influence of the thermomechanical history - purespeciﬁc volume of polymers inﬂuence of the...

Specific volume of polymers : influence of thethermomechanical historyCitation for published version (APA):van der Beek, M. H. E. (2005). Specific volume of polymers : influence of the thermomechanical history.Eindhoven: Technische Universiteit Eindhoven. https://doi.org/10.6100/IR590887

DOI:10.6100/IR590887

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https://doi.org/10.6100/IR590887

https://doi.org/10.6100/IR590887

https://research.tue.nl/en/publications/specific-volume-of-polymers--influence-of-the-thermomechanical-history(efe315d5-2543-4f9b-b740-e0d826e9dc7c).html

Specific volume of polymers

Influence of the thermomechanical history

CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN

Beek, Maurice H.E. van der

Specific volume of polymers : influence of the thermomechanical history/by Maurice H.E. van der Beek. - Eindhoven : Technische UniversiteitEindhoven, 2005.Proefschrift. – ISBN 90-386-2567-7NUR 971Subject headings: isotactic polypropylene / semi-crystalline polymers /specific volume / PVT behavior / cooling rate / pressure dependence /flow induced crystallization / dilatometry

Printed by Universiteitsdrukkerij TU Eindhoven, Eindhoven, The Netherlands.

Specific volume of polymers

Influence of the thermomechanical history

PROEFSCHRIFT

ter verkrijging van de graad van doctoraan de Technische Universiteit Eindhoven,

op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn,voor een commissie aangewezen door het College voor Promoties

in het openbaar te verdedigen opdinsdag 14 juni 2005 om 16.00 uur

door

Maurice Hubertus Elisabeth van der Beek

geboren te Roermond

Dit proefschrift is goedgekeurd door de promotoren:

prof.dr.ir. H.E.H. Meijerenprof.dr.ir. J.M.J. den Toonder

Copromotor:dr.ir. G.W.M. Peters

Veur mien maedje

Contents

1 Introduction 11.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Concentric cylinder dilatometer: design and testing 92.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Design and instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Comparison with confining fluid baseddilatometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5 Example: isotactic polypropylene . . . . . . . . . . . . . . . . . . . . . . 262.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.A Appendix: material properties . . . . . . . . . . . . . . . . . . . . . . . 30

3 The influence of cooling rate on specific volume 333.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2 Experimental part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Dilatometer experiments . . . . . . . . . . . . . . . . . . . . . . . . . 36X-ray analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Density measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Specific volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Crystalline morphology . . . . . . . . . . . . . . . . . . . . . . . . . . 43Modelling aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

vii

viii CONTENTS

3.A Appendix: specific volume of the melt . . . . . . . . . . . . . . . . . . . 58

4 The influence of shear flow on specific volume 614.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.2 Experimental part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Dilatometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Density gradient column . . . . . . . . . . . . . . . . . . . . . . . . . 64X-ray analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Scanning electron microscopy . . . . . . . . . . . . . . . . . . . . . . 65

4.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Specific volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Crystalline morphology . . . . . . . . . . . . . . . . . . . . . . . . . . 74


5 Classification of the influence of flow on specific volume: The Deborahnumber. 855.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Deborah number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Dimensionless transition temperature . . . . . . . . . . . . . . . . . . 88Dimensionless transition rate . . . . . . . . . . . . . . . . . . . . . . . 88

5.3 Experimental part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Crystalline morphology . . . . . . . . . . . . . . . . . . . . . . . . . . 90Specific volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94


6 Conclusions and recommendations 1016.1 Main conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1016.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Samenvatting 107

Dankwoord 111

Curriculum Vitae 113

Summary

Nowadays, semi-crystalline polymers are widely used in many product applica-tions that display high dimensional accuracy and stability. However, the relation-ship between processing conditions and the main property determining macroscopicshrinkage, i.e. specific volume, is still not understood in sufficient detail to predictthe resulting dimensions of a product dependent on the selected material and cho-sen processing conditions. In this thesis, the dependence of the specific volume ofcrystallizing polymers on the thermomechanical history as experienced during pro-cessing is investigated. Emphasis is placed on selecting and reaching those process-ing conditions that are relevant for industrial processing operations such as injectionmolding and extrusion. To extent the interpretation of the results obtained on the de-velopment of specific volume, structure properties of the resulting crystalline mor-phology are investigated using wide angle X-ray diffraction (WAXD) in combinationwith scanning electron microscopy (ESEM).

A custom designed dilatometer is presented in chapter 2, which is used to quanti-tatively analyze the dependence of specific volume on temperature (up to 260 C),cooling rate (up to 100 oC/s), pressure (up to 100 MPa), and shear rate (up to 80 1/s).The dilatometer is based on the principle of confined compression, using annularshaped samples with a radial thickness of 0.5 mm. To quantify the measurement er-ror arising from friction forces between the solidifying sample and dilatometer walls,a comparison is made with measurements performed on a dilatometer based on theprinciple of confining fluid (Gnomix). Measurements performed in the absence offlow, at isobaric conditions, and at a relatively low cooling rate of about 4-5 oC/minagree quite well with respect to the specific volume in the melt, temperature at whichthe transition to the semi-crystalline state starts, and the specific volume of the solidstate. Detailed analysis shows a relative difference in specific volume of the melt of0.1 - 0.4 %. An identical relative difference is assumed for specific volume measuredduring the first part of crystallization, since the ratio of shear and bulk modulus isstill small and the influence of friction forces and loss of hydrostatic pressure can beneglected. The relative difference in the specific volume of the solid state ranges from0.1− 0.2%. However, especially for higher cooling rates, this part of the measuredspecific volume curve should be taken as qualitative rather than quantitative.

ix

x SUMMARY

The influence of cooling rate on the evolution of specific volume and the resultingcrystalline morphology of an isotactic polypropylene is investigated in chapter 3.Experiments performed at cooling rates ranging from 0.1 to 35 oC/s, and elevatedpressures ranging from 20 to 60 MPa show a profound influence of cooling rate onthe transition temperature, i.e. the temperature at which the transition from the meltto the semi-crystalline state starts, and on the rate of transition. With increasingcooling rate and constant pressure, the transition temperature shifts towards lowertemperatures and the transition itself is less distinct and more wide spread. Addi-tionally, an increasing cooling rate causes the final specific volume to increase, whichagrees with a decrease in the degree of crystallinity determined from WAXD anal-ysis. For the relatively small pressure range that was experimentally accessible, acombined influence of pressure and cooling rate on the specific volume or crystallinemorphology was not found. Experimental validation of numerical predictions of theevolution of specific volume showed at first large deviations in the calculated startand rate of the transition. These deviations increase with increasing cooling rate.Deviations in the rate of transition could partly be explained from small variationsin model parameters, and can be justified from possible inaccuracies in the experi-mental characterization of important input parameters, i.e. the spherulitic growthrate G(T, p) and the number of nuclei per unit volume N(T, p), or from determiningmodel parameters to describe these quantities numerically. Especially in the pre-diction during fast cooling, G(T, p) and N(T, p) should be characterized for a suf-ficiently large temperature range, including temperatures typically lower than thetemperature where the maximum in G(T, p) occurs. Deviations in predicted tran-sition temperature are however quite unexplained and could only be improved byintroducing an unrealistic larger number of nuclei than determined experimentallyat relatively high temperatures. This is subject to future investigation.

The influence of shear flow on the evolution of the specific volume is investigatedin chapter 4. The combined influence of shear rate, pressure and temperature dur-ing flow is investigated at non-isothermal conditions using two grades of isotacticpolypropylene with different weight averaged molar mass (Mw). In general, shearflow has a pronounced effect on the evolution of specific volume. The temperaturemarking the transition in specific volume and the rate of transition are affected. Theinfluence of flow increases with increasing shear rate, increasing pressure, decreasingtemperature at which flow is applied, and higher Mw. Although the degree of ori-entation and the overall structure of the resulting crystalline morphology are greatlyaffected by the flow, the resulting specific volume and degree of crystallinity are onlymarginally affected by the processing conditions employed. If shear flow is appliedat a temperature near the material’s equilibrium melting temperature T0

m, i.e. at lowundercooling, dependent on material and applied shear rate remelting of flow in-duced crystalline structures and relaxation of molecular orientation is able to fullyerase the effect of flow. With increasing Mw, the effect of flow applied at low under-cooling is prevailed longer. Although not investigated in this study, we think that anincreased cooling rate (i.e. less time to remelt flow induced structures) would alsoenlarge the resulting effect on the evolution of specific volume when applied at low

SUMMARY xi

undercooling.

In chapter 5, the use of the dimensionless Deborah number is investigated to analyzeand classify the influence of shear flow on the specific volume and resulting crys-talline morphology. Classification of the influence of flow on the orientation of theresulting crystalline morphology as visualized by WAXD could be performed if flowwas applied at relatively large undercooling. With increasing Deborah number, theorientation of crystals increases and the classification of the flow strength resultingin a spherulitic, row nucleated, or shish-kebab morphology is possible. However, incase flow was applied at low undercooling, the influence of remelting and relaxationof molecular orientation yields the Deborah number of little use. The influence offlow could be erased totally, even when strong flow is applied, i.e. high Deborahnumbers. For large undercooling, remelting and relaxation has little effect on thedevelopment of the flow-induced crystalline morphology as was already observedby others. These conclusions also hold for the classification of flow on the evolutionof specific volume. If flow is applied at large undercooling, Deborah numbers Des(based on the process of chain retraction) or Derep (based on the process of reptationof chains) can equally well be used to classify the influence of flow on the evolutionof specific volume, e.g. characterized by the dimensionless transition temperature θcand dimensionless rate of transition λ. Even relatively large differences in coolingrate have little effect on the classification of the influence of flow on the evolution ofspecific volume, when applied at large undercooling.

Finally, in chapter 6 the main conclusions of this thesis are outlined together withrecommendations for future research.

xii SUMMARY

CHAPTER ONE

Introduction

1.1 Context

Polymers are widely used in many products that require accurate dimensions, eitherbecause of their functionality or for esthetic reasons. Examples range from mediafor data storage such as CD’s and DVD’s, to the housing of a cellular phone, to carbumpers. A new and growing field of application for polymers in which high dimen-sional accuracy is required is that of micro systems. Typically, the polymer compo-nents used in these systems have features with dimensions in the sub-millimeter tomicrometer range, or even overall dimensions in the sub-millimeter range (see figure1.1), demanding dimensional accuracy in the order of micrometers.

However, especially for crystallizing polymers, it is still impossible to predict thefinal dimensions of a product in detail based on the polymer used, the design ofthe product, and the processing conditions applied. One of the main properties thatdetermine the final dimensions of a product is the specific volume of the polymer,and its evolution during processing. Like any other physical property of crystalliz-ing polymers, it is to a large extend determined by the crystallization process andcrystalline morphology that results after processing. This thesis is a contribution tounderstanding the specific volume and the related crystalline morphology of semi-crystalline polymers, that depends on the thermomechanical history experienced,and on the relevant molecular parameters.

1.2 Background

Injection molding is the most common technique for the mass production of complexshaped products that require accurate dimensions. Typically, the polymer is plasti-cized by being heated to elevated temperatures, and injected into a mold where the

1

2 1 INTRODUCTION

( a)

( b)

Figure 1.1: (a) Micromechanical component (gearbox) made from Polyoxymethylene,(b) gearbox and individual components compared to a needle [1].

molten polymer acquires the product shape. Subsequently, mold and polymer arecooled to room temperature, during which the polymer solidifies and stabilization ofthe product shape occurs. In practice the dimensions of the solidified polymer differfrom the mold dimensions due to shrinkage. This is the result of several phenom-ena that cause a decrease in the material’s volume during cooling to room tempera-ture such as thermal contraction, physical phase changes (e.g. crystallization, vitri-fication), and sometimes chemical reactions. The resulting change in density of thepolymer in the mold, is captured by the specific volume, which is expressed in m3/kg.Quantitatively measuring the evolution of the specific volume as experienced duringprocessing, and understanding its dependence on molecular and processing param-eters, is an important prerequisite in predicting the shrinkage behavior of polymers.Quantitative prediction of product shrinkage in its turn will strongly contribute totime and costs reduction of process and mold optimizations and time to market ofhigh precision polymer products in general.

Commonly, the specific volume of polymers is measured as a function of pressureand temperature using the technique of dilatometry. It is therefore often referred toas Pressure-Volume-Temperature behavior or PVT-behavior. Figure 1.2 is reproducedfrom Zoller and Walsh [2] and shows this behavior for an amorphous and a semi-crystalline polymer. For crystallizing polymers, the dependence of the specific vol-ume on processing conditions is however complex. This is because the crystallinitydetermines the specific volume to a large extend, and this crystallinity strongly de-pends on the thermal history [3–7] and the experienced flow [8–16]. This has twomajor implications. First, in contrast with characterization of specific volume as afunction of pressure and temperature only, additional parameters such as coolingrate and flow (e.g. deformation rate, total deformation, viscoelastic stress, amountof experienced mechanical work, etc.) should be taken into account to adequatelycharacterize a material. Secondly, if specific volume data are to be used for (numeri-cal) analysis of processing operations, e.g. injection molding or extrusion, the poly-

1.2 BACKGROUND 3

( a) ( b)

Figure 1.2: The typical PVT-behavior of an amorphous (a) and semi-crystalline poly-mer (b), measured using a bellows type dilatometer operating in isother-mal mode. Data are reproduced from [2].

mer should be characterized at conditions as (locally) experienced during processing.This means that characterization should include elevated pressures of O

(102) MPa

in combination with cooling rates of O(102) C/s and shear or elongation rates of

O(102 − 104) 1/s. Dilatometry is still the most important technique to determine the

evolution of specific volume as a function of processing conditions. However, com-mercially available dilatometers (Gnomix, PVT100) are not sufficiently equipped tosubject polymers to cooling rates relevant for industrial processes or to impose flow.This necessitates the development of new experimental methods.

The constitutive modelling of the specific volume of crystallizing polymers has seenimportant developments the last decade [17–19]. In contrast to early constitutivemodels such as developed by Tait [20] and Spencer and Gilmore [21], present modelscombine an (empirical) description of the specific volume of the amorphous and crys-talline phases with a description of the evolution of the degree of crystallinity. Exam-ples include the Scheider rate equations [22] for non-isothermal quiescent crystalliza-tion and the (modified) Eder rate equations [23, 24] for flow-induced crystallization.These models are in principle able to predict the evolution of the specific volumeof crystallizing polymers as a function of the complete thermomechanical historyexperienced during processing. Moreover, the differential form of these rate equa-tions makes numerical implementation easy and, next to evolution of crystallinity,provides additional information about the crystalline morphology. Unfortunately,further development of the models is hampered by the general lack of experimentaldata necessary for validation purposes.

4 1 INTRODUCTION

1.3 Scope

An experimental study is performed to measure the specific volume and the relatedcrystalline morphology of semi-crystalline polymers, dependent on the experiencedprocessing conditions and relevant molecular parameters. Dilatometry is chosen asthe main experimental technique to study specific volume as a function of temper-ature, pressure level, cooling rate, and shear rate. This technique provides a directway of measuring the evolution of the specific volume, serving for the validationof constitutive equations and fitting of model parameters. A density gradient col-umn (DGC) is used to compare with the dilatometer experiments. Besides, the crys-talline morphology of samples is analyzed ex situ using Wide Angle X-ray Diffrac-tion (WAXD) and Scanning Electron Microscopy (ESEM). The modelling part of thiswork concerns the validation of existing constitutive equations for specific volume;new constitutive models will not be introduced. The materials investigated are twogrades of isotactic polypropylene (iPP), differing in molar mass distribution. Inno-vations with respect to other studies are: a) design and building of a new type ofdilatometer capable of measuring the influence of temperature, pressure, coolingrate, and shear rate on the specific volume of polymers, b) measuring the evolu-tion of specific volume in an extended range of cooling rates and elevated pressurerelevant to industrial polymer processing operations, c) measuring the influence ofrelatively high shear rates on the evolution of specific volume, d) the combinationof specific volume measurements with characterization (WAXD) and visualization(ESEM) of the resulting crystalline morphology.

1.4 Outline

In chapter 2, the design and first testing of the dilatometer is presented. Thisdilatometer enables the analysis of the temperature evolution of specific volume as afunction of pressure (up to 100 MPa), cooling rate (up to 100 C/s), and shear rate (upto 80 1/s). Chapter 3 discusses in depth the influence of cooling rate on the specificvolume of iPP, using experimental data obtained via dilatometry performed at con-stant elevated pressures and using the results of the density gradient column experi-ments. The crystalline morphology resulting from processing conditions is analyzedusing wide angle X-ray diffraction (WAXD). Numerical predictions of the specificvolume are validated experimentally at various cooling rates and critical model pa-rameters are identified. Chapter 4 discusses the influence of shear rate on the specificvolume of two grades of iPP, differing in molar mass distribution. Combined effectsof shear rate and pressure level, and shear rate and temperature at which the shearflow is applied are investigated per material grade. Wide angle X-ray diffraction(WAXD) and scanning electron microscopy (ESEM) are used to investigate the crys-talline morphology resulting from the various flow conditions. Chapter 5 deals withthe use of the dimensionless Deborah number to quantify and compare the strengthof flow applied at various processing conditions. Furthermore, the use of the Deborah

1.4 OUTLINE 5

number as an analytical tool is investigated, to help analyze and compare the influ-ence of flow on the evolution of specific volume for various processing conditions.Finally, chapter 6 summarizes the most important conclusions and gives recommen-dations for future research.

6 1 INTRODUCTION

References

[1] Homepage Institut für Mikrotechnik Mainz (IMM), www.imm-mainz.de.[2] Zoller, P., Walsh, D.J. Standard Pressure-Volume-Temperature Data for Polymers.

Technomic, (1995).[3] Piccarolo, S. Morphological changes in isotactic Polypropylene as a function of

cooling rate. Journal of Macromolecular Science - Phys., B31(4):501-511, (1992).[4] Zuidema, H., Peters, G.W.M., Meijer, H.E.H. Influence of cooling rate on PVT-

data of semicrystalline polymers. Journal of Applied Polymer Science, 82(5):1170-1186, (2001).

[5] Brucato, V., Piccarolo, S., La Carrubba, V. An experimental methodology tostudy polymer crystallization under processing conditions. The influence ofhigh cooling rates. Chemical Engineering Science, 57:4129-4143, (2002).

[6] La Carrubba, V., Brucato, V., Piccarolo, S. Phenomenological approach to com-pare the crystallization kinetics of isotactic Polypropylene and Polyamide-6under pressure. Journal of Polymer Science: Part B: Polymer Physics, 40:153-175,(2002).

[7] Pantani, R., Titomanlio, G. Effect of pressure and temperature history on volumerelaxation of amorphous Polystyrene. Journal of Polymer Science: Part B: PolymerPhysics, 41:1526-1537, (2003).

[8] Alfonso, G.C., Verdona, M.P., Wasiak, A. Crystallization kinetics of orientedpoly(ethylene terephthalate) from the glassy state. Polymer, 19:711-716, (1978).

[9] Vleeshouwers, S., Meijer, H.E.H. A rheological study of shear induced crystal-lization. Rheologica Acta, 35:391-399, (1996).

[10] Keller, A., Kolnaar, J.W.H. Flow-induced orientation and structure formation, in:Processing of Polymers, Meijer, H.E.H. (Ed.), VCH: New York, vol. 18, p.189-268,(1997).

[11] Somani, R.H., Hsiao, B.S., Nogales, A. Structure development during shearflow-induced crystallization of i-PP: In situ small angle X-ray scattering study.Macromolecules, 33:9385-9394, (2000).

[12] Wang, Z.G., Wang, X.H., Hsiao, B.S., Phillips, R.A., Medellin-Rodriquez, F.J.,Srinivas, S., Wang, H., Han, C.C. Structure and morphology development insyndiotactic Polypropylene during isothermal crystallization and subsequentmelting. Journal of Polymer Science, Part B: Polymer Physics, 39:2982-2995, (2001).

[13] Koscher, E., Fulchiron, R. Influence of shear on Polypropylene crystallization:morphology development and kinetics. Polymer, 43:6931-6942, (2002).

[14] Acierno, S., Palomba, B., Winter, H.H., Grizutti, N. Effect of molecular weighton the flow-induced crystallization of isotactic Poly(1-butene). Rheologica Acta,42:243-250, (2003).

[15] Swartjes, F.H.M., Peters, G.W.M., Rastogi, S., Meijer, H.E.H. Stress inducedcrystallization in elongational flow. International Polymer Processing, 18(1):53-66,(2003).

REFERENCES 7

[16] Watanabe, K., Suzuki, T., Masubuchi, Y., Taniguchi, T., Takimoto, J., Koyama, K.Crystallization kinetics of Polypropylene under high pressure and steady shearflow. Polymer, 44:5843-5849, (2003).

[17] Hieber, C.A. Modelling the PVT behavior of isotactic Polypropylene. Interna-tional Polymer Processing, 12(3):249-256, (1997).

[18] Zuidema, H., Peters, G.W.M., Meijer, H.E.H. Development and validation ofa recoverable strain based model for flow induced crystallization of polymers.Macromolecular Theory and Simulation, 10(5):447-460, (2001).

[19] Han, S., Wang, K.K. Use of the fast-cool PVT data for shrinkage analysis in in-jection molding. International Polymer Processing, 17(1):67-75, (2002).

[20] Tait, P.G. Physics and Chemistry of the Voyage of H.M.S. Challenger. UniversityPress, Cambridge, (1888).

[21] Spencer, R.S., Gilmore, G.D. Equation of state for high polymers. Journal of Ap-plied Physics, 21:523-526, (1950).

[22] Schneider, W., Köppl, A., Berger, J. Non-isothermal crystallization. Crystalliza-tion of polymers. International Polymer Processing, 2(3):151-154, (1988).

[23] Eder, G., Janescitz-Kriegl, H., Liedauer, S. Crystallization processes in quiescentand moving polymer melts under heat transfer conditions. Progress in PolymerScience, 15:629-714, (1990)

[24] Zuidema, H. Flow Induced Crystallization, PhD thesis Eindhoven University ofTechnology (2000).

’Design A’

CHAPTER TWO

Concentric cylinder dilatometer:design and testing 1

We developed a dilatometer to investigate the specific volume of polymersas a function of pressure (up to 100 MPa), temperature (up to 260 oC), cool-ing rate (up to 100 oC/s), and shear rate (up to 80 1/s). The dilatometer isbased on the principle of confined compression and comprises of a pressurecell used in combination with a tensile testing machine with rotation capa-bility. The design of the pressure cell is a mixture of a traditional ’piston-dietype’ dilatometer and a Couette rheometer, i.e. piston and die make up an an-nular shaped sample spacing. Specific volume measurements at low coolingrate using an isotactic polypropylene (iPP) are compared with measurementsperformed using a commercial bellows type dilatometer, showing relativedifferences in the range of 0.1-0.4 %. Finally, results are presented showinga profound influence of cooling rate and melt shearing on the evolution ofspecific volume.

2.1 Introduction

Dilatometry is the most common technique to measure the bulk specific volume ofpolymers, both in the melt and solid state. Two measuring principles can be dis-tinguished. The first is the principle of confining fluid. Here the polymer is put intoa rigid sample chamber where it is submerged into a fluid, to which the polymermust be inert. Usually mercury or silicon oil are used for this purpose. The sam-ple chamber is sealed off by a flexible wall or bellows for: a) applying hydrostaticpressure to fluid and polymer by reduction of the sample chamber volume, b) sens-

1Reproduced in part from: Van der Beek, M.H.E., Peters, G.W.M., Meijer, H.E.H. A dilatometer tomeasure the influence of cooling rate and melt shearing on specific volume. International PolymerProcessing, XX(2), (2005).

9

10 2 CONCENTRIC CYLINDER DILATOMETER

Reference Pmax Tmax¦Tmax ε 4νmin

[MPa] [oC] [oC/s] [%] [cc/g][1] 200 250 - 3 -[2] 200 200 0.0056 0.04 0.0002[3] 220 350 - - 0.0015[4] 300 55 - 0.1 0.002[5] 500 270 - - -

Table 2.1: Characteristic processing conditions (Pmax, Tmax, cooling rate), accuracy (ε),and resolution (4νmin) for conventional CF-dilatometers.

ing the cumulative volume change of fluid and polymer. Dilatometers based on thisprinciple will be referred to as CF-dilatometers [1–8]. The advantage of this principleis the ability to apply a true hydrostatic pressure to the polymer, both in melt andsolid state. The disadvantage is that the volumetric changes measured are not thatof the polymeric sample only. Points of concern are sealing of the pressurized fluidand (chemical)reactions occurring between polymer and fluid. The second principleis called confined compression. Here the polymer is enclosed in a rigid cylinder. Apiston, closely fitting into the cylinder, is used both to pressurize the polymer and tomeasure volumetric changes. Dilatometers based on this principle will be referredto as PD-dilatometers (Piston-Die dilatometers) [9–15]. The advantage of this princi-ple is the simplicity in design that can be achieved. A disadvantage is that frictionalforces can arise between the polymer and cylinder wall leading to loss of hydrostaticpressure in the sample in its solid state [3, 16]. A point of concern is the reductionof frictional forces by applying an anti-friction coating or lubricant, which should benon-reactive with the polymer.

Tables 2.1 and 2.2 list the characteristics of just a limited number of CF and PD typedilatometers reported in literature. The dilatometers listed here are referred to as’conventional’ because specific volume is measured only as a function of pressureand temperature. Dependent on design, elevated pressures up to 870 MPa and tem-peratures up to 370 oC can be achieved. Relative errors in measured specific vol-ume are reported ranging from 0.04 to 1.0 % with the lower values reported forCF-dilatometers. The study of Luyé et al. [12] listed in table 2.2 is an example ofthe dilatometer originally developed by Menges et al. [14] and until recently madecommercially available by SWO Polymertechnik GmbH (Krefeld, Germany). In theoriginal work of Menges et al. there is no mentioning of characteristics or accuracy ofthe method. Typically, both types of conventional dilatometers do not accommodateto analyze specific volume as a function of cooling rate or deformation (e.g. shear,extension).

Dilatometers to analyze the influence of cooling rate on specific volume are reportedby Zuidema et al. [8] and Chakravorty [15], see table 2.3. Zuidema et al. used aCF-dilatometer, analyzing the influence of cooling rate as high as 54.2 oC/s on the

2.1 INTRODUCTION 11

Reference Pmax Tmax¦Tmax ε 4νmin

[MPa] [oC] [oC/s] [%] [cc/g][9] 500 300 - 0.1 - 0.2 0.008

[10] 870 370 - ≤ 1.0 -[11] 180 350 - 0.5 -[12] 120 240 0.5 ≤ 0.8 -

Table 2.2: As table 2.1 now for PD-dilatometers.

specific volume of isotactic polypropylene (iPP). Unfortunately, a maximum pressureof only 17.7 MPa could be reached. Chakravorty used a PD-dilatometer reaching amaximum cooling rate of 2.5 oC/s in combination with a maximum pressure of 40MPa. Both authors do not report on the accuracy or resolution of the dilatometers.Also Bhatt and McCarthy [17] developed a dilatometer to study the influence of cool-ing rate but failed to mention any dilatometer characteristics.

Dilatometers to study the influence of deformation, i.e. shear and shear rate, onspecific volume are reported by Fritzsche and Price [13], Pixa et al. [6], Duran andMcKenna [7], and Watanabe et al. [18] (see table 2.4). Fritzsche and Price developeda PD-dilatometer with an annular sample chamber. This mixture in design betweena conventional PD-dilatometer and a Couette rheometer was used to study the in-fluence of steady shear on the crystallization kinetics of several polyethylene oxides(PEO). Unfortunately, the specific volume data used to derive the evolution of crys-tallinity as a function of shear rate and shear are not reported. Pixa et al. and Duranand McKenna developed a so called torsional dilatometer to study the effect of stepshear, and subsequent stress relaxation, on the specific volume of PVC and epoxyresins in the solid state. The design of these dilatometers is dedicated to the appli-cation of solid state samples and not suited for analyzing the influence of processingconditions on specific volume such as encountered in injection molding or extrusion.All these experiments were performed at ambient pressure and the influence of cool-ing rate was not studied. Only Watanabe et al. investigated the influence of shearflow on the evolution of crystallinity, derived from specific volume, at elevated pres-sures but isothermal conditions. They modified a standard PD-dilatometer (ToyoSeiki Seisaku-sho, Ltd.) such that samples could be subjected to steady shear flowusing a plate-plate geometry. However, applied shear rates are relatively low to amaximum of 0.5 1/s and the plate-plate geometry is not very well suited to apply ahomogenous deformation to the sample.

If specific volume data are to be used to gain better understanding of what is happen-ing during industrial processing of polymers or as input for constitutive modelingused in simulation software, it is necessary to measure specific volume at conditionscomparable to industrial processing conditions. Dilatometry is one of the main tech-niques available to achieve this. However, there is a general lack of suitable dilatome-ters able to measure specific volume as a function of both thermal and mechanical


Reference Dilatometer Pmax Tmax¦T ε

Type [MPa] [oC] [oC/s] [%][8] CF 17.7 180 0.21 - 54.2 -

[15] PD 40 220 0.5 - 2.5 -

Table 2.3: Characteristic processing conditions (Pmax, Tmax, cooling rate), and accu-racy (ε) for dilatometers used to analyze the influence of cooling rate onspecific volume.

Reference Dilatometer Pmax Tmax¦γmax γmax ε

Type [MPa] [oC] [1/s] [−] [%][6] CF 0.1 0.1 0.1 0.15 0.001[7] CF 0.1 60 0.12 0.15 0.0025

[13] PD 0.1 95 168 - -[18] PD 20 200 0.5 450 -

Table 2.4: Characteristic processing conditions (Pmax, Tmax, maximum shear rate,γmax) and accuracy (ε) of dilatometers used to analyze the influence of de-formation on specific volume.

history. In this chapter, the design and performance of a dilatometer based on theprinciple of confined compression is presented with the ability to measure specificvolume as a function of elevated pressure, temperature, cooling rate, and shear flowin the range of processing conditions as found in injection molding or extrusion. Themain goal is not to reach the maximum accuracy possible but rather the ability toanalyze specific volume for this combination of processing conditions.

2.2 Design and instrumentation

In order to measure specific volume at processing conditions as found in injectionmolding or extrusion, a dilatometer should allow for elevated pressures of O(102)MPa, temperatures of O(2− 3 · 102) oC, cooling rates of O(102) oC/s, and shear orelongation rates of O(102 − 104) 1/s. Incorporating all these functional demandsinto one dilatometer is a challenging task. The principle of piston-die is chosen asa basis for the dilatometer because of the relative simplicity in design that can bereached. The design of piston and die is chosen such that an annular shaped samplespacing is created, similar to dilatometers developed by Fritzsche and Price [13] andChakravorty [15]. This particular sample shape is preferred for two reasons. First,since polymers are bad heat conductors, one of the sample dimensions has to besufficiently small to enable rapid cooling without introducing thermal gradients [12,

2.2 DESIGN AND INSTRUMENTATION 13

19]. An annular sample shape has the advantage that the radial thickness can bechosen small while independently the height of the sample can be chosen such toguarantee enough sample volume necessary for a good signal to noise ratio. Based ona heat conduction analysis, the maximum allowable sample thickness is determinedto be of O(10−4) m in case a cooling rate of O(102) oC/s is applied and homogeneouscooling is enforced. Secondly, similar to a Couette rheometer, an annular sample caneasily be subjected to drag flow by rotating the outer wall of the sample spacingwith respect to the inner. The dimensions of the annulus and material propertiesof the sample determine the shear rate that can be reached dependent on speed ofrotation [20]. Finally, a Couette geometry allows for ex situ structure analysis (e.g.via SAXS, WAXS) given the relatively uniform structure over the thickness.

The assembled piston and die make up a pressure cell that is used in combinationwith a hydraulically operating tensile testing machine (MTS 858 Mini Bionix) toform the dilatometer. Figure 2.1 shows a schematic drawing of the pressure cell asmounted to the tensile testing machine. Figure 2.2 shows the individual componentsand the polymer sample used. Important features of the tensile testing machine areits ability to subject samples simultaneously to compressive force and angular rota-tion while measuring axial displacement, angular displacement, and axial force. Theadvantage of this combination is that only the fairly simple pressure cell is customdesigned while the tensile testing machine incorporates already the necessary actu-ators, instrumentation, and provides a platform with a stiff frame for mounting thepressure cell. This last feature is not a trivial one. Since the axial displacement is ameasure for the volume of the sample, deformation of the frame due to mechanicalloading introduces errors and should be minimized. The axial displacement is mea-sured by a linear variable differential transformer (LVDT), and the angular rotation,applied to the die to shear the sample, is measured with an angular differential trans-former (ADT). The pressure cell can also be mounted on a more conventional tensiletesting machine without the ability of applying angular rotation. In that case, therotation should be realized in a different way, e.g. manually or by using an externaldevice.

The pressure cell has a height of approximately 110 mm and outer diameter of 60mm. The piston (A), see figure 2.1, is made from tungsten carbide for optimal ther-mal and mechanical properties (for detailed material properties see Appendix 2.A).It has an outer diameter of 22.0 mm, respectively 21.0 mm at the sample spacing,and is hollow with an inner diameter of 12.0 mm to enable fast cooling from theinside via a nozzle. The die (B) is constructed from three concentric cylinder parts(not shown). The most inner cylinder has an inner diameter identical to the outerdiameter of the piston, 22.0 mm, respectively 21.0 mm. It is also made from the sametungsten carbide as the piston. This part of the die and the piston fit together closelywith a spacing of about 1 µm and, when assembled, form an annular sample spacing(C) with a radial thickness of 0.5 mm. The two outer parts of the die are made fromstainless steel and contain 22 cooling channels with a diameter of 2.0 mm. Becauseof differences in thermal expansion between the various parts of the die, the individ-ual parts are held together between two plates using tensile rods (see figure 2.2b).


Load Cell

(0 - 15 kN)

Linear actuator

& LVDT

Rotary actuator

& ADT

ressure Cell

Load Cell

Ωω

F

A

B

CD

E

F

G

H

Figure 2.1: Schematic representation of the tensile testing machine with instrumen-tation (top) and a cross section of the pressure cell (bottom). A: piston,B: die, C: sample, D: thermocouple locations, E: PTFE seal, F: electricalheater, G: ceramic insulator, H: water cooled interface. Arrows indicateflow of cooling medium.


( a) ( b)

( c) ( d)

Figure 2.2: (a) piston with interface, (b) die with thermocouples, (c) annular samplewith PTFE sealing, (d) drawing of piston-die assembly.


For heating purposes, the die is equipped with an electrical band heater (Watlow,750 W) controlled by a HASCO heater unit (F). Since the dilatometer is only used inthe so called isobaric-cooling mode, see section 2.3, accuracy of temperature controlis not critical. The temperature of the sample is sensed with custom made K-typethermocouples having a thread diameter of 0.1 mm for fast thermal response. Tem-perature readings (D) are taken at three locations in the die (outer sample surface)and three locations in the piston (inner sample surface). The locations correspondto top, middle, and bottom of the sample. The distance between temperature read-ings and actual sample surface is about 0.5 mm. Because the temperatures are notrecorded inside the polymeric sample, a correction has to be applied. The tempera-ture of the sample is calculated using the energy balance equation and the heat con-ductive properties of tungsten carbide. To prevent polymeric material from leakingduring experiments at high pressure and temperature, the sample spacing is sealedwith PTFE rings (E) with a height of 2.0 mm. The interfaces (H) between pressure celland tensile testing machine are actively cooled to prevent the machine from warmingduring experiments at elevated temperature. Both interfaces are made of aluminiumand are continuously cooled using tap water. To apply rotation to the pressure cell,the upper interface is connected to the tensile testing machine via a semi-permanentconstruction shown in figure 2.3. Stainless steel rods at the sides of the interface con-nect with ’fork-like’ constructions of component X. The latter is permanently screwedto the tensile testing machine. For additional thermal insulation, ceramic rings (G)made of Al2O3 are placed between the aluminium interfaces and piston and die.

A schematic drawing of the pressure cell and cooling system is shown in figure 2.4.The flow rates of cooling medium through piston and die can be adjusted indepen-dently to improve control over homogeneity of sample cooling. Variation in flowrate and type of cooling medium (i.e. water, pressurized air) determines the effec-tive cooling rate of the sample. Flow controllers (Kytölä Oy, 10 l/ min) are used incase water is used as cooling medium. In case of pressurized air, the flow rate isadjusted by a pressure control. The use of electromagnetic valves (ASCO, 1/4”, NC,maximum pressure 13 bar) which are situated as close as possible to the pressure cellenable quick cooling response. The piston is cooled from the inside using a nozzleconstruction. The cooling medium enters through three inlets, located at an angleof 120 with respect to each other. The die has two inlets for the cooling medium,each one distributing the cooling medium over half of the 22 cooling channels. Asdepicted in figure 2.4 where only a few of the 22 channels are shown. The flow di-rection per cooling channel is chosen such to minimize cooling gradients in the axialdirection. The pressure cell is connected to the cooling system using fast connectors(Staubly) for easy assembly.

The characteristics of the tensile testing machine instrumentation and custom madethermocouples are listed in table 2.5. Accuracy of instrumentation is given for typicalexperimental range, i.e. −2 ≤ X ≤ 2 mm, −135 ≤ α ≤ 135 deg, and 0 ≤ F ≤ −3300N. Note: X is the absolute position of the LVDT’s core with respect to its coil, deter-mining the accuracy of the measured relative displacement 4x. For data acquisitionpurposes a PC with I/O board (National Instruments, PCI-6031E, 32 channels, 16 bit)


( a) ( b)

( c)

Figure 2.3: (a) interface, (b) component X, (c) assembly.


Drain

Cooling

medium

= Electromagnetic Valve

Flow controller

Cooling

medium

Figure 2.4: Schematic representation of the cooling system and detail of flow throughthe cooling channels of the die.

2.3 EXPERIMENTAL 19

Property Instrumentation Supplier Type Accuracy

4x LVDT TransTek series 210 (long stroke) ±5.0E− 6 [m]α ADT TransTek model 605 (300 [deg]) ±1.4 [deg]F FT MTS 662.20D-04/15 (SG) ±10 [N]T TC custom K-type ±1.7 [oC]

Table 2.5: Characteristics of used instrumentation. 4x = axial displacement, α = an-gle of rotation, F = axial force, T = temperature, FT = force transducer, TC= thermocouple, SG = strain gage type.

and shielded BNC connector block (National Instruments, SCB-100) is used.

2.3 Experimental

Dilatometers can be used in several modes of operation: isothermal compressiontaken in order of increasing temperature, isothermal compression taken in order ofdecreasing temperature, isobaric heating, and isobaric cooling [12]. For isobaric cool-ing, the polymeric sample is first heated above its melting temperature, next the sam-ple is pressurized, and finally the volume of the sample is measured while coolingto ambient conditions during which the pressure is maintained constant. If specificvolume data are to be used in the analysis of industrial processes such as injectionmolding, the isobaric cooling mode should be applied [12]. The main reason for thisis that during injection molding, the material transitions observed are crystallizationor vitrification. Contrary to for example isobaric heating where the transition ob-served is melting. Secondly, when heating the polymer above its melting point for asufficiently long time, the thermomechanical history of the material is erased. Thisrules out any influence of the sample preparation procedure on the measured spe-cific volume. Furthermore, in case of PD-dilatometers, melting of the sample prior tothe actual experiment ensures that the polymer completely fills the sample spacing.This is a necessary prerequisite for this type of dilatometers. Finally, Leute et al. [21]measured large deviations from hydrostatic pressure inside a polypropylene sampleduring isobaric heating experiments in a PD-dilatometer. They concluded that onlycooling experiments are suited to get reliable results using a PD-dilatometer.

The measured displacement, i.e. the relative displacement of the core with respect tothe coil of the LVDT, is influenced by many factors other than the volume of the poly-meric sample. All these factors are functions of temperature and mechanical load-ing, e.g. thermal expansion of the rod carrying the core of the LVDT, deformationof the dilatometers frame, deformation of the pressure cell and its sample spacing,etc. It would be an impossible exercise to accurately account for all these influencesby calculating appropriate correction functions. Instead, the measured displacementof an experimental run is corrected using the measured displacement of an experi-ment performed at identical conditions but in the absence of sample material. This


so called ’calibration run’ is unique for every processing condition.

Experiments performed with the present dilatometer have shown that the repro-ducibility of measurements improved greatly if the specific volume is based on therelative volume change of the sample during cooling instead of the absolute volume.The relative specific volume measurements have to be completed with absolute spe-cific volume data measured using standard techniques. To be exact, the specific vol-ume of the polymer melt at maximum temperature is set equal to a value measuredwith a conventional dilatometer operating in isobaric mode at an identical pressurelevel. It can be assumed that the specific volume of the polymer melt at tempera-tures sufficiently high above the melting temperature is only a function of pressureand temperature [3]. This procedure can be used independent of the conditions ap-plied during cooling.

Based on the instrument accuracies listed in table 2.5, the accuracy for specific vol-ume can be determined using equation 2.1.

ν =4X · A

m+ vmelt_c f =

(4x1 −4x2) · π4

(d2

o − d2i)

m+ vmelt_c f (2.1)

where 4x1 is the displacement measured in the experimental run, 4x2 the displace-ment measured in the calibration run, do the outer diameter of the sample spacing,di the inner diameter of the sample spacing, m the sample mass, and νmelt_c f theabsolute specific volume for the melt phase measured with a CF-dilatometer. Theabsolute accuracy of specific volume, δν, is determined from the individual accura-cies according to:

δν=∣∣∣∣

∂ν

∂ (4x1)

∣∣∣∣ δ4x1+∣∣∣∣

∂ν

∂ (4x2)

∣∣∣∣ δ4x2+∣∣∣∣

∂ν

∂do

∣∣∣∣ δdo+∣∣∣∣

∂ν

∂di

∣∣∣∣ δdi+∣∣∣∣

∂ν

∂m

∣∣∣∣ δm+δvmelt_c f

(2.2)

Both the diameters do and di are shaped with a maximum tolerance of ±2.5 · 10−3

mm, the sample mass is measured with an accuracy of δm = ±5.0 · 10−7 kg, and thedisplacement is measured with an accuracy δ4x1 = δ4x2 = ±5.0 · 10−3 mm. Theaccuracy of measuring specific volume with the CF-dilatometer δvmelt_c f is estimatedto be about 1.25 · 103 mm3/kg. This results in an absolute accuracy δν = 7.04 · 103

mm3/kg for the specific volume.

Sample preparation

Samples are prepared from standard sized pellets using compression molding. If theglass transition temperature of the material to be investigated is below room temper-ature, rectangular strips are molded with dimensions 2.5 x 65 x 0.4 mm. Because the

2.3 EXPERIMENTAL 21

Medium ‘Flux’ (Piston / Die) Cooling time [s](none) - 4600Pressurized Air 2 / 2 [bar] 600Water 4.0 / 2.0 [l/ min] 15

Table 2.6: Examples of applied cooling media and cooling times needed to reach am-bient conditions.

material is in its rubbery state at room temperature, the strips can be bend into ringswhen loaded into the dilatometer. If the glass transition temperature of the materialto be investigated is above room temperature the material is molded into cylindri-cally shaped samples with dimensions ∅ 23 x 22 mm. After demolding, the samplesare machined into rings with dimensions ∅ 22.0−0.05 x ∅ 21.0+0.05 x 2.5 mm.

Procedure

Since the dilatometer is used in the isobaric cooling mode, the pressure cell is firstheated to a temperature above the melting point of the sample. This is done with anaverage heating rate of about 5 oC/min. Once the maximum temperature is reached,it is kept constant for a certain time to ensure complete melting of the material (e.g.for polypropylene this takes about 10 minutes at 210 oC). This time should be mini-mized rather than maximized in order to prevent thermal degradation of the mate-rial. Next, a compressive force is applied to the pressure cell to pressurize the sample.Since the sample’s cross section in direction of the applied force equals A = 33.77mm2, a compressive force of about 3300 N is sufficient to reach a sample pressureof 100 MPa. The compressive force applied is corrected for the weight that the dieexerts on the sample. The temperature control unit is shut off after the sample is fullypressurized and with a 5 seconds delay the data acquisition is started. After another10 seconds, the electromagnetic valves are opened to start cooling. During coolingof the sample to ambient conditions, the compressive force is maintained constantto within ±10 N. Shear can be applied during cooling either as a step or oscillat-ing. The effective cooling of the sample is fully determined by the cooling mediumand cooling flux applied. Because the flux of the cooling medium is constant, theresulting cooling rate is time dependent (see figure 2.5). Table 2.6 shows examplesof the cooling medium used and the resulting cooling time when cooling from 210oC to ambient conditions. As mentioned before, the flux of cooling medium throughpiston and die are adjusted separately to optimize for thermal homogeneity of thesample during cooling.

After the sample is completely cooled down, it is taken out of the dilatometer and thesame procedure is repeated in the absence of a sample. This calibration measurementis used to correct the measured volumetric change of the sample for external influ-ences such as thermal expansion of the dilatometer, deformation of the dilatometerdue to mechanical loading, etc.


0 2 4 6 8 10 12 14 16

50

100

150

200

T [

C]

0 2 4 6 8 10 12 14 16−100

−80

−60

−40

−20

0

t [s]

Coo

ling

Rat

e [C

/s]

Figure 2.5: Example of measured temperature (top) and (derived) cooling rate (bot-tom) when using water as cooling medium.

2.4 Comparison with confining fluid baseddilatometer

As a check on the general experimental procedure described above, specific volumemeasurements of an isotactic polypropylene, Mw = 365000 g/mol and Mw/Mn =5.4 (grade K2xmod, Borealis), are compared with isobaric cooling experiments per-formed using a CF-dilatometer. Additionally, the comparison helps to quantify theinfluence of friction forces that arise between sample and PD-dilatometer walls dur-ing solidification of the sample [16]. Experiments with the CF-dilatometer are per-formed at Moldflow Plastics Labs (Ithaca, USA) using a commercial dilatometer(Gnomix). Here the experimental procedure applied is as follows: loading of thesample to the desired pressure level, heating of the polymer to a temperature of 210oC, holding the material for 10 min at maximum temperature, cooling at a constantcooling rate. The pressure levels applied are 10, 40, 80 MPa and cooling rates are 1.0and 4.0 oC/min. Although the material is already pressurized during melting, thecrystalline microstructure is regarded to be completely melted after 10 min at 210 oC.This is based on results of Nakafuku [22], showing the melting temperature of themost stable α−monoclinic crystalline phase in iPP to be approximately 198 oC at apressure of 100 MPa.

Results of the measurements performed with the CF-dilatometer are shown in fig-ure 2.6. Although both cooling rates are relatively low, the transition where crystal-lization becomes effective clearly shifts towards lower temperatures with increasingcooling rate. This agrees with results found by Luyé et al. [12], measuring specificvolume in isobaric mode at 40 MPa and cooling rates ranging from 5 to 30 oC/min.

2.4 COMPARISON WITH CONFINING FLUID BASED

DILATOMETER 23

They conclude that the transition temperature not only depends on pressure but onthe entire thermal history (especially the cooling rate). The experiments performedwith our PD-dilatometer are performed at the lowest non-constant cooling rate, i.e.cooling in still air, at pressures of 10, 40, 60 MPa. Silicon grease is applied to thesamples to reduce the friction between sample and dilatometer walls. DSC measure-ments performed after the experiment on samples treated with grease and untreatedsamples, show no effect of the silicon grease on the crystallization kinetics of theiPP. Prior to cooling, the polymer is kept for 10 min at a maximum temperature of210 oC to assure fully melting of the crystalline morphology. Figure 2.7 shows theresults of experiments performed with the PD-dilatometer and the CF-dilatometer,respectively cooled in still air and with a constant cooling rate of 4.0 oC/min. Inthe molten state the comparison is good, as expected. More interesting is the goodcomparison with respect to the temperature where the transition from the melt tothe semi-crystalline state becomes effective. This indicates that the effective thermal-histories experienced are comparable, despite the different cooling rates applied. Thegood comparison during crystallization is explained because the experienced coolingrates are almost the same in this range of temperatures, i.e. the average cooling rateduring crystallization in the measurements using the PD-dilatometer is about 5− 6oC/min. Because the effective thermal histories of both measurements before andduring crystallization show such good comparison, differences in solid state specificvolume are considered negligible. Closer comparison of the specific volume for meltand solid state are shown in figure 2.8. For comparison, data of the CF-dilatometerare interpolated to values corresponding to 60 MPa. The relative differences in spe-cific volume are calculated using equation 2.3 and results are listed in table 2.7.

ε =∣∣∣∣νPD − νCF

νCF

∣∣∣∣ ∗ 100% (2.3)

where:νPD : specific volume measured with PD-dilatometerνCF : specific volume measured with CF-dilatometer

For the specific volume measured in the melt state, the relative differences range

P [MPa] εmelt [%] εsolid [%]10 0.36 0.1640 0.12 0.0860 0.23 0.19

Table 2.7: Average values of the relative difference in specific volume for melt (εmelt)and solid state (εsolid).


80 100 120 140 160 180 200 220 240 2601.05

1.1

1.15

1.2

1.25

1.3

1.35x 10

6

T [C]

ν [

mm

3 /Kg]

80 MPa

40 MPa

10 MPaCF−1CF−4

Figure 2.6: Specific volume of iPP (K2xmod, Borealis) measured in isobaric modewith a CF-dilatometer at pressures 10, 40, 80 MPa and constant coolingrates of 1.0 oC/min (O) and 4.0 oC/min (¤).

80 100 120 140 160 180 200 220 240 2601.05

1.1

1.15

1.2

1.25

1.3

1.35x 10

6

T [C]

ν [

mm

3 /Kg]

40 MPa

10 MPaPDCF

Figure 2.7: Comparison of specific volume of iPP (K2xmod, Borealis) measured inisobaric mode at 10, 40 MPa with a CF-dilatometer at a constant coolingrate of 4.0 oC/min (¤) and the custom designed PD-dilatometer coolingin still air (5).

2.4 COMPARISON WITH CONFINING FLUID BASED

DILATOMETER 25

140 150 160 170 180 190 200 210 220 2301.15

1.2

1.25

1.3

1.35x 10

6

ν am

[mm

3 /Kg]

10 MPa

40 MPa

60 MPa

90 100 110 120 130 140 150 1601.06

1.08

1.1

1.12

1.14

1.16

x 106

T [C]

ν cr

[mm

3 /Kg]

10 MPa

40 MPa

60 MPa

Figure 2.8: Comparison of specific volume of iPP (K2xmod, Borealis) for melt (top)and solid state (bottom). Measurements performed with CF-dilatometerat a cooling rate of 4.0 oC/min (2) and PD-dilatometer (5) cooling in stillair. Data CF-dilatometer for 60 MPa are interpolated (¦).

from about 0.1-0.4%. This can be related to the experimental procedure of the PD-dilatometer since the influence of friction forces [16] and cooling rate [3] on specificvolume measurements in melt state can be neglected. Remarkably, εsolid is generallyless than εmelt. The opposite is expected because of an additional error arising fromfriction forces and the resulting loss of hydrostatic pressure inside the sample. Mostprobably this is the result of the fairly narrow temperature range of specific volumedata measured in solid state.

In conclusion, the relative differences between specific volume data measured witha CF-dilatometer (Gnomix) and the PD-dilatometer are in the range of 0.1− 0.4% inmelt state including the temperature range where transition to the semi-crystallinephase becomes effective. Generally, the relative differences decrease with increasingpressure level. Furthermore, identical relative differences are assumed for specificvolume measured during the first part of crystallization, since the ratio of shear andbulk modulus is still small and the influence of friction forces and loss of hydro-static pressure can be neglected [16]. Although the relative differences in specificvolume for the solid state range from 0.1 − 0.2%, these results are regarded to bemore of qualitative than quantitative value. That is why the relative differences inspecific volume for the latter part of crystallization and for solid state specific volumeare assumed to be larger than 0.4% and this part of the measured specific volumecurve should be taken as qualitative rather than quantitative. Finally, in case thePD-dilatometer is subjected to higher cooling rates, the influence of friction forceson the specific volume in the solid state is believed to increase. It is, however, dif-ficult to quantify this increase because comparison with data performed with a CF-


dilatometer at equally high cooling rates is not possible.

2.5 Example: isotactic polypropylene

Figures 2.9 and 2.10 show, respectively, the influence of cooling rate and melt shear-ing on the specific volume of a linear iPP (grade HD120MO, Borealis) characterizedby Mw = 365000 g/mol, Mw/Mn = 5.2. For reasons of comparison, in the latterfigure the normalized specific volume ν∗ is plotted, defined as:

ν∗ =ν − νs

νm − νs(2.4)

Here νs represents the value of the specific volume at room temperature in the solidstate, in case the sample is not subjected to flow. Identically, νm represents the valueof the specific volume in the melt state at 210 oC. Samples are prepared by compres-sion molding into strips with dimensions 2.5 x 65 x 0.4 mm (see section 2.3). First,pellets are melted at atmospheric pressure. Next, the material is compressed for 3minutes at 210 oC with a force of 50 kN. The samples are cooled in a water cooledpress during 5 minutes from 210 to 25 oC again with a force of 50 kN.

0 50 100 150 200 2501.05

1.1

1.15

1.2

1.25

1.3x 10

6

T [C]

ν [

mm

3 /kg]

Figure 2.9: Influence of cooling rate on the specific volume of iPP at a pressure of 40MPa. Average cooling rates during crystallization are given in the figure.

Cooling rate and melt shearing clearly have a pronounced effect on the evolutionof specific volume as a function of temperature, with opposing influences on thetemperature where the transition from the melt to the semi-crystalline state becomeseffective. The dependence of this transition as a function of processing conditions

2.6 CONCLUSIONS 27

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

Figure 2.10: Influence of shear flow on the normalized specific volume of iPP. Shearis applied as a step function at 139 oC, with a shear rate of 39.0 1/s to atotal shear of 117. Specific volume with (4) and without shear flow (O)is obtained at an average cooling rate during crystallization of 1.4 oC/sand a pressure of 40 MPa.

is for example of importance for the choice of the ’No Flow’ temperature, as usedin numerical simulation codes. Furthermore, the resulting specific volume in thesolid state clearly increases with increasing cooling rate. This agrees with results ofothers [23–25]. The shear flow applied only marginally affects the resulting specificvolume in the solid state.

2.6 Conclusions

This chapter described the construction and first testing of a new device to studythe influence of pressure, cooling rate, shear rate, and total shear on the specific vol-ume. Comparison of results, measured at low cooling rates without applying shear,shows very good agreement with results obtained using a commercial bellows typedilatometer. First experiments using an isotactic polypropylene show a profound in-fluence of both cooling rate and shear flow on the evolution of specific volume. Thespecific volume in the solid state increases with increasing cooling rate but is onlymarginally affected by the shear flow applied.


References

[1] Hellwege, K.H., Knappe, W., Lehmann, P. Die isotherme Kompressibilitäteiniger amorpher und teilkristalliner Hochpolymerer im Temperaturbereichvon 20-250 [oC] und bei Drucken bis zu 2000 Kp/Cm2. Kolloid-Zeitschrift undZeitschrift für Polymere, 183(2):110 - 120, (1961).

[2] Quach, A., Simha, R. Pressure-Volume-Temperature properties and transitionsof amorphous polymers; polystyrene and poly (orthomethylstyrenes). Journal ofApplied Physics, 42(12):4592-4606, (1971).

[3] Zoller, P., Bolli, P., Pahud, V., Ackermann, H. Apparatus for measuring Pressure-Volume-Temperature relationships of polymers to 350 oC and 2200 Kg/Cm2.Review of Scientific Instruments, 47(8):948-952, (1976).

[4] Barlow, J.W. Measurement of the PVT behavior of cis-1,4-polybutadiene. Poly-mer Engineering and Science, 18(3):238-245, (1978).

[5] Taki, S., Takemura, T., Matsushige, K. Development of high-pressure dilatome-ter for polymer studies. Japanese Journal of Applied Physics, 30(4):888-889, (1991).

[6] Pixa, R., Le Du, V., Wippler, C. Dilatometric study of deformation induced vol-ume increase and recovery in rigid PVC. Colloid Polymer Science, 266(10):913-920,(1988).

[7] Duran, R.S., Mckenna, G.B. A torsional dilatometer for volume change mea-surements on deformed glasses: instrument description and measurement onequilibrated glasses. Journal of Rheology, 34(6):813-839, (1990).

[8] Zuidema, H., Peters, G.W.M., Meijer, H.E.H. Influence of cooling rate on PVT-data of semicrystalline polymers. Journal of Applied Polymer Science, 82(5):1170-1186, (2001).

[9] Foster, G.N., Waldmann, N. Griskey, R.G. Pressure-Volume-Temperature behav-ior of polypropylene. Polymer Engineering and Science, 6:131 -, (1966).

[10] Waldmann, N., Beyer, G.H., Griskey, R.G. A dilatometer for measuring com-pressibilities of polymers in their melting range. Journal of Applied Polymer Sci-ence, 14:1507-1513, (1970).

[11] Karl, V.H. and Asmussen, F. and Überreiter, K. Über die Druckabhängigkeit derViskoelastischen und Physikalisch-Chemischen Eigenschaften von Polymeren.Markomolecular Chemistry, 178:2037-2047, (1977).

[12] Luyé, J.F., Regnie, G., Le Bot, P.H., Delaunay, D., Fulchiron, R. PVT measure-ment methodology for semicrystalline polymers to simulate injection-moldingprocess. Journal of Applied Polymer Science, 79:302-311, (2001).

[13] Fritzsche, A.K. and Price, F.P. Crystallization of polyethylene oxide under shear.Polymer Engineering and Science, 14(6):401-412, (1974).

[14] Menges, G., Thienel, P. Eine Messvorrichtung zur aufnahme von P-V-T Di-agrammen bei praktischen Abkühlgeschwindigkeiten. Kunststoffe, 65:696-699,(1975).

[15] Chakravorty, S. PVT testing of polymers under industrial processing conditions.Polymer Testing, 21:313-317, (2002).

REFERENCES 29

[16] Lei, M., Reid, C.G., Zoller, P. Stresses and volume changes in a polymer loadedaxially in a rigid die. Polymer, 29:1784-1788, (1988).

[17] Bhatt, S.M., McCarthy, S.P. Pressure, Volume and Temperature (PVT) appara-tus for computer simulations in injection molding. Annual Technical ConferenceSociety of Plastics Engineers (ANTEC), 1831-1832, (1994).

[18] Watanabe, K., Suzuki, T., Masubuchi, Y., Taniguchi, T., Takimoto, J., Koyama, K.Crystallization kinetics of polypropylene under high pressure and steady shearflow. Polymer, 44:5843-5849, (2003).

[19] Ding, Z., Spruiell, J.E. An experimental method for studying nonisothermalcrystallization of polymers at very high cooling rates. Journal of Polymer Science,34:2783-2804, (1996).

[20] Macosko, C.W. Rheology, Principles, Measurements, and Applications, VCH Pub-lishers, New York (1994).

[21] Leute, U., Dollhopf, W., Liska, E. Dilatometric measurements on some poly-mers: the pressure dependence of thermal properties. Colloid and Polymer Sci-ence, 254:237-246, (1976).

[22] Nakafuku, C. High pressure D.T.A. study on the melting and crystallization ofisotactic polypropylene. Polymer, 22:1673-1676, (1981).

[23] Piccarolo, S. Morphological changes in isotactic polypropylene as a function ofcooling rate. Journal of Macromolecular Science - Phys., B31(4):501-511, (1992).

[24] Brucato, V., Piccarolo, S., La Carrubba, V. An experimental methodology tostudy polymer crystallization under processing conditions. The influence ofhigh cooling rates. Chemical Engineering Science, 57:4129-4143, (2002).

[25] La Carrubba, V., Brucato, V., Piccarolo, S. Phenomenological approach to com-pare the crystallization kinetics of isotactic polypropylene and polyamide-6under pressure. Journal of Polymer Science: Part B: Polymer Physics, 40:153-175,(2002).

30 2 CONCENTRIC CYLINDER DILATOMETER: DESIGN AND TESTING

2.A Appendix: material properties

Both the piston and the most inner part of the die are fabricated from tungsten car-bide for optimal thermomechanical properties. The specific grade of tungsten car-bide used, consists of 90 % tungsten carbide particles having a size smaller equal 0.8µm embedded in a 10 % Cobalt matrix. Relevant material properties are given intable 2.8.

Property Symbol Value DimensionYoungs Modulus E 4.2 · 105 [N/mm2]Heat conductivity λ 80 [W/mK]Density ρ 1.44 · 104 [kg/m3]Heat capacity Cp 277.2 [J/kgK]Transverse rupture strength TRS 3.0 · 103 [N/mm2]Thermal expansion α 5.4− 5.6 · 10−6 [1/K]

Table 2.8: Material properties of tungsten carbide used for the fabrication of pistonand most inner part of the die.

2.A APPENDIX: MATERIAL PROPERTIES 31

‘Design B’

CHAPTER THREE

The influence of cooling rate onspecific volume 1

The influence of cooling rate on the evolution of specific volume is stud-ied. Average cooling rates imposed during crystallization of the materialvary from 0.1 to 35 C/s while pressures range from 20 to 60 MPa. Resultsshow the well known profound influence of pressure and cooling rate onspecific volume. An increasing cooling rate shifts the transition temperatureTc towards lower temperatures, increases the final specific volume, and thetransition due to crystallization is more gradual and widespread. Increasingpressure has an opposite effect on the shift in Tc, while the final specific vol-ume after pressure release also increases. Finally, comparison of numericalpredictions with experimental data show that the predicted transition tem-perature Tc is consistently too low and that predictions at high cooling ratesare sensitive to (small) variations in model parameters.

3.1 Introduction

Experimental studies investigating the influence of cooling rate on the specific vol-ume of polymers can roughly be divided into dilatometric studies investigating theevolution of the specific volume with temperature and studies investigating the finalspecific volume. Table 3.1 shows a (limited) overview of dilatometric studies per-formed on polypropylene at various cooling rates and elevated pressures. However,most cooling experiments listed in table 3.1 are performed at cooling rates far lessthan (locally) expected during processing. Only recent studies report on the influ-ence of medium (up to 3 C/s) and high cooling rate on specific volume [1–3]. In

1Reproduced in part from: Van der Beek, M.H.E., Peters, G.W.M., Meijer, H.E.H. The influence ofcooling rate on the specific volume of isotactic polypropylene at elevated pressures. MacromolecularMaterials and Engineering, accepted, (2005).

33

34 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

Reference¦Tmax Pmax Mn Mw/Mn

[C/s] [MPa] [g/mol] [-][1] 0.5 120 - -[2] 54.0 18 67000 5.45[3] 2.5 40 - -[5] 0.003∗ 200 - -[6] 0.0017 98 470000 1.03 - 1.61[7] 0.019∗ 157 - -[8] 0.042∗ 200 47000 6.38[9] 0.042 200 47000 6.38

[10] 0.033 150 - -[11] 0.017∗ 100 75100 6.43

Table 3.1: Overview of dilatometric studies on the specific volume of polypropyleneobtained at various cooling or heating rates and elevated pressures. Dataindicated by * are obtained by increasing temperature from ambient condi-tions. Polypropylene grades used are characterized by Mn and Mw/Mn.

general, results of these studies show the transition due to crystallization to shifttowards lower temperatures and the specific volume after complete cooling to in-crease with increasing cooling rate. Unfortunately, the data of Chakravorty [3] aremost likely influenced by thermal gradients in the sample considering the sampledimensions and cooling rates employed. This means that their data do not repre-sent intrinsic material behavior. Even at the relatively low cooling rates, up to 0.5C/s, employed in the study of Luyé et al. [1], thermal gradients between 5 - 15 Cwhere found resulting from the large sample dimensions, i.e. a cylindrical samplewith diameter 7.4 mm. Zuidema et al. [2] used samples with a thickness ≤ 0.35 mm,to guarantee homogeneous cooling of the sample at the applied cooling rates. How-ever, the pressure levels employed at are relatively low with respect to pressure levelsencountered during processing.

Studies reporting on the influence of cooling rate on the final specific volume aremostly performed in the frame work of understanding the crystallization kinetics ofpolymers. The final density, i.e. reciprocal value of specific volume, is typically mea-sured ex situ using the technique of density gradient column (DGC). Table 3.2 showssome studies performed in this field. All studies characterize the applied (time de-pendent) cooling rate by its value at 70 C, i.e. T70. In the studies of Piccarolo [12,13],Pantani et al. [14], and Brucato et al. [15] a specially designed setup is used to quench100-150 µm thin samples at atmospheric pressure. Cooling rates achieved are of or-der O(102 − 103) C/s. La Carrubba et al. [16] used a modified injection moldingmachine to investigate the combined influence of cooling rate and pressure on finalspecific volume. From the injection molded samples microtome slices were taken,representing material subjected to cooling rates of O(102) C/s and elevated pres-sure to 40 MPa. All studies clearly show a decrease in final density, i.e. an increase

3.2 EXPERIMENTAL PART 35

Reference¦T70 Pmax Mn Mw/Mn

[C/s] [MPa] [g/mol] [-][12] 0.28 - 311 0.1 79300 6.00[13] 0.083 - 311 0.1 79300 6.00[14] 0.02 - 1130 0.1 - -[15] 0.1 - 1000 0.1 - -[16] 1 - 100 40 75100 6.43

Table 3.2: Overview of studies reporting on the final specific volume and crystallinemorphology of polypropylene resulting from processing conditions.

in specific volume, with increasing cooling rate associated to a decrease in degreeof crystallinity. Interesting are the results of La Carrubba et al. [16] showing that in-creased pressure and increased cooling rate have a qualitatively similar effect on thespecific volume of polypropylene.

The studies mentioned in tables 3.1 and 3.2 are representative for the work done re-garding the influence of cooling rate on the specific volume of polymers but most arefar outside the range of processing conditions. Dilatometric studies typically investi-gate the influence of pressure on the evolution of specific volume with temperature.In general, the range of cooling rates applied is limited with respect to industrial pro-cesses such as injection molding. Only Zuidema et al. [2] were able to impose highcooling rates but, unfortunately, at relatively low pressure. Except for the study ofLa Carrubba et al. [16], the final specific volume of polymers is generally investigatedat high cooling rates but atmospheric pressure. We conclude that the combined in-fluence of cooling rate and elevated pressure, as encountered during industrial pro-cessing operations, is insufficiently investigated. In this chapter, the influence ofcooling rate on the specific volume of isotactic polypropylene is investigated at el-evated pressures. Numerical predictions of the temperature dependent behavior ofspecific volume using the model of Zuidema et al. [2] are compared with experimen-tal data. Also the resulting crystalline morphology is investigated by means of wideangle X-ray diffraction (WAXD) experiments.

3.2 Experimental part

Materials

The material used in this study is a linear isotactic polypropylene (grade HD120MO,Borealis), characterized by Mw = 365000 g/mol, Mw/Mn = 5.2. Sheets with di-mensions 2.5 x 65 x 0.4 mm are prepared by compression molding. First, pellets aremelted at atmospheric pressure. Next, the material is compressed for 3 minutes at210 C with a force of 50 kN. The samples are cooled in a water cooled press during 5


minutes from 210 to 25 C again with a force of 50 kN. Within minutes after finishingthe dilatometric experiments, samples are stored in a freezer at −5 C for later usein density gradient column (DGC) and wide angle X-ray diffraction (WAXD) experi-ments.

Dilatometer experiments

The combined influence of cooling rate and pressure on the specific volume of iso-tactic polypropylene (iPP) is investigated using the custom dilatometer presentedin chapter 2. A schematic representation of the dilatometer is shown in figure 3.1.Experiments are performed in isobaric cooling mode according to the following pro-cedure: a) the sample is heated with an average heating rate of 5 C/min to a tem-perature of 210 C, b) kept for 10 minutes at 210 C to ensure fully melting of thecrystalline microstructure, c) pressurized to the desired level, d) cooled to room tem-perature during which the pressure is maintained constant to within±0.3 MPa. Priorto the experiment, a synthetic grease (Krytox GPL 207, Dupont) is put on the surfaceof the sample to reduce the friction between sample and dilatometer wall duringthe experiment. The basis of this grease is a perfluoropolyether (PFPE) synthetic oilthickened with polytetrafluoroethylene (PTFE) and is chosen for non-reactive behav-ior and thermal stability (-30 to 288 C). DSC measurements performed on samplestreated with grease and untreated samples, show no effect of the silicon grease onthe crystallization kinetics of the iPP. The cooling rate is determined by the type andflux of the cooling medium. The piston and die of the dilatometer are cooled inde-pendently to optimize for thermal homogeneity of the sample during cooling. Sincethe dilatometer is cooled with a constant flux of cooling medium, the cooling rate istime dependent (see also figure 2.5).

X-ray analysis

Wide Angle X-ray Diffraction (WAXD) experiments are performed at the materialsbeam-line ID 11 of the European Synchrotron Radiation Facility (ESRF) in Greno-ble, France. The size of the X-ray beam is 0.2 x 0.2 mm2 having a wavelength of0.4956 Å. The detector used is a Frelon CCD detector with 1024 x 1024 pixels. Bothhorizontal and vertical pixels are 164.4 µm in size. From calibration experimentsusing Lanthanum Hexaboride (LaB6) a sample-to-detector distance of 439.9 mm isdetermined. The exposure time for all images is 30 seconds. Finally, all images arecorrected for spatial distortion using the ’Fit2d’ software [17] and background noiseis subtracted.

3.3 RESULTS AND DISCUSSION 37

F

Force / rotationcontrolled die

Sample

Fixed piston

Cooling die

Cooling piston

Temperaturereading

Ωω

Figure 3.1: Working principle of the custom designed dilatometer.

Density measurements

Density gradient column (DGC) experiments are performed to determine the densityof samples subjected to dilatometer experiments. The column is prepared accord-ing to ASTM D1505 using water and isopropanol (IPA), establishing a linear densitydistribution ranging from 0.87-0.94 g/cc. Measurements are performed at a columntemperature of 23 C. Prior to submergence into the column, samples are subjected toan ultrasonic bath for 20 minutes, which consists of a representative mixture of waterand IPA, in order to minimize the presence of air bubbles on the sample surface.

3.3 Results and discussion

Specific volume

Dilatometer experiments are performed at 20, 40, and 60 MPa and three differentcooling profiles. These profiles are achieved either by cooling the dilatometer pas-sively to the surrounding air (Tlow), or actively using either pressurized air (Tmedium)or water (Thigh) as cooling medium. Temperatures are recorded at 6 positions outsidethe polymeric sample, corresponding to respectively top, middle, and bottom of thesample measured at both the inner and outer sample surface (see figure 3.1). Thecorresponding (surface) temperatures of the sample are determined via heat conduc-


tion analysis using the experimentally measured temperatures, the heat conductingproperties of the set up material, and the known distance (0.5 mm) between the tipof the thermocouples and the sample surface. Based on these corrected tempera-tures, an averaged temperature profile in time is determined which represents thethermal history of the sample and which is used in further analysis of the data. Asa characteristic value for the thermal history experienced by the material, the valueof the cooling rate at 70 C, T70, is often used [12–15, 18]. Studies of the crystallinemorphology of iPP resulting from quenching experiments [12, 13] have shown thatthe maximum of the crystallization rate for iPP is found at 70 C. This is why T70is regarded as a characteristic processing parameter for iPP, used to indicate quencheffectiveness and for comparing crystalline morphology and resulting material prop-erties obtained at different processing conditions [11]. These studies have been per-formed at ambient pressure. However, it is known that with increasing pressurethe polymer’s equilibrium melting temperature T0

m increases [19], leading to crystal-lization at higher temperatures. Consequently, as the cooling rate is highest at hightemperature, the effective cooling rate experienced by the material will increase incase the polymer is subjected to a time-dependent cooling rate. Any changes in ma-terial properties resulting from a change in pressure at an identical time-dependentcooling rate, i.e. constant T70, could be explained from a ‘processing point of view’ asa pressure effect. However, from a ‘material point of view’ this is at most a combinedeffect of cooling rate and pressure, since we can not distinguish for the pressure ef-fect solely. To better discriminate for pressure effects from a material point of view,in this study the average cooling rate during crystallization is used as a characteristicvalue for the experienced thermal history of the polymer, i.e. the average of the cool-ing rates present during the transition in the specific volume. Our experience showsthat this approach is a useful one, see also chapter 2, figure 2.7. Characteristic valuesfor cooling rate are listed in table 3.4. Additionally, values for T70 are given to en-able comparison with other studies such as listed in table 3.2. As already outlined inchapter 2, the measured specific volume data are completed with conventional pVT-data of the amorphous phase. These data are measured with a conventional bellowstype dilatometer at low cooling rates (see Appendix 3.A).

Figure 3.2 shows specific volume as a function of pressure and temperature mea-sured at different cooling profiles. Each curve depicts the mean of 3 measurementswith standard deviation. In case of Thigh, curves represent the mean of 5 measure-ments. Figure 3.2a shows the specific volume of iPP measured at Tlow and isobars20, 40, 60 MPa. Characteristic for these measurements performed at a cooling rateof 0.1 C/s is the sharp transition in the specific volume associated to the crystal-lization of the polymer. The temperature marking the start of this transition, furtherreferred to as the transition temperature Tc, is defined arbitrarily as the temperaturewhere the change in specific volume due to crystallization has reached 5 % of the to-tal change. With increasing cooling rate, the characteristic shift of Tc towards lowertemperatures is observed and the transition itself is getting less distinct and morewide spread [1–3].

Both the shift in Tc and the less distinct and more wide spread transition are re-


0 50 100 150 200 2501.05

1.1

1.15

1.2

1.25

1.3

1.35x 10

6

T [C]

ν [

mm

3 /kg]

20 [MPa]40 [MPa]60 [MPa]

( a)

0 50 100 150 200 2501.05

1.1

1.15

1.2

1.25

1.3

1.35x 10

6

T [C]

ν [

mm

3 /kg]

20 [MPa]40 [MPa]60 [MPa]

( b)

0 50 100 150 200 2501.05

1.1

1.15

1.2

1.25

1.3

1.35x 10

6

T [C]

ν [

mm

3 /kg]

20 [MPa]40 [MPa]60 [MPa]

( c)

Figure 3.2: Influence of cooling rate on the specific volume of iPP measured at variouspressure levels: (a) 0.1 C/s, (b) 1.2 - 1.4 C/s, (c) 30.0 - 34.8 C/s. For exactcooling rates per pressure level see table 3.4.


0 50 100 150 200 2501.05

1.1

1.15

1.2

1.25

1.3x 10

6

T [C]

ν [

mm

3 /kg]

Figure 3.3: Influence of cooling rate on the specific volume of iPP at a pressure of 40MPa. Characteristic cooling rates are respectively: 0.1 (O), 1.4 (4), 32.5(¤) C/s.

lated to the suppression of the crystallization process, and can be explained by thecompetition between the time of cooling and the time necessary to crystallize. Withincreasing cooling rate, the time for spherulites to grow and new nuclei to form at acertain undercooling is less.

Figure 3.3 more clearly illustrates the suppression of the crystallization process withincreased cooling rate. The specific volume is measured at a constant pressure of40 MPa and cooling rates 0.1, 1.2, and 32.5 C/s. The transition temperature Tc,shifts respectively -13.5 C and -29.0 C when the cooling rate is increased from 0.1to respectively 1.2 and 32.5 C/s. The real driving force for crystallization is theundercooling 4T = T0

m − T, which scales with temperature when the pressure isconstant. Since the start of the transition can be regarded as a measure for the on-set of crystallization, the shift in Tc towards lower temperatures indicates a delay inthe onset of crystallization, i.e. crystallization starts at higher undercooling. Withincreased pressure, Tc shifts towards higher temperatures due to the pressure de-pendence of the equilibrium melting temperature T0

m [19]. However, independent ofpressure the onset of crystallization will occur at the same undercooling for identi-cal characteristic cooling rate, i.e. identical thermal history. For the relatively smallpressure range that was experimentally accessible, the influence of pressure on Tc isabout linear with a pressure dependence of 0.2700 C/MPa. This is very similar tothe pressure dependence of PP found by other authors: 0.2287 oC/MPa obtained ata cooling rate of 0.042 C/s [8], 0.2625 oC/MPa obtained at a cooling rate of 0.083C/s [1], and 0.2536 oC/MPa obtained at a cooling rate of 0.10 C/s [20]. This lastvalue is obtained from applying a linear fit to data of crystallization temperature Tc1,i.e. samples crystallized below a pressure of 340 MPa.


10−2

10−1

100

101

102

100

110

120

130

140

150

160

Cooling rate [C/s]

Tc ,

T1/

2 [C

]

20 [MPa] 40 [MPa] 60 [MPa] Luye − 40 [MPa]Luye − 80 [MPa]Luye − 120 [MPa]

Figure 3.4: Influence of cooling rate and pressure on the transition temperature Tc.For comparison, measurements of the half-crystallization temperature,T1/2, of Luyé et al. [1] are included.

Figure 3.4 shows the transition temperature Tc as a function of both cooling rate andpressure. Solid lines represent a linear fit of the data according to equation (3.1) withcoefficients a0 and a1 as listed in table 3.3.

Tc = a0 + a1 log(¦T) (3.1)

The influences of pressure and cooling are of an opposite nature. The cooling ratedependence changes only little with pressure. The data obtained at 60 MPa show asomewhat different trend, which is mainly caused by determining Tc at the highestcooling rate. This is subject to small variations due to the less distinct transition inspecific volume. Luyé et al. [1] analyzed the influence of pressure and cooling rateon the half-crystallization temperature T1/2. They performed measurements for apressure range of 40-120 MPa at cooling rates ranging from 0.083 to 0.5 C/s. Com-paring both data sets, the cooling rate dependence of Tc and T1/2 shows very goodagreement. Differences in temperature values could be resulting from the differentmaterial grades used and the different definitions used for Tc and T1/2.

Finally, the specific volume at room temperature increases with increasing coolingrate. This is in agreement with results of the DGC experiments shown in figure 3.5,and confirms the results of others [11–13]. Again, the offset between both data sets ismost likely the result of differences in material grade used.


10−2

10−1

100

101

102

0.89

0.895

0.9

0.905

0.91

0.915

0.92

Cooling rate at 70 [C] [C/s]

ρ [g

/cm

3 ]

20 [MPa] 40 [MPa] 60 [MPa] LaCarrubba 24 [MPa]LaCarrubba 40 [MPa]LaCarrubba 60 [MPa]

Figure 3.5: Influence of cooling rate and formation pressure on the resulting densityof iPP measured at atmospheric pressure and 23 C. Filled symbols repre-sent data of La Carrubba [11].

P a0 a1[MPa] [oC] [s]20 125.8 -12.322640 129.2 -11.489060 135.6 -9.569140∗ 116.1 -13.069480∗ 127.8 -11.5269120∗ 136.1 -13.1736

Table 3.3: Fitting coefficients for the cooling rate dependence of the transition tem-perature Tc according to equation 3.1. Data indicated with ∗ are obtainedfrom Luyé et al. [1].


X-ray(Single shot)

X-ray(Scanning)

T

Figure 3.6: Schematic representation of an annular sample used in dilatometer exper-iments with indication of cooling direction. WAXD analysis is performedex situ either in scanning mode (perpendicular to direction of cooling) orin single shot mode (parallel to direction of cooling).

Crystalline morphology

Wide angle X-ray diffraction (WAXD) experiments are performed to investigate thecrystalline morphology depending on cooling rate and pressure. These experimentsare performed in single shot mode, parallel to the direction of cooling. Additionally,the homogeneity of samples subjected to Tmedium and Thigh is analyzed by performingexperiments in scanning mode, perpendicular to direction of cooling (see figure 3.6).Here a step size of 0.05 mm is used. The step size is chosen smaller than the beamsize to study possible heterogeneities at the edge of the sample. From the two dimen-sional WAXD images, one dimensional scattering (1D WAXD) profiles are obtainedby integration of the Debye-Scherrer rings along the azimuthal angle. Furthermore,to correct for small variations in sample thickness and fluctuations of the beam, theintensity is normalized such that the area underneath the curve equals unity accord-ing to:

I∗ (2θ) =I (2θ)∫

I (2θ) d (2θ)(3.2)

The degree of crystallinity is determined by subtracting the scattering pattern ofa nearly 100% amorphous sample from the scattering patterns of semi-crystallinesamples. To do this, the intensity is scaled such that the maximum of the amor-phous halo equals the minimum between the (110)α / (111)γ and (040)α / (008)γ

diffraction peaks (see figure 3.7). Additionally, values for the relative fractions of thecrystalline phases in iPP (α-monoclinic, γ-orthorhombic crystalline phase) are deter-mined from single shot experiments according to the method of Van der Burgt etal. [24]. Changes in the (130)α scattering peak, which is located at 2θ = 5.94o forλ = 0.4956 Å, are taken as indicative for changes in α-monoclinic crystalline phase.For the γ-orthorhombic crystalline phase the (117)γ peak at 2θ = 6.49o is used (see


figure 3.7). The relative fractions are determined from the area beneath the respectivescattering peaks in the 1D-WAXD patterns, which are indicated as shaded areas infigure 3.7.

Homogeneity of crystalline morphology

Figure 3.8 shows the running average of the degree of crystallinity χ as distributionacross the sample thickness. The sample’s core corresponds to x=0. First of all, an un-usual high variation of 15% in the distribution of χ is observed for samples subjectedto Thigh and 60 MPa. This is quite unexplained. A possible explanation could be thecombined influence of spatial temperature gradients ∂T

∂x across the thickness of thesample, that increase with higher temperature values because of the time-dependentnature of the cooling rate, and the shift of T0

m towards higher temperatures with in-creasing pressure, i.e. with increasing pressure the polymer is subjected to highercooling rates that could result in significant spatial temperature gradients due to therelatively bad heat conductive properties of the polymeric sample. Samples sub-jected to Tmedium show a very homogeneous morphology while samples subjectedto Thigh and 20, 40 MPa display a somewhat larger, but still acceptable, variation.Table 3.4 shows the degree of crystallinity determined by both types of WAXD ex-periments. When comparing the degree of crystallinity determined from single shotexperiments (χ) with the averaged degree of crystallinity determined from scanningexperiments (χµ), differences of ≤ 1.1% are observed except for 20 MPa and a cool-ing rate 1.2 oC/s where a difference of 2.4% is seen. Since χ and χµ should be equal,these differences are subscribed to the accuracy of the method used to determine thedegree of crystallinity. The standard deviation σ increases with cooling rate but isstill acceptable small considering the accuracy of the method.

Degree of crystallinity and crystalline phase fractions

With respect to the influence of cooling rate and pressure on the degree of crys-tallinity χ and the relative fractions of the various crystalline phases present in iPP,our results confirm the findings of other authors (see table 3.4). As expected, thedegree of crystallinity decreases significantly with increasing cooling rate. The influ-ence of pressure is however marginal for the pressure range employed, especially forTmedium and Thigh. Furthermore, a combined influence of pressure and cooling rate isnot observed. This agrees with results of La Carrubba et al. [25] who found the effectof pressure on (α-)crystallinity to be largest in the pressure range to about 10 MPa forcooling rates exceeding 1.5 C/s. For pressures exceeding roughly 10 MPa at thesecooling rates, the observed influence of pressure was negligible and no combinedinfluence of cooling rate and pressure was detected.

With respect to changes in the relative fractions of the α- and γ-crystalline phaseswe observe an increase in the relative amount of γ-crystalline phase with increasingpressure at low cooling rates [19, 20, 26, 27], and a rapid decrease in γ-crystalline


( a)

( b)

Figure 3.7: 1D WAXD profiles showing the normalized intensity I∗ versus Bragg’s an-gle 2θ for samples crystallized at a pressure of 40 MPa and a characteristiccooling rate of (a) 0.1 C/s and (b) 32.5 C/s. The scaled amorphous halois represented by the dashed line.


−0.2 −0.1 0 0.1 0.225

30

35

40

45

50

55

60

65

X [mm]

χ [%

]

Figure 3.8: The running average of the degree of crystallinity χ plotted against scan-ning position (x = 0 corresponds to sample core). Symbols represent: (o)20 MPa - 1.2 C/s, (¤) 40 MPa - 1.4 C/s, (4) 60 MPa - 1.4 C/s, (•) 20MPa - 30.0 C/s, (¥) 40 MPa - 32.5 C/s, (N) 60 MPa - 34.8 C/s.

P Cooling¦T70

¦T χ χµ σ f rac α f rac γ

[MPa] Profile [oC/s] [oC/s] [%] [%] [−] [%] [%]20 0.1 63.7 - - 91.2 8.2

40¦Tlow 0.03 0.1 63.5 - - 82.0 18.0

60 0.1 62.3 - - 56.3 43.720 1.2 59.2 61.6 0.18 98.6 1.4

40¦Tmedium 0.5 1.4 60.1 59.0 0.34 99.2 0.8

60 1.4 59.4 59.9 0.38 99.1 0.920 30.0 54.2 54.1 0.88 100.0 0.0

40¦Thigh 18.1 32.5 54.0 52.9 1.55 100.0 0.0

60 34.8 34.1 33.9 5.79 100.0 0.0

Table 3.4: Influence of cooling rate and pressure on the degree of crystallinity and rel-ative crystalline fractions: χ = degree of crystallinity determined from sin-gle shot experiments, χµ = the average value of the degree of crystallinitydetermined from scanning experiments, σ = the standard deviation corre-sponding to values of χµ, f rac α = relative fraction of α-crystallinity, f rac γ

= relative fraction of γ-crystallinity.


Parameter Melt state (i=a) Solid state (i=sc) Dimensionνre f ,i 1.1379·106 1.0805·106 [mm3/kg]

∂νi∂T 7.7028·102 4.3988·102 [mm3/kgC]∂νi∂P -1.1232·10−3 -2.7242·10−2 [mm3/kgPa]

∂2νi∂T∂P -1.3400·10−6 -3.0343·10−6 [mm3/kgCPa]∂2νi∂T2 0·0 0·0 [mm3/kgC2]∂2νi∂P2 1.5443·10−11 2.6749·10−12 [mm3/kgPa2]∂3νi

∂T∂P2 -5.3721·10−14 1.5359·10−14 [mm3/kgCPa2]

Table 3.5: Partial derivatives for Taylor series description of the specific volume inmelt and solid state.

phase with increasing cooling rate [24,28]. The presence of a smectic or mesomorphicphase, was analyzed using a WAXD-deconvolution method similar to La Carrubbaet al. [25]. However, because of the large number of fitting parameters introducedby taking all crystalline phases (α−, γ−crystallinity), mesomorphic and amorphousphase into account, this method failed to produce reliable results with respect toquantifying the presence of the mesomorphic phase. Optimization of this method issubject of future research.

Modelling aspects

The specific volume data measured at a pressure of 40 MPa are used for comparisonwith numerical predictions that are based on the following constitutive model forspecific volume [2]:

ν = ξgνsc + (1−ξg)νa (3.3)

where νsc is the specific volume of the solid (semi-crystalline) state, νa the specificvolume of the amorphous phase assumed equal to the specific volume of the polymermelt, and ξg the degree of space filling of spherulites. Both νsc and νa are describedas a Taylor series in pressure and temperature.

νi = νre f ,i +∂νi

∂T4T +

∂νi

∂P4P +

∂2νi

∂T∂P4T4P +

∂2νi

∂T2 4T2 +

∂2νi

∂P2 4P2 +∂3νi

∂T∂P24T4P2 i = a, sc (3.4)

4T = T− Tre f (3.5)


4P = P− Pre f (3.6)

with Tre f =0 C and Pre f =20 MPa. Values for the partial derivatives are determinedby fitting (3.4) to specific volume data obtained during slow cooling (Tlow) and arelisted in table 3.5. The degree of space filling ξg is calculated using the Schneider rateequations for the description of quiescent crystallization kinetics in non-isothermalconditions [22]:

·φ3 = 8πα (φ3 = 8πN) ′rate′ (3.7)·φ2 = Gφ3 (φ2 = 4πRtot) ′radius′ (3.8)·φ1 = Gφ2 (φ1 = Stot) ′sur f ace′ (3.9)·φ0 = Gφ1 (φ0 = Vtot) ′volume′ (3.10)

φ0 = − ln(1−ξg

) ′space f illing′ (3.11)

These rate equations are based on the generalized Kolmogoroff equation [23], trans-forming the original integral form of Kolmogoroff’s equation to a set of differentialequations. Auxiliary functions φi are introduced by the step wise differentiationwith respect to time, each of which can be related to the crystalline morphology: φ0is equal to the undisturbed total volume Vtot of the spherulites per unit volume, φ1is the total surface Stot of the spherulites per unit volume, φ2 is 4π times the sumof the radii of the spherulites per unit volume, and φ3 is 8π times the number ofspherulites N per unit volume. Impingement and swallowing of spherulites are dis-regarded, i.e. unbounded growth of spherulites, which also implies that the rate ofnucleation α is independent of the volume fraction of already crystallized material.An Avrami model, equation (3.11), is used to correct for impingement and swal-lowing of spherulites. Important input data for these rate equations are the experi-mentally measured thermal history (see figure 2.5) and the, degree of undercoolingdependent, spherulitic growth rate G(T) and the number of nuclei per unit volumeN(T) determined from polarized optical microscopy experiments. To describe spe-cific volume at elevated pressure, both G(T) and N(T) are corrected for pressuredependence and modelled in the following way:

G(T, p) = Gmax exp[−b(T− Tre f − fg(p))2] (3.12)

N(T, p) = 10[n0+n1(T− fn(p))] (3.13)

where

fi(P) = pi04P + pi14P2 i = g, n (3.14)

4P = P− Pre f (3.15)


Parameter Fit1 Fit2 Fit3 DimensionGmax 2.9669·10−6 2.9669·10−6 2.9669·10−6 [m/s]b 1.3000·10−3 1.3000·10−3 1.3000·10−3 [1/oC]Tre f 9.00·101 9.00·101 9.00·101 [oC]pg0 2.7000·10−7 2.7000·10−7 7.0333·10−8 [K/Pa]pg1 0·0 0·0 -4.7000·10−15 [K/Pa2]pn0 2.7000·10−7 -7.4287·10−7 2.7000·10−7 [K/Pa]pn1 0·0 1.3870·10−14 0·0 [K/Pa2]n0 1.9067·101 1.9067·101 1.9067·101 [1/m3]n1 -4.9800·10−2 -4.9800·10−2 -4.9800·10−2 [1/m3K]Pre f 1.0000·105 1.0000·105 1.0000·105 [Pa]

Table 3.6: Model parameters for the spherulitic growth rate G(T,p) and effective num-ber of nuclei N(T,p) for iPP (HD120MO, Borealis).

In a first approach, the pressure dependence of both spherulitic growth rate G(T, p)and number of nuclei N(T, p) is taken equal to the pressure dependence of the crys-tallization temperature Tc. The reason for this is that the pressure dependence of Tcis related to the pressure dependence of the (equilibrium) melting temperature T0

m,which in its turn affects the undercooling4T, being the real driving force for G(T, p)and N(T, p). Values for the various modelling parameters are listed in table 3.6 andare indicated with ‘Fit 1’.

The predicted specific volume for a pressure of 40 MPa and Tlow is shown in figure3.9a, and for Tmedium and Thigh in figures 3.10a and 3.10b, respectively. Except forThigh, the predicted specific volume agrees rather well with experimental data. ForThigh a large mismatch in the predicted start and evolution of the transition withrespect to the experimental data is observed. A second and third approach to modelthe pressure dependence of G(T, p) and N(T, p) is to: i) adjust N(T, p) such thatthe predicted specific volume fits to the experimental data obtained at Tlow, whileG(T, p) is based on the pressure dependence of Tc (=fit 2), ii) adjust G(T, p) such thatthe predicted specific volume fits to the experimental data obtained at Tlow, whileN(T, p) is based on the pressure dependence of Tc (=fit 3). Although both approachesshow similar results as fit 1 for Tlow and Tmedium, only fit 3 shows improvement ofthe predicted specific volume for Thigh. The predicted evolution of the transition isquite improved using fit 3, while the mismatch in predicted start of the transitionstays rather unaffected for all three approaches. These deviations could be resultingfrom experimental inaccuracies determining G(T) and N(T). See for example thecompilation of growth speeds for the α-crystallinity of iPP as reported by Eder andJaneshitz-Kriegl [30] Here differences of up to a factor 2 in the reported Gmax of theα-crystalline phase of iPP can be observed.


0 50 100 150 2001.05

1.1

1.15

1.2

1.25

1.3x 106

T [C]

ν [m

m3 /k

g]

Fit 1Fit 2Fit 3

( a)

0 50 100 150 2001.05

1.1

1.15

1.2

1.25

1.3x 106

T [C]

ν [m

m3 /k

g]

Fit 3 n1 −10% n1 +10% Tref −5%Tref +5%

( b)

Figure 3.9: (a) Measured (¤) and calculated specific volume for a pressure of 40 MPaand a cooling rate of 0.1 C/s, (b) influence of small variations in modelparameters on the predicted specific volume at a cooling rate of 0.1 C/s.Calculations are indicated in the same way as the used numerical descrip-tion for G(T) and N(T) in figure 3.11.


0 50 100 150 2001.05

1.1

1.15

1.2

1.25

1.3x 106

T [C]

ν [m

m3 /k

g]

Fit 1Fit 2Fit 3

( a)

0 50 100 150 2001.05

1.1

1.15

1.2

1.25

1.3x 106

T [C]

ν [m

m3 /k

g]

Fit 1Fit 2Fit 3

( b)

Figure 3.10: Measured (¤) and calculated specific volume for a pressure of 40 MPaand a cooling rate of (a) 1.4 C/s and (b) 32.5 C/s.


Another reason for the observed mismatch between the experimentally measuredand numerically predicted specific volume could be because of inaccuracies in deter-mining numerical descriptions for G(T, p) and N(T, p). To study the influence of thelatter on predictions of specific volume, small variations in the parameters describingG(T, p) and N(T, p) are introduced (see figure 3.11). With respect to the modellingof G(T, p), variations of ±5% in Tre f are introduced. Similarly, variations of ±10%in n1 are introduced when modelling N(T, p). The effect of these variations on thepredicted specific volume are shown in figure 3.9b and figure 3.12. Again, the pre-diction of the specific volume at Thigh shows the largest susceptibility to variations inthe model. If we focus on predictions for Thigh (figure 3.12b), variation of parametern1 with -10% does not show any change in predictions with respect to fit 3 (curveson top of each other). Variation of n1 with +10% gives a slightly worse prediction ofthe evolution of the transition. Changes of ±5% in Tre f result in larger differences inpredicted transition. Because these changes in Tre f mainly affect the description ofG(T, p) for temperature values lower than the temperature where Gmax is occurring(see figure 3.11), we can conclude that especially the description of G(T, p) for theselow temperatures is of importance for the correct prediction of specific volume athigh cooling rates.

The mismatch in predicted start of the transition is however almost unaffected by allvariations. Only (unrealistically large) variations of N(T, p), such that a larger num-ber of nuclei becomes available at high temperatures, is able to improve this mis-match. This can be accomplished for example by choosing a constant and relativelylarge value for N(T, p), in combination with a description of G(T, p) according to fit3. Here a value of 1015.25 1/m3 is chosen for parameter n0 (see figure 3.11b). Thesedeviations in predicted specific volume compared to experimentally determined val-ues are still not well understood and are subject of future investigations.


0 50 100 15010

−8

10−7

10−6

T [C]

G [

m/s

]

Exp. dataBest fit Tref −5% Tref +5%

( a)

0 50 100 15010

10

1015

1020

T [C]

N [

1/m

3 ]

Exp. data Best fit n1 +10% n1 −10% N = 1015.25

( b)

Figure 3.11: Spherulitic growth rate G(T) and effective number of nuclei N(T) deter-mined from polarized optical microscopy measurements at atmosphericpressure (O) and various numerical descriptions characterized by smallvariations in model parameters.


0 50 100 150 2001.05

1.1

1.15

1.2

1.25

1.3x 106

T [C]

ν [m

m3 /k

g]

Fit 3 n1 −10% n1 +10% Tref −5%Tref +5%

( a)

0 50 100 150 2001.05

1.1

1.15

1.2

1.25

1.3x 106

T [C]

ν [m

m3 /k

g]

Fit 3 n1 −10% n1 +10% Tref −5% Tref +5% N = 1015.25

( b)

Figure 3.12: Influence of small variations in model parameters on the predicted spe-cific volume at a cooling rate of (a) 1.4 C/s and (b) 32.5 C/s. Calcula-tions are indicated in the same way as the used numerical description forG(T) and N(T) in figure 3.11.


3.4 Conclusions

The influence of cooling rate and pressure on the specific volume of isotacticpolypropylene was investigated using a custom designed dilatometer. A profoundinfluence of both cooling rate and pressure on the crystallization temperature Tc andthe final specific volume after cooling was observed. Comparison of these resultswith different literature sources showed good agreement. The need for homoge-neous cooling restricts the maximum cooling rate that can be used. The influenceof possible thermal gradients in the sample on the resulting crystalline morphologyis however dependent on the actual undercooling. Because of the time-dependentnature of the cooling rate and the pressure dependence of the melting temperatureof the polymer, also the pressure puts indirect restrictions to the maximum coolingrate to be used. In our study using isotactic polypropylene, analysis of the crystallinemorphology via WAXD showed good homogeneity of samples up to a cooling rateof 32.4 C/s and a pressure of 40 MPa.Finally, comparison of model predictions with experimental data at medium andhigh cooling rate showed at first large deviations in the prediction of start and evo-lution of the transition, i.e. the predicted crystallization temperature Tc and rate ofcrystallization. Deviations in the rate of crystallization could partly be explainedfrom small variations in model parameters. These variations were justified frompossible inaccuracies in the experimental characterization of G(T, p) and N(T, p),or from determining model parameters to describe these quantities numerically. Es-pecially in the prediction of crystallization kinetics during fast cooling, G(T, p) andN(T, p) should be characterized for a sufficiently large temperature range, includingtemperatures typically lower than the temperature where the maximum in G(T, p)occurs. Deviations in predicted crystallization temperature Tc are however quite un-explained and could only be improved by introducing an unrealistic larger numberof nuclei than determined experimentally at relatively high temperatures. This issubject to future investigation.


References

[1] Luyé, J.F., Regnie, G., Le Bot, P.H., Delaunay, D., Fulchiron, R. PVT measure-ment methodology for semicrystalline polymers to simulate injection-moldingprocess. Journal of Applied Polymer Science, 79:302-311, (2001).


[3] Chakravorty, S. PVT testing of polymers under industrial processing conditions.Polymer Testing, 21:313-317, (2002).

[4] Piccarolo, S. Morphological changes in isotactic Polypropylene as a function ofcooling rate. Journal of Macromolecular Science - Phys., B31(4):501-511, (1992).

[5] Baer, E., Kardos, J.L. Melting of homopolymers under pressure. Journal of Poly-mer Science, 3:2827-, (1965).

[6] Leute, U., Dollhopf, W., Liska, E. Dilatometric measurements on some poly-mers: the pressure dependence of thermal properties. Colloid and Polymer Sci-ence, 254:237-246, (1976).

[7] Karl, V.H. and Asmussen, F. and Überreiter, K. Über die Druckabhängigkeit derViskoelastischen und Physikalisch-Chemischen Eigenschaften von Polymeren.Markomolecular Chemistry, 178:2037-2047, (1977).

[8] He, J. Zoller, P. Crystallization of Polypropylene, Nylon-66 and Poly(ethyleneterephtalate) at pressures to 200 MPa: kinetics and characterization of products.Journal of Polymer Science: Part B, Polymer Physics, 32:1049-1067, (1994).

[9] Zoller, P., Fakhreddine, Y.A. Pressure-Volume-Temperature studies of semicrys-talline polymers. Thermochimica Acta, 238:397-415, (1994).

[10] Ito, H., Tsustumi, Y., Minagawa, K., Takimoto, J., Koyama, K. Simulationsof polymer crystallization under high pressure. Colloid and Polymer Science,273:811-815, (1995).

[11] V. La Carrubba, Polymer Solidification under Pressure and High Cooling Rate, PhD-thesis University of Palermo, (1997).

[12] Piccarolo, S. Morphological changes in isotactic Polypropylene as a function ofcooling rate. Journal of Macromolecular Science - Phys., B31(4):501-511, (1992).

[13] Piccarolo, S., Saiu, M., Brucato, V., Titomanlio, G. Crystallization of polymermelts under fast cooling. II: High-purity iPP. Journal of Applied Polymer Science,46:625-634, (1992).

[14] Pantani, R., Titomanlio, G. Description of PVT behavior of an industrialpolypropylene-EPR copolymer in process conditions. Journal of Applied PolymerScience, 81:267-278, (2001).

[15] Brucato, V., Piccarolo, S., La Carrubba, V. An experimental methodology tostudy polymer crystallization under processing conditions. the influence of highcooling rates. Chemical Engineering Science, 57:4129-4143, (2002).

[16] La Carrubba, V., Brucato, V., Piccarolo, S. Phenomenological approach to com-pare the crystallization kinetics of isotactic Polypropylene and Polyamide-6

REFERENCES 57

under pressure. Journal of Polymer Science: Part B: Polymer Physics, 40:153-175,(2002).

[17] The Fit2D homepage, www.esrf.fr/computing/scientific/FIT2D.[18] Coccorrullo, R., Pantani, R., Titomanlio, G. Crystallization kinetics and solidi-

fied structure in iPP under high cooling rates. Polymer, 44:307-318, (2003).[19] K. Mezghani, P. Phillips, The γ-phase of high molecular weight isotactic

polypropylene: III. the equilibrium melting point and the phase diagram. Poly-mer, 39(16):3735-3744, (1998).

[20] Nakafuku, C. High pressure D.T.A. study on the melting and crystallization ofisotactic Polypropylene. Polymer, 22:1673-1676, (1981).

[21] Angelloz, C., Fulchiron, R., Douillard, A., Chabert, B., Fillet, R., Vautrin, A.,David, L. Crystallization of isotactic polypropylene under high pressure (γphase). Macromolecules, 33:4138-4145, (2000).

[22] Schneider, W., Köppl, A., Berger, J. Non-isothermal crystallization. Crystalliza-tion of polymers. International Polymer Processing, 2(3):151-154, (1988).

[23] Kolmogoroff, A.N. On the Statistical Theory of the Crystallization of the Metals.Izvestiya Akad. Nauk SSSR, Ser. Math., 1:355, (1937).

[24] Van der Burgt, F.P.T.J., Rastogi, S., Chadwick, J.C., Rieger, B.J. Influence of ther-mal treatments on the polymorphism in stereoirregular isotactic polypropy-lene: effect of stereo-defect distribution. Journal of Macromolecular Science. PartB: Physics, B41:1091-1104, (2002).

[25] La Carrubba, V., Brucato, V. , Piccarolo, S. Isotactic Polypropylene solidificationunder pressure and high cooling rates. A master curve approach. Polymer Engi-neering and Science, 40(11):2430-2441, (2000).

[26] Campbell, R.A., Philips, P.J., Lin, J.S. The gamma phase of high-molecularweight polypropylene: 1. morphological aspects. Polymer, 34(23):4809-4816,(1993).

[27] Brückner, S., Philips, P.J., Mezghani, K., Meille, S.V. On the crystallization ofγ-isotactic polypropylene: A high pressure study. Macromolecular Rapid Commu-nications, 18:1-7, (1997).

[28] Foresta, T., Piccarolo, S., Goldbeck-Wood, G. Competition between α and γ

phases in isotactic Polypropylene: effects of ethylene content and nucleationagents at different cooling rates. Polymer, 42:1167-1176, (2001).


[30] G. Eder, H. Janeschitz-Kriegl. Crystallization, in: Processing of Polymers, Meijer,H.E.H., (Ed.), VCH: New York, vol.18, p. 269-342, (1997).


3.A Appendix: specific volume of the melt

Specific volume data obtained with a conventional ’bellows’ type dilatometer(Gnomix Inc.) are used to complete measurements performed with our custom de-signed dilatometer. Figure 3.13 shows the data, which are measured in isobaric modeat a constant cooling rate of 1.0 C/min. Experiments are performed at MoldflowPlastics Labs (Ithaca, USA). The material used is an iPP (grade K2Xmod, Borealis)which is characterized by Mw = 365000 g/mol, Mw/Mn = 5.2. This material isvery similar in molecular weight and molecular weight distribution compared to theinvestigated polypropylene grade HD120MO, except that the latter does not includenucleation agent. The specific volume of the melt is assumed identical. A polynomialfit is determined to describe the specific volume of the melt as function of pressureand temperature:

ν (T, p) = a0 + a1T + a2T4P + a3T4P2 + a44P + a54P2 (A.1)

with

4P = P− Pre f (A.2)

Values for the various parameters are given in table 3.7. This fit serves to translatethe relative specific volume data measured with our dilatometer to absolute specificvolume, i.e. the specific volume of the melt at the highest temperature is set equalto the specific volume determined with the fit using the highest temperature andpressure as input.

Parameter Value Dimensiona0 1.1348·106 [mm3/kg]a1 8.6387·102 [mm3/kg oC]a2 −7.3487·10−6 [mm3/kg oCPa]a3 4.0480·10−14 [mm3/kg oCPa2]a4 −1.4359·10−4 [mm3/kgPa]a5 −1.7185·10−12 [mm3/kgPa2]Pre f 1.0·107 [Pa]

Table 3.7: Parameters for the polynomial description of the specific volume in themelt.

3.A APPENDIX: SPECIFIC VOLUME OF THE MELT 59

50 100 150 2001.05

1.1

1.15

1.2

1.25

1.3

1.35x 10

6

T [C]

ν [

mm

3 /kg]

p = 10 [MPa]p = 40 [MPa]p = 80 [MPa]p = 100 [MPa] Fit

Figure 3.13: Specific volume data of iPP (grade K2xmod, Borealis) measured in iso-baric mode at a constant cooling rate of 1.0 C/min. Solid lines representthe fit for the specific volume of the melt.

‘Design C’

CHAPTER FOUR

The influence of shear flow onspecific volume 1

The influence of shear flow on the temperature evolution of the specific vol-ume of two iPP’s, differing in weight averaged molar mass Mw, was inves-tigated at non-isothermal conditions and elevated pressures, using a customdesigned dilatometer. These conditions are typically in the range of condi-tions as experienced during polymer processing. A pronounced influenceof flow on the temperature marking the transition in specific volume andthe rate of transition could be observed. In general, this influence increasedwith increasing shear rate, decreasing temperature where flow was applied,increasing pressure, and increased weight averaged molar mass Mw of thepolymer. Although the degree of orientation and the overall structure of theresulting crystalline morphology were greatly affected by the flow, the result-ing specific volume was only little affected by the thermomechanical condi-tions presently investigated. Finally, when flow was applied at sufficientlyhigh temperature, in some cases the polymer was able to fully erase the ef-fect of flow. This is attributed to remelting of the flow-induced crystallinestructures.

4.1 Introduction

During processing operations such as injection molding, extrusion, fiber spinning,etc., polymers are subjected to different types of flow fields (shear, extension, mixed)[1]. For semi-crystalline polymers, it is known that these flow conditions strongly in-fluence the process of crystallization and the resulting crystalline morphology [2–14].This is expected to also have a major influence on the evolution of specific volumeand on the final mechanical and dimensional properties. The number of studies re-

1Submitted to: Macromolecules.

61

62 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

garding the influence of flow on the specific volume of polymers is, however, limited.Fritzsche and Price [15] used a concentric cylinder dilatometer to quantitatively fol-low the crystallization process of polyethylene oxide (PEO) grades as a function ofundercooling, shear rate, and molecular weight. This was derived from specific vol-ume data. Steady shear experiments, with shear rates applied up to 140 1/s, wereperformed at isothermal conditions and atmospheric pressure. Results showed thestart in crystallization, i.e. the transition in the specific volume, to occur at smallertimes with increasing shear rate, increasing molecular weight, and higher undercool-ing. Fleishmann and Koppelmann [16] performed injection molding experimentsand compared measured cavity pressure levels with calculated pressures, to drawconclusions with respect to the dependence of specific volume on applied flow. Theagreement of calculated and experimental pressure data showed large deviations ifstandard ’slow cooling PVT-data’ were used as input for the model. A better agree-ment was obtained by shifting the transition temperature of specific volume towardshigher temperatures to correct for the influence of flow. Watanabe et al. [17] useda dilatometer consisting of a mixture of a conventional piston-die dilatometer anda plate-plate rheometer, to study the influence of (steady) shear rate and elevatedpressure at isothermal conditions on the relative degree of crystallinity as derivedfrom specific volume data. The start of the transition in the specific volume of iPPwas found to occur at smaller times with increasing shear rate and with increasingpressure. The influence of pressure was explained by the shift in the experimentalmelting temperature Tm towards higher temperatures leading to increased under-cooling at a constant temperature. Unfortunately, only shear rates up to 0.5 1/s wereapplied at a maximum pressure of 20 MPa. These conditions are not very repre-sentative for the processing conditions as encountered during, for instance, injectionmolding. Moreover, the plate-plate geometry is not very well suited to study theinfluence of shear rate on specific volume because of its dependence on the sampleradius, i.e. inhomogeneous distribution across the sample.

This chapter deals with the influence of shear flow on the specific volume of isotacticpolypropylene measured at conditions close to industrial processing conditions. Thecombined influence of shear rate, pressure, cooling rate, and the polymer’s molec-ular weight distribution on the temperature-dependent development of the specificvolume is studied, using the technique of dilatometry. The results are explained us-ing the present knowledge of (flow induced) crystallization and are related to thecrystalline morphology, as investigated ex situ using wide angle X-ray diffraction(WAXD) and visualized by scanning electron microscopy (ESEM).


Materials

The materials used are two commercial isotactic polypropylenes (iPP). The first ma-terial (iPP-1) is supplied by Borealis (grade HD120MO), the second material (iPP-2)

4.2 EXPERIMENTAL PART 63

3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

log Mw

[g/mol]

Am

ount

[%

]

iPP−1iPP−2

Figure 4.1: Molecular weight distribution determined via gel permeation chromatog-raphy (GPC). Data were provided by Gahleitner/Königsdorfer (Borealis,Linz, Austria).

Material Mw Mw/Mn Tm[g/mol] [−] [oC]

iPP-1 365000 5.2 162.7iPP-2 636000 6.9 163.0

Table 4.1: Characterization of the materials used in this study. iPP-1: HD120MO (Bo-realis, Austria), iPP-2: Stamylan P 13E10 (DSM, The Netherlands).

by DSM (grade Stamylan P 13E10). Figure 4.1 shows the molecular weight distribu-tion of both materials determined via GPC, and table 4.1 lists some main propertiesof both materials. Note that although iPP-2 was also used by Swartjes et al. [14], re-sults of GPC characterization are somewhat different. For dilatometer experiments,samples with dimensions 2.5 x 65 x 0.4 mm are prepared by compression molding.These dimensions are chosen to facilitate the sample loading into the dilatometer.Samples are prepared from standard sized pellets using compression molding. First,pellets are melted at atmospheric pressure. Next, the material is compressed for 3minutes at 210 C with a force of 50 kN. The samples are cooled in a water cooledpress during 5 minutes from 210 to 25 C again with a force of 50 kN.


T[ C]O

Gg[1/ ]s

Tt [s]

Tt [s]

B

A

D

E

P[Mpa]

C

Tt [s]

Figure 4.2: Schematic representation of the employed experimental procedure.

Dilatometry

The influence of shear flow on specific volume at elevated pressures is investigatedusing the custom designed dilatometer as described in chapter 2. Dilatometer ex-periments are performed in the isobaric cooling mode according to the procedureschematically depicted in figure 4.2: A) the sample is heated with an average heat-ing rate of 5 C/min to a temperature of 210 C, B) kept for 10 minutes at 210 C toensure fully melting of the crystalline microstructure, C) pressurized to the desiredlevel, D) cooled to room temperature during which the pressure is maintained con-stant to within ±0.3 MPa, E) and during cooling subjected to shear flow for a certaintime and constant shear rate. After the sample is completely cooled down, it is takenout of the dilatometer and the same procedure is repeated in the absence of a sample.This calibration measurement is used to correct the measured volumetric change ofthe sample for external influences such as thermal expansion of the dilatometer, de-formation of the dilatometer due to mechanical loading, etc. Within minutes afterfinishing the experiments, the samples are removed from the dilatometer and storedin a freezer at −5 C for later analysis of the crystalline morphology and resultingdensity.

Density Gradient Column

Density gradient column (DGC) experiments were performed according to ASTMD1505, establishing a linear density distribution ranging from 0.87-0.94 g/cc using


water and isopropanol (IPA). Measurements were performed at a column tempera-ture of 23 C. Prior to submergence into the column, samples were subjected to anultrasonic bath, consisting of a representative mixture of water and isopropanol, for20 minutes in order to minimize the presence of air bubbles on the sample surface.

X-ray analysis

Wide Angle X-ray Diffraction (WAXD) experiments were performed at the materialsbeam-line ID 11 of the European Synchrotron Radiation Facility (ESRF) in Grenoble,France. The size of the X-ray beam is 0.2 x 0.2 mm2 having a wavelength of 0.4956Å. The detector used is a Frelon CCD detector with 1024 x 1024 pixels. Both hor-izontal and vertical pixels are 164 µm in size. From calibration experiments, usingLanthanum Hexaboride, a sample-to-detector distance of 439.9 mm was determined.The exposure time for all images was 30 seconds.

Scanning Electron Microscopy

Microtome cuts were taken from samples under cryogenic conditions. These weresubsequently etched for 4 hours in a mixture of potassium permanganate (KMnO4)and acid (4 vol.-% H3PO4, 10 vol.-% H2SO4) and coated with gold (Au). Finally,imaging of the etched sample surfaces was done with a Philips XL30 ESEM using aSE-detector and operated at 5 kV.


Specific volume

Dilatometer experiments were performed to study the combined influence of shearflow, pressure, and molecular parameters on the specific volume of iPP. Parametersthat were varied are: a) average temperature during flow, b) shear rate at constanttotal shear, c) the molecular weight distribution (MWD) of the polymer, d) pressureduring flow. In the following analysis of the results, the specific volume is normal-ized to make comparison of results obtained at various processing conditions moreeasy. The normalized specific volume ν∗ is defined as:

ν∗ =ν − νs

νm − νs(4.1)

where ν is the measured specific volume, νs is the value of the specific volume in thesolid state at room temperature (in case the sample was not subjected to flow), andνm represents the value of the specific volume in the melt state at 210 C.


0 100 200 300 400 500 600

50

100

150

200

T [

C]

0 100 200 300 400 500 600

−4

−2

0

t [s]

Coo

ling

Rat

e [C

/s]

Figure 4.3: Recorded temperature (top) and derived cooling rate (bottom).

iPP-1 iPP-2Tγ 4Tγ Tγ 4Tγ

[C] [C] [C] [C]139 59.2 133 65.2154 44.2 153 45.2193 5.2 193 5.2

Table 4.2: Temperatures Tγ where shear flow is applied and associated undercooling4Tγ for both iPP’s.

Influence of temperature during flow

The influence of thermomechanical history on the specific volume of iPP was investi-gated by subjecting the polymer to shear flow at various temperatures. The pressureduring the experiments was kept constant at 40 MPa and cooling as depicted in fig-ure 4.3 was applied. Shear flow was applied as a step-function during cooling, with ashear rate of 39.0 1/s for a shear time ts = 3.0 s or a shear rate of 78.0 1/s for ts = 1.5s, i.e. the total shear is approximately constant. Flow was applied at various temper-atures, i.e. different degrees of undercooling. Since shear flow was applied duringcooling over a small temperature range, the average value of this range is taken asa characteristic value and further referred to as Tγ. Values for Tγ and the associatedundercooling, 4Tγ = T0

m − Tγ, are listed in table 4.2. For the equilibrium meltingtemperature T0

m at a pressure of 40 MPa a value of 198.2 C is used [24].


0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( a)

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( b)

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( c)

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( d)

Figure 4.4: Influence of shear flow on the normalized specific volume ν∗ of iPP-1.Shear flow is applied as a step function with a shear rate of 39.0 1/s dur-ing 3.0 s (4) or a shear rate of 78.0 1/s during 1.5 s (¤) at various tem-peratures, indicated by the arrows: (a) no shear flow applied, (b) Tγ = 193C, (c) Tγ = 154 C, (d) Tγ = 139 C. Measurements performed in absenceof flow are represented by (O). All measurements are performed at a con-stant pressure of 40 MPa. WAXD images show the influence of shear flowon the orientation of the resulting crystalline morphology, using a shearrate of 39.0 1/s during 3.0 s.


Figures 4.4 and 4.5 show the influence of shear flow applied at various tempera-tures Tγ on the normalized specific volume of respectively iPP-1 and iPP-2. Arrowsindicate the temperature Tγ where flow is applied. The WAXD patterns give an in-dication of the orientation of the resulting crystalline morphology (flow direction isvertical). Furthermore, in each sub-figure the specific volume measured in the ab-sence of flow is incorporated for reference. Figure 4.4 shows that, dependent on Tγ,shear flow can have a profound influence on the temperature Tc marking the onsetof the transition, whereas the specific volume of the solid state is hardly affected. Ifshear flow has an effect, then Tc shifts towards higher temperatures and associatedto this WAXD analysis shows arcing of the Debye-Scherrer rings. This is an indica-tion for orientation of the resulting crystalline morphology. From a thermodynamicpoint of view, the shift in Tc towards higher temperatures can be explained from theorientation of polymer chains due to shear flow, causing a decrease in melt entropy.This can be reflected in an effective increase of the melting temperature [18]. At agiven temperature the effective undercooling 4T is therefore higher. From a crystal-lization kinetics point of view, molecular orientation yields an enhanced formationof (flow induced) primary nuclei [2, 3, 6, 9, 11, 19]. The number of flow induced nu-clei can be some orders of magnitude higher than the number of nuclei formed atquiescent conditions [13]. Both effects will enhance the crystallization kinetics, en-abling the process of crystallization to start at higher temperatures. Furthermore,with increasing Tγ the resulting crystalline morphology shows less orientation andthe temperature interval between Tγ and Tc increases. Note that if iPP-1 is subjectedto a shear rate of 39.0 1/s at Tγ = 193 C, the effect of flow can be fully erased (figure4.4b). This ability of the melt to erase the influence of flow on the process of crys-tallization was also observed by others [20–22], and is attributed to remelting of theflow induced crystalline structure and relaxation of oriented chains. However, if thepolymer is subjected to a shear rate of 78.0 1/s at Tγ = 193 C, the influence of flowis not fully erased as indicated by a small shift in Tc.

If shear flow is applied at increased undercooling (figures 4.4c and 4.4d), remelting offlow induced structures can be ignored [20]. The evolution of the specific volume incase the polymer is subjected to a shear rate of 39.0 1/s applied either at Tγ = 154 Cor Tγ = 139 C matches surprisingly well. The temperature marking the start of thetransition and the evolution of the transition itself are almost identical. This is morecoincidence than rule and is treated in more detail in chapter 5. If the temperature atwhich shear flow is applied is taken as a reference, the polymer needs an additionalundercooling of about 17 C for the transition to start in case shear flow is appliedat Tγ = 154 C. If shear flow is applied at Tγ = 139 C, the transition starts almostimmediately, i.e. the time needed to start crystallization after application of flowreduces. There are several reasons for that. First, viscoelastic stresses arising fromshear flow at lower temperature are higher, therefore leading to a higher numberof shear induced nuclei [13]. Secondly, at lower Tγ, or higher undercooling 4Tγ,a larger number of quiescently formed nuclei is present, which are believed to linkmolecules into a physical network [23]. Shear flow applied will thus have a largerorienting effect throughout the melt, potentially forming more flow induced nuclei.


0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( a)

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( b)

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( c)

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( d)

Figure 4.5: Influence of shear flow on the normalized specific volume ν∗ of iPP-2.Shear flow is applied as a step function with a shear rate of 39.0 1/s dur-ing 3.0 s (4) at various temperatures, indicated by the arrows: (a) no shearflow applied, (b) Tγ = 193 C, (c) Tγ = 153 C, (d) Tγ = 133 C. Measure-ments performed in absence of flow are represented by (O). All measure-ments are performed at a constant pressure of 40 MPa. WAXD imagesshow the influence of shear flow on the orientation of the resulting crys-talline morphology.


130 140 150 160 170 180 190 200

1.096

1.098

1.1

1.102

1.104

1.106

1.108x 10

6

Tγ [C]

ν [m

m3 /k

g]

iPP−1 / 39.0 [1/s]iPP−2 / 39.0 [1/s]iPP−1 / Quiescent iPP−2 / Quiescent

( a)

10 20 30 40 50 60 70

1.096

1.098

1.1

1.102

1.104

1.106

1.108x 10

6

P [MPa]

ν [m

m3 /k

g]

iPP−1 / Quiescent iPP−1 / 78.0 [1/s]

( b)

Figure 4.6: (a) The influence of shear flow, applied with a shear rate of 39.0 1/s during3.0 s at a pressure of 40 MPa for various Tγ on the specific volume aftercomplete cooling, (b) the influence of pressure on the resulting specificvolume of iPP-1 when shear flow is applied with a shear rate of 78.0 1/sduring 1.5 s at Tγ = 140 C. Lines are used to guide the eye.

Thirdly, the spherulitic growth rate is larger at higher undercooling. These effectsexplain the enhanced crystallization process from the moment flow is applied andthe higher degree of orientation visualized by WAXD in figure 4.4d compared tofigure 4.4c. This agrees qualitatively with the resulting crystalline morphology asvisualized by ESEM (figure 4.7). Pictures (a-c) correspond to iPP-1, and show theinfluence of flow applied at various temperatures Tγ. All images are taken close tothe core of the sample. When shear flow is applied at lower Tγ, smaller spherulitesare formed and the orientation of the morphology increases (row nucleation). Figure4.4d furthermore shows that by increasing the shear rate to 78.0 1/s, the crystalliza-tion kinetics are more enhanced, i.e. the whole transition process takes place muchfaster.Finally, figure 4.6a shows the influence of Tγ on the resulting specific volume mea-sured via DGC. The specific volume resulting from quiescent conditions, i.e. no shearflow applied, is represented by filled symbols plotted at the highest temperature Tγ.In general, the influence of shear flow on the resulting specific volume can be ne-glected. This despite the observed differences in the evolution of specific volumeand differences in the orientation and structure of the crystalline morphology.

Influence of molar mass distribution

Figure 4.5 shows the influence of Tγ on the normalized specific volume and resultingcrystalline morphology of iPP-2. With respect to iPP-1, this material has a higherweight averaged molar mass Mw. Comparing figures 4.4a and 4.5a we conclude thatthe normalized specific volume of both (polydisperse) iPP’s at quiescent conditionsis practically identical. As expected, the effect of shear flow on the specific volume


and the resulting crystalline morphology is significantly enhanced by the increasein Mw [4, 7, 8, 10, 12, 21]. If shear flow is applied to the undercooled melt of iPP-2, the transition to the semi-crystalline state is significantly faster (figure 4.5d), orthe temperature interval between Tγ and Tc decreases compared to the iPP-1 results,(figure 4.5c). Even when shear flow is applied at Tγ = 193 C, i.e. close to theequilibrium melting temperature T0

m, the specific volume and crystalline morphologyare affected (figure 4.5b).

Figure 4.7 (d-f), confirms the large influence of Mw on the crystallization kineticsafter flow. Contrary to iPP-1, significant orientation of the morphology is alreadyseen when shearing at Tγ = 193 C (figure 4.7d), which was already observed inthe WAXD patterns in figure 4.5. With decreasing temperature of flow, (bundles) ofhighly oriented structures can be observed at Tγ = 154 C, and finally a denselypacked highly oriented structure results across the whole sample thickness in case ofTγ=139 C.

Finally, the influence of Tγ on the specific volume after complete cooling (figure 4.6a)shows the same trend as for iPP-1. The molecular weight distribution seems to playa minor role in this.

Influence of pressure during flow

The influence of the pressure during flow is investigated either for a constant tem-perature Tγ and for a constant undercooling 4Tγ. In both cases polymer iPP-1 issubjected to a step shear with a shear rate of 78.0 1/s during 1.5 s at pressure levels20, 40, and 60 MPa. Figure 4.8 shows the results if shear flow is applied at Tγ = 140C. All pressure levels display the typical shift of Tc towards higher temperatureswhile the effect on the specific volume of the solid state is small to negligible. Addi-tionally, we see the small temperature interval between Tγ and Tc to decrease evenfurther with increasing pressure and the transition in specific volume is getting moreabrupt. These last observations point to enhancement of the crystallization processafter and during flow with increased pressure level. If the specific volume is an-alyzed as a function of time (see figure 4.8d), an increase in the transition rate isobserved with respect to the quiescent situation by a factor 1.4, 4.6, and 6.0 for pres-sure levels of 20, 40, and 60 MPa, respectively. Figure 4.6b shows the specific volumeafter complete cooling, measured with DGC. Lines are used to guide the eye. The de-crease in specific volume with respect to quiescent conditions is the same for everypressure level applied, about 0.28-0.29 %.

Figure 4.9 shows the influence of shear flow applied on the specific volume measuredat pressure levels 20, 40, and 60 MPa and an almost identical undercooling. Becauseof the pressure dependence of the equilibrium melting temperature T0

m of iPP [24],the temperature at which the flow is applied increases with increasing pressure. Forpressure levels 20, 40, 60 MPa, the temperature where flow is applied Tγ is 150.1 C,153.6 C, and 160.7 C, respectively. Again using the data of Mezghani and Philips[24] for the pressure dependence of iPP’s T0

m, this resulted in an undercooling during


( a) ( d)

( b) ( e)

( c) ( f)

Figure 4.7: Crystalline morphology close to the core of the samples visualized usingESEM. Pictures (a-c) correspond to iPP-1 subjected to a shear rate of 39.01/s for 3.0 s applied at Tγ = 193 C (a), Tγ = 154 C (b), and Tγ = 139 C(c), respectively. Pictures (d-f) correspond to iPP-2 and Tγ = 193 C (d),Tγ = 153 C (e), and Tγ = 133 C (f), respectively. The flow direction isvertical.


0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( a)

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( b)

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

( c)

0 20 40 60 80 100

0

0.2

0.4

0.6

0.8

1

t [s]

ν* [ −

]

Quiescent − 20MPaQuiescent − 40MPaQuiescent − 60MPaFlow − 20MPa Flow − 40MPa Flow − 60MPa

( d)

Figure 4.8: Influence of the pressure during shear flow on the normalized specific vol-ume of iPP-1. Shear flow is applied as a step function with a shear rate of78.0 1/s during 1.5 s at Tγ = 140 C. Pressure levels are: (a) 20 MPa, (b)40 MPa, and (c) 60 MPa. Normalized specific volume as a function of timeis shown in (d) and illustrates the effect of pressure on the rate of crystal-lization.


−50 0 50 100 150 200

0

0.2

0.4

0.6

0.8

1

∆T [C]

ν* [ −

]

Figure 4.9: The influence of pressure on the normalized specific volume when ap-plying a step shear of 78.0 1/s during 1.5 s at a undercooling 4Tγ =41.9− 44.6 C (see text for explanation). Pressure levels are: (4) 20 MPa,(O) 40 MPa, (¤) 60 MPa. Specific volume measured at quiescent condi-tions is represented by open symbols, while the filled symbols representspecific volume subjected to shear flow.

flow of 41.9, 44.6, and 43.1 C, respectively. For all pressure levels we see an identicalshift of Tc with respect to quiescent conditions (open symbols). Also the transitionitself shows hardly any differences between the various pressure levels.

Crystalline morphology

Degree of orientation

The degree of crystal orientation, visualized by WAXD analysis in figures 4.4 and4.5, can be further quantified using the Herman orientation factor f. The orientationfunction is defined as:

f =3

⟨cos2 φ

⟩− 12

(4.2)


where φ is the angle between a reference direction (e.g. the direction of applied flow)and the normal to a set of hkl-reflective planes. The term 〈cos2 φ〉 is defined as:

⟨cos2 φ

⟩=

π/2∫0

I(φ) cos2 φ sinφdφ

π/2∫0

I(φ) sinφdφ

(4.3)

where I(φ) is the pole concentration representing the relative amount of crystallinematerial having plane normals in the direction of φ, ψ, such that:

I (φ) =2π∫

0

I (φ, ψ) dψ (4.4)

Regarding the crystal orientation, we are interested in the orientation of the α-crystalline phase, i.e. the orientation of the chain axis or c-axis of molecules withrespect to the direction of flow (see also figure 4.10a). The α-crystalline phase ofpolypropylene does not have a hkl-reflective plane which directly reveals the c-axisorientation. Therefore, the method of Wilchinsky [25] is used to derive the c-axisorientation using the (110) and (040) reflections and the angle of 72.5 between theb-axis and the (110) plane. For the angle σ between the c-axis and the direction offlow, the corresponding 〈cos2 σ〉 is now calculated according:

⟨cos2 σ

⟩= 1− 0.901 ·

⟨cos2 φ040

⟩− 1.099 ·

⟨cos2 φ110

⟩(4.5)

When the c-axis is perfectly aligned to the direction of flow, f = 1, if the c-axis isaligned perpendicular to the direction of flow f = −1/2, and for random orientationf = 0. For both iPP’s, the Herman orientation factor f is given in figure 4.11 incase shear flow is applied with a shear rate of 39.0 1/s. Furthermore, to differentiatebetween c-axis orientation and a∗-axis orientation, caused by lamellar branching, therelative fraction of a∗-axis component [A∗] is calculated according to Fujiyama [26].This fraction can be evaluated from the relative intensity of the (110) reflection versusazimuthal angle, depicted in figure 4.10b, following:

[A∗] =A∗

C + A∗(4.6)

where C is taken as the area around an azimuthal angle of 0 and A∗ the area aroundan azimuthal angle of 90, after subtraction of the base line area B.

Figure 4.11 shows the Herman orientation factor f as a function of the temperatureTγ where flow is applied with a shear rate of 39.0 1/s for ts = 3.0 s. For both iPP’s,the orientation increases when flow is applied at lower temperatures. Shear flowapplied at lower temperature leads to higher viscoelastic stresses enabling a higherdegree of orientation of the molecules. As expected, the higher molecular weight


( a)

0 20 40 60 800

0.2

0.4

0.6

0.8

1

Azimuthal angle [ o]

Rel

ativ

e in

tens

ity [

−]

C

A*

B

I(φ110

)

( b)

Figure 4.10: (a) Lamellar branched shish-kebab structure [27], (b) Method to deter-mine fraction [A∗] from the relative intensity of the (110) reflective planeaccording to Fujiyama [26].

iPP-2 consistently shows higher values for f. Because of the higher rheological relax-ation times, molecular orientation resulting from flow is prevailed for a longer time.Furthermore, the fraction [A∗] decreases with decreasing Tγ. At lower temperatures,or higher undercooling, the process of flow-induced crystallization is faster, leavingless time for secondary crystallization processes such as lamellar branching. Notethat the Herman orientation factor only takes the oriented α-crystals into account,while also a significant amount of β-crystals show orientation in the WAXD imagesshown in figures 4.4 and 4.5. These (300)β reflections show the same arcing patternas the (040)α reflections. The orientation of the c-axis of the β-crystals can howevernot directly be determined from the (300)β reflection.

Polymorphism

The degree of crystallinity and the presence of the crystalline phases (α-monoclinic,β-hexagonal, γ-orthorhombic crystalline phase) are investigated as a function of Tγ,in case samples are subjected to shear flow with a shear rate of 39.0 1/s for ts = 3.0s at a pressure of 40 MPa. The degree of crystallinity χ and the relative amountsof α- and γ-crystalline phases are determined in the same way as described in sec-tion 3.3, a method also used for instance by Somani et al. [28] to derive the degree ofcrystallinity of oriented samples. The relative amount of the β-crystalline phase isdetermined from the (300)β diffraction peak which can be discerned as a shoulderto the (040)α / (008)γ diffraction peak at approximately 2θ = 5.14o for λ = 0.4956Å. The relative fractions are determined from the area beneath the respective scat-tering peaks in the 1D-WAXD patterns. Figure 4.12 shows a detail of the 1D-WAXDscattering profiles with the relevant diffraction peaks depicted, and the degree ofcrystallinity with relative amount of crystalline phases. For both iPP’s, the degree


130 140 150 160 170 180 190 2000

0.2

0.4

0.6

0.8

1

Tγ [C]

f , [A

* ] [−

]

Figure 4.11: The Herman orientation factor f (open symbols) and fraction [A∗] (filledsymbols) as a function of temperature Tγ where flow is applied, at a pres-sure of 40 MPa: (O) iPP-1, (¤) iPP-2.

of crystallinity χ is hardly affected by shear flow, and with a value of about χ = 60% very close to the value obtained after quiescent crystallization (see table 3.4). Therelative amount of β- and γ-crystals, next to the more common α-crystals, is howeversubject to significant changes dependent on the temperature where flow is applied.Figures 4.12a and 4.12b show the strong increase in relative amount of β-crystals ifiPP-1 is subjected to shear flow at lower temperatures. This relates to the increase inorientation of (α-)crystals, i.e. increase in the Herman orientation factor, which wasalso found by Somani et al. [28], as according to [29–32], the surface of these orientedα-crystals would provide nucleation sites for β-crystals to grow. The 2D-WAXD pat-terns in figure 4.4 show an identical arcing pattern for the (300)β and (040)α reflec-tions. The relative amount of γ-crystals is also enhanced with respect to quiescentconditions (see table 3.4). For iPP-2, figures 4.12c and 4.12d, the relative amount ofβ-crystals shows however a completely different dependence on the temperature Tγ.This in spite of a larger amount of oriented α-crystals as quantified by the Hermanorientation factor (figure 4.11). For Tγ = 193 C, the relative amount of β-crystals iscomparable to the amount present in iPP-1 when sheared at identical temperature.A possible reason for the absence of β-crystals after shearing at Tγ = 154 C andTγ = 133 C could be that the generally weak (300)β reflections are over powered bythe very strong (040)α reflections. Another reason could be that because of the fastercrystallization kinetics, the time is too short for the β-crystals to grow on the alreadyformed α-crystals.


5 5.5 6 6.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2θ [deg]

I* [ −

]

β (300)α (130)

γ (117)

Quiescent Tγ=139 [C]

Tγ=158 [C]

Tγ=193 [C]

( a)

140 160 180 2000

20

40

60

80

100

Tγ [C]

crys

talli

nity

and

frac

tions

[ %

]

χ frac αfrac β frac γ

( b)

5 5.5 6 6.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

2θ [deg]

I* [ −

]

β (300)

α (130)

γ (117)

Quiescent Tγ=133 [C]

Tγ=154 [C]

Tγ=193 [C]

( c)

140 160 180 2000

20

40

60

80

100

Tγ [C]

crys

talli

nity

and

frac

tions

[ %

]

χ frac αfrac β frac γ

( d)

Figure 4.12: 1D-WAXD diffraction plots showing the normalized intensity I∗, crys-tallinity χ, and relative amounts of the α-, β-, and γ-crystalline phasesdependent on temperature of applied flow: (a,b) iPP-1, (c,d) iPP-2.


4.4 Conclusions

The influence of shear flow on the evolution of specific volume of two iPP gradesat non-isothermal conditions and elevated pressures was investigated, via the tech-nique of dilatometry. In general, shear flow has a pronounced effect on the evolutionof specific volume. Especially the temperature marking the transition in specific vol-ume Tc and the rate of transition are affected. The effect of flow on the evolutionof specific volume increases with increasing shear rate, increasing pressure, decreas-ing temperature at which flow is applied, and higher Mw. Although the degree oforientation and the overall structure of the resulting crystalline morphology weregreatly affected by the flow, the resulting specific volume was not significantly af-fected by the processing conditions employed and shows a clear link to the degreeof crystallinity which was also hardly affected by shear flow. It is clear that flow canstrongly enhance the occurrence of the β-crystalline phase. Crystallization modelsconsisting of one crystalline phase are therefore most probably not sufficient to de-scribe the crystallization kinetics during flow. If shear flow is applied at a sufficientlyhigh temperature, dependent on material and shear rate applied, remelting of flowinduced crystalline structures and relaxation of oriented chains is able to fully erasethe effect of flow. With increasing Mw, the effect of flow is prevailed longer. Althoughnot investigated in this study, we think that an increased cooling rate (i.e. less timeto remelt flow induced structures) will also enlarge the resulting effect of flow.


References

[1] Lee, O. and Kamal, M.R. Experimental study of post-shear crystallization ofpolypropylene melts. Polymer Engineering and Science, 39:236-248, (1999).

[2] Jerschow, P. and Janeschitz-Kriegl, H. On the development of oblong particlesas precursors for polymer crystallization from shear flow: origin of the so-calledfine grained layers. Rheologica Acta, 35(2):127-133, (1996).

[3] Tribout, C., Monasse, B., and Haudin, J.M. Experimental study of shear-inducedcrystallization of an impact polypropylene copolymer. Colloid and Polymer Sci-ence, 274:197-208, (1996).

[4] Vleeshouwers, S. and Meijer, H.E.H. A rheological study of shear induced crys-tallization. Rheologica Acta, 35:391-399, (1996).

[5] Keller, A. and Kolnaar, J.W.H. Flow-Induced Orientation and Structure Forma-tion, in: Processing of Polymers, Meijer, H.E.H., (Ed.), VCH: New York, vol.18, p.189-268, (1997).

[6] G. Eder, H. Janeschitz-Kriegl. Crystallization, in: Processing of Polymers, Meijer,H.E.H., (Ed.), VCH: New York, vol.18, p. 269-342, (1997).

[7] Jay, F., Haudin, J.M., and Monasse, B. Shear-induced crystallization ofpolypropylenes: effect of molecular weight. Journal of Materials Science, 34:2089-2102, (1999).

[8] Somani, R.H., Hsiao, B.S., and Nogales, A. Structure development during shearflow-induced crystallization of i-PP: in situ small angle X-ray scattering study.Macromolecules, 33:9385-9394, (2000).

[9] Kumaraswamy, G., Kornfield, J.A., Yeh, F., and Hsiao, B.S. Shear-enhanced crys-tallization in isotactic polypropylene. Part 3. Evidence for a kinetic pathway tonucleation. Macromlecules, 35:1762-1769, (2002).

[10] Seki, M., Thurman, D.W., Oberhauser, J.P., and Kornfield, J.A. Shear-mediatedcrystallization of isotactic polypropylene: the role of long chain - long chainoverlap. Macromolecules, 35:2583-2594, (2002).

[11] Koscher, E., and Fulchiron, R. Influence of shear on polypropylene crystalliza-tion: morphology development and kinetics. Polymer, 43:6931-6942, (2002).

[12] Elmoumni, A., Winter, H.H., and Waddon, A.J. Correlation of material and pro-cessing time scales with structure development in isotactic polypropylene crys-tallization. Macromolecules, 36:6453-6461, (2003).

[13] Janeschitz-Kriegl, H., Ratajski, E., and Stadlbauer, M. Flow as an effective pro-moter of nucleation in polymer melts: a quantitative evaluation. Rheologica Acta,42:355-364, (2003).

[14] Swartjes, F.H.M., Peters, G.W.M., Rastogi, S., Meijer, H.E.H. Stress inducedcrystallization in elongational flow. International Polymer Processing, 18(1):53-66,(2003).

[15] Fritzsche, A.K. and Price, F.P. Crystallization of Polyethylene oxide under shear.Polymer Engineering and Science, 14(6):401-412, (1974).

REFERENCES 81

[16] Fleischmann, E. and Koppelmann, J. Effect of cooling rate and shear in-duced crystallization on the Pressure-Volume-Temperature diagram of isotacticpolypropylene. Journal of Applied Polymer Science, 41:1115-1121, (1990).

[17] Watanabe, K., Suzuki, T., Masubuchi, Y., Taniguchi, T., Takimoto, J., Koyama, K.Crystallization kinetics of Polypropylene under high pressure and steady shearflow. Polymer, 44:5843-5849, (2003).

[18] Flory, P.J. Thermodynamics of crystallization in high polymers. Journal of Chem-istry and Physics, 15:397-408, (1947).

[19] Pogodina, N.V., Lavrenko, V.P., Srinivas, S., and Winter, H.H. Rheology andstructure of isotactic polypropylene near the gel point: quiescent and shear-induced crystallization. Polymer, 42:9031-9043, (2001).

[20] Eder, G., Janeschitz-Kriegl, H., and Liedauer, S. Crystallization processes in qui-escent and moving polymer melts under heat transfer conditions. Progress inPolymer Science, 15:629-714, (1990).

[21] Jerschow, P. and Janeschitz-Kriegl, H. The role of long molecules and nucleatingagents in shear induced crystallization of isotactic polypropylenes. InternationalPolymer Processing, 12(1):72-77, (1997).

[22] Janeschitz-Kriegl, H., Ratasjski, E., and Wippel, H. The physics of athermal nu-clei in polymer crystallization. Colloid Polymer Science, 277:217-226, (1999).


[24] K. Mezghani, P. Phillips, The γ-phase of high molecular weight isotacticpolypropylene: III. the equilibrium melting point and the phase diagram. Poly-mer, 39(16):3735-3744, (1998).

[25] Wilchinsky, Z.W. Measurement of orientation in polypropylene film. Journal ofApplied Physics, 31:1969-1972, (1960).

[26] Fujiyama, M. and Wakino, T. Structure of skin layer in injection-moldedpolypropylene. Journal of Applied Polymer Science, 35:29-49, (1988).

[27] Fujiyama, M. and Wakino, T.J. Distribution of higher-order structures ininjection-molded Polypropylenes. Journal of Applied Polymer Science, 43:57-81(1991).

[28] Somani, R.H., Hsiao, B.S., Nogales, A., Fruitwala, H., Srinivas, S., and Tsou,A.H. Structure development during shear flow induced crystallization of i-PP:in situ wide-angle X-ray diffraction study. Macromolecules, 34:5902-5909, (2001).

[29] Lovinger, A.J., Chua, J.O., and Gryte, C.C. Studies on the α and β forms ofisotactic Polypropylene by crystallization in a temperature gradient. Journal ofPolymer Science: Part B, Polymer Physics, 15:641, (1977).

[30] Lovinger, A.J. Microstructure and unit-cell orientation in alpha-polypropylene.Journal of Polymer Science Physics Edition, 21,97-110, (1983).

[31] Varga, J. and Karger-Kocsis, J. Interfacial morphologies in carbon fibre-reinforced polypropylene microcomposites. Polymer, 36:4877-4881, (1995).


[32] Varga, J. and Karger-Kocsis, J. Rules of supermolecular structure formation insheared isotactic polypropylene melts. Journal of Polymer Science: Part B, PolymerPhysics, 34:657-670, (1996).

REFERENCES 83

‘Design D’

CHAPTER FIVE

Classification of the influence of flowon specific volume: The Deborah

number 1

The use of the Deborah number in classifying the effect of shear flow on theevolution of the specific volume and resulting crystalline morphology is in-vestigated. If flow is applied at large undercooling, the Deborah number canprovide a good classification of the influence of flow on the orientation andstructural properties of the resulting crystalline morphology as well as forthe influence of flow on the evolution of specific volume. For the latter, theDeborah number related to the process of chain retraction (Des) or the Debo-rah number related to reptation of chains (Derep) can equally well be used toclassify the influence of flow on the evolution of specific volume, as charac-terized by the dimensionless transition temperature and dimensionless rateof transition. If flow is applied at relatively low undercooling, remelting offlow-induced crystalline structures and relaxation of molecular orientationcan play a significant role after cessation of flow. Therefore, in these casesthe use of the Deborah or Weissenberg number is regarded of little use inclassifying the effect of flow.

5.1 Introduction

In chapter 4, shear flow was shown to have a significant influence on the evolution ofspecific volume. Characteristic features of this evolution, e.g. the transition tempera-ture Tc, the time needed for the transition to start after flow is applied, and the rate ofcrystallization, are influenced not only by the shear rate but also by the pressure and

1In preparation for: Rheologica Acta.

85

86 5 CLASSIFICATION OF THE INFLUENCE OF FLOW

temperature during flow, and the material’s molecular weight distribution (MWD).It is the combination of these process and material parameters that is indicative forthe evolution of specific volume. This makes predictions regarding the evolution ofspecific volume as influenced by flow rather complicated. In recent studies concern-ing the influence of flow on the process of crystallization, the dimensionless Deborahand Weissenberg numbers have proven to be helpful in quantifying the strength ofthe flow applied at various processing conditions [1,2] and in classifying flow condi-tions with respect to their influence on the resulting crystalline morphology [3]. Thedimensionless Weissenberg (We) and Deborah (De) number are respectively definedas:

We =·γτ (5.1)

De =τ

t(5.2)

where τ is a characteristic rheological relaxation time of the material,·γ is the shear

rate, and t a characteristic time of the process. Both numbers are identical when thecharacteristic time of the process t is chosen equal to the reciprocal value of the shearrate

·γ. Acierno et al. [1] used We to study the influence of shear flow on the crys-

tallization behavior of various grades of isotactic poly(1-butene) (iPB), differing inmolecular weight distribution (MWD), using a rotational rheometer equipped withplate-plate geometry. They determined We by setting τ equal to the maximum re-laxation time resulting from small angle oscillatory shear (SAOS) rheological charac-terization. During isothermal crystallization experiments at 103 C, the time neededto start crystallization and the (dimensionless) half-time for crystallization decreasedwith increasing We. Furthermore, a transition from spherulitic to ‘rod-like’ crystal-lite growth was observed for roughly We > 150. Elmoumni et al. [2] performedisothermal flow-induced crystallization experiments on various grades of isotacticpolypropylene (iPP) at a temperature of 145 C, also using a rotational rheometerbut with cone-plate geometry. Here We was based on the relaxation time associatedto the cross over of G’ and G". They also found the induction time of crystalliza-tion to decrease and the rate of crystallization to increase with increasing We. Ad-ditionally the orientation of the c-axis in the direction of flow and the nucleationdensity increased with increasing We. For We < 1 the resulting morphology showeda spherulitic structure, while for We > 1 shish-kebab formation was observed. How-ever, they note that if We was defined based on the longest relaxation time, this criti-cal value could shift with as much as 1 order of magnitude (We > 10). Van Meerveldet al. [3] proposed a classification of flow-induced crystallization (FIC) experiments,regarding their effect on the resulting crystalline morphology, based on values forDe associated to the process of reptation (Derep) and chain retraction (Des) of themolecules in the high molecular weight (HMW) tail, i.e. Derep and Des should corre-spond to the relaxation dynamics of the HMW-tail. Roughly, Derep can be regardedas a measure for the ability of the flow to orient the contour path of molecules while

REFERENCES 87

Des is a measure for the ability of the flow to stretch the contour path of molecules.From the analysis of FIC experiments reported in literature that used iPP, the effectof flow on the number density of nuclei was observed to start already at Derep > 1,Des < 1 while for Derep > 1, Des = 1 − 10 a transition from spherulitic to shish-kebab formation was observed.

The above mentioned studies use the Deborah and Weissenberg number to analyzeand classify the influence of flow on the resulting crystalline morphology, when flowis applied during isothermal conditions and atmospheric pressure. Furthermore,classification of the influence of flow on the morphology of iPP [2, 3] typically isdone for experiments performed at a fairly large undercooling 4T = 36 − 46 C,if an equilibrium melting temperature T0

m at atmospheric pressure of 186 C is as-sumed [4]. However, the question arises if the Deborah and Weissenberg numbercan similarly be used to classify the influence of flow on the crystalline morphologywhen flow is applied during conditions relevant for industrial processing of poly-mers, i.e. elevated pressures and non-isothermal conditions. Moreover, can thesedimensionless numbers be used to classify the influence of flow applied on the evo-lution of specific volume? In this chapter, the use of the Deborah number to analyzeand classify the influence of shear flow on the resulting crystalline morphology andevolution of specific volume is studied, when flow is applied at elevated pressures,various degrees of undercooling, and non-isothermal conditions.

5.2 Methods

Deborah number

To quantify the strength of the shear flow applied at various elevated pressures andtemperatures, the Deborah number is defined as:

De = aT aP τ·γ (5.3)

where τ is a characteristic rheological relaxation time of the material at a referencetemperature Tre f and reference pressure Pre f ,

·γ is the shear rate applied, aT is the

temperature shift factor, and aP the pressure shift factor. Temperature shifting is doneaccording to a WLF-description [5, 6] and the pressure shift aP is defined accordingto [7]:

aP = exp(κPT

) (5.4)

where κ = 8.405 · 10−6 K/Pa and assumed a generic value for polypropylene, P thepressure, and T the absolute temperature. The shear flow experiments performed inthis study are classified according to the method proposed by Van Meerveld et al. [3],because Deborah numbers Derep and Des are closely correlated to the dynamics of


the chains in the HMW-tail, which are known to greatly influence the crystallizationprocess under flow [8–10]. The relaxation times τrep and τs of the longest chains ofthe MWD are estimated according to [11, 12]:

τrep = 3τeZ3(

1− 1.51√Z

)2

(5.5)

τs = τeZ2 (5.6)

with τe the equilibrium time which is independent of the molecular weight of thechain [11, 13, 14], and Z representing the number of entanglements per chain:

Z = MHMW/Me (5.7)

with MHMW the largest molecular weight of the MWD measured via gel permeationchromatography (GPC), and Me the molar mass between entanglements.

Dimensionless transition temperature

The transition temperature Tc is a characteristic feature of the evolution of specificvolume that is significantly influenced by the combination of shear rate, temperatureand pressure during flow (see chapter 4). To be able to compare the influence of flowapplied at various processing conditions on the transition temperature, we introducethe dimensionless transition temperature θc defined as:

θc =Tcγ − Tγ

TcQ − Tγ(5.8)

where Tcγ is the transition temperature in case shear flow is applied, Tγ the averagetemperature during shear flow, and TcQ the transition temperature in case no shearflow is applied, i.e. quiescent conditions (see also figure 5.1).

Dimensionless transition rate

In analogy to the dimensionless transition temperature θc, we introduce a dimen-sionless rate of transition λ defined as:

λ =(

∂ν

∂T

)

γ

/

(∂ν

∂T

)

Q(5.9)

REFERENCES 89

0 50 100 150 200 250

0

0.2

0.4

0.6

0.8

1

T [C]

ν* [ −

]

21 3

Figure 5.1: Example of the normalized specific volume ν∗ measured during quiescentconditions (O) and when applying shear flow at a temperature of 154 C(4): 1) transition temperature TcQ, 2) transition temperature Tcγ, 3) tem-perature where shear flow is applied Tγ.

where ∂ν∂T is the average transition rate of the specific volume with temperature. The

suffix γ indicates the transition rate obtained when shear flow is applied, and thesuffix Q indicates the rate of transition resulting from quiescent conditions. Note thatboth θc and λ refer to a relative change in Tc and the rate of transition with respect toquiescent conditions, the latter being dependent on cooling rate and pressure.


Materials

Two commercial grades isotactic polypropylenes (iPP) with various molecularweights (Mw) are used. The first material (iPP-1) is supplied by Borealis (gradeHD120MO), and is characterized by Mw = 365000 g/mol, Mw/Mn = 5.2. The sec-ond material (iPP-2) is supplied by DSM (grade Stamylan P 13E10) and is character-ized by Mw = 636000 g/mol, Mw/Mn = 6.9. Samples with dimensions 2.5 x 65 x0.4 mm are prepared by compression molding: the materials are compressed for 3minutes at 210 C with a force of 50 kN, and subsequently cooled in a water cooledpress during 5 minutes from 210 to 25 C again with a force of 50 kN.

In accordance with Van Meerveld et al. [3], for both iPP’s an equilibrium time τe =3.54 · 10−8 s is assumed and the molar mass between entanglements Me = 4400g/mol for a reference temperature of 190 C. Time-temperature shifting is performedusing the temperature shift factor aT. Table 5.1 lists the values for relaxation times


Material MHMW Z τe τrep τs[g/mol] [−] ·10−8[s] ·104[s] [s]

iPP-1 107.38 5469 3.54 1.7 1.0iPP-2 107.64 9891 3.54 10.0 3.5

Table 5.1: Equilibrium time τe, relaxation time τrep associated to the process of repta-tion, and relaxation time τs associated to the process of retraction of chainsin the HMW-tail, at a reference temperature of 190 C and reference pres-sure of 1.0·105 Pa.

τrep and τs. Deborah numers Derep, Des are determined using (5.3) and replacing τ

with τrep, τs respectively.

Techniques

The influence of shear flow on the specific volume of both iPP’s is measured usingthe dilatometer described in chapter 2, using the experimental procedure depictedin figure 4.2, and processing conditions as listed in table 5.2. Note: shear flow is ap-plied over a range of temperatures because of non-isothermal conditions. ThereforeTγ refers to the average temperature during flow and the thermal shift factor aT isdetermined using Tγ.

The final crystalline structure formed is evaluated ex situ with wide angle X-raydiffraction (WAXD). WAXD experiments were performed at the materials beam-lineID 11 of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France.The size of the X-ray beam is 0.2 x 0.2 mm2 having a wavelength of 0.4956 Å. Thedetector used is a Frelon CCD detector with 1024 x 1024 pixels. Both horizontal andvertical pixels are 164 µm in size. From calibration experiments, using LanthanumHexaboride, a sample-to-detector distance of 439.9 mm was determined. The expo-sure time for all images was 30 seconds. The final crystalline morphology is adi-tionally visualized via scanning electron microscopy (ESEM) performed on a PhilipsXL30 ESEM using a SE-detector and operated at 5 kV.


Classification of the resulting crystalline morphology

Classification of the resulting crystalline morphology using Des and Derep is done forsamples of both iPP’s subjected to a shear rate of 39 1/s, a pressure of 40 MPa, anda cooling rate of 1.4 C/s. Variation in Deborah numbers is achieved by applyingshear flow at different temperatures (see table 5.2). Note that the values for Des andDerep are typically larger than found by Van Meerveld et al.. Figure 5.2 shows the

REFERENCES 91

Material Code P¦T

¦γ Tγ Derep Des

[MPa] [C/s] 1/s [C] ·106 [ - ] ·102 [ - ]iPP-1

20S78 20 0.1 78 141.5 7.8 5.0142.5 7.5 4.8

40S78 40 0.1 78 140.2 12.2 7.720M78 20 1.2 78 127.4 11.7 7.4

131.0 9.6 6.1140.0 8.3 5.3150.1 5.9 3.8169.6 3.1 1.9210.0 1.3 0.8

40M39 40 1.4 39 138.6 6.4 4.1154.1 3.7 2.4193.0 1.3 0.8

40M78 40 1.4 78 131.8 13.9 8.8141.2 12.0 7.7153.6 7.7 3.9200.6 2.4 1.5

60M78 60 1.4 78 140.2 18.4 11.7150.4 12.9 8.2151.3 12.2 7.7160.7 9.2 5.9

iPP-240M39 40 1.4 39 133.0 39.2 13.6

152.5 24.2 8.4192.5 7.5 2.6

Table 5.2: Overview of applied processing conditions during flow and resulting Deb-orah numbers Derep, Des.


iPP-1

(110)

(040)

(130)

1A: Des = 0Derep = 0

1B: Des = 80Derep = 1.3 · 106

1C: Des = 237Derep = 3.7 · 106

1D: Des = 412Derep = 6.5 · 106

iPP-2

2A: Des = 0Derep = 0

2B: Des = 260Derep = 7.5 · 106

2C: Des = 842Derep = 24.2 · 106

2D: Des = 1364Derep = 39.2 · 106

Figure 5.2: Orientation of the crystalline morphology of samples subjected to a shearrate of 39 1/s, a pressure of 40 MPa, and a cooling rate of 1.4 C. Vari-ation in Deborah numbers Des,Derep is the result of shearing at differenttemperatures, see also table 5.2.

orientation of crystals as visualized by WAXD analysis. The main reflections of thecrystallographic planes (110), (040), and (130) of the α-crystalline phase are indicatedfor reference. The direction of flow in all pictures is vertical.

Sub-figures 1A and 2A show WAXD images of samples crystallized in quiescent con-ditions, i.e. Des = 0, Derep = 0. Generally, an increase in the orientation of crystalsis observed with higher Des and Derep. When subjecting iPP-1 to a flow character-ized by Des = 80 and Derep = 1.3 · 106 the influence of flow on the resulting ori-entation of crystals is negligible (sub-figure 1B). However, the presence of the (300)βreflection, located between the (110)α and (040)α reflections, is evidence of the flowapplied. Compared to results of Van Meerveld et al., who observed shish-formationfor Derep > 1 and Des = 1− 10, the flow applied can be regarded as strong. How-ever, because of the fairly low undercooling at which this flow is applied, i.e. for

REFERENCES 93

Tγ = 193 C an undercooling of 4Tγ = 5.2 C results when assuming T0m = 198.2

C at a pressure of 40 MPa [4], remelting of flow induced crystalline structures andrelaxation of molecules after cessation of flow are thought to play a significant rolesuch that the influence of flow on the orientation of the crystalline morphology iscompletely erased. By comparison, flow applied on iPP-2 at identical undercooling(sub-figure 2B) does have a significant effect on the orientation of crystals. This isexplained by the higher Mw and associated larger relaxation times of iPP-2, resultingin a stronger flow and slower relaxation of molecular orientation after cessation offlow. The increased strength of flow will not only result in a higher orientation ofchains, but also in a higher number of chains to be oriented [15], potentially lead-ing to a higher number of flow-induced nuclei. Comparing the Deborah numbersof sub-figure 2B with sub-figures 1C and 1D, a somewhat higher degree of orienta-tion is expected. This also points to a noticable influence of remelting and molecularrelaxation, (partially) erasing the effect of flow. Flow applied at undercooling rang-ing from 44.2 ≤ 4Tγ ≤ 65.2 is depicted in sub-figures C and D (see also table5.3). The influence of remelting and relaxation is expected to be negligible at theseundercoolings [2]. Consistent with an increase in Des and Derep, an increase in ori-entation is observed. Important features that can be related to orientation of chainsin the direction of flow are the equatorial reflections of the (110)α and (040)α crystal-lographic planes. These can already be observed for Des = 237 but are significantlypresent for Des ≥ 842. A more detailed classification of the orientation and structuralproperties of the crystalline morphology is possible by visualizing the morphologyusing ESEM, figure 5.3. The numbering of sub-figures corresponds to figure 5.2. Asalready discussed, for iPP-1 the influence of shear flow applied at small undercool-ing is negligible (sub-figure 1B). Large spherulites are visible of up to 50 µm in sizeacross the sample. However, iPP-2 samples subjected to shear flow applied at iden-tical conditions already show significant orientation of the morphology. The brightlines in figure 2B are thought to be short row nucleated structures, observed at thecore of the sample. At the edges, a somewhat stronger row nucleated morphologyis observed with row lengths exceeding 20 µm and width of about 500 nm. If shearflow is applied to iPP-1 at an undercooling 4Tγ = 44.2C, figure 1C, a mixture ofspherulites and row nucleated structures is observed. Spherulites are typically about10 - 20 µm in size while rows are about 30 µm in length and 500 nm wide. Again, themorphology of iPP-2 is much more affected by the shear flow at 4Tγ = 44.2C. Fig-ure 2C clearly shows an abundant presence of densely packed and highly orientedcrystallites (‘shish-kebabs’). Finally, shearing iPP-1 at an even higher undercoolingof 4Tγ = 59.2C, figure 1D, results in a mixed morphology of row nucleated andspherulitic crystallites in the core while additionally sporadic shish-kebab formationis observed at the edge. The morphology of iPP-2 sheared at 4Tγ = 65.2C con-sists completely of shish-kebabs, both at the core and edges of the sample. Typically,these shish-kebabs are about 270 nm wide and have a periodicity of kebabs rangingfrom 200 - 450 nm. Table 5.3 summarizes the observed morphology as a a functionof Deborah numbers. The presence of spherulitic (S), row-nucleated (R), and shish-kebab (K) morphology shows a logical order with increasing Deborah numbers. Be-cause of the expected remelting present in sub-figures 1B and 2B, these data can not


iPP-1

1B : Des = 80Derep = 1.3 · 106

1C : Des = 237Derep = 3.7 · 106

1D : Des = 412Derep = 6.5 · 106

iPP-2

2B : Des = 260Derep = 7.5 · 106

2C : Des = 842Derep = 24.2 · 106

2D : Des = 1364Derep = 39.2 · 106

Figure 5.3: Crystalline morphology visualized by ESEM of samples subjected to ashear rate of 39 1/s, a pressure of 40 MPa, and a cooling rate of 1.4 C.Variation in Deborah numbers Des,Derep is the result of shearing at differ-ent temperatures, see also table 5.2.

be used to determine the transition from spherulitic to row-nucleated morphology.However, the transition to shish-kebab morphology can be determined and occursfor 240 ≤ Des ≤ 410. Saturation of the morphology with shish-kebab structureshappens for 842 ≤ Des ≤ 1364.

Classification of the evolution of specific volume

Figure 5.4 shows the dimensionless transition temperature θc and dimensionless rateof transition λ as a function of Deborah number Des. The use of Derep gives quali-tatively the same trend of θc and λ, since for the values of Z of the materials usedthe ratio of Derep and Des is approximately constant and equal to 3 times Z. Linesare drawn to guide the eye. If Des is lower than a minimum value of approximatelyDes = 150, the influence of flow on the evolution of specific volume is negligible

REFERENCES 95

Material Sub-figure 4Tγ Des Derep Morphology[C] ·102 [ - ] ·106 [ - ]

iPP-1 1B 5.2 0.8 1.3 SiPP-1 1C 44.2 2.4 3.7 R, SiPP-2 2B 5.2 2.6 7.5 R, SiPP-1 1D 59.2 4.1 6.4 K, R, SiPP-2 2C 45.2 8.4 24.2 K, RiPP-2 2D 65.2 13.6 39.2 K

Table 5.3: Summary of the morphology features observed in figure 5.3 as a functionof Deborah numbers Derep, Des: S = spherulitic, R = row nucleated, K =shish-kebab.

(θc = 1, λ = 1). Typically, in our experiments this corresponds to shear flow ap-plied to iPP-1 at small undercooling. When this value is superseded, at first only ashift of the transition temperature towards higher values is observed (0.6 ≤ θc ≤ 1),while the average rate of transition is unaffected (λ = 1). In our experiments, thiscorresponds to flow applied to iPP-1 at large undercooling and flow applied to iPP-2 applied at small undercooling. With increasing Des, the influence of flow on theshift of the transition temperature shows a strong increase (0.6 < θc ≤ 0). Addi-tionally, the rate of transition increases with maximum a factor 2. Interestingly, theupswing of λ at about Des = 500 correlates rather well with the transition fromspherulitic to shish-kebab morphology (240 ≤ Des ≤ 410). Finally, for approxi-mately Des ≥ 800, the crystallization process is enhanced such that the transitionfrom the melt to the semi-crystalline state starts almost instantaneously the momentflow is applied (θc = 0). Therefore, a significant part of the flow is applied duringcrystallization. This is associated to a significant increase in the rate of transition(4.5 ≤ λ ≤ 5). Note that the classification of flow applied at large undercooling ishardly affected by differences in cooling rate.


101

102

103

104

0

0.2

0.4

0.6

0.8

1

log Des [ − ]

θ c [ −

]

iPP1 − 20S78iPP1 − 40S78iPP1 − 20M78iPP1 − 40M78iPP1 − 60M78iPP1 − 40M39iPP2 − 40M39

( a)

101

102

103

104

1

2

3

4

5

6

log Des [ − ]

λ [

− ]

iPP1 − 20S78iPP1 − 40S78iPP1 − 20M78iPP1 − 40M78iPP1 − 60M78iPP1 − 40M39iPP2 − 40M39

( b)

Figure 5.4: The dimensionless transition temperatureθc and the dimensionless rate oftransition λ as a function of Deborah number Des. Data are coded corre-sponding to table 5.2.

REFERENCES 97

5.5 Conclusions

Classification of the influence of flow on the resulting crystalline morphology wasperformed for samples of two iPP grades, subjected to flow at constant elevatedpressure and during non-isothermal conditions. Variation in the strength of the flowapplied was reached by shearing at different degrees of undercooling. Classificationof the influence of flow on the orientation of the resulting crystalline morphology asvisualized by WAXD could be performed if flow was applied at relatively large un-dercooling. However, the influence of remelting and relaxation of molecular orien-tation yields the Deborah number of little use if flow is applied at high temperaturesand relatively low undercooling. For large undercooling, remelting and relaxationhas little effect on the development of the flow-induced crystalline morphology aswas already observed in a previous study [2]. These conclusions also hold for theclassification of flow on the evolution of specific volume. If flow is applied at largeundercooling, Des and Derep can equally well be used to classify the influence of flowon the dimensionless transition temperature and dimensionless transition rate. Evenrelatively large differences in cooling rate have little effect on the classification offlow applied at large undercooling.


References

[1] Acierno, S., Palomba, B., Winter, H.H., and Grizutti, N. effect of molecularweight on the flow-induced crystallization of isotactic Poly(1-butene). RheologicaActa, 42:243-250, (2003).

[2] Elmoumni, A., Winter, H.H., and Waddon, A.J. Correlation of material and pro-cessing time scales wth structure development in isotactic Polypropylene crys-tallization. Macromolecules, 36:6453-6461, (2003).

[3] Van Meerveld, J., Peters, G.W.M., and Hütter, M. Towards a rheological classifi-cation of flow induced crystallization experiments of polymer melts. RheologicaActa, 44:119-134, (2004).


[5] Swartjes, F.H.M., Peters, G.W.M., Rastogi, S., and Meijer, H.E.H. Stress inducedcrystallization in elongational flow. International Polymer Processing, 18:53-66,(2003).

[6] Vega, J.F. Personal communication, (2004).[7] Kadijk, S.E. and Van Den Brule, B.H.A.A. On the Pressure Dependency of the

Viscosity of Molten Polymers. Polymer Engineering and Science, 34:1535-1546,(1994).

[8] Vleeshouwers, S. and Meijer, H.E.H. A rheological study of shear induced crys-tallization. Rheologica Acta, 35:391-399, (1996).

[9] Seki, M., Thurman, D.W., Oberhauser, J.P., and Kornfield, J.A. Shear-mediatedcrystallization of isotactic Polypropylene: the role of long chain - long chainoverlap. Macromolecules, 35:2583-2594, (2002).

[10] Janeschitz-Kriegl, H., Ratajski, E., and Stadlbauer, M. Flow as an effective pro-moter of nucleation in polymer melts: a quantitative evaluation. Rheologica Acta,42:355-364, (2003).

[11] Doi, M. and Edwards, S.F. The theory of polymer dynamics. Claredon Press, Ox-ford, (1986).

[12] Ketzmerick, R. and Öttinger, H.C. Simulation of a non-markovian process mod-eling contour length fluctuation in the Doi-Edwards model. Continuum Mechan-ics and Thermodynamics, 1:113-124, (1989).

[13] Watanabe, H. Viscoelasticity and dynamics of entangled polymers. Progress inPolymer Science, 24:1253-1403, (1999).

[14] Tube theory of entangled polymer dynamics. Advances in Physics, 51:1379-1527,(2002).

[15] Somani, R.H., Hsiao, B.S. and Nogales, A. Structure Development During ShearFlow-Induced Crystallization of I-PP: In Situ Small Angle X-Ray ScatteringStudy. Macromolecules, 33:9385-9394, (2000).

[16] Eder, G., Janeschitz-Kriegl, H., and Liedauer, S. Crystallization processes in qui-escent and moving polymer melts under heat transfer conditions. Progress inPolymer Science, 15:629-714, (1990).

REFERENCES 99


[18] Ziabicki, A. and Alfonso, G.C. A simple model of flow-induced crystallizationmemory. Macromolecular Symposia, 185:211-231, (2002).

‘Final’

CHAPTER SIX

Conclusions and recommendations

6.1 Main conclusions

In this thesis, the dependence of the specific volume of crystallizing polymers onthe thermomechanical history as experienced during processing is investigated. Thetechnique of dilatometry is used to study the combined influence of temperature,cooling rate, pressure, and shear flow, on the evolution of specific volume. Empha-sis is placed on selecting and reaching those processing conditions that are relevantfor industrial processing operations such as injection molding and extrusion. To ex-tent the interpretation of the results obtained on the development of specific vol-ume, structure properties of the resulting crystalline morphology are investigatedusing wide angle X-ray diffraction (WAXD) in combination with scanning electronmicroscopy (ESEM).

In chapter 2 a custom designed dilatometer is presented as a new experimental toolto quantitatively investigate the evolution of specific volume as a function of tem-perature (up to 260 C), cooling rate (up to 100 oC/s), pressure (up to 100 MPa), andshear rate (up to 80 1/s). The dilatometer is based on the principle of confined com-pression, and allows the use of annular shaped samples having a radial thickness of0.5 mm. A possible source of error known to dilatometers based on this principle isthe occurrence of friction forces arising between solidifying sample and dilatometerwall. To quantify this error, a comparison was made with measurements performedon a dilatometer based on the principle of confining fluid (Gnomix). The specific vol-ume was measured in the absence of flow, at isobaric conditions, and at a relativelylow cooling rate of about 4-5 oC/min. Both sets of data agreed quite well with respectto specific volume in the melt, the temperature at which the transition to the semi-crystalline phase started, and the specific volume of the solid state. Detailed analysisshowed a relative difference in specific volume of the melt of 0.1 - 0.4 %. An identicalrelative difference was assumed for the specific volume measured during the first

101

102 6 CONCLUSIONS AND RECOMMENDATIONS

part of crystallization, since the ratio of shear and bulk modulus is still small andthe influence of friction forces and loss of hydrostatic pressure can be neglected. Therelative difference in the specific volume of the solid state ranged from 0.1− 0.2%.However, especially for higher cooling rates, this part of the specific volume curvemeasured should be taken as qualitative rather than quantitative.

In chapter 3, the influence of thermal history, i.e. the influence of cooling rate, on thespecific volume and the resulting crystalline morphology of an isotactic polypropy-lene is investigated. Measurements are performed at cooling rates ranging from 0.1to 35 oC/s, and at elevated pressures ranging from 20 to 60 MPa. A profound in-fluence of cooling rate on the temperature at which the transition from the melt tothe semi-crystalline state starts is found. With increasing cooling rate and constantpressure, this transition temperature shifts towards lower temperatures. At constantpressure, the transition temperature scales with the undercooling, i.e 4T = T − T0

m.Since the transition temperature can be regarded as a measure for the onset of crys-tallization, an increased cooling rate causes the crystallization to start at a higherundercooling. This is explained as a ‘suppression’ of crystallization. Additionally,an increasing cooling rate causes the final specific volume to increase, which agreeswith a decrease in the degree of crystallinity determined from WAXD analysis. Incontrast to results of Zuidema et al. [1], for the relatively small pressure range thatwas experimentally accessible, a combined influence of pressure and cooling rate onthe specific volume or crystalline morphology was not found. Finally, comparisonof numerical predictions with experimental data of the evolution of specific volumewere performed using a constitutive description for specific volume as proposed byZuidema et al. [1]. Predictions showed at first large deviations in the calculated startand rate of the transition. These deviations increased with increasing cooling rate.Deviations in the rate of transition could partly be explained from small variationsin model parameters, that were justified from possible inaccuracies in the experi-mental characterization of important input parameters, i.e. the spherulitic growthrate G(T, p) and the number of nuclei per unit volume N(T, p), or from determiningmodel parameters to describe these quantities numerically. Especially in the pre-diction during fast cooling, G(T, p) and N(T, p) should be characterized for a suf-ficiently large temperature range, including temperatures typically lower than thetemperature where the maximum in G(T, p) occurs. Deviations in predicted transi-tion temperatures are however quite unexplained and could only be improved byintroducing an unrealistic larger number of nuclei than determined experimentallyat relatively high temperatures. This is subject to future investigation.

Next, the influence of thermo-mechanical history on the evolution of the specific vol-ume is investigated in chapter 4. The combined influence of shear rate, pressure andtemperature during flow is studied at non-isothermal conditions using two grades ofisotactic polypropylene with different weight averaged molar mass (Mw). In general,shear flow has a pronounced effect on the evolution of specific volume. Especiallythe temperature marking the transition in specific volume Tc and the rate of transi-tion are affected. The effect of flow on the evolution of specific volume increases withincreasing shear rate, increasing pressure, decreasing temperature at which flow is

REFERENCES 103

applied, and higher Mw. Although the degree of orientation and the overall structureof the resulting crystalline morphology are greatly affected by the flow, interestinglyand remarkably the resulting specific volume is not and shows a clear link to thedegree of crystallinity which is also hardly affected by shear flow. Analysis of thecrystalline morphology shows that flow can strongly enhance the occurrence of theβ-crystalline phase. Crystallization models consisting of one crystalline morphologytype can therefore be insufficient to describe the crystallization kinetics during flow.If shear flow is applied at a temperature near to the material’s equilibrium meltingtemperature T0

m [2], i.e. at low undercooling, dependent on material and appliedshear rate remelting of flow induced crystalline structures and relaxation of molec-ular orientation was able to fully erase the effect of flow. With increasing Mw, theeffect of flow applied near T0

m prevailed longer. Although not investigated in thisstudy, we think that an increased cooling rate (i.e. less time to remelt flow inducedstructures) would also enlarge the resulting effect on the evolution of specific volumewhen applied at low undercooling.

In chapter 5, the use of the dimensionless Deborah number is investigated to analyzeand classify the influence of shear flow on the specific volume and resulting crys-talline morphology, when flow is applied at different processing conditions. Clas-sification of the influence of flow on the orientation of the resulting crystalline mor-phology as visualized by WAXD could be performed if flow was applied at relativelylarge undercooling. However, the influence of remelting and relaxation of molecularorientation yields the Deborah number of little use if flow is applied at high tempera-tures and relatively low undercooling. Even when strong flows are applied, i.e. highDeborah numbers, the influence of flow can be erased totally. For large undercool-ing, remelting and relaxation has little effect on the development of the flow-inducedcrystalline morphology as was already observed in a previous study [3]. These con-clusions also hold for the classification of flow on the evolution of specific volume.If flow is applied at large undercooling, Deborah numbers Des based on the processof chain retraction or Derep based on the process of reptation can equally well beused to classify the influence of flow on the evolution of specific volume, e.g. char-acterized by the dimensionless transition temperature θc and dimensionless rate oftransition λ. Even relatively large differences in cooling rate have little effect on theclassification of flow applied at large undercooling. Furthermore, classification of theresulting crystalline morphology can be performed. With increasing Des, Derep theorientation of crystals increases and a differentiation in spherulitic, row nucleated,and shish-kebab structures is possible.

6.2 Recommendations

The custom made dilatometer presented in chapter 2 was designed to analyze theinfluence of thermomechanical history on the evolution of specific volume as expe-rienced during processing operations, i.e. non-isothermal conditions. This does notrequire extensive control of the procedure of cooling. However, improved and auto-


mated control of cooling would enable isothermal experiments after an initial periodof fast cooling. In this way, well defined analysis of the combined influence of flow,pressure, and temperature on crystallization kinetics can be performed. Addition-ally, a redesign of the piston and die, such that the annular thickness of the sampleis in the order of 0.1 mm with a larger radius of the sample, would enable evenbetter homogeneous cooling conditions at high cooling rates and the application ofincreased shear rates. Finally, an alternative way for the application of pressure androtation has to be found such that the use of the tensile testing machine is no longernecessary.

In chapter 3, experimental validation of numerical constitutive modelling of the spe-cific volume still showed deviations in predicted temperature of transition, espe-cially at high cooling rates. This mismatch between experimentally determined andpredicted specific volume could only be improved by introducing an unrealisticallylarge number of nuclei at higher temperatures. Experimental characterization of thespherulitic growth rate G(T, p) and the number of nuclei per unit volume N(T, p) asa function of temperature and pressure could improve these predictions and wouldprovide better understanding of the modelling. This characterization was alreadyinitiated and a proof of principle provided by the author of this thesis using opticalmicroscopy in combination with a high pressure cell.

The experiments performed in chapter 4 can be regarded as simplified injectionmolding experiments, i.e. the polymer is melted to above its melting temperature,subjected to flow, and finally cooled with relatively high cooling rate. The exper-imentally determined evolution of specific volume provides a direct way of vali-dating constitutive modelling of specific volume or modelling of the evolution ofcrystallinity, based on a combination of the Schneider rate equations for quiescentcrystallization and the (modified) Eder equations for flow-induced crystallization.In combination with ex-situ techniques to visualize the crystalline morphology, e.g.ESEM, optical microscopy, SALS, experimental validation of the numerically pre-dicted crystalline morphology is possible.

In chapter 4 it was shown that shear flow did not have a significant effect on the re-sulting specific volume, for the processing conditions applied and a cooling rate of1.4 oC/s. This agreed with the degree of crystallinity which was about constant dur-ing all shear flow experiments. However, the enhancement of crystallization kineticsby flow could give a significant difference with crystallization in quiescent condi-tions if an increased cooling rate is applied, e.g. a cooling rate where in quiescentconditions a significant suppression of crystallization occurs. Additionally, variationin cooling rate while applying shear flow near the equilibrium melting temperatureT0

m would provide better understanding of the remelting of flow-induced crystallineentities and their effect on the evolution of specific volume.

In chapters 3 and 4 it was shown that the annular shape of the samples resulted ina homogeneous crystalline morphology, even when subjected to high cooling ratesand shear flow. For instance, in chapter 4 visualization with ESEM showed thatsamples with a homogeneous shish-kebab morphology could be prepared. Samples

REFERENCES 105

subjected to a well controlled thermomechanical history could serve as basis for ex-perimental studies investigating the influence of crystalline structure properties onintrinsic material properties such as dimensional accuracy and stability, yield stress,Young’s Modulus, etc.

In chapter 5, a classification of flow-induced crystallization experiments using theDeborah number as proposed by Van Meerveld et al. [4] was applied on the evo-lution of specific volume. Shear induced crystallization experiments in isothermalconditions and elevated pressures would provide an additional way for experimen-tal validation of this classification.


References



[3] Elmoumni, A., Winter, H.H., and Waddon, A.J. Correlation of material and pro-cessing time scales wth structure development in isotactic Polypropylene crys-tallization. Macromolecules, 36:6453-6461, (2003).

[4] Van Meerveld, J., Peters, G.W.M., and Hütter, M. Towards a rheological classifi-cation of flow induced crystallization experiments of polymer melts. RheologicaActa, 44:119-134, (2004).

Samenvatting

Semi-kristallijne polymeren worden veelvuldig gebruikt in produkten die een grotedimensie-nauwkeurigheid en -stabiliteit vereisen. Het verband tussen procescon-dities en de belangrijkste eigenschap die bepalend is bij de controle van dimensie-nauwkeurigheid, te weten het specifieke volume, is echter nog steeds onvoldoendebegrepen. In dit proefschrift wordt het specifieke volume van kristalli- serende poly-meren onderzocht als functie van de thermomechanische geschiedenis zoals onder-vonden tijdens verwerking. Hierbij wordt de nadruk gelegd op procescondities dierelevant zijn voor industriële verwerkingsprocessen zoals spuit- gieten en extrusie.Dilatometrie wordt gebruikt om de gecombineerde invloed van temperatuur, afkoel-snelheid, druk, en afschuifstroming op het specifieke volume te onderzoeken. Tevenswordt het verband tussen het specifieke volume en de kristallijne microstructuur dieresulteert uit deze procescondities onderzocht. De eigenschappen van de kristalli-jne microstructuur worden ex situ onderzocht door gebruik te maken van röntgen-diffractie (WAXD) en elektronen-microscopie (ESEM).

In hoofdstuk 2 wordt een dilatometer ontworpen, die de kwantitatieve analyse vanhet specifieke volume toelaat als functie van temperatuur (tot 260 C), afkoelsnelheid(tot 100 oC/s), druk (tot 100 MPa), en afschuifsnelheid (tot 80 1/s). De dilatome-ter is gebaseerd op het principe van ‘confined compression’ en maakt gebruik vanringvormige proefstukken met een dikte van 0.5 mm. De fout in het gemetenspecifieke volume, die onstaat ten gevolge van wrijvingskrachten tussen het proef-stuk en de wand van de dilatometer, wordt gekwantificeerd door een vergelijkingte maken met metingen uitgevoerd op een dilatometer gebaseerd op het principevan ‘confining fluid’ (Gnomix). Het specifieke volume gemeten in de afwezigheidvan stroming, bij constante druk en bij een relatief lage afkoelsnelheid van ongeveer4-5 oC/min komt goed overeen in de smelt fase, de temperatuur waarbij de transi-tie naar de semi-kristallijne fase begint en het specifieke volume van de vaste fase.Een gedetailleerde analyse toont relatieve verschillen in de smelt van 0.1 - 0.4 %,terwijl het relatieve verschil in de vaste fase varieert van 0.1 − 0.2%. Het is echterte verwachten dat voor hoge afkoelsnelheden de fout ten gevolge van wrijving zaltoenemen, waardoor het specifieke volume in de vaste fase meer van kwalitatievedan van kwantitatieve waarde is.

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108 SAMENVATTING

In hoofdstuk 3 is de invloed van de afkoelsnelheid op het specifieke volume en deresulterende kristallijne microstructuur van een isotactisch polypropyleen (iPP) on-derzocht. Experimenten uitgevoerd bij afkoelsnelheden variërend van 0.1 tot 35 oC/sen drukken variërend van 20 tot 60 MPa tonen een grote invloed op de temperatuurdie de transitie van de smelt naar de semi-kristallijne fase markeert en op het ver-loop van het specifieke volume als functie van temperatuur tijdens de transitie. Mettoenemende afkoelsnelheid en constante druk, verschuift deze transitietemperatuurnaar lagere waardes en het verloop van de transitie zelf is minder opvallend en overeen groter temperatuurtraject uitgestrekt. Daarnaast zorgt een hogere afkoelsnel-heid voor een toename in het specifieke volume gemeten bij kamertemperatuur, het-geen overeenstemt met een afname van de graad van kristalliniteit zoals bepaald uitWAXD metingen. Onder de gebruikte meetcondities werd er geen gecombineerdeinvloed van druk en afkoelsnelheid op het specifieke volume en op de kristallijnemicrostructuur gevonden. Experimentele validatie van numerieke voorspellingenvan het specifieke volume tonen aanvankelijk grote afwijkingen in de berekendetransitietemperatuur en het verloop tijdens de transitie. Deze afwijkingen nementoe met toenemende afkoelsnelheid. De afwijkingen in het specifieke volume tijdensde transitie kunnen gedeeltelijk verklaard worden uit de gevoeligheid voor kleinevariaties in modelparameters. Deze volgen uit mogelijke onnauwkeurigheden in deexperimentele karakterisering van belangrijke input parameters, zoals de groeisnel-heid van sferulieten G(T, p) en het aantal nuclei per volume eenheid N(T, p), of on-nauwkeurigheden in het bepalen van een numerieke beschrijving van deze groothe-den. Met name wanneer het specifieke volume wordt voorspeld bij hoge afkoel-snelheden, moeten G(T, p) en N(T, p) gekarakteriseerd worden voor een voldoendegroot temperatuurtraject, inclusief temperaturen die typisch lager zijn dan de tem-peratuur waar het maximum in de groeisnelheid van sferulieten G(T, p) optreedt.Afwijkingen in de voorspelde transitietemperatuur kunnen echter niet geheel wor-den verklaard en kunnen alleen worden verbeterd door een onrealistisch en groterdan experimenteel waargenomen aantal nuclei bij relatief hoge temperatuur voor teschrijven. Dit blijft een onderwerp voor toekomstig onderzoek.

De invloed van stroming op het verloop van het specifieke volume is onderzochtin hoofdstuk 4. De gecombineerde invloed van afschuifsnelheid, druk en temper-atuur tijdens stroming is gemeten onder niet-isotherme condities gebruikmakend van twee typen isotactisch polypropyleen met verschillend gemiddeldmoleculairgewicht (Mw). Afschuifstroming heeft een groot effect op het verloopvan het specifieke volume. De temperatuur die de transitie markeert en het ver-loop tijdens de transitie worden beïnvloed. De invloed van stroming neemt toemet hogere afschuifsnelheid, hogere druk, lagere temperatuur tijdens stroming, ofeen hoger gemiddeld moleculairgewicht Mw. Hoewel de mate van oriëntatie ende algemene opbouw van de kristallijne microstructuur in grote mate beïnvloedwordt door stroming, worden het resulterende specifieke volume en de graad vankristalliniteit nauwelijks beïnvloed door de toegepaste procescondities. Als stromingwordt toegepast bij relatief hoge temperatuur of lage onderkoeling, dan smeltenstromingsgeïnduceerde kristallijne structuren en relaxeert de moleculaire orientatie.

6.2 RECOMMENDATIONS 109

Met toenemend gemiddeld moleculairgewicht Mw wordt de invloed van stroming,ook wanneer toegepast bij relatief hoge temperatuur, langzamer uitgewist. Hoewelniet onderzocht in deze studie, denken we dat een grotere afkoelsnelheid, hetgeenovereenkomt met minder tijd voor het smelten van stromingsgeïnduceerde struc-turen, ook het effect van stroming toegepast bij hoge temperatuur op het specifiekevolume doet toenemen.

In hoofdstuk 5 is onderzocht of het dimensieloze Deborah getal kan worden gebruiktvoor de klassificatie van de invloed van stroming op het specifieke volume en opde resulterende kristallijne morfologie. Alleen bij een relatief grote onderkoelingvolgt een zinvolle klassificatie van de invloed van stroming op de oriëntatie van demorfologie, gemeten via röntgen-diffractie technieken (WAXD). Bij lage onderkoel-ing volgt smelten van stromingsgeïnduceerde kristallijne structuren en relaxatie vangeoriënteerde moleculen en beperkt het gebruik van het Deborah getal. Zelfs de in-vloed van sterke stroming, gekenmerkt door een hoog Deborah getal, kan bij lage on-derkoeling volledig worden uitgewist. Deze conclusies gelden ook voor de klassifi-catie van stromingsinvloed op het verloop van het specifieke volume. Als stromingwordt toegepast bij grote onderkoeling, kunnen Deborah getallen Des (gebaseerd ophet proces van relaxatie van moleculen na rek) en Derep (gebaseerd op het proces vanreptatie van moleculen) gelijkelijk worden gebruikt. Zelfs relatief grote verschillen inafkoelsnelheid hebben dan slechts weinig invloed op de klassificatie wanneer stro-ming wordt aangebracht bij grote onderkoeling. Met toenemend Des, Derep neemt deoriëntatie van kristallen toe en is een differentiatie in sferulitische, rij-genucleëerdeen shish-kebab structuren mogelijk.

Dankwoord

Graag wil ik hier iedereen bedanken die meegeholpen heeft aan het tot stand komenvan dit proefschrift. Allereerst wil ik Gerrit Peters bedanken voor zijn begeleiding,enthousiasme en zijn altijd kritische houding. Dit is de kwaliteit van dit werk zekerten goede gekomen. Mocht er ooit een ’GA(I)M Bv.’ worden opgericht dan mag jij,Gerrit, bij deze de functie van Scientific Director bekleden. Ook wil ik Han Meijerbedanken voor het vertrouwen dat hij gedurende al deze jaren in mij heeft gestelden voor het mogelijk maken van dit promotie project. Het DPI en TNO Industrie enTechniek wil ik bedanken voor het financieel mogelijk maken van dit project en hetcreëren van een goede onderzoeksomgeving.

Dank ook aan allen die meegeholpen hebben bij de uitvoering van de vele experi-menten, het maken en aanpassen van opstellingen en andere technische werkzaam-heden die nodig waren als essentieel onderdeel van dit experimentele promotie-werk. Speciaal dank aan Sjef Garenfeld, die een grote steun was bij het realiserenvan de dilatometer en Denka Hristova voor haar hulp bij het uitvoeren van WAXDen ESEM experimenten. Tevens dank aan Anne Spoelstra, Luigi Balzano, Jan-WillemHousmans, Guido Heunen, Reinhard Forstner, Leon Govaert, Dejan Mitrovic, UrsulaKroesen, Johan van der Velden, Meindert Janszen, Jos de Laat, Rob van de Berg enToon van Gils voor hun bijdragen. Ook dank aan Leo Wouters en Patrick van Brakelvoor de numerieke ondersteuning.

Daarnaast bedank ik Sanjay Rastogi voor alle hulp en het beschikbaar stellen van tijdvoor het uitvoeren van WAXD experimenten, Gaetano Lamberti voor de interessantediscussies op het gebied van röntgen-diffractie technieken, Frank van der Burgt voorhet ter beschikking stellen van WAXD metingen aan amorf iPP, Markus Gahleitnervoor het uitvoeren van GPC metingen, Jan van Meerveld voor zijn kritisch kommen-taar en alle collega’s van TNO (groep POW) voor hun getoonde interesse en onder-steuning. Speciaal Jos Kunen voor zijn hulp in de eerste jaren van het onderzoek,Roland Kals die een goede afronding van dit proefschrift mogelijk maakte, Pieter JanBolt voor begeleiding en Ed Berben voor zijn tomeloze inzet toen ik zo nodig naarGrenoble moest.

Dank aan mijn (ex)kamergenoten (Richard Schaake, Marco van den Bosch,Alexander Sarkessov, Alpay Aydemir, Marcel Meuwissen, Marlies Terlouw, Georgo

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Angelis) en andere MaTe collega’s (Vinny Khatavkar, Roel Janssen, Jesus Mediavilla,Alexander Zdravkov, Edwin Klompen, Christophe Pelletier, Frank Swartjes) voorde altijd interessante discussies, levenswijsheden en Bulgaarse geschiedenislessen.Zonder jullie was de koffie lang zo lekker niet geweest.

Ik wil mijn ouders, familie en vrienden bedanken voor hun interesse als ’de studie’van Maurice weer eens ter sprake kwam en voor hun steun. Tot slot wil ik mijn lieveAngela bedanken voor haar vertrouwen, geduld en altijd volwaardige steun, ook intijden dat het niet zo lekker liep. Jij bent mijn beste ’promotor’.

Maurice van der BeekEindhoven, 21 april 2005

Curriculum Vitae

Maurice van der Beek (Roermond, november 7 1970) graduated from secondaryschool in 1989 at B.C. Schöndeln, Roermond. From 1989 to 1996, he studied Biomedi-cal Engineering at the Eindhoven University of Technology and obtained his mastersdegree in the group of prof.dr.ir. H.E.H. Meijer on the analysis of constitutive equa-tions for the prediction of viscoelastic stresses in complex polymer melt flow. After atwo year working period at Raytheon Engineers and Constructors, he was employedat TNO Industrial Technology in 1998, working in the field of polymer processingwith main focus micro injection molding. In 2000 he was offered the opportunityto pursue a PhD-degree within the research program of the Dutch Polymer Institute(DPI-project #160), of which the results are presented in this thesis.

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influence of the thermomechanical history - purespeciﬁc volume of polymers inﬂuence of the...

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