Flow Field

In the course of an interfacial material flowing through a constantly chang-ing flow field, the change of the flow field and the orientation of the interfacerelative to the flow field must be tracked. If the instantaneous growth of a ma-terial interface is given by:

(3)

where � is the interfacial line length, D is the rate of deformation tensor, and nis undeformed unit normal vector. Then, orientation of that interface relative tothe flow is given by:

(4)

where F is force at the interface and N is deformed unit normal vector. By dif-ferentiating the above equation, the rate of change of the interface is given by:

(5)

where D is the rate-of-deformation tensor and W is the rate-of-rotation tensor.The above expression can be said to quantify the reorientation of a material in-terface as it is deformed in the flow field. A physical understanding of thenature of reorientation of the interface can be garnered by reviewing a simpli-fied version of this equation as applied to a Couette flow, which is given by thefollowing:

(6)

By inspection, it can be seen that the rate-of-change of the angle is zero whenthe interface is either parallel or perpendicular to the flow direction. The rate-of-change of the angle is maximum when the line is at a 45° and 135° angle.The rate of change becomes very small when the angle approaches 7°. In otherwords, in a steady shear flow, an interface, when placed in an arbitrary orienta-tion, will quickly rotate to an orientation of approximately 7°. After that, thedecrease in the angle proceeds slowly. We will discuss screw designs later inthe chapter. The estimation of the time it takes for a fluid element to achievethis angle would help in determining frequency of screw disruption.

��

�t� �Sin2 �

�u

�y

n#

� (D � W)n ��#

� n

n �F

�� N

�#

�� D : nn


9.3.1.2.3 Reorientation in Laminar Mixing Theory

The previous discussion of reorientation, from continuum mechanics princi-ples, quantified the change of orientation on an interfacial area with respect toa deforming coordinate system. The effect of the reorientation on the rate-of-stretch of an interface, although directly calculable, is never characterized. Inthe 1970s, using laminar mixing principles, Erwin showed that reorientatingthe interface, with respect to the direction of the flow, can alter the linear rateof mixing. In a simple shear flow, as the interfacial area deforms, it orientsitself parallel to the direction of shear, which is least favorable for mixing.Erwin showed that subsequent reorientations produced a relationship for thefinal area growth, after k reorientations as follows:

(7)

It was shown later that the reorientation did not produce new interface itself,rather it produced an increased efficiency in the linear mixing. The total areagrowth in a simple shear flow, which is characterized with a linear relation-ship, can tend toward exponential growth rates after sufficient reorientations.The nonintermeshing twin-screw extruder has been shown to be a greater-than-linear mixer by Bigio et al. [17]. This can be understood in terms of theprevious discussion. As material moves from one screw into the apex region, itreorients as it enters into the channel of the other screw.

9.3.1.2.4 Distribution of Mixing

In addition to the rate of stretching, it is important to consider the spatial dis-tribution of stretching. A nonuniform distribution means that different portionsof the system exhibit different extents of mixing at a given time (hence, differ-ent local striation thickness), resulting in poor global mixing. Until recently, itwas believed that mixing in chaotic regions was always fast and efficient. Thisis not necessarily true, because first, the effects of islands can span regions thatare much larger than the islands themselves [18], and second, for systems suchas the cavity flow, segregated high stretching regions can develop within thechaotic region and persist for many periods. Since particles can remain trappedfor long times within these high stretching regions, such regions can act as bar-riers to mixing. These regions develop as a result of singularities at the cornersof the cavities [19]. Singularities are also present in the upper corners of thewavy channel flow, where the top wall slips past the vertical walls, and also inextruder flows at the locations where the screw contacts the shell.

Af

Ai� q

k

i�1 fi a(s

k)bk


In the previous sections, we have presented the fundamental physics associ-ated with distributive mixing. The difficulty lies in understanding how to applythe fundamentals to complex flow situations. To demonstrate this point, thereader is directed to the following exercise. Figure 9.2 shows the mixing intwo different geometries. The initial condition shows a single fluid that is pig-mented with titanium dioxide or carbon black and fed into a flow channel. Thebottom two figures show the mixing at the end of the flow path. Both of theflow channels have wavy walls, with the mixing pattern on the right beingcaused by the channel with the walls with the greater amplitude. Since thevolume fraction of the pigment is very small and the interfacial tension isminimal, this is a good example of distributive mixing. The question is asfollows: Which one is better mixed? Which one is better mixed from the prin-ciples of laminar mixing?

Based on the principles of laminar mixing theory, mixing is defined by theincrease of interfacial area between the black and white fluids. The picture on

FIGURE 9.2 Cross-channel images before and after mixing.


the left was caused by flow in a channel with a mildly wavy wall. It was foundthat the interfacial area growth was linear with the average applied fluid strain.So, the flow was essentially linear and the mixing was not very efficient. Onthe other hand, the area growth of the flow on the right-hand side was expo-nential with the applied strain. In terms of the theory, the mixing on the right-hand side was greater. In fact, it can be shown that the nature of the mixing waschaotic.

But, the concept of well-mixed has another connotation. How well is it dis-tributed inside of the control volume? To that criterion, the answer is that thesample on the left is better mixed. There is a more even distribution of the areathickness, and it is better distributed inside of the volume. The sample on theright would continue to have the large unmixed area in the middle of thechannel, so in fact, it would not go away, and although the area would continueto increase, there would be a large unmixed region. This region is called an“island” in the chaos literature, which refers to a region of the flow in whichthe fluid inside of this region does not interchange with the fluid outside of theregion.

One final comment about the question of which one is better mixed. Theanswer may depend on the process you are performing. In the case of mixingcolor, for example, the flow on the left is preferred; whereas, if you are inter-ested in a reaction where the diffusion scales need to be small, the sample onthe right would be preferred.

9.3.1.3 Experimental

This section describes experimental investigations into the mechanism ofdistributive mixing in a corotating intermeshing twin-screw extruder and acounterrotating nonintermeshing twin-screw extruder. Previous work hasshown the pronounced effect of percent channel fill (or percent drag flow) ondistributive mixing in each machine and no effect of screw speed [17, 20]. Totranslate the percent channel fill variable into machine operating parameters, itimplies that the specific throughput (i.e., volumetric throughput divided byscrew speed, Q/N) is the more appropriate operating parameter for distributivemixing than just screw speed alone. Thus, the following experimental studieswill demonstrate the importance and effect of specific throughput on distribu-tive mixing.

Experiments were run on two clear-barreled extruders. One is a fully inter-meshing, 30 mm corotating twin-screw extruder (CoTSE), provided byKrupp-Werner & Pfleiderer. The other is a 20 mm, square-pitched, noninter-meshing twin-screw extruder (NITSE), provided by Welding Engineers Inc.(now called NFM/Welding Engineers Inc.).

Silicone oils with viscosities of 60, 100, and 300 Pa-sec, supplied by GEPlastics, were tested in the experimental apparatus. The viscosities were suffi-


cient to operate at starve-fed conditions without producing gravitational droopat the operating screw speeds. At the rate-of-strain levels employed in the ex-periment, the fluids performed like a Newtonian, nonviscoelastic, isothermalfluid. Screw speeds of 7 to 50 rpm were reported. A small volume of siliconeoil, pigmented with carbon black, was injected on one screw and then video-taped as it was transported through the extruder. Feeding the dyed fluid ontoone screw allowed for observation of the screw-to-screw transfer of the fluidand for tracking its specific path through the extruder.

For partially-filled channels, the flow field is purely a function of drag flow.Drag flow is defined as the cross-sectional area of the channel times the down-stream velocity, which is modeled as flat plate flow. This area of the flow fieldis modeled as a semi-ellipse for the CoTSE and a rectangle for the NITSE withthe width being the distance between two flights perpendicular to the helicalaxis and the height being the distance between the screw root and the inner di-ameter of the barrel. Flow downstream is parallel to the helical axis, then de-scribed as the product of screw geometry, barrel diameter, rotational velocity,and cosine of the helical angle. This expression is given for each extruder:

(8)

(9)

where, width, height, of barrel,of screw revolutions, flow factor,

, , and .Percent channel fill is then found as the pump flow rate divided by drag flow

rate. Both the flow rate, Q, and the screw speed, N, were varied to give a con-stant Q/N ratio over a range of screw speeds. For the CoTSE, the ratios rangedfrom 2.0 to 5.0 (equivalent to 30% channel fill to 70% channel fill) and for theNITSE, the ratios ranged from 1.0 to 4.0 (equivalent to 30% channel fill to90% channel fill).

Analysis of the dye distribution employed a quasi-quantitative technique ofmeasurement for each machine. For the CoTSE, this technique was themeasure of the increase in linear length of the tracer. An injected pulse stays inone channel in conveying elements for the CoTSE and thus stretches into aline, wrapping around the elements. The length of this line could be deter-mined and plotted against strain as a measure of mixing where average totalstrain is defined as the integral of strain rate over time. For partially filledchannels, the flow field is generated by drag alone, and the average strain rateis constant. Strain is defined as follows:

(10)� ��3 NDb

2

4Qp� n

� � helix anglef � 1 � (nip height/barrel circumference)4f/(1�3f)FD � nip factor �fd � dragN � number

Db � diameterH � channelW � channel

QNITSE � �WHNDb fdFD cos �

QCoTSE � �WHNDb cos �


where N is the screw speed, Db is the barrel diameter, Qp is the volumetric flowrate, and n is the number of screw revolutions. For the NITSE, an injectedpulse quickly enters many channels on each screw (as opposed to the CoTSE)so the measure of mixing is the number of channels containing dye (whereeach L/D is broken into eighths for analysis). Channels containing dye is pre-sented as a function of screw revolutions, which is analogous to impartedstrain.

9.3.1.4 Results

9.3.1.4.1 Corotating Twin-Screw Extruder (CoTSE)

Figure 9.3 is a plot of averaged line length versus strain for a 30mm CoTSE.There is a pronounced effect of percent channel fill on mixing. A jump in linelengths appears between 40% and 50% fill. This is due to the way that theCoTSE channel physically filled with fluid. Since the channel of the CoTSE isnear parabolic, at a given screw speed slight increases in the flow rate will tendto fill the bottom of the channel, only slightly increasing the wetted barrel

FIGURE 9.3 Averaged line length versus strain in a 30 mm CoTSE. (Adapted from Bigio et al.[20].)


surface. Since the shearing force is imparted to the fluid via the wetted barrelsurface, for channel fills of less than 30%, slight increases in barrel surfacecontact translate into only slight increases in mixing. However, at above about30% channel fill, the bottom of the channel is filled and increases in flow ratewill yield proportionate increases in the wetted barrel surface. In other words,increased flow rate yields rapid increases in mixing for percent channel fillsabove 30%.

Figure 9.4 shows normalized line length versus percent channel fill. Thenormalized line length is the line length divided by strain. It can be seen thatthe rate of mixing is very much dependent on the degree of fill of the machine.Above about 40% fill, slight increases in the flow rate (at constant screwspeed) yield rapid increases in mixing. However, below about 40% fill (espe-cially around 30% fill), only slight increases in mixing are seen from increasesin flow rate, and the rate of mixing is nearly constant. To optimize mixing inpartially filled conveying sections in the CoTSE, the channels must be filled togreater than 40%. By running the machine over 40% fill, dramatic mixingresults can be achieved when compared to the lower percent fills.

9.3.1.4.2 Nonintermeshing Twin-Screw Extruder (NITSE)

Figure 9.5 is a plot of channels containing dye versus screw speed for the 20mm NITSE run at various percent channel fills while keeping the screw speed

FIGURE 9.4 Normalized line length versus percent channel fill in a 30 mm CoTSE. (Adaptedfrom Bigio et al. [20].)


constant at a given screw stagger. As can be seen, there is an increase in mixingas the degree of channel fill is increased. This is due to the nature of the screw-to-screw transfer that depends on the relation between the screw stagger andthe percent channel fill [17]. If the percent fill is less than the percent stagger,there is no fluid-to-fluid contact across the screws. The only mode of transferis deposition where fluid from one screw gets deposited into the nip regionbetween the two screws and is picked up by the opposite screw. This is a rela-tively inefficient mode of transfer (as is seen by the few channels containingdye for low percent channel fills). When the percent fill is greater than thescrew stagger, there is direct fluid-to-fluid contact and highly efficient screw-to-screw transfer. Thus, for high percent channel fills—when the percent fill isgreater than the percent screw stagger—there is enhanced transfer; hence, en-hanced distributive mixing. Figure 9.6 is a similar plot for a constant percentchannel fill at various screw speeds. Mixing is obviously not a function ofscrew speed, given pure positive conveying elements. Even though the fluidsees a high shear stress at high screw speeds, the residence time decreases suchthat the fluid sees the high shear region for a shorter time.

9.3.2 DISPERSIVE MIXING

Processing of materials for foam applications requires the successful addi-tion of a foaming agent into the polymer matrix. The requirements for theprocess vary as a function of the additive and the desired application. In somecases where a physical blowing agent is used, the additive is a lower viscositymaterial that needs to be distributed throughout the polymer. In other caseswhere a chemical foaming agent is used, the material is very stress sensitive

FIGURE 9.5 Extruder volume containing dye versus screw speed at various percent channelfills in a 20 mm NITSE. (Adapted from Bigio et al. [17].)


and over mixing could result in loss of efficiency. On the other extreme, the ad-ditive could be a pseudo-solid that requires strong forces to overcome the ag-glomeration so that it could be distributed throughout the polymer matrix. Inboth of these examples, force is required to achieve the desired mixing.

What is similar in both of these cases is that there is a range of forces that allof the dispersed phase elements must see in order to be sufficiently distributedthroughout the flow field. Similarly, there are maximum stresses and tempera-tures to which the chemical foaming agents must not be exposed to avoid pre-mature decomposition. In this section, we will present some of the basicphysics associated with the dispersive mixing process. In subsequent sections,the effects of screw design and operating conditions in extruders will be dis-cussed.

9.3.2.1 Relationship of Dispersive and Distributive Mixing

When people discuss mixing, they often say that they first need to break upthe large particles and then distribute them throughout the flow volume. The

FIGURE 9.6 Extruder volume containing dye versus percent channel fill at various screwspeeds in a 20 mm NITSE.


way it is described in practice, it would seem that the two types of mixing areseparate and distinct and driven by different forces. In fact, the opposite is true.In the simplest sense, the difference between distributive and dispersivemixing is that the latter requires a minimum force to overcome adhesiveforces, whereas distributive mixing has no resistance to the process. Themeasure for mixing with dispersive mixing is morphology or solid diameter;the measure for mixing with distributive mixing is interfacial area or scale ofseparation.

Distributive mixing is related to the shear rate; the dispersive mixing isrelated to the stress. But, the stress is given by the viscosity multiplied by theshear rate, or

(11)

In the locations where there are large shear rates, there are also large stresses.So, the locations for good distributive mixing are also those with good disper-sive mixing. The only caveat to that statement is that with dispersive mixing,there needs to be a minimum stress to overcome the adhesive forces.

9.3.2.2 Liquid-Liquid Mixing

The process of mixing a liquid additive into a liquid matrix is fulfilledthrough the competition of forces—surface tension forces that tend to hold thedrop together and viscous forces imparted by the fluid motion that tend tobreak them apart. The dimensionless parameters that describe the processinclude capillary number and viscosity ratio.

Capillary number (or Weber number) is a nondimensional number that isthe ratio of the viscous forces to the surface tension forces or

(12)

Where matrix viscosity, local shear rate, character-istic drop length scale, and tension.

Viscosity ratio is the ratio of the disperse phase to the continuous phase or

(13)

In the case of mixing of Newtonian fluids, the critical capillary number, as afunction of the viscosity ratio, describes the critical diameter of a drop in aflow field above which the drop can be broken into smaller, daughter, drops.

� ��d

�m

� � interfaciald � the�

#� the�m � the

Ca ��m�

#d

�

� ��#


As the viscosity ratio changes between the dispersed and continuous phases,so does the value of the critical capillary number. Taylor [21] showed that for

, the dispersed drop will not break because the matrix fluid could notimpart a sufficient stress. Figure 9.7 shows the critical capillary number versusviscosity ratio curves in a simple shear flow and an extentional flow [22]. Fora miscible fluid system with a hydrocarbon blowing agent, the interfacialtension is essentially zero, so the capillary number is not determinable.

9.3.2.2.1 Viscoelastic Effects

Most polymers exhibit viscoelastic effects that affect the process of dropbreakup. Literature reported contradictory results in the effect of viscoelastic-ity on drop deformation and breakup. It was generally assumed that viscoelas-ticity retards the process of deformation and breakup.

The critical capillary numbers have been reported for viscoelastic drops in aviscous matrix [23–25]. Their results showed that for viscosity ratios on theorder of one, no significant difference (e.g., a factor of 2) from Newtonian dropswas found. Viscoelasticity plays a significant role only if the deformation is fastand large enough. In most drop breakup experiments, the total strain may belarge, but the rate of deformation may be too small to build up a significant level

� � 3.7

FIGURE 9.7 Critical capillary number versus viscosity ratio for simple shear flow and exten-sional flow. (Adapted from Grace [22].)


of orientational stresses. In addition, the stresses that have built up could relaxquickly. Then the deformed drops retract back to initial shape.

Tipstreaming breakup phenomenon was observed by Milliken and Leal [23]for viscoelastic drops. Janssen [26] reasoned that this type of phenomenon wasnot caused by the viscoelastic behavior of the fluid. The polymer moleculesadded to modify and make the model fluid viscoelastic may accumulate at theinterface and act as a surfactant [27, 28]. The inhomogeneities in the interfa-cial concentration of this surfactant and the interfacial tension cause nonuni-form drop breakup observed as tipstreaming. That is, an extended drop breaksup into a major drop with a few much smaller satellite drops at both ends.

Mighri et al. [29] examined the deformation and critical breakup in a simpleshear flow of two viscoelastic fluids. They developed empirical relationshipsbetween the elasticity ratio, k�, the ratio of the drop and matrix relaxationtimes, and the Capillary number. Their results showed that for , theelastic drops deform less than Newtonian drops; whereas for , thedrops deform more than Newtonian drops. In general, they concluded that the matrix elasticity helps to deform the drops, whereas the drop elasticityresists the drop deformation. Elasticity ratio affected drop breakup in the fol-lowing manners. The critical Capillary number and breakup time increase withincreasing elasticity ratio. For , the critical Capillary number increasesrapidly, increasing k�. Above , the critical Capillary number is about1.75 that corresponds to the maximum contribution of elasticity on dropbreakup.

Wu [30] studied the interfacial and rheological effects for incompatiblepolymer blends in a corotating intermeshing twin-screw extruder. The disper-sion process was investigated using nonreactive and reactive ethylene pro-pylene rubbers as the dispersed phase. Polyamide (nylon 6,6 resin) andpoly(ethylene terephthalate) were used as the matrix phase. Based on experi-mental data, he established a master curve that similarly correlated the criticalcapillary number with viscosity ratio. The portion of the curve for viscosityratio greater than one can be expressed as a straight line.

(14)

Although there lacked sufficient data available for , a linear curve canbe tentatively drawn for the portion. Then, the whole range of themaster curve becomes V-shaped as the elasticity of the system increases. Fur-thermore, he found that viscoelastic drops can break up even for in theextruder. He suggested that this arose from a combination of several factors:the viscoelastic effects, complex transient shear, complex viscosity/tempera-ture profile along the extruder, and the presence of elongational flow field inthe extruder.

� � 4

� � 1� � 1

Cacrit � 4�0.84 for � � 1

k� � 4k� � 4

k� � 0.37k� � 0.37


9.3.2.3 Application to Complex Flow

The fundamentals for drop breakup have been developed in simple, steady-state flows in order to distinguish the breakup mechanisms. The trouble occurswhen these models are used to predict the resultant morphology in a complexflow where there is no constant value for shear rate. Even in a simple flow likethe flow in a screw channel, the shear rate for a fluid element varies as it flowsaround the cavity. So, from a rigorous point of view, one would have to track anumber of drops over various streamlines and then apply some criteria forbreakup to generate a prediction for the final morphology. Bastian et al. [31]are beginning to look into developing that approach.

Therefore, how much time a fluid drop is at a particular shear rate becomes acritical factor for trying to predict average drop sizes using established theory.Bigio et al. [32] applied an experimentally derived model for drop breakup inthe steady shear flow of a screw channel. The result shows the conditions underwhich drop breakup would occur and the final average drop sizes.

To further complicate the issue, in many of the reported experiments, theaverage particle sizes are smaller than what is predictable by the abovemodels. What, then, is the cause of the breakup? It is possible that the sourceof breakup is the folding and breaking of the drop fibers as they translate fromone flow field to another in a complex flow regime as might be found in themixing elements of an extruder. Ottino [33] has shown the physics associatedwith this mechanism.

9.3.2.4 Solid-Liquid Breakup

In the case of solid-liquid breakup for foaming agent and/or nucleatingagent in the polymeric melt, the primary forces involved are particle cohesiveforce, flow shear, and extensional force. When the breaking force is greaterthan the holding force, agglomates tend to break up into smaller ones. The at-tractive van der Waals force between two spheres with same radius, R, is

(15)

Where, Adenotes Hamaker constant , and z sepa-ration distance, 4 Afor adhering particles. Considering void fraction, �, the cohe-sive force in the rupture cross-sectional area, S, can be expressed as follows [34]:

(16)

When the sum of breaking forces, shear force, hydrodynamic force, and exten-sional force, is greater than Fc, smaller particle clusters in the flow area canthus be anticipated.

Fc � (9/16)(1�e)/e(A/(12z2R)S

(� 5 � 10�20 to 5 � 10�19 J)

F � AR/12/z2


Since shear rate and elongation play critical roles in the breaking force, thedesign of mixer, flight tip clearance, and multiple passage of the high-shearregion, become very important factors in solid-liquid dispersion. The criteria,

, can be used to calculate the solid agglomarate size. Based upon theparticle density and mass rate, the solid cluster distribution becomes a straight-forward calculation.

9.4 MIXING PRACTICES IN SINGLE- AND TWIN-SCREWEXTRUDERS

Thiele [5] has reviewed the machinery features for thermoplastic foam ex-trusion. He asserted that there is really no standard device or process method tomake foamed products. He used a “think-through” machinery approach todevelop a processing protocol for a specific foamed product. One cannotdesign proper mixing sections to meet specific process demands and productrequirements without understanding the common machinery employed.

The above sections have reviewed the theory of mixing and the operatingprinciples for dispersive and distributive mixing. The mixing sections insingle- and twin-screw extruders utilized in thermoplastic foam extrusion arecovered in the following. The screw configurations for achieving required dis-persive and distributive mixing intensities are demonstrated. Table 9.1 listscommon mixing elements available in various extruders.

9.4.1 MIXING SECTIONS IN SINGLE-SCREW EXTRUDERS

The standard screws in single-screw extruders provide very limited mixingcapability. The linear rate of mixing generated by the simple shear flow in thestandard single-screw extruder is a very poor mixing mechanism [10, 35]. Theextruder machine makers, screw designers, and processors have recognizedthis fact. Modifications have been made to the standard screws to improvetheir mixing capability. New screw designs to accomplish different processdemands or product quality requirements have been evolving in the market.Rauwendaal [36] listed common types of screw elements for dispersive anddistributive mixing in single-screw extruders. Maddock mixing section, Eganmixing section, and blister ring are some common dispersive mixing elements.Common distributive mixing elements include pin, Saxton, Dulmage, Pinap-ple, slotted screw, and cavity transfer mixing sections (see Figure 9.8) [36].

Rauwendaal [37] discussed the screw design for good control of melt tem-perature, mixing, and melting in foam extrusion systems. One of the criticalsteps in foam extrusion is the distributive mixing of the physical blowingagents into the polymer melt. He compared several distributive mixing ele-ments commonly used in single-screw extruders. (see Table 9.2) [37]. The best

Fb � Fc


TABLE 9.1 Mixing Elements in Various Extruders.

Corotating Counterrotating CounterrotatingExtruder Type and Intermeshing Intermeshing NonintermeshingMixing Elements Single-Screw Extruder Twin-Screw Extruder Twin-Screw Extruder Twin-Screw Extruder

Dispersive Mixing Maddock, Egan, blister Discontinuous discs Intermeshing calendering Cylindrical elementrings screws, discontinuous

discs, mixing rings, hexalobal mixing screw

Distributive Mixing Pin mixer, Saxton, Dulmage, Discontinuous discs, Discontinuous discs, Staggered non-intermeshingPinapple, slotted screw, toothed mixing slotted screw, pin mixer screws, double-reverse flight cavity transfer mixing element mixing ring, vane mixer, element, slotted double-element gear mixer reverse element


overall mixing section is the Saxton mixer that combines forward conveyingcapability and a streamlined geometry with frequent flow path splitting and re-orientation. The cavity transfer mixer (CTM) also provides the features for fre-quent splitting and reorientation [38]. New special screw designs for achievingimproved dispersive and distributive mixing in single-screw extruders havebeen available from various manufacturers.

9.4.2 MIXING SECTIONS IN COROTATING INTERMESHINGTWIN-SCREW EXTRUDERS

Corotating intermeshing twin-screw extruders have been widely used asplastics compounding machines. They provide flexible design of screw config-

FIGURE 9.8 Some common dispersive and distributive mixing elements for single-screw ex-truders. (Adapted from Rauwendaal [36].)


urations and modular barrel assembly to balance the various process tasks inthe machine. The common mixing elements in corotating intermeshing twin-screw extruders are discontinuous discs (so-called “kneading blocks”) andspecial mixing elements. The mixing zones are often arranged in combinationsof mixing elements of different geometries to achieve the desired level ofmixing intensity.

Each discontinuous disc is characterized by its axial width, number of discs,staggering angle between the discs, and whether it is constructed for forwardconveying or for reverse flow restriction. Distributive mixing is said to be en-hanced by narrow discontinuous to maximize the number of flow divisions fora given machine length. Dispersive mixing utilizes wide discontinuous discsthat maximize the flow of fluid that is affected by the stagnation points onevery disc. The polymer stream must first be mixed distributively to allowuniform stress input. As the stagger angle increases, the amount of materialthat can backflow through the gaps is increased, which increases the percent ofmaterial seeing the high stress and the total residence time in the mixingsection. For both types of mixing sections, reverse discontinuous discs, neutraldiscontinuous discs, or reverse screw elements can be used to restrict the ma-terial flow and build up pressure, thereby increasing the mean residence time,broadening the residence time distribution, and enhancing the mixing inten-sity. They also create a melt seal to separate the subsequent process functions.One caveat is that the mixing elements should not be arranged in such a waythat excessive polymer melt temperature rise and subsequent material degra-dation are caused. For the same mixing sections, the mixing intensity increasesas the flow is restricted by the following elements in ascending order: neutralkneading blocks, reverse discontinuous discs, and reverse screw elements.Figure 9.9 shows several screw configurations that illustrate the screw designconcepts for dispersive and distributive mixing.

TABLE 9.2 Comparison of Distributive Mixing Elements for Single-Screw Extruders [37].

Pres- Splitting,sure Dead Barrel Operator Machining Shear Reori-

Mixers Drop Spot Wiped Friendly Cost Strain enting

Pins 2 2 3 4 5 2 4Dulmage 4 2 2 4 4 4 5Saxton 4 4 5 4 4 4 5CTM 1 3 2 1 1 4 5TMR 1 3 4 3 3 4 5Axon 4 4 4 4 5 4 3D-Wave 4 4 4 4 2 4 2Pulsar 4 4 4 4 3 3 2Stratabl. 4 3 4 4 3 3 2

(Rating scale: )5 � very good, 1 � very poor


One of the processing challenges in foam extrusion is the injection and rapidmixing of physical blowing agents. The distributive mixing for this functionmay be beyond the capabilities of narrow discontinuous discs. Special mixingelements are available for higher intensity distributive mixing. For instance,Krupp W&P’s ZSK twin-screw compounders utilize toothed distributivemixing elements such as the TME (turbine mixing element) or ZME (Zahn-mischelement) design [39]. Note that other suppliers of corotating intermesh-ing twin-screw extruders also provide similar mixing element design. Theseelements are defined by the number of teeth around the circumference and thetooth angle. Both mixing elements provide the maximum amount of distribu-tive mixing with minimal energy input by providing flow splitting and reorien-tation. One difference between these two mixing elements is that the TMEmixing elements do not have flight advancements, so their conveying capabil-ity is poor. The polymer material may stagnate and degrade in these regions.

FIGURE 9.9 Screw configurations for distributive and dispersive mixing.


Some conveying screw elements are normally staged between zones of TMEmixing elements to provide forward conveying capability. On the other hand,ZME mixing elements have flight advancements that provide better conveyingcapabilities than TME elements. TME or ZME mixing elements can bearranged in combinations of alternating patterns of forward and reverse ele-ments to balance the degree of fill, back pressure, and distributive mixing in-tensity. Similar to the discontinuous discs, flow restriction and pressurebuildup can be utilized at the end of TME or ZME mixing zones to increasemixing intensity. ZMEs, reverse TMEs, neutral discontinuous discs, reversediscontinuous discs, and reverse screw elements can be used to provide mixingwith increasing intensity. Figure 9.9 shows several screw configurations thatutilize TME mixing elements for distributive mixing.

As pointed out by Dreiblatt and Eise [40], the design of a screw configura-tion for twin-screw extruders is more of an art than a science. The above dis-cussions merely provide general guidelines for mixing in corotating inter-meshing twin-screw extruders. When designing a screw configuration formixing, one has to consider the physical properties and compatibility of the in-gredients, temperature profile and mechanical energy management, shear sen-sitivity of the polymer materials, and required mixing intensity.

9.4.3 MIXING SECTIONS IN COUNTERROTATINGINTERMESHING TWIN-SCREW EXTRUDERS

Counterrotating intermeshing twin-screw extruders are often used inprocesses that require short mean residence time, narrow residence time distri-bution, good control over material temperatures, and relatively positivepumping capacity. As a result of the above advantages, these extruders havebeen used in extrusion of temperature-sensitive materials, such as profile ex-trusion of rigid PVC, with minimum degradation. These extruders are wellsuited for foam extrusion processes where thermal history control is importantto make quality foamed products.

In counterrotating screws, the roll-off process between the screw flight andscrew root and between the screw flanks creates a calender effect. The matingin the intermeshing region between the root of one screw and the flight ofanother screw forms a chamber shaped like a capital letter “C.” The C-shapedchambers in the classical counterrotating intermeshing twin-screw extrudersprovide better sealing between the two screws and efficient forward pumpingcapability. However, high pressure can develop in the intermeshing region dueto the locked C-shaped chambers. This pressure works to push the two screwshafts apart. In addition, the wear of the screws increases as the screw speedincreases. As a result, these extruders have to run at low speeds around 10 to50 rpm, generally limited to 150 rpm [1, 42]. New design concepts have madeit possible to run high speeds in the range of 300 to 500 rpm in counterrotating


intermeshing twin-screw extruders [42]. The high shear and elongational flowin the classical counterrotating calender gap offer an effective dispersivemixing mechanism. Three book volumes [43–45] are good references for de-scribing the development history, screw designs, process functions, and appli-cation examples in counterrotating intermeshing twin-screw extruders.

Classical counterrotating intermeshing twin-screw extruders use slottedscrews, pin mixers, and mixing rings to achieve distributive mixing, whereasthe intermeshing calendering and mixing rings are utilized for dispersivemixing. Similar to corotating intermeshing twin-screw extruders, discontinu-ous discs are available to assemble appropriate screw configurations for dis-persive and distributive mixing. Vane or gear mixers are available for distribu-tive mixing [42]. Solid and slotted hexalobal mixing screws were invented toimprove the mixing capability in counterrotating intermeshing twin-screw ex-truders [42, 46].

9.4.4 MIXING SECTIONS IN COUNTERROTATINGNONINTERMESHING TWIN-SCREW EXTRUDERS

The Counterrotating Nonintermeshing Twin-Screw Extruder, manufacturedby NFM/Welding Engineers enjoys wide usage in reactive processing, espe-cially devolatilization and latex processing. This is due to the high free-volumecapabilities and the flow path in the apex region between the two screws [47].The extruder has been shown to have excellent distributive mixing character-istics [17, 20, 48, 49]. They showed that in the apex region, flow transferoccurs from one screw to another and in the back flow direction. The drivingforce was suggested to be due to a local pressure gradient that occurs when thescrews are staggered that places the pushing flight of one screw (high pressure)near the trailing flight of the adjacent screw (low pressure). The transfer of10–15% of the material in the channel results in a reorientation of the materialin the channel and an enhanced mixing rate [50, 51]. As mentioned earlier, thedistributive mixing in counterrotating nonintermeshing twin-screw extruderscould be a greater-than-linear type. In other words, mixing can be greater thanjust doubling two single-screw extruders as long as the mixer is operated underconditions where the degree of fill is greater than the screw stagger.

One standard element available for dispersive mixing in counterrotatingnonintermeshing twin-screw extruders is a cylinder or a cylindrical com-pounder. The cylinders offer no forward conveying capabilities. The pressureflow through the cylinders can occur either in the annular region between thecylinder and the barrel wall or through the apex region. The pressure dropacross the cylinders also provides the melt seal function. The cylinders areavailable with different clearance to vary the level of pressure drop and degreeof shear stress. A tighter gap results in a higher material flow in the apexregion. The advantage of the cylinders is that the flow that passes in the


annular region experiences an equal amount of stress. The limiting factor isthat the tighter the gap that is needed, the more the material will flow throughthe apex rather than the annular region. Hagberg et al. [52] conducted a scale-up study of dispersive mixing on cylindrical compounders using 30 mm and51 mm counterrotating nonintermeshing twin-screw extruders. They foundthat dispersive mixing was scaled up with increasing extruder size. The pres-sure drop across the cylinder is an indication of stresses necessary for disper-sive mixing. To obtain a higher dispersive mixing, one would run the extruderat the higher pressure drop conditions where tighter apex barrels with tightercylinders are used.

9.5 PROCESS CHALLENGES

9.5.1 INJECTION AND MIXING OF PHYSICAL BLOWING AGENTS

Injection and mixing of physical blowing agents is one of the challengingprocess tasks in foam extrusion. The process requires pumping and injection ofthe blowing agent in liquid form (or supercritical fluids) into the extruder at aconsistent rate without much fluctuation. Once the blowing agent is injectedinto the extruder, the next task is to mix the blowing agent into the polymer inan efficient and uniform distributive mixing mechanism. Due to the large vis-cosity difference between the low-viscosity blowing agent and the high-vis-cosity polymer (i.e., small viscosity ratio), higher energy input is required toachieve good mixing [22, 30, 53–55]. Their data showed that droplet breakupfor mixing (as characterized by a critical capillary number or Weber number)is ineffective for low-viscosity ratio fluids subject to a simple shear flow field.On the other hand, elongational flow significantly reduced the critical capillarynumber for improved drop breakup.

Distribution mixing involves the reduction in segregation of scale, flow di-vision, and reorientation of the minor component (blowing agent) in the majorcomponent (polymer). A good distributive mixing process is beneficial if start-ing with a smaller domain of the minor component. This can be achieved byusing an injection nozzle with a smaller diameter port. Another alternative is tosplit-inject the liquid into two or more injection nozzles. Each injection nozzlehandles a smaller quantity of liquid. A third option is to use a multi-injectionport as described by Park et al. [56]. They utilized the multi-injection ports inthe supercritical gas injection nozzle to increase the interfacial area betweenthe gas and the polymer melt. As a result, the diffusion of gas into the polymermelt is improved and the diffusion time required to complete the polymer/gassolution formation is decreased [57].

To further improve mixing of the blowing agent, the above practices arecomplemented by injecting the blowing agent over distributive mixing ele-


ments (e.g., narrow discontinuous discs, toothed mixing elements, gearmixers) under high pressure. The blowing agent immediately divides intosmaller domains when injected over mixing elements. By contrast, theblowing agent flowing from the injection nozzle to the flighted screw elementsmay form large drops and coalesce into larger drops. Then, it would requiremore mixing elements, longer screw, and higher energy input in the down-stream to achieve the same level of mixing as injection over mixing elements.In other words, the preferred distributive mixing process is one starting with assmall a length or area for stretching and orientation as possible. It is importantthat the blowing agent is finely divided without relaxation to prevent it fromforming larger drops due to coalescence. A rapid reduction in scale of domainincreases the diffusion rate of the blowing agent into the polymer and shortensthe diffusion time required to complete dissolution.

Mass transfer properties of the materials used in foam extrusion are also im-portant in determining the intensity of mixing required for achieving rapid dis-solution. In foam extrusion, diffusivity and solubility of the blowing agent inthe polymer are two key properties. Diffusivity determines the rate of diffusionof the blowing agent in the polymer. Solubility determines the equilibriumlevel of blowing agent dissolving in the polymer at given conditions. Forexample, isopentane has higher solubility than carbon dioxide in polystyrenefor the same given conditions. Besides, isopentane is in a liquid phase at roomtemperature and, thus, can be easily metered when injected using a positivedisplacement pump, as opposed to the gaseous carbon dioxide. A more con-trollable process can be achieved. It is easier to mix isopentane with poly-styrene because they are more compatible to each other. As long as the scale ofsegregation for mixing is reduced sufficiently, the dissolution process takesplace quickly. By contrast, higher mixing intensity is required for dissolvingcarbon dioxide. Sometimes, the injection pressure also has to be maintained atthousands of psi’s to obtain the same level of dissolution as with isopentane.The intensity of mixing has to be maintained and also sustained and pro-longed. This may occur to an undesirable degree causing excessive shear-heating. As a result, the downstream cooling of the polymer system could bedifficult and that would limit machine throughput.

Figure 9.9 has shown some of the screw configurations for distributionmixing in a corotating intermeshing twin-screw extruder. One can assemble adistributive mixing screw by alternating the right-handed and reverse mixing el-ements to give the desired flow division and reorientation. For single-screw ex-truders and other types of extruders where modular barrel and screw assemblyare not available, commercial systems utilize suitable distributive mixing ele-ments for mixing the blowing agent. Static mixers are used after the distributivemixing elements to further improve mixing of the blowing agent. The materialsflowing into a static mixer are divided by baffles, and mixing occurs by contin-ual flow splitting and recombination. Most commonly used static mixers rely on


shear flows and high shear stresses to split and redistribute the materials uni-formly. They tend to cause excessive temperature rise while mixing the materi-als. The excessive temperature rise reduces the melt viscosity and makescooling even more difficult. As a result, throughput and productivity are limited.Some special temperature control devices for static mixers are available thatoffer efficient heat transfer to reduce downstream cooling and line length [58].A new type of static mixer that provides dispersive and distributive mixing ca-pabilities in one device has been described in the literature [59].

As the blowing agent is injected into the extruder under high pressure, itmay blow back upstream and interfere with the process. It is necessary to havea melt seal before to the blowing agent mixing section. Because liquid pumpsare used to deliver and inject the blowing agents, it is important that theyprovide enough positive pumping capacity to overcome the pressure over themixing elements. Otherwise, the blowing agents could back up from the ex-truder to the injection nozzle. The precision of the metering device is critical insupplying consistent flow rate of the blowing agents. The injection tube isideally short, rigid, and in smaller diameter to minimize pressure loss.

9.5.2 EXTRUDER COOLING

Since the viscosity of the polymer system may drop by as much as half afterbeing mixed with the blowing agent, it is necessary to cool the polymer systemand develop proper rheological properties for die forming. As mentionedearlier, the extraction of heat from the polymer for cooling conflicts with therequirements for mixing and limits the throughput capability. So far, commer-cial foam extrusion systems have been utilizing a longer plasticating extruderor a second oversized extruder in tandem to attain the cooling requirementbefore die forming. Therefore, one of the processing challenges in foam extru-sion is rapid and uniform cooling of the polymer system.

Several books and articles have covered the subject on heat transfer ofpolymer systems in extruders [36, 45, 60–63]. However, there was little engi-neering analysis as to how to achieve good mixing and rapid cooling for agiven extruder at the same screw speed and throughput [64, 65]. It is easy toidentify that there are two major heat transfer mechanisms providing theheating source for the polymer systems. They are conductive heat throughbarrel surfaces and the heat generated by viscous energy dissipation. For thesame given extruder and high screw speed requirement for mixing, the onlysource of heat exchange for cooling is heat conduction through barrel surfaces.The process requirements for these two tasks conflict with each other.

Han [65] developed a mathematical model and performed computer simula-tion of cooling extruder performance in thermoplastic foam extrusion. Basedon the computation results on a 6-inch, 32 L/D single-screw extruder, heshowed that the screw temperature can be 30°C higher than the barrel temper-


ature while the polymer melt temperature is 20°C higher than the screw tem-perature. In other words, the temperature difference between the barrel and themelt is 50°C. Such a large temperature difference indicates that it is not suffi-cient to rely on the cool barrel temperature to reduce melt temperature effec-tively. In addition, the computer simulation showed that the melt temperaturedifference from the screw root to the highest temperature point (about 2/3channel height from the screw root) in the cross channel can be 40 to 50°C.Each fluid element follows the velocity distribution profile and circulatesinside the cross-channel melt pool while conveying downstream in themachine direction. The higher melt temperature fluid elements circulate nearthe center of the pool and never have the opportunity to cross the flow path tolow-temperature areas near the screw and barrel surfaces. This mode of heattransfer is not efficient due to poor mixing and the relatively large distancebetween the maximum melt temperature region to both screw and barrel.

This problem can be alleviated by using efficient mixing elements andproper process conditions. One can use mixing elements that are capable of ef-ficient flow reorientation and surface renewal. Rapid surface renewal increasesthe surface area for efficient heat transfer. Flow reorientation gives an opportu-nity for the fluid elements inside the circulating melt pool to travel to cool sur-faces near the screws and barrel for heat transfer. The screw design factors af-fecting surface renewal include the helix angle, number of flights, and theflight clearance [36, 37]. Efficient heat transfer is favored by multiple flights, asmall flight clearance, and a large screw pitch.

Todd [63] reported heat transfer in partially filled twin-screw extruders. Hederived an overall heat transfer correlation equation based on a classical heattransfer approach. The equation expresses Nusselt number (hD/k) as a functionof Reynolds number (D2N�/�) and Prandtl number (c�/k) with no effects fromdegree of fill or flight clearance:

(17)

where coefficient, diameter, conductivity,speed, melt density, viscosity (�w at

wall), and .The above equation can be further simplified when lumping the Reynolds

and Prandtl numbers together:

(18)

Experimental results with cooling polyethylene in a single-screw extrudershowed good agreement with the above heat transfer equation [61]. Notice thatthis equation does not include the effects of screw flight clearance and degreeof fill.

(hD/k) � 1.02(D2 N �c/k)0.33 (�/�w)0.14

c � specific heat� � effective� � polymerN � screw

k � thermalD � barrelh � film

(hD/k) � 0.94(D2 N�/�)0.28 (c�/k)0.33 (�/�w)0.14


Table 9.3 compares the relative effects of various parameters on the processfunctions in foam extrusion. They show either positive or negative effects ofincreasing throughput, screw speed, barrel temperature, screw pitch, channeldepth, number of flights, and flight clearance on mixing, melt temperature,torque (energy input), and conveying capacity (throughput). The effect on melttemperature increase is the opposite of melt cooling. It is seen that the parame-ters used to cool the melt temperature compete with better mixing and higherthroughput.

9.6 SUMMARY

This chapter presents the design of dispersive and distributive mixing forfoam extrusion. Mixing plays important roles in foam extrusion by dispersive-melting the raw materials, distributive-mixing the foaming agent, homogeniz-ing the polymer system, and cooling the polymer system for die forming. Thefundamentals of dispersive and distributive mixing are covered. The mixingsections in various extruders are described: single-screw extruders, corotatingintermeshing twin-screw extruders, counterrotating intermeshing twin-screwextruders, and counterrotating nonintermeshing twin-screw extruders. Twoprocess challenges in foam extrusion are described. One is the injection andmixing of physical blowing agents. The other is rapid and uniform cooling ofthe polymer system. This chapter intends to give a guideline as to how todesign mixing sections to achieve the various process tasks in foam extrusionrather than to give a detailed engineering analysis.

TABLE 9.3 The Relative Effects of Process Parameters on Extruder Performance.

Increase in the Melt Energy ConveyingFollowing Parameters Mixing Temperature Input Capacity

ThroughputScrew speedBarrel temperatureScrew pitchChannel depthNumber of flightsFlight clearance ��

��

��

��

�

��


9.7 NOMENCLATURE

A interfacial area; Hamaker constantc specific heatCa Capillary or Weber numberd characteristic drop length scaleD diameter; rate of deformation tensorfd drag flow factorF forceFD nip factorh film coefficientH channel heightk� elasticity ration number of screw revolution; undeformed unit normal vectorN screw speed; deformed unit normal vectorR radiuss shear strainS cross-sectional areaQ volumetric throughputW channel width; rate of rotation tensorz distance

Greek Letters� angle of orientation� angle of orientation� void fraction� strain� viscosity� viscosity ratio; interfacial line length�i principal elongation ratio� helix angle� density� interfacial tension shear stress

9.8 REFERENCES

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10. Erwin, L. 1978c. “Theory of Mixing in Single Screw Extruders,” Polym. Eng. Sci., 18: 572.

11. Erwin, L. 1978d. “New Fundamental Considerations on Mixing in Laminar Flow,” SPEANTEC Tech. Papers.

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19. Liu, M., F. Muzzio and R. Peskin. 1994. “Fractal Structure of a Dissipative Particle-FluidSystem in a Time-Dependent Chaotic Flow,” Am. Phys. Soc., 50: 4245.

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22. Grace, H. P. 1982. “Dispersion Phenomena in High Viscosity Immiscible Fluid Systems andApplication of Static Mixers as Dispersive Devices in Such Systems,” Chem. Eng. Commun.14: 225.

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30. Wu, S. 1987. “Formation of Dispersed Phase in Incompatible Polymer Blends: Interfacial andRheological Effects,” Polym. Eng. Sci., 27: 335.

31. Bastian, M., M. Stephan and H. Potente. 1999. “Morphology Development of PolymerBlends in Twin Screw Extruders,” 15th Polym. Proc. Soc. Ann. Meeting, Paper 275.

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35. Bigio, D. I. and L. Erwin. 1987. “Criteria for the Prediction of Mixing in Laminar Mixers,”SPE ANTEC Tech. Papers, pp. 164–169.

36. Rauwendaal, C. 1994. Polymer Extrusion. New York, NY: Hanser.

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40. Dreiblatt, A. and K. Eise. 1991. “Intermeshing Corotating Twin-Screw Extruders,” in Mixingin Polymer Processing. C. Raunwendaal, ed. New York, NY: Marcel Dekker.

41. Raudendaals, C. 1995. “Which Twin Screw Extruder Is for You?” Plastics Formulating &Compounding. Nov./Dec.: 15.

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47. Nichols, R. J. 1983. “Pumping Characteristics of Counter-Rotating Tangential Twin-ScrewExtruders,” SPE ANTEC Tech. Papers, p. 69.

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CHAPTER 10

Foaming Agents for Foam Extrusion

THOMAS PONTIFF

10.1 INTRODUCTION

FOAMING agents are a vital and necessary ingredient used in the productionof extruded foamed thermoplastics. Foaming agents have several different

but similar definitions. Most generally, a foaming agent is a material that, in thevapor phase, expands a thermoplastic melt upon reduction in pressure. Physicalfoaming agents are materials that are injected into the process as either liquidsor gasses. Chemical foaming agents are materials that decompose to generategasses during the processing. Some physical foaming agents are low boilingpoint liquids, such as pentane or isopropyl alcohol, that remain liquids in thethermoplastic melt while the melt is under pressure. When the pressure isreduced, the foaming agent quickly changes from liquid to vapor and comes outof solution with the polymer to expand the melt. Another type of foaming agentincludes the so-called inert gasses, such as carbon dioxide or nitrogen. Thesematerials dissolve as vapors in the plastic melt and come out of solution asvapors to expand the plastic melt. Chemical foaming agents utilize a decompos-able material that produces a gas or gasses during decomposition. In this case,chemical foaming agents must first decompose, then the gas produced behavesmuch like a physical foaming agent but with some effects influenced by theresidual material from the chemical foaming agent decomposition.

10.2 PHYSICAL FOAMING AGENTS

Almost as early in the history of thermoplastics processing as the develop-ment of polystyrene thermoplastic resin is the advent of foamed polystyrene.


The first public disclosure of foamed polystyrene might have been made byMunters and Tandberg, who obtained U.S. patent 2,023,204 on December 3,1935 [1]. Early processes for production of foamed polystyrene utilized lowboiling point liquids, such as methyl chloride or butylene, which was used todissolve the polystyrene resin in a large vessel. The heated and pressurizedpolystyrene/solvent solution was then released to atmospheric conditionswhere the solvent volatilized and expanded the polystyrene. Eventually, thisprocess was transferred to extrusion processes in which polystyrene, whichwas preimpregnated with a foaming agent, was extruded to produce foamedproducts used for food and protective packaging and flotation [2]. Later, thedirect gassing process was developed in which the foaming agent was injecteddirectly into the extruder and dissolved into the thermoplastic melt [3, 4]. Thefoaming agent dissolved into the melt and then was extruded to atmosphericconditions to expand and form a foam product. Several different variations ofextruders have been developed for this process, including long single-screwextruders, tandem extruders, twin-screw extruders, and several specializedsystems. All of the extrusion systems must be capable of melting and mixingthe polymer and additives, dissolving and dispersing the physical foamingagent, cooling the melt containing the foaming agent, and maintaining suffi-cient pressure until extrusion from the die. These are the necessary steps forsuccessful production of low-density foams using the direct gassing process.These methods have been used to produce a wide variety of foam productsfrom many types of thermoplastic resins, including LDPE (low-density poly-ethylene), PP (polypropylene), PET (polyethylene terapthalate), and others.

Over the years, many types of physical foaming agents have been used inthe production of thermoplastic foams. In the early years of the technology,hydrocarbons, such as pentane, and chlorinated hydrocarbons, such as methylchloride and CFCs were most popular. CFCs were desirable because they werenonflammable and performed well in the process. They had the disadvantagesof being more expensive than hydrocarbons, and it was later determined in the1970s and 1980s that they were contributing to the destruction of the Earth’sozone layer. Efforts have been made to list important physical foaming agentproperties. One list, proposed by James Burt of E. I. Du Pont de Nemours &Co., lists the following as important properties [5]:

• boiling point: • inertness• safety• adequate solubility in molten resin• low permeability through resin• low solubility in solid resin• economical

The boiling point range is defined by reasonable processing temperatures. If aphysical foaming agent is chosen that has a higher boiling point, it is too diffi-

�50°F to �150°F


cult to vaporize. In fact, a better upper limit for boiling point might be about100°F (37.8°C). Even materials that are candidates to be physical foamingagents that have boiling points around 100°F (37.8°C) do not possess suffi-cient vapor pressures at room temperature to maintain sufficient pressurewithin the cells to keep them inflated. An example is n-pentane. This is a com-monly used physical foaming agent in extrusion of polystyrene foam. As thefoam cools to room temperature, its vapor pressure drops, creating low pres-sure within the foam cells. Polystyrene foam produced with n-pentane doesnot collapse as the polystyrene has enough rigidity to support the cellularstructure. However, LDPE foam extruded with n-pentane will collapse as thetemperature approaches room temperature, as the LDPE is not rigid enough tosupport the cellular structure with reduced internal pressure. Other factors willinfluence this collapsing phenomenon, and they will be discussed later. As theboiling point becomes lower, the volatility of the material increases. Highervolatility or vapor pressure requires more pressure to keep the material in theliquid phase in the polymer melt. Therefore, the use of propane requires ahigher melt pressure than the use of pentane.

Inertness relates to the material’s reactivity and corrosiveness to thepolymer being foamed, any additives, the machinery, or surrounding environ-ment. It is best, for obvious reasons, that the physical foaming agent be as inertas possible.

Safety is important, again, for obvious reasons. The ideal physical foamingagent would be completely safe, nontoxic, inflammable, and noncorrosive.However, the use of a material that might be considered unsafe, such as analkane hydrocarbon, is accomplished by employing appropriate safety mea-sures.

Good solubility in the polymer melt is important for a physical foamingagent. As the foaming agent dissolves into the melt, it will plasticize the melt,lowering its viscosity. This allows the melt temperature to be reduced. In anextruder, as the solubility of the foaming agent in the melt increases, the“minimum” melt pressure needed to get and to keep the foaming agent in so-lution decreases. If the foaming agent has poor solubility, high amounts ofenergy must be used to force the foaming agent into solution. This is usuallyaccomplished by running the equipment so that the melt is kept under highermelt pressure, which facilitates the dissolving of the foaming agent into themelt. The higher pressure causes the polymer melt to be exposed to more shearheat, and therefore, it is more difficult to cool to the optimum foaming temper-ature. The end result is that the lowest density achievable with a poorly solublefoaming agent is higher than that for a foam produced with a highly solublefoaming agent.

Once the foam is formed, enough foaming agent vapor must remain insidethe cells to prevent the cells from collapsing. This is obviously more criticalwith flexible foams, such as LDPE, than for more rigid foams, like PS. If thefoaming agent escapes from the flexible foam at a rate much greater than the


rate that air diffuses into the cells, the foam can collapse due to the lower totalpressure inside the cells. In the past, the preferred physical foaming agent forLDPE was dichlorotetrafluoroethane (CFC 114). It had a very slow permeationrate through the LDPE and allowed collapse-free foams to be produced. Nowthat CFC 114 is not available due to its impact on the environment, the mostcommon physical foaming agents for LDPE are alkanes, such as butane andpropane. These have high permeation rates through the LDPE and foams pro-duced with them collapse. However, permeation modifiers, such as glycerolmonostearate are used to slow the permeation of the foaming agent from thefoam.

Low solubility of the physical foaming agent in the solid resin is importantto prevent the polymer to be weakened by the solvent effect. If too muchfoaming agent remains in solution in the cell walls, the foam structure will bemade weaker and subject to creep and poor physical properties.

The fact that the physical foaming agent needs to be economical is obvious.However, there are some factors that need to be considered. CFCs, likedichlorodifluoromethane (CFC 12) or CFC 114, were quite popular in spite oftheir cost being roughly two to five times that of alkanes, such as butane orpentane. The main reason is that the CFCs are not flammable and are thereforemuch easier to use and handle. To utilize alkanes, several steps must be takento ensure safety, which can be quite costly [6, 7, 8].

Table 10.1 lists properties of the commonly used physical foaming agentsfor thermoplastic foam extrusion and some materials that are similar but arenot used for various reasons. The properties, molecular weight, boiling point,vapor pressure, liquid density, and thermal conductivity of the vapor all affectthe function of the physical foaming agent in the process. While these materi-als do not act as exactly ideal gasses, their behavior can generally be approxi-mated by ideal gas behavior. Therefore, one mole of propane vapor willoccupy approximately the same volume as one mole of chlorodifluoromethane(HCFC 22), assuming that their vapor pressures are about the same. Referringto Table 10.1, 44.1 grams of propane should occupy the same volume as 86.5grams of HCFC 22. This would mean that propane is roughly two times moreefficient than HCFC 22 on the basis of weight required for the same expansion.Of course, other factors (such as solubility in the polymer melt and vapor pres-sure at the expansion temperature) affect the efficiency and will be discussed,but molecular weight can provide an estimate of the relative efficiency of aphysical foaming agent compared to other similar materials.

The boiling point of the physical foaming agent is important in severalways. First of all, the boiling point (at atmospheric pressure) of the foamingagent must be below the processing temperature in order to expand thepolymer. Generally, the higher the boiling point, the lower the vapor pressureof the foaming agent. The effects of vapor pressure will be discussed later. Asdiscussed previously, once the foam is formed and cooled to room tempera-


TABLE 10.1 Properties of Physical Foaming Agents [9].

VaporBoiling Vapor Liquid Thermal

Molecular Point Pressure Density Conductivity Flam-Name Formula CAS # Weight (°C) (psi) (g/cc) (W/mK) mable

Propane C3H8 74-98-6 44.1 �42.1 137.89 0.49 0.0179 Yesn-Butane C4H10 106-97-8 58.1 �0.5 35.26 0.57 0.0159 Yesi-Butane CH3(CH3)CHCH3 75-28-5 58.1 �11.7 50.53 0.55 0.0161 Yesn-Pentane C5H12 109-66-0 72.2 36.1 9.90 0.621 0.0141 Yesi-Pentane CH3(CH3) 78-78-4 72.2 27.0 14.23 0.615 — Yes

CHCH2CH3

HCFC-22 CHF2Cl 75-45-6 86.5 �40.8 151.4 1.194 0.0106 NoHCFC-142b CF2ClCH3 75-68-3 100.5 �9.2 49.16 1.11 0.0108 YesHFC-152a CHF2CH3 75-37-6 66.0 �24.7 86.81 0.899 0.0136 YesHCFC-123 CHCl2CF3 306-83-2 153.0 27.1 13.27 1.46 0.0095 NoHCFC-123a CHFClCF2Cl 354-23-4 153.0 28.2 12.61 1.467 0.0111 NoHCFC-124 CHFClCF3 2837-89-0 136.5 �12.0 55.85 1.356 0.0106 NoHFC-134a CH2FCF3 811-97-2 102.0 �26.5 96.52 1.207 0.0127 NoHFC-143a CH3CF3 420-46-2 84.0 �46.7 182.5 1.089 0.0137 YesCFC-11 CFCl3 75-69-4 137.4 23.8 15.32 1.476 0.0082 NoCFC-12 CF2Cl2 75-71-8 120.9 �29.8 94.51 1.311 0.0100 NoCFC-113 CFCl2CF2Cl 76-13-1 187.4 47.6 6.46 1.565 0.0097 NoCFC-114 CF2CLCF2Cl 76-14-2 170.9 3.6 30.96 1.456 0.0112 NoMeCl CH3Cl 74-87-3 50.5 �24.2 82.16 1.098 0.0106 YesMeCl2 CH2Cl2 75-09-2 84.9 40.1 8.22 1.322 0.0084 No

CO2 124-38-9 44.0 �78.5 N/A N/A 0.0165 NoN2 7727-37-9 28.0 �195.8 N/A N/A 0.0258 NoO2 7782-44-7 32.0 �183.0 N/A N/A 0.0266 No


ture, the foaming agent should have a sufficiently high boiling point to main-tain sufficient pressure inside the foam cells to keep the foam from collapsing.This is very important for flexible foams, such as LDPE, but not as importantfor more rigid foams, such as PS.

As stated before, the vapor pressure of the physical foaming agent is in-versely related to the boiling point, and there must be sufficient vapor pressureat room temperature to keep the foam from collapsing. The vapor pressure isalso important at the foam expansion temperature or melt temperature. Thehigher the vapor pressure at the expansion temperature, the higher the pressureon the melt must be to prevent it from expanding inside the die or extrusionequipment, a behavior called prefoaming. Of course, the amount of pressurerequired to keep the physical foaming agent in solution is also related to thesolubility of the foaming agent in the melt, but the vapor pressure also has animpact. For example, in the production of LDPE foam using either propane orisobutane (foaming agents with similar solubilities in LDPE), the propane re-quires a higher die pressure to prevent prefoaming than does the butane.

The liquid density of the physical foaming agent is important for storageconsiderations and for when a volumetric flow measurement device is used.

The thermal conductivity of the foaming agent vapor (K-vapor) is importantfor thermal insulation applications. Polystyrene foam boards have been pro-duced in the past using CFC 12 and methylene chloride. These materials invapor phase inside the foam cells provide a structure with a much betterthermal insulation capability than foam with cells containing air [10]. Eventhough the foaming agent vapors would escape over some years, the lowerinitial thermal conductivity of the PS insulation board was used as a sellingpoint. Of course, after several years, the air replaced the foaming agent vapor,reducing the thermal insulating performance slightly. Currently, many thermalinsulation applications are utilizing chlorodifluoroethane (HCFC 142b) undera special exemption from the UN Montreal protocol on halogenated hydrocar-bons [11]. HCFC 142b offers some advantage over other materials, such asCO2 and alkane hydrocarbons in terms of thermal insulation performance, butthis material is being phased out so processors will need to find suitable alter-natives.

In the 1970s, the scientific community determined that the CFCs were de-composing high in the Earth’s atmosphere and causing the ozone layer tobecome depleted. It was determined that this effect was basically due to thechlorine atoms in the molecule. Later, in the 1980s, programs were imple-mented to phase out the halogenated alkanes that contain chlorine atoms.Therefore, foam processors were required to seek alternative materials.

The chemical structure of the physical foaming agent has effects on its per-formance. For example, isobutane is slightly less soluble in polymer melts andslightly less permeable in the polymer than n-butane because of the differencesin molecular structure. Further, the presence of halogens substituted for hydro-gen has a similar effect, reducing the solubility and permeability.


10.3 CHEMICAL FOAMING AGENTS

Chemical foaming agents (CFAs) have their history based in explosive andbakery products. Endothermic CFAs were originally used as nucleating agentsfor direct-gassed polystyrene foam production. Their use as effective CFAswas discovered some time later. CFAs are solid or liquid materials that decom-pose under certain conditions to generate vapors. It is the vapor material thatthen behaves like a physical foaming agent in the plastics process. Most CFAsare finely divided solid materials, and most decompose within a certain tem-perature range. The decomposition temperature of the CFA should be in thesame range as the melt temperature of the polymer being processed. Thisensures that the CFA does not prematurely decompose and that the decompo-sition is complete.

The gas that is yielded as a result of the CFA decomposition has severaleffects on the process and product. Because carbon dioxide is more soluble inplastics and has a lower vapor pressure than nitrogen, it is generally easier towork with. CFAs that generate carbon dioxide generally give finer cells, lowerdensities, better surface appearance, and shorter cycle times than CFAs thatgenerate nitrogen. However, for example, for plastics with high melt viscosi-ties or for injection molding parts that are difficult to fill, nitrogen generatingCFAs can be advantageous. In this case, the higher pressure generated by thenitrogen gives a more efficient and complete expansion that more effectivelyfills the mold.

The gas yield, a measure of the volume of gas generated by a given mass, ofthe CFA is important in determining its relative efficiency compared with othergrades or types. Most commonly used CFAs predominately generate carbondioxide or predominately generate nitrogen. Please refer to Table 10.1 for de-tailed properties of nitrogen and carbon dioxide. As temperatures used forplastics processing are above the critical points of both gasses, specific volumecan be used to compare the behavior of the two gasses in expansion of plasticfoams. Nitrogen occupies more volume for the same mass of the material, andthis fact partially illustrates why the expansion of nitrogen during the foamingof plastics is more explosive and difficult to control.

Another factor that effects the efficiency or explosiveness of the expansionis the solubility of the gas in the polymer. The solubility of a gas in a moltenpolymer is governed by the following equation [12].

Where , law constant, and pressure. TheHenry’s law constant for each gas is different for each of the various polymers.For commonly used polymers, the Henry’s law constant for carbon dioxide is1.5 to 4 times than that for nitrogen. For polyethylene, , (cc(STP)/gmatm), , and carbon . Therefore, carbon diox-dioxide � 0.275nitrogen � 0.111

gas � H

P � gasH � Henry’sS � solubility

S � H * P


ide is about 2.5 times more soluble in polyethylene than nitrogen. This illus-trates that it is necessary to keep more pressure on a melt that contains nitrogenthan on a melt that contains carbon dioxide to keep the gas in solution. It alsoshows that, during expansion, nitrogen is going to come out of solution andexpand the plastic melt faster, and coupled with the greater specific volume fornitrogen, the expansion of nitrogen will be more efficient in terms of volumeper mass of gas but will be more difficult to control.

Chemical foaming agents are generally divided into two categories, exo-thermic and endothermic. Exothermic CFAs generate thermal energy (heat)during their decomposition, and endothermic CFAs consume thermal energyduring their decomposition. The fact that the CFA decomposition reaction gen-erates or consumes heat generally has very little, if any, effect on the tempera-ture of the polymer melt or the product. The main effect of the heat generationor absorption is manifested in the rate and temperature range of decomposi-tion. Generally, once an exothermic CFA begins to decompose, it is difficult tostop it before it reaches full decomposition. This results in a faster decomposi-tion in a narrow temperature range. Of course, when the exothermic CFA isdispersed at low levels (below about 5%) in the polymer, the reaction can bestopped by rapid cooling or insufficient temperature for processing. Endother-mic CFAs, on the other hand, require additional heat to support their continu-ing decomposition. This results in a broader decomposition time and tempera-ture range.

The main foaming gas generated by the CFA has a great effect on itsfoaming and processing behavior. Considering the most commonly usedCFAs, the endothermic CFAs generate carbon dioxide as the main foaminggas, and the exothermic CFAs generate nitrogen as the main foaming gas.Most CFAs generate other gasses, but they do not have as much effect on theprocessing and foaming behavior as the main foaming gas. Below are some ofthe common CFAs with some of their typical properties.

10.3.1 AZODICARBONAMIDE [13]

Azodicarbonamide decomposes in a temperature range of about 205°C to215°C. There are many materials that act as activators for the decompositionof the CFA, lowering its decomposition temperature range by up to about40°C. Common activators include zinc oxide, zinc stearate, urea, and many tinor zinc-containing PVC stabilizers. The reaction of azodicarbonamide canleave residual materials, referred to as plateout, on die and mold tooling.Proper use of additives can minimize or alleviate this problem.

Chemical formula: O OL L

2H2NCN � NCNH2


Gas composition: 65% Nitrogen24% Carbon monoxide5% Carbon dioxide5% Ammonia (NH3)

Solid decomposition products include Urazol, Biurea, Cyamelide, and Cya-nuric acid.

Gas yield: 220 cc/gmFDA Status:

Regulation Number Use175.300 (2.0% max.) Resinous and polymeric coatings, (can end

cements)177.1210 (2.0% max.) Closure sealing gaskets in contact with food

(repeated use)177.2600 (5.0% max.) Rubber articles in contact with food

10.3.2 ACID/CARBONATE BLEND

The most commonly used formulation for these endothermic CFAs is ablend of citric acid and sodium bicarbonate. The materials are encapsulated orcoated in a material that prevents or inhibits the decomposition reaction andexposure to moisture. The materials are generally blended in stoichiometri-cally correct proportions. The ratio of the blend components can be modifiedto affect changes in the decomposition temperature range for the CFA. Theequation for the decomposition can be generally written as follows:

In practice, some of the sodium citrate is probably in the pentahydrate form,but some free water vapor is always generated. The reaction takes place in twotemperature ranges, one at about 160°C and the second one at about 210°C.The gas yield is 120 cc/gm and the FDA status is that both components aregenerally recognized as safe (GRAS) for any food contact use.

Many CFAs also generate other gas by-products aside from the mainfoaming gas, such as water. If the plastic being processed is sensitive to hy-drolysis, decomposition by water, it is important to use either a CFA, whichgenerates very little or no water in the decomposition, or one that can effec-tively bind the water chemically. Examples of hydrolytically unstable plasticsinclude polycarbonate and polyesters.

C6H8O7 � 3NaHCO3 � (C6H5Na3O7) � 2(H2O) � 3(CO2) � H2O

� Sodium citrate dihydrate � Carbon dioxide � WaterCitric acid � Sodium bicarbonate


Table 10.2 lists commercially used CFAs. The proper choice of CFA notonly depends upon the main foaming gas evolved but also on the decomposi-tion temperature. Basically, in the processing equipment, the same sequence ofsteps must take place in order to ensure proper performance. First, the CFA isadded to the process in the same fashion as other additives or colorants. TheCFA, whether powder or pelletized masterbatch, can be blended with thepolymer resin prior to addition to the hopper or it can be metered into the feedthroat of the extruder/injection molder. The CFA additive must then be dis-persed into the polymer as the polymer begins to melt. Once the polymer ismelted and the CFA (and any other additives) is dispersed, sufficient melt tem-perature must be achieved to decompose the CFA. As the gas is evolving, thepressure on the melt must be sufficient to allow the gas to dissolve into themelt. Once the gas is formed and dissolved into the melt, the melt must be keptunder sufficient pressure to keep the gas in solution. The pressure sufficient tokeep the gas in solution depends on several factors, including the solubility ofthe gas in the polymer and the temperature of the solution. The gas should bekept in solution until the expansion of the melt is desired, generally uponexiting from the die or injection into the mold. If the melt is allowed to expandprior to this (inside the extruder barrel or injection molding machine barrel ornozzle), poor foam will result.

Temperature control in several areas of the process is critical to good foamproduction using CFAs. If the temperature in the feed section of the process,

TABLE 10.2 Commercially Used Chemical Foaming Agents [13, 14].

Decompo- Main Endo sition Gas Foaming

Common or Temper- Evolution, Gas Name Chemical Name Exo ature, °C cc/gm Evolved

Citric acid/ Endo 160–210 120 CO2

SodiumbicarbonateADCA Azodicarbonate Exo 205–212 220 N2

OBSH p,p’-Oxybis Exo 158–160 125 N2

(benzene) sulfonylhydrazide

TSH p-Toluene sulfonyl Exo 110–120 115 N2

hydrazideTSS p-Toluene solfonyl Exo 228–235 140 N2

semicarbazideDNPT Dinitrosopenta- Exo 190 190 N2

methylenetetramine5PT 5-Phenyltetrazole Exo 240–250 220 N2

SBH Sodium borohydride Endo * 2000 H2

* SBH is chemically activated by exposure to water.


the first or second zone, is too high, the CFA can decompose before thepolymer has completely melted. In this case, the gas evolved can escapethrough the feed hopper and not dissolve in the melt. The temperature in themetering/mixing sections of the process should be high enough to ensure com-plete decomposition of the CFA. If either the decomposition of the CFA iscarried out too early or not completely, the resultant product will be foamed in-consistently or not at all. Once the CFA is completely decomposed and the gasis dissolved in the melt, the melt temperature can be adjusted to suit theprocess so long as sufficient melt pressure is maintained to keep the gas in so-lution. Generally, the melt temperature is reduced, especially in extrusion pro-cessing, to increase the melt viscosity. The higher melt viscosity generally alsoincreases the melt strength of the melt, thereby improving the foam quality anddensity reduction.

Because of the temperature considerations described above, the CFA chosenfor a particular polymer resin must be matched to the resin in terms of its de-composition temperature. The melting point and processing temperatures of aparticular resin must be considered when choosing the CFA to ensure that theCFA does not predecompose or insufficiently decompose. For example, forLDPE processing that takes place at temperatures generally in the range of 150to 180 °C, the CFA should have a decomposition temperature that is in thatgeneral range. If a CFA is used that decomposes at a higher temperature, suchas 5PT, no decomposition of the CFA will be realized.

CFAs are also used as high-performance nucleating agents for direct-gassedfoam extrusion. The performance of endothermic CFAs for nucleation is betterthan so-called inactive nucleators, such as talc. Generally, endothermic CFAsare three to five times more effective than talc in nucleating direct-gassedfoams, but can be up to eight times more efficient [15]. Endothermic CFAs(sodium bicarbonate and citric acid) are the most commonly utilized types fornucleation and are used over less expensive nucleators, such as talc, whenfiner-celled foam products are required. Exothermic CFAs (mainly azodicar-bonamide) are used for nucleation of direct-gassed wire and cable insulation asthe residual materials from the decomposition have the least effect on the elec-trical properties of the insulating material when considering all available nu-cleators. While the mechanism of the nucleation effect of CFAs is not entirelyunderstood, it must be a combination effect of the residual material and the gasgenerated by the decomposition [16].

The future for foaming agents is quite exciting. The constant search for easyto use environmentally friendly physical foaming agents will continue. Thisendeavor will bring about improvements in processing equipment andpolymer morphology/formulation as well as new and unique physical foamingagent materials/blends. The difficulties in using inert gasses, such as carbondioxide or nitrogen, over the traditional physical foaming agents, like isobu-tane or CFCs, should be obvious from the text of this chapter.


The desire to foam polymers other than polystyrene and low-density poly-ethylene such as polypropylene, polyethylene terapthalate, and thermoplasticelastomers continues to challenge processors to find new foaming agent alter-natives. Chemical foaming agents are constantly being modified by reformula-tion or blending. The use of CFAs in the form of pelletized masterbatches in apolymer carrier is becoming more popular. The use of masterbatches improvesthe accuracy of dosing the additive to the process and also greatly improvestheir use in terms of handling and cleanliness.

Foaming agents are a vital ingredient for the production of foamed plastics.The interaction between the foaming agent and the rest of the process can bequite complex, but when the proper choice of foaming agent is coupled withthe right polymer, equipment, and processing parameters, unique and interest-ing products can be produced.

10.4 REFERENCES

1. Munters, C. G. and Tandberg, J. G., U. S. Patent 2,023,204.

2. Collins, F. H., “Controlled Density Polystyrene Foam Extrusion”, SPE 16th Annual TechnicalConference, 1960.

3. Jacobs, W. A. and Collins, F. H., U. S. Patent 3,151,192.

4. Carlson, Jr., F. A., U. S. Patent 2,797,443.

5. Burt, J. G., “The Blowing Agent in Polystyrene Foam Sheet,” E. I. Du Pont de Nemours &Co., Inc., Technical Paper (publication and date unknown).

6. Kolosowski, P. A., U. S. Patent 5,424,016.

7. Pontiff, T. M. and Rapp, Joseph P., U. S. Patent 5,059,376.

8. Miyamoto, A., Akiyama, H. and Usuda, Y., U. S. Patent 3,808,380.

9. E. I. DuPont de Nemours & Co., Inc. (various product bulletins).

10. Levy, S., “Extruding Plastics Foam Insulation,” Plastics Machinery and Equipment, August,1979.

11. Suh, K. W., U. S. Patent 4,916,166.

12. Throne, J. L., Thermoplastic Foams, Sherwood Publishers, Hinckley, OH, 1996.

13. Uniroyal Chemical Company, Inc., Product Bulletin: “Technology of Celogen BlowingAgents,” August, 1992.

14. Hamel, R. G. and Poulin, S. P., U. S. Patent 4,520,137.

15. Pontiff, T. M., “Nucleation in Direct Gassed PS Foam Using Chemical Foaming Agents,”Dubai Plast Pro ‘98, Maack Business Services, May 11–13, 1998.

16. Colombo, E. A., “Controlling the Properties of Extruded Polystyrene Foam Sheet,” Scienceand Technology of Polymer Processing, edited by N. P. Suh and N. Sung, The MIT Press,1979.


CHAPTER 11

Continuous Production of High-Density and Low-Density Microcellular Plastics in Extrusion

CHUL B. PARK

11.1 INTRODUCTION

THIS chapter describes a continuous extrusion process for the manufactureof high-density and low-density microcellular plastics. Microcellular

plastics are foamed polymers characterized by a cell density greater than 109

cells/cm3 and a fully grown cell size on the order of 10 micrometers. The basicapproach to the production of microcellular structures is to continuously forma polymer/gas solution, to nucleate a large number of bubbles using thermody-namic instability via a rapid pressure drop, to suppress cell coalescence by in-creasing the melt strength, and to induce a volume expansion to a desired ex-pansion ratio. All the processing requirements and the approaches to achievethe required processing steps are described in detail. The experimental resultsobtained at various processing conditions are presented to elucidate the effectof each processing parameter on the cell morphology. With careful tailoring ofthe processing conditions, microcellular foamed plastics with a cell-populationdensity higher than 109 cells/cm3 and a controlled volume expansion ratio inthe range of 1.5 to 43 times for the high-density and low-density applicationsare obtained.

Microcellular plastics are characterized by a cell density higher than 109

cells/cm3 and a cell size on the order of 10 micrometers. A typical fractographof a microcellular plastic part is shown in Figure 11.1. The concept for mi-crocellular plastics was created by Suh [1] in response to industrial need forreducing materials cost for certain polymer products without major compro-mise to mechanical properties. The central idea was to create a large numberof bubbles, smaller than the preexisting flaws in a polymer. Typically, micro-cellular plastics exhibit high Charpy impact strength (i.e., up to a fivefold


increase over unfoamed plastic [2–5]), high toughness (i.e., up to a five-fold increase over unfoamed plastic [5–7]), high fatigue life (i.e., up to a fivefold increase over unfoamed plastic [8]), high thermal stability [9], highlight reflectability, low dielectric constant, and low thermal conductivity [10].Because of these unique properties, a large number of innovative applicationsof microcellular plastics can be imagined. These include food packaging withreduced material costs, airplane and automotive parts with high strength-to-weight ratio and acoustic dampening, sporting equipment with reduced weightand high energy absorption, insulative fibers/filaments for fabric, moleculargrade filters for separation processes, light reflecting boards, surface modifiersfor low friction, and biomedical materials.

Conventional foams use a nucleating agent or a chemical blowing agent tonucleate gas bubbles. The quality of the foam produced depends on the amountand the distribution of these agents. A nonuniform distribution of the agentsresults in a foam that has a high concentration of gas bubbles or cells in agent-rich areas and a low concentration in agent-poor areas. The density of cells isdetermined by the concentration of the foaming agent. The large bubbles havea lower internal pressure, and there is a steeper gas concentration gradient inthe vicinity. Larger bubbles will then be energetically favored to grow at a

FIGURE 11.1 Typical scanning electron micrograph of a microcellular plastic.


faster rate than smaller bubbles because gas will preferentially diffuse towardthe low-pressure area [11,12]. As a result, larger bubbles grow at the expenseof smaller bubbles, and the bubble size distribution becomes highly nonuni-form in the foam structure. Because the number and the size of the bubbles aredetermined by the concentration of the foaming agent, the uniformity of thecell structure and the cell density are limited by the method used to mix theagents and the polymer. In fact, it is rather hard to obtain a uniform cell struc-ture with a high cell density in a conventional foam processing with a chemi-cal or physical blowing agent. For conventional foams, a typical cell density isin the range of 102 to 106 cells/cm3, the cell size is larger than 100 microme-ters, and the cell size distribution is very nonuniform.

Over the past decade, substantial research and development have been con-ducted to gain knowledge about the physical phenomena governing microcel-lular processing of microcellular polymers. This knowledge has successfullyled to the implementation of microcellular batch processes [13–25] and semi-continuous processes [26–28]. Some significant structure and property charac-terization studies have been carried out as well [2–9, 18, 19, 22–25, 29–35]. Inorder to overcome the high processing cost of microcellular batch and semi-continuous processing due to their long cycle times, continuous extrusionprocesses have also been developed [36–50]. This chapter briefly outlines thecurrent progress of continuous microcellular processing and its futureprospect.

11.2 PREVIOUS STUDIES ON BATCH AND SEMICONTINUOUSMICROCELLULAR PROCESSING

Based on the concept of microcellular plastics [1], the first microcellularplastics technology in a form of batch processing was developed by Martiniand Suh [13,14]. The basic approach of the developed batch microcellular pro-cessing was to saturate a plastic sheet with an inert gas in a high-pressurechamber and to induce thermodynamic instability by rapidly dropping the sol-ubility of gas in the polymer. Martini performed the first experiments and ana-lyzed theoretically the formation and growth of microcellular foams [13].Waldman and Suh then investigated the mechanical properties and processingbehavior of microcellular foams [29]. Process parameters were determined ex-perimentally, and the strategy for process design was presented. A method ofproducing lightweight polyester composites was developed by Youn and Suh[15,16]. Investigations into modeling microcellular thermoplastic nucleationwere made by Colton and Suh [30–33]. Their model explained the effect ofvarious additives and processing conditions on the number of bubbles nucle-ated. Cha and Suh improved the batch microcellular processing by utilizingthe supercritical state of CO2 to enhance its solubility and diffusivity in the


plastic matrix [17,18]. As a result, much finer cell structures were obtainedfrom various thermoplastics including PVC, PETG, PMMA, ABS, PC, TPX,LDPE, HDPE, etc. A similar approach was taken by Goel and Beckman toimprove the foam structure of PMMA [19]. Colton and Suh, Baldwin et al.,and Doroudiani et al. have developed special processing strategies to developmicrocellular foam structures from various semicrystalline polymers [20–22].Matuana et al. studied the microcellular foaming behavior of wood-fiber com-posites [23–25].

Efforts have also been made to develop semicontinuous microcellular pro-cessing with a view to realizing the microcellular processing concept to indus-trial production. Kumar and Suh developed a modified thermoforming micro-cellular process for producing microcellular foamed parts with a geometry [26,27]. The basic approach was to decouple the shaping process from the foamingprocess. Kumar and Schirmer developed a solid-state microcellular batchprocess in which semicontinuous sheets of microcellular polymers are pro-duced by saturating a roll of sheet with the aid of gas permeable material fol-lowed by foaming the roll of sheet as in the batch process [28].

11.3 BACKGROUND ON MICROCELLULAR PLASTICSPROCESSING

Microcellular plastics have been produced using thermodynamic instabilityof a polymer/gas system to promote a large bubble density in the polymermatrix. Microcellular plastics processing involves the following four basicsteps to utilize such thermodynamic instability: polymer/gas solution forma-tion, microcell nucleation, suppression of cell coalescence, and cell growth.These steps are basic to microcellular processing and are applied to both batchand continuous manufacturing processes.

Typically, formation of a polymer/gas solution is accomplished by dissolv-ing an inert gas, such as carbon dioxide or nitrogen, into a polymer matrixunder a high pressure. This creates a solution having a high gas concentration(typically 5 to 20 wt%) in the polymer matrix. Solution formation is governedby gas diffusion in the polymer. Diffusion processes are typically slow, result-ing in long cycle times.

The next phase of microcellular processing involves subjecting thepolymer/gas solution to thermodynamic instability to nucleate microcells. Thisis achieved by lowering the solubility of gas in the solution by controlling thetemperature and/or pressure. The system now seeks a state of a lower freeenergy that results in the clustering of gas molecules in the form of cell nuclei.Formation of cell nuclei provides a relatively small mean free distance for the


gas molecules in the solution to diffuse through before reaching a cell nucleus(i.e., the gas phase). As the gas diffuses into the cells, the free energy of thesystem is lowered. The cell nucleation process can occur homogeneouslythroughout the material or heterogeneously at high energy regions such asphase boundaries [30–33]. In the ideal case, nucleation occurs instantaneously.The cell nucleation process is very important in microcellular plastics produc-tion in that it governs the cell morphology of material, and to a large extent, theproperties of the material.

Although a large number of nuclei have been achieved in the nucleationstage, the final cell density of produced foams might not be the same as theinitial nuclei density if cell coalescence occurs. Cell coalescence is thermody-namically favored because the total surface area of cells is reduced by coales-cence. When the cell density is deteriorated by cell coalescence, the mechani-cal and thermal properties are deteriorated as well. In order to prevent thedeterioration of the properties and to fully utilize the unique properties of mi-crocellular plastics, cell coalescence should be suppressed.

When the cells are nucleated, they continue to grow as available gas diffusesinto cells, provided little resistance is encountered. The cells grow and the totalpolymer density decreases as the gas molecules diffuse into the nucleated cellsfrom the polymer matrix (a distance on the order of 10 microns). The rate atwhich the cells grow is limited by the diffusion rate and the stiffness of the vis-coelastic polymer/gas solution. If the stiffness of the matrix is too high, cellgrowth is extremely slow. In this case, the solution temperature can be in-creased to lower the matrix stiffness. In general, the cell growth process is con-trolled primarily by the time allowed for the cells to grow, the temperature ofthe system, the state of supersaturation, the hydrostatic pressure or stressapplied to the polymer matrix, and the viscoelastic properties of the polymer/gas solution [42].

Microcellular plastics were produced first in a batch process [14]. Figure11.2 shows a typical example of a batch process for producing microcellularplastics. In this process, a polymer sample is first placed in a high pressurechamber where the sample is saturated with CO2 or N2 under high pressure atambient temperature. Then, a thermodynamic instability is induced by rapidlydropping the solubility of gas in the polymer. This is accomplished by releas-ing the pressure and heating the sample. This drives nucleation of a myriad ofmicrocells, and the nucleated cells continue to grow, leading to the foam ex-pansion. One of the disadvantages of the batch process is a very long cycletime required for gas saturation in the polymer because the diffusion rate isvery low at the ambient temperature. In this context, the extrusion-based con-tinuous microcellular process has been developed to reduce the gas saturationtime, and this continuous microcellular processing is described in detail in thefollowing sections.


11.4 FORMATION OF A SINGLE-PHASE POLYMER/GASSOLUTION

One of the critical steps in the continuous production of microcellular plas-tics is formation of a polymer/gas solution at industrial processing rates [38,39]. In order to design a solution formation device, the physical phenomenabehind the solution formation process should be analyzed, and the criticalprocess parameters of solution formation should be identified. Figure 11.3shows the morphology change of polymer and gas system in the solution for-mation process. Initially, a soluble amount of gas is injected into a polymermelt stream, forming a two-phase polymer/gas mixture. Then, the large in-jected gas bubbles are broken into smaller bubbles and stretched through shearmixing. Eventually, the gas diffuses into the polymer matrix, forming a single-phase solution.

11.4.1 ESTIMATION OF GAS SOLUBILITY IN POLYMERS ATELEVATED TEMPERATURES AND PRESSURES

Only a soluble amount of gas should be injected into the polymer meltstream. Excess gas would result in formation of undesirable voids in the melt.Such voids could be detrimental to the cell structure unless hollow cores areintentionally formed in the final product [51]. The existence of voids sup-

FIGURE 11.2 Typical batch process for microcellular foamed plastics. Reproduced with per-mission from Reference [2]. Copyright (c) 1998 Polymer Engineering and Science.


presses homogeneous nucleation because the gas molecules preferentiallydiffuse to larger cells [12,13], resulting in formation of hollow cavities in thefinal product.

In order to inject only a soluble amount of gas into the polymer matrix, thesolubilities of CO2 in various polymers were estimated at 200°C and 27.6 MPa(4,000 psi), which are a typical processing temperature and pressure, respec-tively. Shim and Johnston’s work [52, 53] suggested that the logarithm of theCO2 solubility in polymers at elevated pressures is well correlated to thedensity of CO2 up to 30 MPa for a constant temperature. Durrill and Griskey’sdata [54, 55] was used to derive this correlation, and the solubilities of CO2 at27.6 MPa (4,000 psi) were extrapolated from this correlation. The estimatedsolubilities are summarized in Table 11.1. The solubilities of CO2 in manypolymers are approximately 10 wt%.

FIGURE 11.3 Schematic of the morphology change of polymer/gas systems in the solution for-mation process. Reproduced with permission from Reference [39]. Copyright (c) 1996 PolymerEngineering and Science.

Source: Reproduced with Permission from Reference [39]. Copyright (c) 1996 Polymer Engineeringand Science.

TABLE 11.1 Estimated Solubility of CO2 in Polymers at 200°C and 27.6 MPa (4,000 psi).

Polymer CO2 weight gain (%)

PE 15PP 12PS 12PMMA 15


11.4.2 ESTIMATION OF GAS DIFFUSIVITY IN POLYMERS AT ELEVATED TEMPERATURES

The diffusivity of gas in a polymer was also investigated to determine theprocessing time required for formation of a single-phase polymer/gas solution.In general, the gas diffusivity in a polymer changes with temperature, pressure,and gas concentration [54-61] and can be approximated as follows:

(1)

Since the diffusivity increases as the temperature increases, the rate of gas dif-fusion is enhanced by processing the mixture at a high temperature. Therefore,compared to room temperature, the gas diffusion rate for the polymer mixtureis increased in the heated extrusion barrel.

Only limited data is available for gas diffusion in polymers at high tempera-tures [54–56]. The estimated diffusivities are summarized in Table 11.2. At 200°C, a typical diffusivity of CO2 and N2 in a thermoplastic is approximately

, which is two orders of magnitude greater than a typical diffu-sivity of at room temperature [56].

11.4.3 BASIC CONCEPT OF CONVECTIVE DIFFUSION: MIXING AND DIFFUSION

When a metered amount of gas is delivered to the polymer melt stream, for-mation of a uniform and homogeneous single-phase solution from the two-phase mixture can be accomplished through gas diffusion. Because gas diffu-sion is a very slow process, a technique for rapid solution formation has been

10�8 cm2/s10�6 cm2/sec

D � Do exp (��ED / R T)

Source: Reproduced with Permission from Reference [39]. Copyright (c) 1996 Polymer Engineeringand Science.*Durril and Griskey [54, 55]†van Krevelen [56]

TABLE 11.2 Estimated Diffusivity of CO2 in Polymers at Elevated Temperatures.

Polymer D of CO2 (cm2/s)

at 188°C* at 200°C†

PS —PPPET —HDPELDPE —PTFE —PVC — 3.8 � 10�5

7.0 � 10�61.1 � 10�42.4 � 10�55.7 � 10�52.6 � 10�6

4.2 � 10�51.3 � 10�5


developed in order to produce microcellular plastics at industrial processingrates [38, 39]. The basic strategy for rapid solution formation is to induce con-vective diffusion.

Mass transfer by molecular diffusion is analogous to heat transfer becausethe heat conduction and diffusion equations have the same form [62]. The heattransfer rate is enhanced by convection. A convective flow causes fluid parti-cles of lower (or higher) temperature to be brought into contact with the heatsource, resulting in a higher temperature gradient near the source. The heattransfer rate is promoted by the higher temperature gradient. Similarly, the dif-fusion rate can also be enhanced by convection. Convection brings low gasconcentration polymer into contact with high gas concentration bubbles. Thisconvective flow induces a high concentration gradient that promotes diffusion.

When the diffusion source is stationary and exhibits a simple shape, such asa flat plate as shown in Figure 11.4, the concentration profile is similar to thetemperature profile associated with a similar heat source. Therefore, the con-centration profile may be expressed from known heat transfer solutions withan appropriate change in notation. Typical examples are the concentrationboundary layer on a flat plate, the concentration profile in a flow between theparallel plates, and the concentration profile in a flow through a circular pipe.The diffusion rates are promoted by a forced convective flow.

When the diffusion source is also moving, the analysis of the problembecomes complicated. In investigating the local concentration profile, the firststep is to trace the shape of the source boundary. Since the diffusion sources inthis study are the gas bubbles that are moving along the polymer melt, thedynamic behavior of the gas bubbles and the polymer melt should be investi-gated first. The diffusion phenomena will then be analyzed based on themixing behavior of the gas bubbles and the polymer melt.

FIGURE 11.4 Diffusion boundary layer on a flat plate. Reproduced with permission from Ref-erence [39]. Copyright (c) 1996 Polymer Engineering and Science.


As the gas molecules diffuse into the polymer matrix, the total volume ofthe gaseous phase diminishes in size until the gas completely dissolves into thematrix. Since the size of one phase component is changing, the mixing behav-ior of the two-phase mixture is far more complicated than simple mixing. It isvery difficult to investigate the mixing behavior of the two-phase mixture andthe flow fields of each phase. Since the diffusion phenomenon stronglydepends on mixing behavior, the analysis of the mass transfer phenomena ofdiffusion is also complicated. Therefore, the diffusion of gas into the polymermatrix may not be completely analyzed.

Despite the complication of modeling the dynamic behavior of the mixtureof the two fluids, the diffusion rate is greatly enhanced when the diffusionsource is also moving. As the degree of mixing increases, more polymer meltis brought into contact with the source of the high gas concentration that in-creases the effect of convective diffusion. This convective diffusion effect isenhanced through an increase in the interfacial area per unit volume, a reduc-tion of the diffusion distance, and a redistribution of the local gas concentra-tion profile in the polymer matrix [38, 39]. In addition, since the diffusion ratestrongly depends on the mixing behavior, the diffusion time can be controlledby varying the degree of mixing.

11.4.4 ANALYSIS OF A CONVECTIVE DIFFUSION PROCESS

The concept of convective diffusion can be effectively utilized to enhancethe diffusion rate in an extrusion barrel [38, 39]. One technique for rapid solu-tion formation using convective diffusion employs laminar mixing in themolten polymer shear field. Since the mixing accomplished by the simplescrew motion is limited, efforts were also made to enhance the mixing effec-tiveness by introducing various mixing sections in the extruder [63, 64]. Theidea behind the mixing section is that reorientation of the mixture during pro-cessing will enhance the effectiveness of shear mixing. Using the mixingsection, the diffusion time would decrease due to the enhanced degree ofmixing. Figure 11.5 shows a schematic of the convective diffusion device de-veloped by Park [36].

The shearing action in the extruder draws small bubbles of gas into themolten polymer shear field. The mixing action of the shear field slowly dis-perses a source of high gas concentration (i.e., the gas bubbles) into thepolymer matrix. The gas eventually diffuses into the polymer, forming asingle-phase solution. The convective diffusion effect in the shear field gener-ated by the screw motion is well described for devolatilization of polymer so-lution in a twin-screw extruder [65, 66]. Deformation and movement of theconcentration source and diminishment of the total volume of the gaseousphase component cause it to be very difficult to analyze the mixing behavior ofthe two-phase mixture and the diffusion phenomena. However, we can still es-


timate the diffusion time for completing solution formation based on the esti-mated striation thickness of the gas and polymer mixture.

As an order of magnitude, the diffusion distance (lD) is estimated as

(2)

where tD is the diffusion time. The time at which the diffusion distance is ofthe same order as the striation thickness (s) of the mixture can be estimated asthe diffusion time:

(3)

The estimated diffusion times are shown in Table 11.3 for various striationthicknesses and diffusivities. For example, if the striation thickness is less than100 �m, the diffusion of gas would be completed within 2 minutes for atypical diffusivity of at 200°C.

A fundamental study has been carried out to estimate the striation thicknessof polymer and gas in an extruder. An order of magnitude analysis [38] pre-dicts that when the polymer/gas system is fully mixed, the striation thicknessof the mixture would be 45 �m. Based on this striation thickness, the requireddiffusion time is estimated to be

(4)tD �s2

D�

(45 � 10�4)2

1 � 10�6 � 20 s

10�6 cm2/s

tD �lD

2

D�

s2

D

lD � 2D tD

FIGURE 11.5 Polymer/gas solution formation in an extrusion barrel. Reproduced with permis-sion from Reference [46]. Copyright (c) 1997 American CHemical Society.


This indicates that formation of a single-phase solution out of the two-phasepolymer/gas mixture would be completed in 20 seconds. Therefore, continu-ous solution formation can be achieved in extrusion systems without substan-tially decreasing the processing rates. However, it should be noted that if theamount of gas injected is more than the solubility at the processing condition,the solution formation could not be completed. In addition, due to the limitedavailable CO2 diffusivity data for high concentration at elevated temperatures,the concentration-dependent nature of the diffusivity could not be accountedfor in this order of magnitude analysis. In order to develop a better model ofcontinuous formation of a single-phase polymer/gas solution, fundamental re-search on the diffusivity and the solubility of a gas at high temperatures andpressures and the polymer/gas mixing behavior in the mixing elements shouldbe carried out.

11.5 MICROCELLULAR NUCLEATION CONTROL

The next critical step in the continuous production of microcellular plasticsis promotion of high bubble nucleation rates in the polymer/gas solution. Nu-cleation of bubbles is transformation of small clusters of gas molecules intoenergetically stable pockets of molecules with distinct walls. The microcellu-lar process requires that the nuclei density be larger than 109 cells/cm3 so thatthe fully grown cell size will be less than 10 �m. The key to producing the re-quired cell density is inducing a very high rate of cell nucleation in thepolymer/gas solution [40].

High nucleation rates have been achieved in batch processes by using ther-modynamic instability of the gas and polymer system. In order to make use of

Source: Reproduced with Permission from Reference [39]. Copyright (c) 1996 Polymer Engineeringand Science.

TABLE 11.3 Estimated Diffusion Time at Various Striation Thicknesses and Diffusivities.

StriationThicknesses (s) Diffusivity (D)

10�5cm2/sec 10�6cm2/sec 10�7cm2/sec 10�8cm2/sec

1 �m 0.01 sec 0.1 sec 1 sec10 �m 0.1 sec 1 sec 10 sec 100 sec50 �m 2.5 sec 25 sec 4 min 42 min

100 �m 10 sec 100 sec 17 min 3 hrs250 �m 63 sec 10 min 2 hrs 17 hrs500 �m 4 min 42 min 7 hrs 3 days750 �m 9 min 94 min 16 hrs 7 days

1000 �m 17 min 3 hrs 28 hrs 12 days

1 � 10�3 sec


thermodynamic instability in a continuous process, a rapid drop in the gas sol-ubility as in the batch process must be induced in the polymer/gas solution.The solubility of gas in a polymer changes with pressure and temperature[52–56]. Therefore, thermodynamic instability can be induced by rapidlyvarying the pressure, temperature, or both. Since, in the typical range of inter-est, the solubility of gas in a polymer decreases as the pressure decreases, ahigh cell nucleation rate can be promoted by subjecting the polymer/gas solu-tion to a rapid pressure drop. The solubility drop due to a change of pressure ortemperature is illustrated in Figure 11.6.

The greatest possible number of cells for a given pressure difference wouldbe nucleated out of a given polymer/gas solution if the pressure drops instan-taneously. However, in reality, the pressure drops over a finite time period asshown in Figure 11.7. It is expected that the more rapidly the pressure drops,the greater the number of cells that would be nucleated, because greater ther-modynamic instability would be induced. A rapid pressure drop element con-sisting of a nozzle (shown in Figure 11.8) has been utilized in Park et al.’sstudies to demonstrate the effect of the pressure drop rate on cell nucleation[39, 40]. When a viscous polymer/gas solution passes through the long, narrownozzle, the pressure drops almost linearly with distance due to friction. Inorder to be able to maximize the pressure drop rate and, therefore, to inducethe greatest thermodynamic instability, the pressure drop and the pressure droprate are analyzed in an order of magnitude analysis. To compensate for the

FIGURE 11.6 Solubility change of polymer and gas systems in batch and continuous pro-cessing.


error involved in the theoretical model, an experimental calibration has beenperformed.

11.5.1 EFFECT OF THE PRESSURE DROP RATE ONNUCLEATION

The homogeneous nucleation theory [31] predicts that the cell nucleationrate is given by

(5)

(6)

where Nhom is the homogeneous nucleation rate and �P is the pressure drop ofthe gas/polymer solution. Equations (5) and (6) predict that, for a larger pres-sure drop, the cell nucleation rate will increase. If an instantaneous pressuredrop and instantaneous homogeneous nucleation are assumed, then the nucle-

�Ghom � 16� �3bp/3 �P2

Nhom � fo Co exp (��Ghom/kT)

FIGURE 11.8 Typical pressure drop element for microcellular nucleation.

FIGURE 11.7 Pressure drop profile in a rapid pressure drop device. Reproduced with permis-sion from Reference [40]. Copyright (c) 1995 Polymer Engineering and Science.


ation rate and the number of nucleated cells correspond. Thus, for a constantpressure drop with an instantaneous pressure drop rate, the cell density shouldbe constant. However, in reality, the pressure drop is not instantaneous buthappens over a finite time period. It is expected that the nucleation time periodis affected by the time period over which thermodynamic instability is inducedin the system, and that the pressure drop rate will affect the nucleation timeperiod, and therefore, will affect the nucleation rate.

To explain the pressure rate effect, one must consider microcell nucleationand growth of the cells with respect to the competition between these mecha-nisms [36, 40]. The basic concept is the following. During the course of thepressure drop, which instigates thermodynamic instability, some stable cellsnucleate early during the residence time of the polymer in the nozzle. The gasin solution will diffuse to the nucleated cells to lower the free energy of thesystem. As the gas diffuses to these cells, low gas concentration regions wherenucleation cannot occur are generated adjacent to the stable nuclei as shown inFigure 11.9. As the solution pressure drops further, the system will nucleate

FIGURE 11.9 Competition between nucleation of new cells and growth of existing cells. Re-produced with permission from Reference [40]. Copyright (c) 1995 Polymer Engineering andScience.


additional microcells and expand the existing cells by gas diffusion or onlyexpand the existing cells. To determine whether further microcells are nucle-ated, one must look closely at the depleted gas regions around the previouslynucleated cells [13]. If the depleted regions of adjacent cells impinge uponeach other, then no further nucleation will tend to occur. This follows since thegas preferentially diffuses to the existing cells, depleting the gas between cells.In this state, the gas concentration between the existing cells is below the crit-ical level needed to nucleate additional cells. However, if the size of the de-pleted gas regions is less than the dimension between existing cells, then addi-tional cells will tend to nucleate between existing cells.

Here, the effect of the pressure drop rate on the competition of nucleationand cell growth is considered. Consider the pressure drop profiles for Nozzle iand Nozzle j as shown in Figure 11.10. At time t1, where to-t1 is an arbitrarilysmall time period, the pressure drop for Nozzle j, , is larger than the pres-sure drop for Nozzle i, . Since the nucleation rate is inversely sensitive to�P according to Equations (5) and (6), the nucleation rate in Nozzle j is higherthan the nucleation rate in Nozzle i as illustrated in Figure 11.11 (a) and (b). Atthe next time step, t2, the previously nucleated cells have grown, thus, reduc-ing the available gas for nucleating additional cells. In the region of thepolymer/gas solution where the gas has not been depleted, the nucleation rates

�P1i

�P1j

FIGURE 11.10 Comparison of pressure drop between nozzle j (narrow and short) and nozzle i(wide and long).


FIGURE 11.11 Nucleation of new cells and growth of the depleted zones in Nozzle i andNozzle j at each time step [36].


for Nozzle i and Nozzle j increase exponentially. However, for any given time,the nucleation rate for Nozzle j is higher than that for Nozzle i due to the addi-tional pressure drop experienced by Nozzle j. This is illustrated in Figure 11.11(c) and (d). Since the nucleation rates for Nozzle j are much higher than forNozzle i, the total nucleation time for Nozzle j will be less than for Nozzle i.This follows since the number of cells nucleated increases exponentially as thesizes of the depleted gas regions increase with time. Thus, the depleted zonesimpinge upon one another more rapidly for Nozzle j than Nozzle i as illus-trated in Figure 11.11 (e) and (f). For Nozzle i, the depleted zones impingeupon one another at a much later time. Since nucleation for Nozzle i takesplace over a long time period, the depleted zones of the previously nucleatedcells must have grown significantly by the time the nucleation stops. There-fore, some of the gas that could have been used for additional nucleation wasused for cell growth for Nozzle i. In other words, more gas was used for cellgrowth in Nozzle i. Since in Nozzle j, nucleation took place over a short timeperiod with high nucleation rates, more gas was used for nucleation of cells.Therefore, the total number of nucleated cells should be higher for Nozzle jthan Nozzle i. This competition between microcell nucleation and cell growthfor gas molecules is determined by the rate of the pressure drop and results inthe different total numbers of nucleated cells even from an identicalpolymer/gas solution [40]. Based on this concept, the pressure drop rate of apolymer melt flowing in a filamentary die is analyzed. The effect of the pres-sure drop rate on the cell density has been examined experimentally (seeSection 11.9.1).

11.5.2 ANALYSIS OF THE PRESSURE DROP RATE IN AFILAMENTARY DIE

The pressure change of flowing, non-Newtonian fluids in a nozzle is brieflyanalyzed in this section [40]. Assuming the viscosity of the polymer/gas solu-tion is shear-rate dependent and described by a “power law” [67, 68], the pres-sure drop over the length of the nozzle for a non-Newtonian fluid can be ex-pressed as follows [69]:

(7)

For a set of filamentary dies that satisfy the following:

(8)L

ro3n�1 �

��p

2m c �

q(a�3)d n � constant

��p �2 m L

ro £ q a3 �

1nb

� r3o

§n


The relationship between the pressure drop and flow rate would be the same.In other words, for a given flow rate, the pressure drop across the dies thatsatisfy the relationship of Equation (8) would be the same. Theoretically, all ofthese nozzles can be replaced with each other without affecting the pre- andpost-flow conditions, i.e., upstream/downstream pressures and flow rates. Itmay be noted that the pressure change at the sudden contraction [70] is notconsidered in this analysis; however, this effect is incorporated in the experi-mental calibration [40].

Now, the pressure drop rate in the die can be derived. The average residencetime, �t, of the flowing polymer/gas solution in the nozzle is expressed asfollows:

(9)

where vavg is the average velocity of the polymer/gas solution in the nozzle.Using this residence time, the average pressure drop rate is estimated asfollows:

(10)

Since the gas solubility is approximately proportional to the pressure[52–56], the solubility drop rate can also be derived in a similar manner:

(11)

where �Cs is the change of the gas solubility in the polymer melt.Park et al. calculated the pressure and solubility drop rates for impact grade

polystyrene (Novacor/Monsanto 3350 HIPS) at 221°C (430°F) flowing inthree different nozzles for a pressure difference of 38.64 MPa (5,600 psi) as atypical application [40]. Table 11.4 summarizes the geometry of the threenozzles and the estimated residence time, pressure drop rate, and solubilitydrop rate for each nozzle at a given pressure difference. Although the length ofnozzle was experimentally calibrated to compensate for the errors involved inthe analysis, the calibrated values of nozzle length, residence time, pressuredrop rate, and solubility drop rate were very close to the estimated ones. Sincethere was approximately an order of magnitude difference in the residencetimes between each of the nozzles, there was about an order of magnitude dif-ference in the pressure drop rates between each nozzle, while the total pressure

dCs

dt�

�Csq

�r2oL

�dp

dt�

��p

�t�

��p q

�r2oL

�t �L

vavg�

Lq

�r2o

��r2

oLq


Source: Reproduced with Permission from Reference [40]. Copyright (c) 1995 Polymer Engineering and Science.

TABLE 11.4 Estimated Geometry, Pressure Drop Rate and Solubility Drop Rate of the Nozzles for a Pressure Drop of 38.64 MPa (5,600 psi).

Residence Pressure SolubilityNozzle Radius Length Flow Rate Time Drop Rate Drop Rate

Nozzle 1 0.60 mm 78.74 mm 0.666 s 0.058GPa/s(0.024 in) (3.100 in)

Nozzle 2 0.39 mm 35.75 mm(0.016 in) (1.407 in) 0.136 s 0.284 GPa/s

Nozzle 3 0.23 mm 12.75 mm(0.009 in) (0.502 in) 0.016 s 2.355 GPa/s 8.75 s�11.28 � 10�7 m3/s

1.03 s�11.28 � 10�7 m3/s

0.21 s�11.28 � 10�7 m3/s§£

dcDC


drops across the length of the three nozzles were the same. Similarly, there wasapproximately an order of magnitude difference in the solubility drop ratesbetween each nozzle.

Since the solubility drop rates were all different, the induced thermody-namic instability for each nozzle was different. Although the solubility dropsof the polymer/gas solution across the three nozzles were the same, the largestthermodynamic instability would result when the solubility drops mostrapidly. Since the third nozzle with the smallest radius and the smallest lengthhas the highest solubility drop rate, it should be the most effective microcellu-lar nucleation element among the three nozzles. This argument was also exam-ined through experiments.

According to Equations (10) and (11), higher pressure and solubility droprates are achieved when the nozzle radius is smaller. Theoretically, when thenozzle radius becomes zero, the pressure and solubility drop rates become in-finitely large. However, the radius reduction is limited by the manufacturabil-ity of the hole and the mechanical strength of the nozzle. According to Equa-tion (8), for the same flow rate and pressure drop, the nozzle length decreaseswith the radius. The nozzle length cannot be arbitrarily reduced because thenozzle must have the mechanical strength to withstand the processing pressureof extrusion.

11.6 SUPPRESSION OF CELL COALESCENCE

Following Park et al.’s early stage research on microcellular nucleation inthe continuous processing of microcellular plastics [36, 38–40], Baldwin et al.[41, 42] carried out a preliminary study on the cell growth control in microcel-lular extrusion processing. Because of the difficulty of inducing a rapid pres-sure drop for microcell nucleation at the die exit, it was proposed that nucle-ation of the microcells be controlled independently in the first stage of the dieby rapidly dropping the pressure of the polymer/gas solution using a nozzleand controlling shaping and cell growth in the second stage of the die. Baldwinet al. proposed to use a high pressure to suppress premature growth in theshaping die and to prevent the bubbles from being stretched along in theshaping direction. Based on this strategy, they demonstrated the feasibility ofthe concept of shaping a nucleated polymer/gas solution under high pressure toprevent distortion of the bubbles and successfully produced 2 mm thick fila-ment and 1 mm thick sheet with a microcellular foamed structure. However,the volume expansion ratios of the extruded foams were relatively low (lessthan two times) and coalescence of nucleated cells was observed to a largeextent. It was expected that when the cells were controlled to be further grown,the cell coalescence problem would be more severe and a lower cell-popula-tion density would be obtained.


In this context, the next critical step in microcellular extrusion processing issuppression of cell coalescence during cell growth. Although a large numberof cell nuclei have been achieved by a high pressure drop rate, this does notguarantee that the final cell density of produced foams will be high enough tobe microcellular. If the cells coalesce during cell growth, the initial cell densitywill be deteriorated. As nucleated cells grow, adjacent cells will touch eachother. These contiguous cells tend to coalesce because the total free energy islowered by reducing the surface area of cells via cell coalescence [11]. It maybe noted that the shear field generated during the shaping process tends tostretch nucleated bubbles, and this will further accelerate cell coalescence[46]. When the cell density is deteriorated, the mechanical and thermal proper-ties are deteriorated as well. In order to prevent deterioration of the propertiesand to fully utilize the unique properties of microcellular plastics, cell coales-cence should be suppressed.

Although Baldwin et al. attempted to prevent cell coalescence in the die bypressurizing the nucleated polymer solution during shaping, the extruded foamstructure showed that many adjacent cells were coalesced and the cell densitywas deteriorated [41]. Maintaining a high pressure in the shaping section toprevent premature cell growth right after the cell nucleation was believed to bea good strategy because the nucleated cells could not grow under high pres-sure. However, considering the difficulty of maintaining a high back pressurein the shaping die for the case of a large cross section of extruded foam, it maynot be realistic to prevent cell coalescence by controlling the pressure alone inthe shaping die.

Park et al. proposed a means for suppressing cell coalescence by increasingthe melt strength of polymer via temperature control in microcellular extrusionprocessing [46]. The melt strength, by definition, may be considered a degreeof resistance to the extensional flow of the cell wall during the drainage ofpolymer in the cell wall when volume expansion takes place. Therefore, thecell wall stability will increase as the melt strength increases [71]. It is knownthat the melt strength of polymer can be enhanced by branching, cross-linking,temperature reduction, control of molecular weight and molecular weight dis-tribution, and blending of polymers and compatibilization of blends [72]. Inthe low-density microcellular extrusion process for PS and HIPS, it was pro-posed that the processing temperature be controlled to increase the meltstrength and to prevent cell coalescence in the cell growth process. Park et al.demonstrated that the increased melt strength due to the lowered melt temper-ature effectively suppressed coalescence of cells, and the high cell nucleationdensities obtained in the microcellular nucleation device were successfullymaintained. The idea of increasing the melt strength to prevent cell coales-cence at the die exit has been well utilized and practiced in conventional foamprocessing, particularly in the low-density foam production [71, 73]. However,temperature control for suppressing cell coalescence was not effectively usedin the early stage of extrusion microcellular processing.


Figure 11.12 shows a schematic of the heat exchanger used to cool theflowing polymer melt. To achieve uniform cooling, static mixers that effec-tively promote convective heat transfer, were used. The temperature of thepolymer melt flowing out of the exit of the heat exchanger was monitoredusing a thermocouple mounted at the die as shown in Figure 11.12. To regulatethe temperature of the polymer melt, a cooling oil was circulated through thechannel machined on the heat exchanger.

11.7 PROMOTION OF LARGE VOLUME EXPANSION

The next critical step in the continuous production of microcellular plasticsis to control volume expansion of extruded foams to a desired ratio. BecauseCO2 easily escapes through the exterior skin of foam during expansion, specialattention needs to be paid to achieve a low-density microcellular foam of ahigh-volume expansion ratio in the extrusion foam processing. It may be notedthat the diffusion rate of a gaseous blowing agent such as CO2 is much higherdue to its smaller molecular size compared to the conventional long-chainblowing agents such as pentane or butane [74]. This section briefly describeshow to prevent loss of CO2 that occurs during the microcellular foam extru-sion for achieving a large volume expansion ratio [47].

11.7.1 PREVIOUS STUDIES OF LOW-DENSITY EXTRUSIONFOAM PROCESSING USING AN INERT GAS

There are a number of well-known extrusion processes for production oflow-density plastic foams using long-chain blowing agents such as CFCs,pentane, butane, etc. [74]. However, there are very few studies on use of aninert gas for low-density foam production. Considering the fact that conven-tional blowing agents are known to be environmentally hazardous, inert gases

FIGURE 11.12 Schematic of a designed heat exchanger for cooling the polymer melt. Repro-duced with permission from Reference [47]. Copyright (c) 1998 Polymer Engineering andScience.


have been considered to be alternatives whether used alone or used togetherwith the conventional agents [75–83].

Jacob and Dey [79] employed inert gases such as CO2, N2, and Ar as ablowing agent in extrusion processing of low-density PS foams. They pro-duced low-density foams of 50 kg/m3 using CO2, which is equivalent to 20-fold volume expansion. Using N2 and Ar, higher foam densities were obtained.For these low-density foams, the cell size was large on the order of 300 �m.Dey et al. [80] also used an inert gas for PP foam processing in extrusion. Theyproduced a medium-density (about 300 kg/m3) foam PP sheet using CO2 as ablowing agent and SAFOAM FP (Reedy International) and talc as a nucleatingagent.

Shimano et al. [81] demonstrated the use of a gaseous blowing agent todevelop a foamed thermoplastic resin article. They described a means to prop-erly inject a constant quantity of gas into the extruder barrel, since one of thedifficulties in injecting gas is variation of the gas flow rate due to fluctuation ofthe barrel pressure. Johnson et al. [82] argued that use of CO2 with pentane isadvantageous because the amount of the hazardous and costly pentaneblowing agent required in the process is reduced. Also, the aging process couldbe simplified and the emission of organic blowing agent into the atmospherecould be reduced. Lee [83] claimed that the mixture of CO2 and isobutanecould be used to produce low-density thermoplastic foams in extrusion. Theachieved foam densities were as low as about 20 kg/m3 in polyolefin foamproducts.

11.7.2 STRATEGY FOR CONTROL OF VOLUME EXPANSION

As the thickness of cell walls decreases in low-density foam production, therate at which gas diffuses out of the foam to the environment increases. Fur-thermore, the high diffusivity of CO2 at an elevated temperature can increasethe blowing agent diffusion rate during expansion. It should be noted that theblowing agent that has diffused into the nucleated cells eventually tends todiffuse out to the atmosphere because complete separation of two phases isthermodynamically more favorable [84]. Gas escape through the thin wallswill decrease the amount of gas available for growth of cells. As a result, if thecells do not freeze, they tend to collapse causing foam contraction. In the mi-crocellular foam extrusion process, this volume contraction is due to gas lossafter an initial volume expansion has been observed [47, 48]. As a conse-quence, the final product had a high foam density. In order to produce low-density foams, gas diffusion through the skin of the foam must be prevented.

One way of preventing gas escape from the foam is to freeze the skin of theextrudate [47]. Since the diffusivity drops as the temperature decreases[54–61], the rate of gas escape can be substantially reduced by freezing theskin of the foam. The surface of the extrudate can be quenched by lowering thedie temperature. Therefore, the basic strategy that has been taken for promot-


ing large volume expansion is to freeze the foam skin by controlling the dietemperature. The die temperature can be precisely controlled by circulating acooling air or a low-temperature oil that is connected to a temperature-controlled oil bath.

It should be noted that the temperature of the polymer melt flowing into thedie also affects the amount of CO2 that escapes to the environment because thediffusion rate of CO2 in the cell walls can be retarded by lowering the temper-ature of polymer melt [47]. Furthermore, the increased stiffness of cell wallscaused by decreasing the melt temperature will also prevent the contraction ofthe foam structure due to gas loss. Therefore, the heat exchanger designed tocool the polymer melt for suppression of cell coalescence will also be helpfulin maintaining high-volume expansion ratios. The effects of the polymer melttemperature on cell coalescence and foam contraction are presented in detail inSection 11.9.3.

11.8 EXPERIMENTAL SET-UP

Based on the proposed processing steps described above, an experimentalextrusion setup has been constructed to produce high-density and low-densitymicrocellular foams. A schematic of the equipment is shown in Figure 11.13. Itconsisted of a 5 hp DC motor, a speed reduction gearbox, a 3⁄4� extruder (C.W.Brabender 05-25-000), and a mixing screw (Brabender 05-00-144). The L/D

FIGURE 11.13 Schematic of the overall experimental equpiment. Reproduced with permissionfrom Reference [47]. Copyright (c) 1998 Polymer Engineering and Science.


ratio and the compression ratio of the screw were 30:1 and 3:1, respectively.The other systems include a positive displacement pump for CO2 injection, adiffusion-enhancing device containing static mixers (Omega ModelFMX8441S), a heat exchanger for cooling the polymer melt that contains ho-mogenizing static mixers (Labcore Model H-04669-12), a cooling sleeve forprecise control of the die temperature, and two hot-oil circulating baths (GrantModel W6-KD). Heat transfer oil (Labcore Model H-01294-40) was used inthe heat exchanger to control the temperature of the flowing polymer melt andin the cooling sleeve to cool the die temperature. Three pressure transducers(Dynisco PT462E-10M-6/18) were also installed: one to measure the pressureof the extrusion barrel where the blowing agent gas is injected, one to measurethe pressure of the mixing and diffusion process between the diffusion en-hancing device and the heat exchanger, and one to measure the pressure ofpolymer melt before exiting the die.

11.9 EXPERIMENTS AND DISCUSSION

A number of semicrystalline and amorphous polymers including HIPS, PS,SPS, ABS, PP, PE, and some proprietary materials have been microcellularprocessed in extrusion for high-density and low-density applications. The cellnucleation and growth behaviors of the extruded foams were studied.

The foam samples were randomly chosen at each processing condition andcharacterized with a scanning electron microscope (SEM, Hitachi 510). Thesamples were dipped in liquid nitrogen and then fractured to expose the cellu-lar morphology. The fractured surface was then coated with gold and the mi-crostructure was examined using SEM. The cell density (i.e., the number ofcells per unit volume of unfoamed polymer), and the volume expansion ratio(or, equivalently, the foam density) were the structural foam parameters mea-sured. The expansion ratio of foam was determined by measuring the weightand volume of the sample.

11.9.1 NUCLEATION EXPERIMENTS

A series of experiments has been conducted to investigate the nucleation be-havior of extruded foams in various processing conditions [36, 38-40]. Itturned out that the critical processing and materials parameters that affect cellnucleation are the type of gas, processing pressure, injected gas amount, andpressure drop rate.

11.9.1.1 Effect of Gases on Cell Nucleation

First, the effect of different gases on the cell morphology was studied [38].The gases injected in these experiments were CO2 and N2, and the processed


polymers were PP (phillips 66 Marlex) and HIPS (Nova 3350). Approximately10 wt% of CO2 and 2 wt% of N2 were injected into each polymer melt basedon the estimated solubilities.

The thermodynamic instability induced through the solubility drop seemssufficient to produce a microcellular structure when the maximum solubleamount of CO2 was injected. When CO2 was processed, the cell densities ofPP and HIPS foams were and , respec-tively. When N2 was processed, the cell densities were and

, respectively, for PP and HIPS foams. The higher cell den-sities of the foams obtained with CO2 injection seemed to be due to the highersolubility of CO2 in the polymers. Because of the higher solubility, it was pos-sible to inject more gas into the polymer when CO2 was injected. It is believedthat the larger amount of dissolved gas induced a greater thermodynamic in-stability and, thereby, a higher cell density.

11.9.1.2 Effect of the Processing Pressure on Cell Nucleation

Next, the effect of the processing pressure on the cell morphology wasstudied [39]. In these experiments, the maximum soluble amount of CO2 wasinjected into the polymer melt at each processing pressure. The polymer usedin these experiments was HIPS. Figure 11.14 shows the micrographs of the ex-truded HIPS at each processing pressure. When the processing pressures were5.4 MPa (780 psi), 10.6 MPa (1,530 psi), 18.6 MPa (2,700 psi), and 28.3 MPa(4,100 psi), the cell densities were , ,

, and , respectively. The results show thatthe cell density increased with the processing pressure as shown in Figure11.15. When the processing pressure was 28.3 MPa (4,100 psi), the foamstructure of the extruded HIPS was microcellular, and the cell density was

.Since the solubility of gas is approximately proportional to the processing

pressure [52–56], more gas could dissolve in the polymer melt when the pro-cessing pressure was higher. The increased amount of dissolved gas induced agreater thermodynamic instability and a larger cell density. Therefore, a largercell density is expected when the processing pressure is higher. However, theprocessing pressure was limited by the capacities of the high-pressure gaspump and the extruder. On the other hand, a lower cell density is expectedwhen the processing pressure is lower. In fact, when the processing pressurefell below 6.9 MPa (1,000 psi), the cell density in the samples was on the orderof .

11.9.1.3 Effect of the Injected Gas Amount on Cell Nucleation

The effect of the amount of gas injected on the cell density was also studiedby Park and Suh [36]. In these experiments, the processing pressure was main-

106 cells/cm3

6 � 109 cells/cm3

6 � 109 cells/cm32 � 108 cells/cm32 � 107 cells/cm37 � 105 cells/cm3

9 � 107 cells/cm33 � 107 cells/cm3



FIGURE 11.14 Scanning electron micrographs of extruded HIPS at different processing pres-sures. Reproduced with permission from Reference [39]. Copyright (c) 1996 Polymer Engineeringand Science.

tained as 27.6 MPa (4,000 psi), while the injected gas amount was varied.When 1 wt%, 5 wt%, and 10 wt% CO2 were injected, the cell densities ofHIPS foams were 107 cells/cm3, , and , re-spectively. These cell densities are plotted as a function of the injected gasamount in Figure 11.16. When the injected gas amount was 10 wt%, the struc-ture of the extruded HIPS foam was microcellular.

For the processing pressure of 27.6 MPa (4,000 psi), 10 wt% is themaximum soluble amount of CO2 (see Section 11.4). Up to this amount, all theinjected gas will dissolve in the polymer. This dissolved gas amount againaffects the cell density of the extruded HIPS foam.

The experimental results shown in Figure 11.15 predict that a microcellularstructure with a cell density larger than 109 cells/cm3 can be produced whenthe processing pressure is higher than 22 MPa (3,200 psi). Since the gas solu-bility is approximately proportional to the processing pressure, the requiredgas amount for microcellular nucleation is estimated to be 7.5 wt%. The ex-perimental results shown in Figure 11.16 predict that the required gas amount



is 6.5 wt%. Similar results were obtained by Shimbo et al. for extruded micro-cellular PS foams [50].

11.9.1.4 Effect of the Pressure Drop Rate on Cell Nucleation

In order to investigate the effect of the pressure drop rate, the three nozzles,theoretically equivalent with respect to the pre- and post-flow conditions as de-scribed in Section 11.5, were calibrated experimentally so that they producedthe same amount of flow rate for a given pressure difference [40]. This cali-bration was needed because the actual experimental relationship between theflow rate and the pressure drop in a nozzle was different from the theoreticallypredicted values. First, Nozzle 3 was chosen as a reference for the calibrationof other nozzles. When Nozzle 3 was mounted, the nozzle pressure and theflow rate were measured as 38.64 MPa (5,600 psi) and , re-spectively. It may be noted that the actual flow rate through Nozzle 3 wasalmost twice the predicted value. Next, the size of Nozzle 1 was calibrated asfollows. Initially, a nozzle of a radius 0.60 mm (0.024 in) and a length 92.23 mm (3.631 in) was used. When the nozzle was mounted, the nozzlepressure and the flow rate were measured as 44.57 MPa (6,460 psi) and

, respectively. The nozzle length was then cut in stages untilthe flow rate and the pressure were measured to be 38.64 MPa (5,600 psi) and1.5 � 10�7 m3/s

1.9 � 10�7 m3/s

FIGURE 11.15 Effect of the processing pressure on the cell density of extruded HIPS. Repro-duced with permission from Reference [39]. Copyright (c) 1996 Polymer Engineering andScience.


. This completed the calibration of Nozzle 1. The length ofNozzle 2 was also determined in a similar manner.

Using the calibrated nozzles, a series of experiments was carried out foreach nozzle to investigate the effects of the pressure drop rate on the cell mor-phology of the extruded microcellular HIPS. In all the experiments, the sameamount of gas, 10 wt% CO2, was injected to form identical polymer/gas solu-tions. The cell densities for the nozzles from 1 to 3 were ,

, and , respectively. The cell densities foreach nozzle are plotted as a function of the pressure drop rate in Figure 11.17.

The residence times of the polymer/gas system in Nozzle 1 and Nozzle 3were 0.19 s and 0.005 s, respectively. The corresponding pressure drop ratesfor Nozzle 1 and Nozzle 3 were 0.18 GPa/s and 6.9 GPa/s, respectively. SinceNozzle 3 experiences a higher pressure drop rate, the nucleation rates forNozzle 3 are higher than for Nozzle 1. Therefore, the total number of nucleatedcells are larger for Nozzle 3 than for Nozzle 1, and the average cell size forNozzle 3 (5 �m) is smaller than for Nozzle 1 (20 �m).

7 � 109 cells/cm31 � 109 cells/cm31 � 108 cells/cm3

2.0 � 10�7 m3/s

FIGURE 11.16 Effect of the injected CO2 amount on the cell density of extruded HIPS [36].


As discussed in Section 11.5, nucleation stops when all the depleted regionsof adjacent cells impinge upon each other and the gas concentration in thepolymer matrix is below the critical level needed to nucleate additional cells.The pressure drop rates that the nozzles experience affect this nucleation timeperiod. For Nozzle 1, the pressure drop rate is low, and therefore, the nucle-ation rates are slow. Since the nucleation rates are governed by the pressuredrop rate, the nucleation time period would be shorter than the total timeperiod over which the pressure drops.

Assume that the nucleation rates for Nozzle 3 are governed by the pressuredrop rate and that nucleation is completed before the pressure drops com-pletely to the downstream pressure as shown in Figure 11.18. In this case, thenucleation time period is shorter than the residence time period in the nozzle.If the residence time period decreases, then the pressure drop rate increases.This will induce higher nucleation rates, and the nucleation time period willdecrease. However, the decrease of the nucleation time period is limitedbecause it takes time for the depleted regions to impinge upon each other. Thegrowth of the depleted region is governed by gas diffusion in the polymermatrix. Therefore, the nucleation time period cannot be reduced infinitelysmall as the pressure drop rate increases infinitely. When the pressure drops

FIGURE 11.17 Effect of the pressure drop rate on the cell density of extruded HIPS. Repro-duced with permission from Reference [40]. Copyright (c) 1995 Polymer Engineering andScience.


almost instantaneously, the nucleation time period may be longer than the res-idence time period. In this case, the pressure drop rate does not affect the nu-cleation rate because most of nucleation takes place after the pressure dropscompletely. Figure 11.18 depicts the nucleation time period for Nozzle 3 to beless than the residence time period. It may be noted that this is a conservativeestimate. The actual nucleation time period for Nozzle 3 may be longer thanthe residence time period. Additional work is required to determine the actualnucleation time period for each nozzle.

The previous argument predicts that some critical pressure drop rate existsabove which the pressure drop rate does not affect the competition betweenmicrocell nucleation and cell growth. This would imply that the graph inFigure 11.17 should reach a maximum constant value. Figure 11.17 shows thatstart of such a maximum, however, due to practical limitations in the manufac-ture of small bore nozzles, as described in Section 11.5, does not permit datapoints verifying the maximum to be obtained.

FIGURE 11.18 Comparison of residence time periods and the nucleation time periods [36].


11.9.1.5 Other Materials

Although HIPS foaming behavior was mainly described above, the nucle-ation behaviors of other materials such as PS [41, 49, 50], PP [44], SPS, andHDPE [48] were also tested. From most of these polymers, a high cell densityon the order of was achieved by injecting CO2 on the ex-truder barrel.

11.9.2 CELL COALESCENCE EXPERIMENTS

The feasibility of suppressing cell coalescence in the microcellular extru-sion foam processing was examined [46]. Figure 11.19 shows a schematic ofthe filament dies used in the experiments that consisted of two stages: nucleat-ing nozzle and shaping section. HIPS was used as the polymer material. Threesets of critical experiments were carried out. In the first experiment, only thenucleating nozzle was attached to the die without any shaping section. In thisexperiment, cell nucleation took place when the polymer/gas solution experi-enced a rapid pressure drop in the nozzle, and the nucleated cells continued togrow in the air after the extrudate exited the nucleating nozzle. In the secondexperiment, a shaping section was attached further to the nucleating nozzle

1 � 109 cells/cm3

FIGURE 11.19 Schematic of the nucleating and shaping device. Reproduced with permissionfrom Reference [46]. Copyright (c) 1997 American Chemical Society.


and the nucleated cells were induced to grow in the shaping section. In the firstand second experiments, the die temperature was maintained at 200°C. In thethird experiment, a shaping section was also attached to the nucleating nozzle.However, the die temperature in the experiment was significantly lowered to125°C. Because of the increased resistance in the die at the low temperature,the length of the nucleating nozzle was reduced from 10.2 mm (0.4 inch) to 2.5mm (0.1 inch) to maintain the same processing pressure of 28 MPa (4,000 psi)as in the first and second experiments. The dimension and the processing tem-perature of each nozzle are presented in Table 11.5.

Figure 11.20(a) shows the microstructure of the foam obtained when noshaping section was attached to the nucleating nozzle (Experiment 1). The celldensity in this case was , which agreed with the previousresults [39, 40]. Since the processing temperature was very high (200°C), it wasobserved that some adjacent cells were coalesced. Figure 11.20(b) shows themicrostructure of the foam obtained from the second experiment. When theshaping section was added to the die, the cell density was dropped to

. This implies that cell coalescence vigorously occurred in theshaping section at the high temperature after a large cell density was achieved atthe nucleating nozzle. If we assume that cells were nucleated in thenozzle as in the other experiments [39, 40], we may conclude that around 50bubbles were coalesced into a single bubble in the shaping section. It was be-lieved that the shear field generated in the shaping section caused this vigorouscoalescence of cells. Finally, Figure 11.20(c) shows the microstructure of thefoam obtained from the third experiment in which a shaping section was also at-tached but the processing temperature was significantly lowered. The celldensity in this case was found to be . This high cell density in-dicates that cell coalescence was substantially prevented by decreasing the tem-perature. Because the melt strength increases as the temperature decreases [72],

5 � 109 cells/cm3

1 � 1010

2 � 108 cells/cm3

1 � 1010 cells/cm3

Source: Reproduced with Permission from Reference [46]. Copyright (c) 1997 American ChemicalSociety.

TABLE 11.5 Nozzle Specifications and the Melt Temperatures Used in the Experiments.

Nucleation Stage Shaping Stage Melt Temperature

Diameter Length Diameter Lengthmm mm mm mm(in.) (in.) (in.) (in.) (°C)

Experiment 1 0.46 10.16 — — 200(0.018) (0.400)

Experiment 2 0.46 10.16 1.52 10.16 200(0.018) (0.400) (0.060) (0.400)

Experiment 3 0.46 2.54 1.52 10.16 125(0.018) (0.100) (0.060) (0.400)


FIGURE 11.20 Microstructures of the foams showing the effect of processing condition on cellcoalescence: (a) Experiment 1, (b) Experiment 2, and (c) Experiment 3. Reproduced with permis-sion from Reference [46]. Copyright (c) 1997 American Chemical Society.


it may be concluded that the increased melt strength by lowering the tempera-ture prevented cell coalescence despite the shear field during shaping. This ex-perimental result confirmed that the previously proposed scheme of indepen-dently controlling cell nucleation, followed by controlling shaping and cellgrowth, can be effectively utilized in the microcellular extrusion foam process-ing. In addition to pressurizing the nucleated polymer/gas solution [41], themelt temperature can be significantly lowered to prevent cell coalescence in theshaping section of the die.

11.9.3 EXPANSION EXPERIMENTS

The feasibility of producing low-density microcellular foams by closelycontrolling the temperature of the polymer melt flowing into the die and thetemperature of die was also examined through experiments [47]. HIPS wasused in the experiments. All the experimental results are summarized in Figure11.21. This figure shows how the melt and nozzle temperatures affect thevolume expansion ratio of the extruded foams. Figure 11.22 shows the mi-crostructures of HIPS foams at various melt temperatures and nozzle tempera-tures, demonstrating the effects of these temperatures on cell coalescence andfoam contraction.

Figure 11.21(a) shows the expansion ratio versus the nozzle temperature atthe three melt temperatures. Equivalently, the foam density is plotted in Figure11.21(b) in terms of the nozzle and melt temperatures. It was observed that thevolume expansion ratio was a strong function of both the melt temperature anddie temperature. When the nozzle temperature was as high as 175°C, theachieved volume expansion ratio was only about 1.5 times, regardless of themelt temperature. This means that when the die temperature was too high, mostof the gas escaped through the hot skin layer of foam during expansion. On theother hand, when the melt temperature was as high as 170°C, the volume expan-sion ratio was also only around 1.5 times irrespective of the nozzle temperature.Even when the nozzle temperature was lowered to 110°C, the volume expan-sion ratio was not changed. This implies that when the temperature of polymermelt was too high, the frozen surface of the extrudate was not effectively block-ing gas escape because the formed frozen skin layer must have been remeltedimmediately by the heat transferred from the hot polymer melt.

However, when the temperature of polymer melt was lowered to 150°C, alow-density microcellular foam was successfully obtained by freezing thesurface of the extrudate. In the nozzle-temperature range of 135°C to 175°C,the expansion ratio increased as the nozzle temperature decreased. In otherwords, the gas diffusion was blocked at the surface and more gas remained inthe foam to contribute to volume expansion as the nozzle temperate waslowered. Very similar results with a larger volume expansion were obtainedwhen the melt temperature was further decreased to 120°C.


When the nozzle temperature was further decreased from 135°C to 110°C,the volume expansion ratio decreased. Even though it was expected that moregas was preserved in the foam at this lower nozzle temperature than at 135°C,the increased stiffness of the frozen skin layer adversely affected volume ex-pansion and limited the achieved expansion ratio of extruded foam. The nozzletemperature could not be lowered below 110°C because the extrudate cloggedin the nozzle. The slight increase of the volume expansion ratio at a melt tem-perature of 150°C with the decrease in the nozzle temperature around 110°Cseems to be due to the melt fracture that occurred on the extrudate.

The experimental results indicate that there exists an optimum nozzle tem-perature to achieve a maximum expansion ratio for each temperature ofpolymer melt. The results shown in Figure 11.21(a) also imply that one can usetwo methods to achieve a desired volume expansion ratio at a fixed gas

FIGURE 11.21 Effect of the nozzle temperature on (a) the Volume Expansion Ratio and (b) thefoam density at various melt temperatures. Reproduced with permission from Reference [47].Copyright (c) 1998 Polymer Engineering and Science.


FIGURE 11.22 Microstructures of HIPS foams at various melt temperatures (Tc) and nozzle temperatures (Tn): (a) , ; (b) , ; (c) ,

; (d) , ; (e) , ; (f) ,; (g) , ; (h) ; ; (i) ,. Reproduced with permission from Reference [47]. Copyright (c) 1998 Polymer Engi-

neering and Science.Tn � 110°C

Tc � 120°CTn � 135°CTc � 120°CTn � 175°CTc � 120°CTn � 110°CTc � 150°CTn � 175°CTc � 135°CTn � 175°CTc � 150°CTn � 110°CTc � 170°CTn � 135°CTc � 170°CTn � 175°CTc � 170°C


amount. First, the amount of gas escape to obtain a desired volume expansionratio can be adjusted by controlling the die temperature above 135°C. Second,below 135°C, the degree of stiffness of the frozen extrudate skin can be ad-justed to control the expansion ratio.

Similar experiments have been conducted on PS [49], HDPE [48], SPS, PP,and other proprietary materials to investigate the volume expansion behaviorsof these materials. Utilizing the strategy of blocking gas loss by freezing thefoam skin, a large volume expansion ratio over 30 times has been achievedwith CO2 as a blowing agent. Very similar volume expansion behaviors as afunction of the melt and die temperatures have been observed for all the amor-phous materials. However, for some semicrystalline materials, the maximumvolume expansion ratio was obtained when the melt and die temperatures werethe lowest [48]. It is believed that this was due to the rheological characteris-tics of semicrystalline polymers above their freezing point [48].

11.10 SUMMARY AND CONCLUSIONS

An extrusion process for manufacturing high-density and low-density mi-crocellular polymers has been presented. This process is cost-effective com-pared to the microcellular batch processes that require a long time for gas sat-uration. The basic approach to the production of microcellular structures is tocontinuously form a polymer/gas solution, to nucleate a large number ofbubbles using thermodynamic instability via a rapid pressure drop, to suppresscell coalescence by increasing the melt strength, and to induce a volume ex-pansion to a desired expansion ratio by blocking gas loss. The main strategyfor the process design was to integrate these processing steps into an extrusionprocess such that the overall process had independently controllable functions.

The kinetics of polymer/gas solution formation, microcell nucleation bythermodynamic instability, suppression of cell coalescence, and volume ex-pansion control were examined through experimental work. An experimentalextrusion setup was built based on the proposed processing strategies. Experi-ments were carried out to verify the design and to identify the critical processparameters. Various semicrystalline and amorphous polymers were processedwith high pressure gases. Microcellular foams of a high nuclei density wereachieved from a variety of thermoplastics when CO2 was processed in thefoam process. It turned out that the amount of gas dissolved in the polymer andthe pressure drop rate across the die are the most critical parameters in deter-mining the nuclei density of extruded foams. The melt and die temperaturesproved to be the most critical parameters that affect the volume expansionratio of the extruded foams. By controlling the melt and die temperatures, avery high volume expansion ratio up to 43 times has been successfullyachieved even with CO2.


11.11 NOMENCLATURE

a Dimensionless characteristic constant of a non-Newtonian fluid

Co Concentration of nucleation sites, #/m3

Ci Concentration of the source, g/gCw Concentration of gas molecules in solution at the cell wall

interface, g/g of polymerC∞ Concentration of the free-stream or initial concentration of gas

molecules in solution, g/g of polymerD Diffusivity or diffusion coefficient, cm2/sDo Diffusion coefficient constant, cm2/sdCs/dt Solubility drop rate across the nozzle, 1/s

Pressure drop rate across the nozzle, Pa/sPressure drop rate across nozzle i, Pa/s

fo Frequency factor for microcell nucleation, 1/sk Boltzman’s constant, J/KL Length of the nozzle, mlD The diffusion distance, cmm Characteristic constant of a non-Newtonian fluid, N-sn/m2

Nhom Homogeneous microcell nucleation rate, cells/m3sn Dimensionless characteristic constant of a non-Newtonian fluidp Pressure of a flowing polymer/gas solution, Paq Volumetric flow rate, m3/sRro Radius of the nozzle, ms Striation thickness of the mixture, cmT Temperature, KTc Melt temperature, KTn Nozzle temperature, KtD Diffusion time, sto Reference time in a nozzle, st1, t2 Arbitrarily small time period during nucleation, sU∞ Velocity of the free-stream, m/svavg Average velocity of the polymer/gas solution in the nozzle�Cs Change of the gas solubility in polymer, g/g of polymer�ED Activation energy for diffusion of a gas in a polymer, J/mol�Ghom Change in Gibbs free energy for homogeneous microcell

nucleation, J�P Difference between initial solution pressure and nucleation

solution pressure, Pa�p Pressure difference, Pa�p1

i Pressure drop at time t1 in Nozzle i, Pa

Universal gas constant � 8.314 J/mol-K

(�dp/dt)i

�dp/dt

( � 1/n)


�p1j Pressure drop at time t1 in Nozzle j, Pa

�t Average residence time of the polymer/gas solution in thenozzle, s

�bp Interfacial energy between gas bubble and polymer, N/m�C Concentration boundary layer, m� Viscosity of a non-Newtonian fluid, Pa-s

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CHAPTER 12

Foam Extrusion of PolyethyleneTerephthalate (PET)

MARINO XANTHOSSUBIR K. DEY

12.1 INTRODUCTION

EXTRUSION foaming of most plastic resins has been carried out successfullyfor some time with physical blowing agents (PBA) or chemical blowing

agents (CBA) in single or tandem lines. CBAs are normally used for the pro-duction of high- and medium-density foams whereas PBAs are generally usedfor the production of lower-density foams—as low as 0.05 g/cc. CBAs releasegaseous products at a required rate over a fairly narrow temperature range,their choice being dictated by the process temperature of the particularpolymer. PBAs are atmospheric gases, volatile hydrocarbons, hydrofluorocar-bons (HFC), or hydrochlorofluorocarbons (HCFC) that are metered and dis-solved in the polymer melt during processing. It is believed that bubble nucle-ation is heterogeneous and begins inside the shaping die [1]. As the gas-ladenmelt emerges from the die, it experiences a sudden pressure drop; this thermo-dynamic instability causes a phase separation. The escaping gas leads to ex-pansion within the fluid matrix in such a manner that individual bubbles growand merge into cells, and through subsequent solidification, stable expandedstructures are produced [2, 3]. The cell size and cell density depend on theamount of gas dissolved into the polymer [4]. More information on the physi-cochemical aspects of bubble nucleation and growth occurring during extru-sion foaming may be found in other sections of this monograph.

The favorable cost/performance characteristics of solid PET (virgin and re-cycled) may be extended to lower density sheet structures produced by single-layer extrusion or coextrusion for thermoforming and lamination. Potential ap-plications would take advantage of the combination of good mechanicalproperties, dimensional stability of the semicrystalline resin at temperatures up


to 200°C, and recyclability. In addition to the food packaging industry wherePET foams have already made advances, other applications would be intendedfor the building/construction, transportation, and other industries currently uti-lizing rigid PUR, PS, or PVC foams. By contrast to the commonly used PS andLDPE resins, extrusion foaming of the relatively high-density, semicrystallinePET is an area presenting several challenges. Difficulties are mostly related tothe required high processing temperatures (260–290°C), the absence of abroad extrusion foaming window as compared to amorphous resins, the ofteninadequate for foaming rheological characteristics of the resin, its slow rate ofcrystallization and limited process stability, and the possible interference ofcrystal nuleation with bubble nucleation. Poor foaming characteristics are ac-centuated by the known sensitivity of the PET ester linkages to hydrolyticdegradation at processing temperatures leading to chain cleavage and reduc-tion in molecular weight. Hydrolytic degradation may be due to inadequatedrying of the base resin or to water given off as a decomposition by-product ofcertain chemical blowing agents. In addition, the sensitivity of PET to thermalor thermooxidative degradation may lead to further reduction in MW and theformation of various by-products that could affect the foaming process.

Significant developmental work has been conducted over the past twentyyears by resin producers and converters to develop suitable resins and extru-sion processes, particularly for low-density foaming. Patents have been issuedto Amoco Corp., Celanese Corp., Dow Chem. Co., E.I. Dupont de Nemours &Co., Eastman Chemical Co., General Electric Co., Goodyear Tire and RubberCo., Sekisui Kaseihin Kogyo Kabushiki Kaisha, M&G Ricerche, Rohm andHaas Co., Teijin Ltd., among others. Since the early 1990s, Shell Chemical Co.(PetliteTM) and Sekisui (CelpetTM) are among suppliers of PET foamed sheets(1–3 mm thick) with different bulk densities and low % crystallinity. Sinco Engineering is among the recent suppliers of foam-grade pellets (CobitechTM).Equipment suppliers for high-volume foam extrusion lines suitable for PET include Battenfeld Gloucester Eng. Co., Berstorff Corp., Cincinnati Milacron/Sano, Wayne Machine and Die, and Leistritz Corp. [5].

Low- to medium-density polymeric sheets or boards are pro-duced by injection of physical blowing agents (PBA) in single extruders or inan extruder of a tandem system. Flat or annular dies may be used. The rheo-logical properties of conventional PET resins with relatively low MW andnarrow MWD are not particularly suitable for low-density extrusion foaming.As a result, modified resins with higher melt viscosity, broader MWD, andhigh melt strength/elasticity are often required to control cell expansion andstabilize the growing bubbles. Such resins can be produced through chain ex-tension/ branching reactions with di- or polyfunctional reagents, as, forexample, pyromellitic dianhydride (PMDA). A variety of blowing agents(CFCs, HCFCs, VOC, atmospheric gases) have been reported to be effectivePBAs for PET. In single extruder foaming processes, a two-stage screw is typ-

(� 0.5 g/cc)


ically used with the blowing agent added usually in the decompression zone ofthe screw [5]. ABA or AB structures, where A is unfoamed skin and B isfoamed core, may be produced by coextrusion with a cap layer to reduce gasloss and, hence, achieve lower density. In a tandem line, the blowing agent isadded in the first extruder, and the mixture is transferred in the second coolingextruder that conveys the melt to the die at appropriate temperature and pres-sure to allow expansion without coalescence. Due to the longer residencetimes in tandem lines, there always exists the possibility of thermal or ther-mooxidative degradation of certain PET resins.

Medium- to high-density extruded PET foams may also beproduced with chemical blowing agents. The rheological characteristics of theresin are less critical than in the case of PBA foaming, and resins with lowerviscosity/melt strength may be acceptable [6]. However, in contrast to otherthermoplastic materials, e.g., PE, PP, PS, PVC, etc, this method is still less ad-vanced.

Following a review of the resin chemistry and current process technologiesfor extruding/forming solid PET sheets, the sections below will discuss the fol-lowing:

• available chemical modification methods to meet the rheologicalrequirements of PET resins for foaming to low densities with PBAs

• available process technologies for foaming with PBAs and CBAs• properties and characteristics of the extruded foams

The processes discussed in this chapter involve macrocellular foam (typically100 �m or larger cell size) and do not cover the so-called microcellularfoaming where resins presaturated with blowing agents, such as CO2, areheated at or above Tg and cooled rapidly to lock in the cellular morphologyand prevent excessive cell growth. Such morphology is characterized byclosed cells up to 25 �m in size with cell density of 108 cells/cm3 [7]. Contin-uous microcellular processes involving extrusion equipment as described invarious patents, e.g. [8], are under development [9].

12.2. REVIEW OF PET CHEMISTRY AND PROCESSINGCHARACTERISTICS

The general information in this section on the characteristics of PET resinsand extrusion processing/forming of solid sheets is extracted from the presen-tations of several authors in Reference [10]. This review will provide a usefulbackground to the foaming processes that will be described in later sections.

PET is prepared by transesterification from dimethyl terephthalate and eth-ylene glycol or direct esterification from terephthalic acid and ethylene glycolin the presence of catalysts; both reactions are followed by a polycondensation

(� 0.5 g/cc)


step. Typical reaction products for textile fiber applications are characterizedby intrinsic viscosity, IV (typically 0.62 IV for MW ranging from 12,000 to20,000). Higher MW can be achieved by longer polycondensation times or bysolid-state polymerization. In the latter process, PET pellets are heated under astream of hot, dry nitrogen to temperatures up to 215°C for 16 hours to reachIVs of 0.80 (MW 30,000–35,000) suitable for bottle applications. In additionto solution viscosity, polymers are characterized by percent crystallinity, glasstransition temperature (about 75°C), melting temperature (approximately260°C), color, barrier properties, and comonomer content. Overall density ofPET homopolymer is high (1.35 g/cc for the amorphous phase, 1.46 g/cc forthe crystalline phase).

PET has a low crystallization rate compared to polymers such as PE or PP;ultimate degrees of crystallinity are also low . Crystalliza-tion kinetics of PET depend primarily on temperature, MW or IV, catalystresidue, and the presence of diethylene glycol formed during synthesis. Effectsof reduced IV are faster crystallization rates and reduced impact resistance. Avariety of plasticizers and nucleating agents, including inorganic and organicsubstances, inorganic minerals, and organic polymers (particularly, polyolefinsfor thermoformable PET) are added at small concentrations to increase crys-tallinity and produce faster rates of crystallization and fine spherulitic structure[11]. Organic plasticizers, including dissolved gases (e.g., CO2), result in in-creased mobility of the polymer chains, reduced Tg, and overall increase ofcrystallization rate. Nucleating agents induce heterogeneous nucleation by in-creasing the density of nucleating sites. Upon cooling from the melt, crystal-lization half-time values for nucleated resins reach minimum values in thetemperature region of 200–180°C (appropriate for thermoforming). For unnu-cleated resins, corresponding values in the same temperature range are signifi-cantly higher. Comonomers such as isophthalic acid, diethylene glycol, or cy-clohexane dimethanol at concentrations up to 5 mole % are used to lowerpercent crystallinity, rate of crystallization and melting temperature withoutcompromising the PET’s desirable properties.

Degradation of PET may be thermal through chain scission reactions in es-sentially air-free environments. Degradation may result in increased carboxylend group content, the formation of acetaldehyde, and eventually the forma-tion of polyene structures. If air is present at these high processing tempera-tures, oxidative processes may occur creating free radicals, gel formation, etc.Predrying to very low moisture levels is required prior to processing to mini-mize hydrolytic degradation. Typical conditions in desiccant dryers to reducemoisture of precrystallized PET pellets to moisture are 150°C forfour to six hours to a dew point of .

The majority of PET applications include bottles, film, strapping, fibers, andsheeting. For sheet extrusion/thermoforming applications, that are particularly

�40°C� 50 ppm

(typically � 40%)


amenable to density reduction by foaming, suitable materials include the fol-lowing:

a. Amorphous PET grades (APET) for “crystal clear” packaging for use attemperatures below Tg.

b. Crystalline PET grades (CPET) for opaque microwavable or dual ovenable.food containers.

APET polymers are typically copolymers with IVs from 0.8 to 1.05 ex-truded to sheets of low crystallinity ; these low crystallinity levels areretained even after thermoforming usually in cold molds (120°F), with 6 seccycle times. Depending on the degree of draw, APET can undergo stress-induced crystallization that may also result in haze and reduced transparency.CPET homopolymers with IVs above 0.7 contain nucleating agents (typically,3% of heat stabilized polyolefins, e.g., LLDPE, LDPE, or PP) to assist in crys-tallization during thermoforming. During extrusion, CPET crystallinity needsto be kept as low as possible by chilling to provide more latitude in consequentheating and forming. Cystallinity of CPET increases from in the ex-truded sheet to about 30–35% on the thermoformed item that is usually pro-duced in hot molds (around 330°F), with cycle times 6–10 sec. CPET trays andcontainers are considered to be heat stable up to 200°C. To improve impactstrength of CPET, particularly at low temperatures, core shell butyl acrylatebased tougheners are employed. For tray thermoforming, an APET layer ex-truded on top of CPET gives improved sealability to MylarTM film and betterimpact resistance. Oxygen and water vapor transmission decrease through ad-ditional crystallization; reported values from materials suppliers [10] are about30–40% lower for CPET trays versus APET sheets.

12.3 FOAMING WITH PHYSICAL BLOWING AGENTS

12.3.1 CHEMICAL MODIFICATION OF PET FOR LOW-DENSITYEXTRUSION FOAMING

Effects related to melt viscoelasticity of thermoplastics can, in general, becontrolled through additives or through changes in MW and MWD duringreactor/post-reactor processing by chain extension, grafting, branching, con-trolled cross-linking or controlled degradation [12]. Modified PET resins withincreased MW, viscosity, and melt strength/elasticity, can be produced throughchain extension/branching reactions, primarily between the carboxyl/hydroxylpolyester end groups and di- or polyfunctional reagents containing anhydride,epoxy, oxazoline, isocyanate, carbodiimide, hydroxyl, tertiary phosphite,

� 5%

(� 5%)


phthalimide, and other groups [13]. The term “melt elasticity” is widely usedin polymer processing where complicated geometric effects and flow fields ne-cessitate the use of linear viscoelastic functions and their nonlinear counter-parts. Changes in melt elasticity have been related to changes in the values ofparameters such as normal stress difference, storage modulus, and extrudateswell [14-16]. For certain polymers, “melt elasticity” has also been related toextensional viscosity [17] and melt strength, the latter being related qualita-tively to extensional rheology [15].

Rheological modification of PET may be carried out during polycondensa-tion, by solid stating in the presence of premixed modifier, or by post-reactormodification via reactive extrusion. Common polyester modifiers listed intechnical publications and the patent literature include polyanhydrides, such aspyromellitic dianhydride (PMDA) (see for example References 18–22) andpolyepoxides, such as diglycidyl esters or copolymers containing glycidylfunctional groups (see for example References 22–28). Within the context oflow-density foaming by PBA injection, the following is a review of modifica-tion methods that have been reported, mostly, in the patent literature.

12.3.1.1 Reactor Polycondensation in the Presence of Modifier

As an example, Muschiatti [18] reported the production of highly branched,high melt strength, non-Newtonian behavior resins suitable for making low-density, closed-cell foams through polymerization in the presence of branch-ing agents (polyols, polyanhydrides, polyacids).

12.3.1.2 Solid Stating in the Presence of Premixed Modifier

The production of PBA extrusion foamable polyesters modified by solid-state polyaddition with a premixed modifier, e.g., PMDA, is discussed in aseries of patents and publications from Sinco Engineering [19, 29–34]. Theseresins are distinguished from nonfoamable resins by increased melt strength,high extrudate swell, increased complex viscosity with non-Newtonian behav-ior in the low-frequency region, and higher storage modulus (G�). Branchedfoamable PET was also prepared by mixing with ethylene copolymers con-taining carboxyl, ester, and alcohol functionalities followed by solid stating toproduce a modified resin with a 10-fold higher melt viscosity and higher dieswell and melt strength than the unmodified resin [35].

12.3.1.3 Post-Reactor Modification by Reactive Extrusion

Extrusion modification of PET with PMDA or other branching additives ina concentrate form results in significant increase in zero shear melt viscosity,increase in melt strength and die swell, increase in molecular weight, and in-


crease in polydispersity from about 4.5 to up to 11 as measured by the z-average/number-average molecular weight ratio [20, 36]. Property changesdepend on the choice of process conditions, additive concentration, and itstype of carrier. Foamable PMDA modified resins had IV of 0.805 dl/g (versus0.70 for the unmodified resin), weight average molecular weight of 85,690,and polydispersity of 10.8. Foams with 0.2 g/cc density were obtained byHCFC injection in the primary extruder of a tandem line equipped with anannular die [20]. In another patent by Hayashi et al. [22], isopentane was in-jected into the molten mixture of PET/PMDA to produce rod-shaped foams.Expansion of the extrudate was proportional to the amount of PMDA added(up to 0.4 %wt); density values for the PMDA-modified foams ranged from0.35 to 0.13 g/cc versus 0.76 g/cc when no PMDA was used. Dianhydrides andmetallic catalysts were used to produce hydrocarbon/inert gas extrusion foam-able PET by substantially increasing its shear viscosity and melt strength [37].PMDA concentrates in different carriers and in the presence of various addi-tives have also been used for improved stability of the foaming process [21,38]. A suggested reaction mechanism [36], with PMDA involves as a first-steplinear extension through reaction of terminal polyester hydroxyl end groupswith the anhydride functionalities and the formation of two carboxyl groupsper incorporated PMDA moiety. Subsequent reactions may involve all func-tionalities of the PMDA molecule through esterification and transreactions toyield branched or even cross-linked structures. Combinations of PMDA/pen-taerythritol/Lewis acid catalyst have also been used to produce resins withmodified rheology [39]. Other modifiers such as multifunctional epoxy chainextending compounds were also used in a tandem line with CO2 to producefoams with 40 kg/m3 density [23]. Tetrafunctional epoxy reactive additiveswere added in a batch mixer to produce PET with increased elongational vis-cosity and melt strength; preliminary batch foaming experiments indicatedthat the modified PET foams obtained by CO2 dissolution at room temperaturewere closed-cell structures [40]. A suggested mechanism [27–28] for chain-ex-tension reactions with the glycidyl functionality includes esterification of car-boxyl end groups and etherification of hydroxyl end groups; secondary hy-droxyls formed from these reactions may further react with carboxyl or epoxygroups leading to branching or cross-linking. A summary of possible reactionsconverting the linear polyesters into partially branched resins may be found inReference [41].

Results of sequential reactive modification/foaming of low-IV recycledresins with premixed branching additives followed by CO2 injection in asingle 40:1 L:D extruder are shown in Table 12.1 [6]. The recycled PET 1 andPET 5 resins having low viscosity (as suggested by low-IV and high-MFIvalues), and low elasticity (as suggested by low die swell values), producedunstable foams in a rod die. By contrast, their counterparts containing pre-mixed modifiers (PET 1M and PET 5M) foamed well and produced predomi-


TABLE 12.1 Materials Characteristics in CO2 Foaming [6].

MFI Die Swell(260°C/ Foam Quality/

Resins Description Nominal IV 2.16 kg) 260°C) Comments

RECYCLED, MODIFIED/PET 1 Recycled post consumer 0.7 26.6 1.29 No foam

pellets (Phoenix)PET 1M Extruder modified N/M 4.38 2.76 Good, uniform; high swell;

PET 1—0.9 phr branching density 0.2 g/cc, aver. celladditives size 410 �m

PET 2 Recycled post-consumer 0.87 6.87 2.66 Good, uniform; high swell; pellets modified by reactive density 0.12 g/cc, aver. cellprocessing (pilot) size 200 �m

PET 4 Recycled post-consumer 0.95 4.38 2.86 Uniform; high swell; pellets modified by reactive density 0.12 g/cc, aver. processing (pilot) cell size 150 �m

PET 5 Recycled green post-consumer 0.7 38 1.23 No foampellets (St. Jude)

PET 5M Extruder modified N/M 1.85 2.97 Good, uniform; high swell; PET 5—2 phr branching density 0.11 g/cc, aver. additives cell size 350 �m

VIRGINPET 6 Bottle grade 0.77 15.9 1.29 Poor/little expansion, large

bubblesPET 7 Copolyester 0.8 15.3 1.43 Poor/little expansion, large

bubblesPET 8 CPET 0.95 10.4 1.39 Poor/little expansion, large

bubblesPET 9 CPET 1.0 7.38 1.43 Poor/little expansion, large

bubbles

(270 s�1/


nantly closed-cell foams with low density and fine cell size. Similarly [42], re-cycled PET was sequentially modified/foamed in a twin-screw extruder with0.25% PMDA, talc nucleating agent, and Freon 12 to produce highly ex-panded extrudates with density of about 0.2 g/cc.

12.3.2 RHEOLOGICAL CHARACTERISTICS OF FOAMABLE PETRESINS

Extrusion foamability of PET resins is usually reported in the literaturethrough single point, single temperature, and single shear rate measurementsof parameters related to melt viscosity and melt strength/elasticity. ASTMstandard methods D4440 for zero shear melt viscosity and D3835 for meltstrength and die swell have been employed [35]. In an earlier publication [6],extrusion foamability of a variety of commercial and experimental resins,virgin and recycled, with different intrinsic viscosity (IV) values was evalu-ated in a single-screw extruder modified for carbon dioxide injection andequipped with a rod die. In addition to molecular weight (through IV), foama-bility was related to melt viscosity through melt flow index and melt elastic-ity/melt strength through die swell measurements under prescribed conditions.The characteristics of the resins and the results of the foaming experiments aresummarized in Table 12.1. As mentioned earlier, the post-consumer recycledmaterials PET 1 and PET 5 were almost impossible to foam due to their verylow viscosity and poor melt strength. The virgin materials (PET 6 to PET 9),although having higher viscosity and fairly good melt strength during extru-sion, did not expand sufficiently to produce satisfactory foams. The recycledmaterials modified with appropriate concentrations of low MW multifunc-tional branching agents (PET 1M, PET 2, PET 4, and PET 5M) swelled signif-icantly at the die exit and foamed well. They produced predominantly closed-cell foams with densities from 0.1 to 0.3 g/cc and fine cell size with fairlyuniform size distribution (Figure 12.1). The obtained data suggested that CO2

foamable PET resins should have die swell values, under the prescribed off-line experimental conditions, approximately 100% higher than those of thepoorly foamable ones; MFI values at 260°C/2.16 kg should also be lower thanabout 7g/10 min for improved foamability.

More complete melt viscoelasticity data for two of the above resins, the un-modified PET8 (poorly foamable) and the chemically modified PET4 (wellfoamable), are reported below. With respect to melt viscosity, by invoking theCox-Merz rule, combined capillary and mechanical spectrometer viscositydata are plotted in Figure 12.2 [43]. The unmodified resin has lower overallviscosity and shows typical Newtonian behavior in the low-frequency regionand significant shear thinning starting at . In contrast, the chemi-cally modified resin seems to behave over almost the entire shear rate region asa power law fluid starting shear-thinning at very low shear rates. Such high-

50–100 s�1


FIGURE 12.1 Cell structure of PET foam. (Courtesy of the CRC for Polymers, Australia.)

FIGURE 12.2 Melt viscosity comparison of unmodified PET8 and modified PET4 at 290°C.


shear sensitivity behavior would be typical of branched or broad MWD poly-mers and very high MW materials [44], also, of high melt strength PET resinsmodified for foaming or extrusion blow molding [29, 30, 45].

With respect to “melt elasticity” criteria, extrudate swell data of the tworesins at 290°C are compared in Figure 12.3. The chemically modified resinhas more than double the extrudate swell of the unmodified resin depending onthe shear rate; extrudate swell is shown to increase with increasing shear rate,as expected. A region of flow instability is noted at high shear rates for thehigh-viscosity chemically modified resin. Storage modulus, G�, as anothermeasure of melt elasticity suggests similar ranking of the two resins (Figure12.4). The values of G� of the chemically modified resin are larger than thoseof the unmodified by a factor of 10 at low frequencies, and they begin to con-verge as frequency increases.

12.3.3 PROCESS TECHNOLOGY AND APPLICATIONS

12.3.3.1 General

Examples of four different extrusion foaming processes described in the lit-erature are summarized in Table 12.2. The systems involve the use of single or tandem lines, premodified resins or resins modified during a sequential

FIGURE 12.3 Extrudate swell versus shear rate for unmodified PET8 and modified PET4 at290°C.


FIGURE 12.4 Comparison of G� and G� for unmodified PET8 and modified PET4 at 290°C.


TABLE 12.2 Examples of PET Foam Extrusion Processes Using PBAs

Parameters/Properties Reference [46] Reference [35] Reference [19] Reference [38]

Resin IV:Chain extension/ Solid stating in presence Solid stating in presence Solid stating in presence During extrusion prior to branching method of modifier of modifier of modifier PBA injectionFoaming nucleator None Talc, TiO2, Na2CO3 Talc Talc, Na2CO3

Extruder system Single-SSE Tandem-SSE Single-SSE Single-TSE(1.25�) (2� and 2.5�) (3.5�) (1.25�)

PBA CO2, N2, Ar Isopentane HCFC Freon 22Product Thin sheets (1.2 mm) Thin sheets (1.5 mm) Thin sheet from annular Thick 15 mm board

from flat die from annular die dieDensity, g/cc Variable to 0.2 min. 0.20 0.15–0.18 About 0.1

depending on resinCrystallinity , 15.3% N/M

depending on resinCell size 0.2–0.3 mm 0.1–0.2 mm 0.05–0.2 mm 0.56 mmPost-processing Press lamination to thick Post-expansion at 175°C — —

boards easier for the to 1.9 mm, 0.16 g/cclow-crystallinity sheet density and 0.2–0.3 mm

cell size

� 15%� 10% or � 15%

� 0.8� 0.85� 0.8� 0.95


extrusion/foaming operation, different size extrusion equipment, and differentblowing agents. Products are thin sheets or thicker boards, all of relatively lowdensity (0.2 g/cc), medium to low percent crystallinity and medium-sized,closed-cell morphology. Talc is the material of choice as a foaming nucleator;it is recognized that talc could also promote crystal nucleation and subsequentcrystallization to different extents during the extrusion or postprocessing steps.Control of crystallinity to low levels through cooling or material formulation(e.g., polyolefin nucleators for crystallinity) is critical when sheets are to beused in thermoforming/lamination. Details on the systems of Table 12.2 aregiven below.

12.3.3.1.1 Example I

In a recent study [46] attempting to provide a better understanding of the pa-rameters affecting foam extrusion with atmospheric gases, a 32 mm dia., 40L/D Killion segmented single-screw extruder equipped with gas injection port,a 250 mm wide flat sheet die, and a three-stack chilled roll assembly (Figure12.5) was used to produce foamed monolayer (about 1.2 mm in thickness)from resins with different rheological characteristics. Carbon dioxide, nitro-gen, or argon were injected at 19D length at different pressures and mixed into

FIGURE 12.5. Schematic of single extruder foaming line equipped with gas injection. (Cour-tesy of the Polymer Processing Institute.)


the PET melt. No additional nucleating agents were used. Process conditionsdepended on the type of gas and the type of resin.

For the chemically modified, high-viscosity, high-melt strength resin (re-ferred to as PET 4 in Table 12.1 and Figures 12.2–12.4) the density of thefoamed extrudates was found to decrease with increasing gas injection pres-sure with a plateau attained at about 5,500–7,000 kPa. The results appear to beindependent of the type of gas (Figure 12.6). Densities as low as 0.2–0.3 g/ccwere obtained at about 5,500 kPa gas pressure regardless of the gas type. Forthe unmodified, lower viscosity and lower melt strength PET 8 resin, thedensity of the foamed extrudates was also found to decrease with increasinggas injection pressure, independently of the type of gas, but with an apparentplateau reached earlier at gas pressures about 4,000 kPa (Figure 12.6). It wasnot possible to produce satisfactory foams at higher gas pressures due to cellcollapse. Densities at about 5,500 kPa were significantly higher (0.7–0.9 g/cc)than the corresponding values obtained with the modified resin. In the absenceof gas solubility data at the processing conditions, gas injection pressures can

FIGURE 12.6 Density versus gas injection pressure for two PET resins foamed with inert gasesin a flat sheet die.


only be considered as indicators of concentration, and final densities are inde-pendent of the type of gas molecules. Injection in the partly filled zone of thesegmented screw would initially lead to a two-phase system that further down-stream could be converted in a combination of a single-phase and undissolvedgas clusters, depending on screw configuration, operating conditions, temper-ature, etc. Such clusters could act as premature nucleators and affect the foammicrostructure. The obtained trends in the density versus gas pressure curvesare similar to the ones observed in the cell density versus gas concentrationcurves by Park and Cheung [47], who suggested that reaching the gas solubil-ity limit was one of the reasons for the observed plateaus. It should be notedthat preliminary results [48] with on-line optical monitors attached at the ex-truder end suggest differences in the solubilities of the three gases used in Ref-erence [46].

An observation in this study was the appearance of corrugation parallel tothe machine direction in all sheets produced from the modified PET 4 andfoamed to densities lower than about 0.5 g/cc. Corrugation was not observedin the case of the 0.7–0.8 g/cc higher density PET 8 sheets. Corrugation in flatsheet dies has also been reported by other authors [49] and is attributed to theuneven directional expansion of gas for a given die/take-up configuration.Ease of expansion in two directions is accompanied by difficulty of the gas ex-panding in the transverse direction resulting in sheet folding. Transverse ex-pansion becomes more difficult in the presence of the larger amounts of gasnecessary to attain low density, a phenomenon that appeared to be amplified bythe particular rheology of the PET 4 resin.

12.3.3.1.2 Example II

As an example of extrusion in a tandem line [35], a prereacted with EVOHbranched PET was fed in a system consisting of a 2 inch primary extruder op-erating at 87 rpm and a 2.5 inch secondary extruder operating at 16.4 rpm andequipped with a 3 inch diameter annular die. Isopentane was introduced in thefirst extruder at 1.6 lb/hour. Temperatures ranged from 260 to 275°C, andpolymer output was 66 lb/hour. The foam was slit and collected as a 36-inch-wide sheet having a density of 0.21 g/cc, a thickness of 59 mils, crystallinity15%, and closed cells 100–200 microns in size. Further heating of the sheet at175°C for three minutes resulted in expansion to about 75 mils, 0.16 g/ccdensity, and 31% crystallinity.

12.3.3.1.3 Example III

Equipment and conditions for producing low-density PET foamed sheetsfrom solid-stated, PMDA chemically modified PET resins with improved meltstrength are described in Reference [19]. In a particular example from this


patent issued to M&G Richerche, a 90 mm single-screw extruder (L:D 30)equipped with an annular 40 mm diameter die was used in combination withtrichlorofluoroethane and talc nucleating agent to produce sheets with proper-ties shown in Table 12.3. Typical operating conditions were 24 rpm, 259°Cmelt temperature, and 9.1 MPa melt pressure. Figure 12.7 shows a pilot plantextrusion line for producing low-density PET foams intended for a variety ofstructural and insulation applications. Thick boards, about 35–40 mm in thick-ness and 230 mm wide, produced by the same technology were found to havethickness dependent percent crystallinity as a result of cooling rates. Crys-tallinity ranged from about 37% in the core to about 25% in the skin [50].

12.3.3.1.4 Example IV

A corotating twin-screw extruder (W&P ZSK-30) was used to produce thickinsulation boards [38]. The screw profile consisted of conveying elements inthe feeding/melting section, a melt seal at the sixth barrel section, and convey-ing elements toward the die. Freon–22 was fed in the seventh barrel section at2 wt% with respect to a resin feed of about 19 lb/hour. Resin feed containedtwo concentrates (PMDA and sodium carbonate, respectively) in PET carriers.

FIGURE 12.7 PET pilot extrusion foam line. (Courtesy of Sinco Engineering.)


TABLE 12.3 Foamable Versus NonFoamable PET—Comparison of Resin and Extrudate Properties [19].

Modified Foamable PET(0.71 IV � 0.15% PMDA Modified Foamable PET

Unmodified PET— Solid Stated � Additional (0.71 IV � 0.3%not Foamable PMDA in Extruder) PMDA Solid Stated)

Resin propertiesIV, dl/g 0.80 0.82 1.95Melt strength, cN 0.2 25 43Complex viscosity, Poise 104 1.05 3.59 40Elastic modulus,G� dyne/cm2 104 1.04 26.0 100Extrudate propertiesDensity, kg/m3 1,300–1,400 150–180 50–80Compession set, MPa N/M 1.5 20Compression Modulus, MPa N/M 15.4 17.0Tensile Strength, MPa N/M 3.3 4.0


Foam was pulled at 40 inches /min to produce a board of about 0.6 inch thick-ness, density of 6.3 pcf, cell size 0.56 mm, compressive strength of 53 psi, andexcellent moisture and thermal dimensional stability. Pressure at the die was440–540 psi, and pressure at the gas injection point was 260–280 psi.

12.3.3.2 Extrusion Followed by Thermoforming

12.3.3.2.1 Extrusion for High-Density Thermoformable Trays

The examples that follow describe extrusion foaming, thermoforming, andproperties of relatively high-density products.

In a patent assigned to the Goodyear Rubber and Tire Co., unmodified PET(IV 0.95) with LLDPE nucleating agent was extruded in a 2.5 inch Egan ex-truder operating at 70 rpm with barrel temperatures 280–330°C, die tempera-ture about 260°C, and nitrogen injected at 3,200 psi. [51]. The foamed sheetwas about 0.03 inch thick having density of about 1 g/cc and low crystallinity(about 5%). Thermoforming of this CPET sheet was carried out utilizing apreheat oven time of about 15 seconds, mold time of 8–10 seconds, sheet tem-perature of 154°C, mold temperature of 154–136°C, top oven temperature of300°C, and bottom oven temperature of 116°C. Thermoforming producedtrays of density 0.85 g/cc due to further expansion of the nitrogen containingcells and additional crystallization to about 25–35% crystallinity. The trayswere heat stable to 200°C and were considered as dual ovenable for use in thefrozen food industry. As mentioned earlier, Shell Chemical Co. commercial-ized in the early 1990s CPET foams with relatively high densities (0.8–0.9g/cc) in 30–40 mil thick sheet form. Petlite IITM intended to be used for ther-moforming food containers met applicable FDA regulations.

In a study conducted by Eastman Chem. Co. [49] on the use of expandedpolyesters for food packaging applications, it was shown that CPET foamscould be thermoformed on conventional PET thermoforming tools. Standard1–1.5� deep trays of foamed CPET could be formed with the same cycle timesas unfoamed CPET. Sheet foam extrusion in the presence of proprietary addi-tives and PBAs was shown to result in reduction of mechanical properties as afunction of density to a 1.5–2 power. Gas barrier properties also decreasedwith decreasing density, for example, oxygen permeability increased fromabout 5 cm2.mm/m2.24 hr.atm for the solid PET to about 15 cm2.mm/m2.24hr.atm for a 0.7 g/cc density foam. Mechanical properties at 0.7 g/cc densitywere as follows:

• tensile strength at break (Machine Direction, MD) about 14 MPa• tensile strength at break (Transverse Direction, TD) about 9 MPa• secant modulus 1%, MD 850 MPa• secant modulus 1%, TD 550 MPa

(� 0.7 g/cc)


12.3.3.2.2 Extrusion for Low-Density Thermoformable Trays

The examples that follow describe extrusion foaming, thermoforming, andproperties of lower density products as well as approaches usedto reduce extractables to meet food regulations.

In the original Sekishui patent [22], a variety of PET resins were extruded todifferent densities by varying the amount of butane injected downstream. Dif-ferent branching additives were used in a 65 mm single-screw extruder (L:D35) equipped with a circular die. Typical barrel temperatures were 280–290°C,die temperatures were 270–280°C, extrusion head pressure was 80–90 kg/cm2,rpm was 30–25, and extrusion rates were 24 kg/hr. The injection pressure ofbutane was 80 kg/cm2 for systems 1 and 2 and 40 kg/cm2 for system 3 (Table12.4). The resulting extrudate was cut open and samples about 1.5 mm thickwere tested. The results summarized in Table 12.4 indicate that the low-densityfoam containing had satisfactory tensile strength, highelongation at break, and high heat resistance. Sheets for thermoforming haddensities 0.16–0.19 g/cc, thickness 1.5–2.6 mm, and crystallinity 10–18%.They were preheated at 175°C for 15 seconds and thermoformed in a plugassist tool for an additional 25 seconds.

In subsequent publications from Sekishui Plastics [37, 52], PET plus diacidanhydride and metal compound were processed in a 65 mm, L/D 35:1 single-screw extruder equipped with a sheet die at 270–280°C. Volatile hydrocarbonsor inert gases were injected downstream. Properties of the extruded foamedsheets (Celpet™) are shown in Table 12.5. Thermoforming to trays wascarried out by preheating to 150°C for 4 seconds, forming and crystallizing at180°C for 6 seconds, and cooling to 20°C for 4 seconds. Crystallinity in-creased from 10 to 22–28% after thermoforming. The formed PET trays hadimproved heat resistance in the presence of food in microwave or electricovens versus equivalent PP or PS foam containers.

In attempts to reduce extractables of thermoformed trays produced fromfoamed PET modified with PMDA, several approaches involving precom-pounded concentrates were used. For example, in a patent assigned to AmocoCorp. [38], an Egan 4.5 single-screw extruder with seven temperature controlzones was used with a flat sheet die. The extruder was modified with a gas delivery system. Barrel set temperatures ranged from 540 to 520°F. Two dif-ferent concentrates containing PMDA and sodium carbonate, respectively, inPET carriers were fed through a side feed hopper. CO2 was injected into thefourth barrel segment, and foam was produced at about 600 lbs/hour. At

, the sheet density was about 30 pcf. Thermo-formed trays had very small amounts of extractable unreacted PMDA in therange of 30–40 ppm, based on the weight of the tray. By contrast, foam traysbelieved to be prepared from a polyester foaming process in which PMDA wasadded directly as a powder had up to sixthfold the extractable PMDA amount.

0.2% PMDA � 0.04% Na2CO3

PMDA � Na2CO3

(� 0.5 g/cc)


TABLE 12.4 Effects of Modifier and PBA Amount on Properties of Extruded Foamed PET Sheets [22].

TensileButane, Expansion Strength, Elongation Dynamic Modulus,

PET Type Additives wt% Ratio Cell Size kg/cm2 at Break, % Pa @ 150°C

#1, PMDA � 1.7 6 medium 63.6 116.6 107

Eastman Na2CO3

9902#2, Diglycidyl 1.7 6 medium 39.3 64.3Eastman terephthalate10388 � Na montanate#3, 0.9 3 medium 81.5 53.3 —Teijin Diglycidyl8580 terephthalate

PMDA �

4 � 106


When the levels of PMDA and sodium carbonate were increased to 0.3% and0.06%, respectively, the resultant extruded foam sheet had a density of 9 pcf,whereas thermoformed trays from the sheet had density of about 28 pcf.

In other publications by Eastman Chemical Co. describing methods toreduce extractables [20, 41], sheets with density of 0.26 g/cc at a thickness of45 mils and low crystallinity of 4.5% were produced by extruding PET in thepresence of a PP/PMDA concentrate, talc and 1,1-difluoroethane in a tandemline. Equipment was similar to that described in Reference [35]. Thermo-formed trays with crystallinities of 28% were subjected to a complete extrac-tion test protocol to evaluate for compliance with European Union and FDAguidelines for total migration, antimony migration, and PMDA migration intofood simulating solvents. Results indicated that the trays complied with alllimits and no migration of PMDA was detected in the extracts.

12.4 FOAMING WITH CHEMICAL BLOWING AGENTS

12.4.1 GENERAL

CBAs can be divided into exothermic and endothermic blowing agents. Ingeneral, CBAs may decompose over a broad temperature range. Exothermicchemical blowing agents include azodicarbonamide, (4,4)-oxy-bis(benzene-

TABLE 12.5 Properties of Extruded Low-Density Foamed PET Sheets [37, 52].

Hydrocarbon Hydrocarbon Inert Gas Property Blowing Agent Blowing Agent Blowing Agent

Thickness, mm 1 3 0.9Density, g/cc 0.3 0.3 0.4Crystallinity, % 10 — 10Tensile strength, 80/65 40/25 105/110kgf/cm2 MD/TDTensile strength, 85/75 25/25 —kgf/cm2

MD/TDElongation at break, 120/110 40/20 129/72% MD/TDElongation at break, 30/30 15/20 —%, MD/TDTear strength, 54/40 25/15 70/46kgf/cm2 MD/TDAver. Cell 0.3/0.34/0.07 — 0.2/0.23/0.05diameter, mmTD/TD/VD

(�20°C)

(�20°C)


sulfonyl hydrazide), p-toluenesulfonyl semicarbazide, and 5-phenyltetrazole.The most common CBA, azodicarbonamide, decomposes between 190°C and230°C and generates mostly nitrogen gas; the exothermic reaction can be cat-alyzed so that gases are produced at lower temperatures. This decompositionrate can be modeled using an Arrhenius-type equation. Decomposition prod-ucts of other exothermic blowing agents may include nitrogen, small amountsof carbon dioxide, carbon monoxide, ammonia, and miscellaneous organiccompounds.

Endothermic chemical blowing agents are usually blends of inorganic car-bonates and polycarbonic acids. The reaction product of these ingredients isprimarily carbon dioxide. The reaction temperature can be varied between150°C and 300°C by altering the chemistry of the system. The endothermicblowing agents yield, in general, lower quantities of gases than the exothermicones. In contrast to the decomposition products of exothermic CBAs, suchgases appear to be more soluble in the polymer. This results in lower levels ofdie pressure required for extrusion foaming with endothermic CBAs.

General advantages/characteristics of CBAs as compared to PBAs in extru-sion foaming are as follows:

(1) Some equipment modification required

(2) Suitable for high- and medium-density foams

(3) Broader operating window

(4) Finer cell sizes

Disadvantages of CBAs are as follows:

(1) Possible moisture as a by-product, particularly critical with hydrolyticallyunstable resins

(2) Changes of polymer rheology, difficulty of recycling nonconformingproducts or contamination due to unreacted CBA or solid residue from thereacted CBA

(3) Relatively higher cost versus most PBAs

12.4.2 EXTRUSION FOAMING OF PET

In contrast to other thermoplastic materials, e.g., PE, PP, PS, PVC, etc., ex-trusion foaming of PET using CBAs is still less advanced. PET homopolymer,being extremely moisture sensitive, requires chemical blowing agents that donot produce moisture as a reaction by-product and decompose in a controlledfashion at the high processing temperatures of PET. There exist several U.S.patents summarized in Reference [41] describing the use of CBAs for foamingPET resins or copolymers with most of the early work reported in the area ofinjection molding. The reference to polycarbonate (PC) resin as CBA for PETto produce relatively high-density foams is noteworthy [53]; PC may appar-


ently undergo an ester interchange reaction with PET with simultaneous de-composition to generate carbon dioxide. The sections below describe recentexperimental work on CBA foaming of thin PET sheeting for the productionby lamination of thicker panels to be evaluated for building applications.

12.4.2.1 Parameters Affecting PET Foaming—Laboratory Scale

Based on vendor’s information and following preliminary thermal analysis(DSC and TGA), three chemical blowing agents were selected (Table 12.6) ina recent work [6, 46]. The effectiveness of the blowing agents with respect toPET foaming was evaluated in two extruders: a 19 mm dia. single-screwBrabender extruder equipped with a 50-mm-wide ribbon die and a 63 mm dia.Welex coextrusion setup equipped with a 860 mm sheet die. PET resins withdifferent rheological characteristics (intrinsic viscosity, melt flow index as aviscosity indicator, and die swell as a melt elasticity indicator) were used. Theresins included a standard post-consumer grade and two recycled materialsmodified by reactive processing for increased melt strength (Table 12.7). The

TABLE 12.6 Materials and Concentrations Used In CBA Foaming [46].

CBA 1 CBA2 CBA3

Description Endothermic Exothermic Endothermic40% Masterbatch; Powder; 40% Masterbatch;2–5 phr 0.5–2 phr 1–5 phr

Decomposition 180–315 190–310 200–270Range by TGA, °CGrade/ Safoam RPC-40 Expandex 5PT HK40B (BoehringerSupplier (Reedy Intern.) (Uniroyal Chem.) Ingelheim)

(Reprinted from Reference [46]).


TABLE 12.7 Resins Used in CBA Foaming [46].

PET 1 PET 2 PET 3

Description Recycled post- Recycled post- Recycled post-consumer pellets consumer pellets consumer pellets

modified by reactive modified by reactiveprocessing (Pilot) processing (Pilot)

Nominal IV 0.7 0.87 1.2MFI 26.6 6.87 N/M(260°C/2.16 kg)Die Swell 1.29 2.66 N/M(270 s�1/260°C)


FIGURE 12.8 Foam density versus resin IV.

CBA was premixed with predried PET resin and fed into the hopper of the ex-truder. The extrudates produced in the 50 mm die were characterized fordensity and the results were fitted into a statistical model. In this case, the in-dependent variables were type of CBA, % CBA, melt temperature, and screwrpm. The dependent variables were die pressure and the density of foam.Results are shown in Figures 12.8–12.11 [6] and are summarized in Table 12.8[46]. As expected, the density was found to be a decreasing function of IV andincreasing function of melt temperature and screw rpm. The % CBA showed aminimum at approximately 1.5 wt%. CBA2 showed the most promise, fol-lowed by CBA1, followed by CBA3. In another publication [54], extrudedPET foams with densities above 0.6 g/cc and uniform and fine cellular struc-ture were produced with endothermic CBAs. Mechanical properties werefound to decrease linearly with decreasing foam density.

12.4.2.2 Parameters Affecting PET Foaming—Large Scale

A PCR PET resin (PET1) with nominal IV of 0.71 was chosen for the scale-up study in the Welex coextrusion line equipped with the 860 mm flat sheet die(Figures 12.12, 12.13). CBA2 and CBA1 were used in two different experi-ments. CBA2 was a non-free-flowing powder that was difficult to feed. At-tempts were made to meter-feed this powder using single- and twin-screw


FIGURE 12.10. Foam density versus CBA type.

FIGURE 12.9. Foam density versus extruder rpm.


powder feeders, including a flexible oscillating wall single-screw feeder,without much success. Consistent feed rate could not be achieved over a longperiod of time. Attempts were also made to precompound a masterbatch into ahigh-melt flow modified PE in a corotating twin-screw extruder with limitedsuccess.

Further experiments with the unmodified PET1 resin and the pelletizedmasterbatch CBA1 indicated that it was difficult to produce monolayer sheetwith reasonable density reduction in the large flat shet die, since the low melt


TABLE 12.8 Summary of CBA Foaming Runs [46].

• Satisfactory foams with densities 0.5–0.9 g/cc were possible at certainmaterial/process condition combinations.

• Average cell size was about 65 �m, but with a broad size distribution from about25 to 190 �m.

From statistical analysis:• Density decreases somewhat with increasing resin IV and die swell and appears

to increase with rpm.• Lower die temperatures appear to result in overall lower foam densities.• CBA 2 yields overall lower densities.• CBA concentrations in excess of about 1.5% do not result in any further density

reduction.

FIGURE 12.11 Foam density versus CBA concentration.


FIGURE 12.12 Schematic of coextrusion line.

FIGURE 12.13 Photograph of coextrusion line equipped with 30 in wide flat die. (Courtesy ofthe Polymer Processing Institute.)


strength of the resin caused escape and/or rapid collapse of the growingbubbles. Better results were obtained with monolayers containing chemicallymodified resins such as PET2 or PET3 at 10–15 phr as rheology modifiers, andABA structures where A was unmodified PET1 and B was PET1 chemicallymodified with a reactive polyethylene copolymer and foamed with 1.5%CBA1. Densities in all cases were relatively high, ranging between 0.8 and 1.1g/cc. For extruded sheets with crystallinity exceeding 10%, lamination tothicker panels about 1� thickness was assisted by incorporating a dry thin ad-hesive film within the layers. Additional crystallization during press or ovenlamination at about 150°C for few minutes resulted in samples with final crys-tallinities of 25–30%.

12.5 CONCLUDING REMARKS

PBA extrusion foaming of PET provides a cost-effective method to producelow-density rigid cellular structures that have some of the attributes of thesolid semicrystalline resin, particularly rigidity, high-temperature dimensionalstability, and recyclability. Although modification of existing sheet lines forgas injection may be costly, advantages of PBAs versus the expensive, spe-cialized CBAs may prove more cost effective. Most of the recent industrialR&D activities have focused in the extrusion forming of expanded CPET forthe food packaging industry in efforts to produce lightweight materials thatcould be more effective versus competitive products, including rigid and ex-panded polyolefins, aluminum foil, and paper /pulp products. The availabilityof extrusion foaming technologies employing environmentally friendly atmo-spheric gases as PBAs, combined with the recyclability of the formed contain-ers/trays may be considered as additional advantages for market penetration.Other markets under development are in the building/construction and trans-portation industries with expanded PET competing with other rigid polymericor nonpolymeric materials in structural sandwich panels or for insulation.

As with other extrusion foaming processes for semicrystalline materials, e.g.,PP, product attributes depend on various parameters including the following:

• obtaining materials with proper melt strength• selecting proper cell and crystal nucleators• obtaining optimum cell size and distribution and spherulitic size and

concentration• optimizing post-processing techniques, e.g., thermoforming

Existing technologies described in this chapter have attained these goals tovarious extents. However, improvements are still desirable and could lead tofurther market penetration. A better understanding of cell nucleation/growthand its differentiation from crystal nucleation/growth in crystallizable poly-


mers is essential. Such phenomena may occur concurrently at different stagesof the extrusion process, competing for the amount of amorphous phasepresent. In addition, extrusion by gas injection produces macrocellular foamswith properties not always adequate for a given application. Selection of gascell nucleators to control type, size, shape, and distribution of gas cellscoupled with the selection of the optimum PBA based on solubility and diffu-sivity measurements could lead to a better control of physical properties, par-ticularly toughness. If cell size reduction can be achieved with a concurrentcontrol of crystal size, impact strength of extrusion produced foams wouldgreatly benefit.

12.6 ACKNOWLEDGEMENTS

The authors wish to acknowledge the assistance of Dr. Victor Tan, Mr. DaleConti and Dr. Q. Zhang of the Polymer Processing Institute and Mr. G. Quintansand Mr. Y. Li of NJIT in several aspects of the experimental work reported inthis chapter. Sinco Engineering kindly supplied various pilot PET resins. Partialfinancial support was provided by the Multi-lifecycle Engineering ResearchCenter (MERC) of the NJ Institute of Technology (NJIT).

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Foam Extrusion Principles and Practice