Specific Volume of Polymers : Influence of the Thermomechanical History

Specific volume of polymers : influence of the thermomechanical history

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

DOI: 10.6100/IR590887

Document status and date: Published: 01/01/2005

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Download date: 30. Sep. 2021 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 Universiteit Eindhoven, 2005. Proefschrift. – ISBN 90-386-2567-7 NUR 971 Subject 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 doctor aan 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 op dinsdag 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. Meijer en prof.dr.ir. J.M.J. den Toonder

Copromotor: dr.ir. G.W.M. Peters Veur mien maedje

Contents

1 Introduction 1 1.1 Context ...... 1 1.2 Background ...... 1 1.3 Scope ...... 4 1.4 Outline ...... 4 References ...... 6

2 Concentric cylinder dilatometer: design and testing 9 2.1 Introduction ...... 9 2.2 Design and instrumentation ...... 12 2.3 Experimental ...... 19 Sample preparation ...... 20 Procedure ...... 21 2.4 Comparison with conﬁning ﬂuid based dilatometer ...... 22 2.5 Example: isotactic polypropylene ...... 26 2.6 Conclusions ...... 27 References ...... 28 2.A Appendix: material properties ...... 30

3 The influence of cooling rate on specific volume 33 3.1 Introduction ...... 33 3.2 Experimental part ...... 35 Materials ...... 35 Dilatometer experiments ...... 36 X-ray analysis ...... 36 Density measurements ...... 37 3.3 Results and discussion ...... 37 Specific volume ...... 37 Crystalline morphology ...... 43 Modelling aspects ...... 47 3.4 Conclusions ...... 55 References ...... 56

vii viii CONTENTS

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

4 The influence of shear flow on specific volume 61 4.1 Introduction ...... 61 4.2 Experimental part ...... 62 Materials ...... 62 Dilatometry ...... 64 Density gradient column ...... 64 X-ray analysis ...... 65 Scanning electron microscopy ...... 65 4.3 Results and discussion ...... 65 Specific volume ...... 65 Crystalline morphology ...... 74 4.4 Conclusions ...... 79 References ...... 80

5 Classification of the influence of flow on specific volume: The Deborah number. 85 5.1 Introduction ...... 85 5.2 Methods ...... 87 Deborah number ...... 87 Dimensionless transition temperature ...... 88 Dimensionless transition rate ...... 88 5.3 Experimental part ...... 89 Materials ...... 89 Experimental techniques ...... 90 5.4 Results and discussion ...... 90 Crystalline morphology ...... 90 Specific volume ...... 94 5.5 Conclusions ...... 97 References ...... 98

6 Conclusions and recommendations 101 6.1 Main conclusions ...... 101 6.2 Recommendations ...... 103 References ...... 106

Samenvatting 107

Dankwoord 111

Curriculum Vitae 113 Summary

Nowadays, semi-crystalline polymers are widely used in many product applications that display high dimensional accuracy and stability. However, the relation- ship between processing conditions and the main property determining macroscopic shrinkage, i.e. specific volume, is still not understood in sufficient detail to predict the resulting dimensions of a product dependent on the selected material and chosen processing conditions. In this thesis, the dependence of the specific volume of crystallizing polymers on the thermomechanical history as experienced during processing is investigated. Emphasis is placed on selecting and reaching those processing conditions that are relevant for industrial processing operations such as injection molding and extrusion. To extent the interpretation of the results obtained on the development of specific volume, structure properties of the resulting crystalline morphology are investigated using wide angle X-ray diffraction (WAXD) in combination with scanning electron microscopy (ESEM). A custom designed dilatometer is presented in chapter 2, which is used to quantitatively 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 annular shaped samples with a radial thickness of 0.5 mm. To quantify the measurement error arising from friction forces between the solidifying sample and dilatometer walls, a comparison is made with measurements performed on a dilatometer based on the principle of confining fluid (Gnomix). Measurements performed in the absence of flow, at isobaric conditions, and at a relatively low cooling rate of about 4-5 oC/min agree quite well with respect to the specific volume in the melt, temperature at which the transition to the semi-crystalline state starts, and the specific volume of the solid state. Detailed analysis shows a relative difference in specific volume of the melt of 0.1 - 0.4 %. An identical relative difference is assumed for specific volume measured during the first part of crystallization, since the ratio of shear and bulk modulus is still small and the influence of friction forces and loss of hydrostatic pressure can be neglected. The relative difference in the specific volume of the solid state ranges from 0.1 − 0.2%. However, especially for higher cooling rates, this part of the measured specific 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 resulting crystalline morphology of an isotactic polypropylene is investigated in chapter 3. Experiments performed at cooling rates ranging from 0.1 to 35 oC/s, and elevated pressures ranging from 20 to 60 MPa show a profound influence of cooling rate on the transition temperature, i.e. the temperature at which the transition from the melt to the semi-crystalline state starts, and on the rate of transition. With increasing cooling rate and constant pressure, the transition temperature shifts towards lower temperatures and the transition itself is less distinct and more wide spread. Addi- tionally, an increasing cooling rate causes the final specific volume to increase, which agrees with a decrease in the degree of crystallinity determined from WAXD analysis. For the relatively small pressure range that was experimentally accessible, a combined influence of pressure and cooling rate on the specific volume or crystalline morphology was not found. Experimental validation of numerical predictions of the evolution of specific volume showed at first large deviations in the calculated start and rate of the transition. These deviations increase with increasing cooling rate. Deviations in the rate of transition could partly be explained from small variations in model parameters, and can be justified from possible inaccuracies in the experimental characterization of important input parameters, i.e. the spherulitic growth rate G(T, p) and the number of nuclei per unit volume N(T, p), or from determining model parameters to describe these quantities numerically. Especially in the prediction during fast cooling, G(T, p) and N(T, p) should be characterized for a sufficiently large temperature range, including temperatures typically lower than the temperature where the maximum in G(T, p) occurs. Deviations in predicted transition temperature are however quite unexplained and could only be improved by introducing an unrealistic larger number of nuclei than determined experimentally at relatively high temperatures. This is subject to future investigation. The influence of shear flow on the evolution of the specific volume is investigated in chapter 4. The combined influence of shear rate, pressure and temperature during flow is investigated at non-isothermal conditions using two grades of isotactic polypropylene with different weight averaged molar mass (Mw). In general, shear flow has a pronounced effect on the evolution of specific volume. The temperature marking the transition in specific volume and the rate of transition are affected. The influence of flow increases with increasing shear rate, increasing pressure, decreasing temperature at which flow is applied, and higher Mw. Although the degree of orientation and the overall structure of the resulting crystalline morphology are greatly affected by the flow, the resulting specific volume and degree of crystallinity are only marginally affected by the processing conditions employed. If shear flow is applied 0 at a temperature near the material’s equilibrium melting temperature Tm, i.e. at low undercooling, dependent on material and applied shear rate remelting of flow induced crystalline structures and relaxation of molecular orientation is able to fully erase the effect of flow. With increasing Mw, the effect of flow applied at low undercooling is prevailed longer. Although not investigated in this study, we think that an increased cooling rate (i.e. less time to remelt flow induced structures) would also enlarge 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 analyze and classify the influence of shear flow on the specific volume and resulting crystalline morphology. Classification of the influence of flow on the orientation of the resulting crystalline morphology as visualized by WAXD could be performed if flow was applied at relatively large undercooling. With increasing Deborah number, the orientation of crystals increases and the classification of the flow strength resulting in a spherulitic, row nucleated, or shish-kebab morphology is possible. However, in case flow was applied at low undercooling, the influence of remelting and relaxation of molecular orientation yields the Deborah number of little use. The influence of flow could be erased totally, even when strong flow is applied, i.e. high Deborah numbers. For large undercooling, remelting and relaxation has little effect on the development of the flow-induced crystalline morphology as was already observed by others. These conclusions 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 process of chain retraction) or Derep (based on the process of reptation of chains) can equally well be used to classify the influence of flow on the evolution of specific volume, e.g. characterized by the dimensionless transition temperature θc and dimensionless rate of transition λ. Even relatively large differences in cooling rate have little effect on the classification of the influence of flow on the evolution of specific volume, when applied at large undercooling. Finally, in chapter 6 the main conclusions of this thesis are outlined together with recommendations for future research. xii SUMMARY CHAPTERONE

Introduction

1.1 Context

Polymers are widely used in many products that require accurate dimensions, either because of their functionality or for esthetic reasons. Examples range from media for data storage such as CD’s and DVD’s, to the housing of a cellular phone, to car bumpers. A new and growing field of application for polymers in which high dimensional accuracy is required is that of micro systems. Typically, the polymer components used in these systems have features with dimensions in the sub-millimeter to micrometer range, or even overall dimensions in the sub-millimeter range (see figure 1.1), demanding dimensional accuracy in the order of micrometers. However, especially for crystallizing polymers, it is still impossible to predict the final dimensions of a product in detail based on the polymer used, the design of the product, and the processing conditions applied. One of the main properties that determine the final dimensions of a product is the specific volume of the polymer, and its evolution during processing. Like any other physical property of crystallizing polymers, it is to a large extend determined by the crystallization process and crystalline morphology that results after processing. This thesis is a contribution to understanding 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 complex shaped 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

( b)

( a)

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 are cooled to room temperature, during which the polymer solidifies and stabilization of the product shape occurs. In practice the dimensions of the solidified polymer differ from 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 temperature such as thermal contraction, physical phase changes (e.g. crystallization, vitrification), and sometimes chemical reactions. The resulting change in density of the polymer 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 during processing, and understanding its dependence on molecular and processing parameters, is an important prerequisite in predicting the shrinkage behavior of polymers. Quantitative prediction of product shrinkage in its turn will strongly contribute to time and costs reduction of process and mold optimizations and time to market of high precision polymer products in general. Commonly, the specific volume of polymers is measured as a function of pressure and temperature using the technique of dilatometry. It is therefore often referred to as Pressure-Volume-Temperature behavior or PVT-behavior. Figure 1.2 is reproduced from Zoller and Walsh [2] and shows this behavior for an amorphous and a semi- crystalline polymer. For crystallizing polymers, the dependence of the specific volume on processing conditions is however complex. This is because the crystallinity determines the specific volume to a large extend, and this crystallinity strongly depends on the thermal history [3–7] and the experienced flow [8–16]. This has two major implications. First, in contrast with characterization of specific volume as a function of pressure and temperature only, additional parameters such as cooling rate and flow (e.g. deformation rate, total deformation, viscoelastic stress, amount of experienced mechanical work, etc.) should be taken into account to adequately characterize a material. Secondly, if specific volume data are to be used for (numerical) 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 polymer (b), measured using a bellows type dilatometer operating in isothermal 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, commercially available dilatometers (Gnomix, PVT100) are not sufficiently equipped to subject 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 seen important developments the last decade [17–19]. In contrast to early constitutive models such as developed by Tait [20] and Spencer and Gilmore [21], present models combine an (empirical) description of the specific volume of the amorphous and crystalline phases with a description of the evolution of the degree of crystallinity. Exam- ples include the Scheider rate equations [22] for non-isothermal quiescent crystallization 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 volume of crystallizing polymers as a function of the complete thermomechanical history experienced during processing. Moreover, the differential form of these rate equations 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 experimental data necessary for validation purposes. 4 1 INTRODUCTION

1.3 Scope

An experimental study is performed to measure the specific volume and the related crystalline morphology of semi-crystalline polymers, dependent on the experienced processing conditions and relevant molecular parameters. Dilatometry is chosen as the main experimental technique to study specific volume as a function of temperature, pressure level, cooling rate, and shear rate. This technique provides a direct way of measuring the evolution of the specific volume, serving for the validation of constitutive equations and fitting of model parameters. A density gradient column (DGC) is used to compare with the dilatometer experiments. Besides, the crystalline morphology of samples is analyzed ex situ using Wide Angle X-ray Diffrac- tion (WAXD) and Scanning Electron Microscopy (ESEM). The modelling part of this work concerns the validation of existing constitutive equations for specific volume; new constitutive models will not be introduced. The materials investigated are two grades 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 of dilatometer capable of measuring the influence of temperature, pressure, cooling rate, and shear rate on the specific volume of polymers, b) measuring the evolution of specific volume in an extended range of cooling rates and elevated pressure relevant to industrial polymer processing operations, c) measuring the influence of relatively high shear rates on the evolution of specific volume, d) the combination of 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. This dilatometer enables the analysis of the temperature evolution of specific volume as a function of pressure (up to 100 MPa), cooling rate (up to 100 C/s), and shear rate (up to 80 1/s). Chapter 3 discusses in depth the influence of cooling rate on the specific volume of iPP, using experimental data obtained via dilatometry performed at constant elevated pressures and using the results of the density gradient column experiments. The crystalline morphology resulting from processing conditions is analyzed using wide angle X-ray diffraction (WAXD). Numerical predictions of the specific volume are validated experimentally at various cooling rates and critical model parameters are identified. Chapter 4 discusses the influence of shear rate on the specific volume of two grades of iPP, differing in molar mass distribution. Combined effects of shear rate and pressure level, and shear rate and temperature at which the shear flow is applied are investigated per material grade. Wide angle X-ray diffraction (WAXD) and scanning electron microscopy (ESEM) are used to investigate the crystalline morphology resulting from the various flow conditions. Chapter 5 deals with the use of the dimensionless Deborah number to quantify and compare the strength of 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 influence of flow on the evolution of specific volume for various processing conditions. Finally, chapter 6 summarizes the most important conclusions and gives recommendations 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 to study polymer crystallization under processing conditions. The influence of high cooling rates. Chemical Engineering Science, 57:4129-4143, (2002). [6] La Carrubba, V., Brucato, V., Piccarolo, S. Phenomenological approach to compare the crystallization kinetics of isotactic Polypropylene and Polyamide-6 under 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 volume relaxation of amorphous Polystyrene. Journal of Polymer Science: Part B: Polymer Physics, 41:1526-1537, (2003). [8] Alfonso, G.C., Verdona, M.P., Wasiak, A. Crystallization kinetics of oriented poly(ethylene terephthalate) from the glassy state. Polymer, 19:711-716, (1978). [9] Vleeshouwers, S., Meijer, H.E.H. A rheological study of shear induced crystallization. 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 shear flow-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 in syndiotactic Polypropylene during isothermal crystallization and subsequent melting. 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 weight on 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 induced crystallization 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 shear ﬂow. 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 of a 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 injection molding. International Polymer Processing, 17(1):67-75, (2002). [20] Tait, P.G. Physics and Chemistry of the Voyage of H.M.S. Challenger. University Press, 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 quiescent and moving polymer melts under heat transfer conditions. Progress in Polymer Science, 15:629-714, (1990) [24] Zuidema, H. Flow Induced Crystallization, PhD thesis Eindhoven University of Technology (2000). ’Design A’ CHAPTERTWO

Concentric cylinder dilatometer: design and testing1

We developed a dilatometer to investigate the specific volume of polymers as a function of pressure (up to 100 MPa), temperature (up to 260 oC), cooling rate (up to 100 oC/s), and shear rate (up to 80 1/s). The dilatometer is based on the principle of confined compression and comprises of a pressure cell 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-die type’ dilatometer and a Couette rheometer, i.e. piston and die make up an annular shaped sample spacing. Specific volume measurements at low cooling rate using an isotactic polypropylene (iPP) are compared with measurements performed using a commercial bellows type dilatometer, showing relative differences in the range of 0.1-0.4 %. Finally, results are presented showing a profound influence of cooling rate and melt shearing on the evolution of specific volume.

2.1 Introduction

Dilatometry is the most common technique to measure the bulk specific volume of polymers, 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 into a rigid sample chamber where it is submerged into a fluid, to which the polymer must be inert. Usually mercury or silicon oil are used for this purpose. The sample chamber is sealed off by a flexible wall or bellows for: a) applying hydrostatic pressure 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 to measure the inﬂuence of cooling rate and melt shearing on speciﬁc volume. International Polymer Processing, XX(2), (2005).

9 10 2 CONCENTRICCYLINDERDILATOMETER

¦ 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 this principle will be referred to as CF-dilatometers [1–8]. The advantage of this principle is the ability to apply a true hydrostatic pressure to the polymer, both in melt and solid state. The disadvantage is that the volumetric changes measured are not that of the polymeric sample only. Points of concern are sealing of the pressurized fluid and (chemical)reactions occurring between polymer and fluid. The second principle is called confined compression. Here the polymer is enclosed in a rigid cylinder. A piston, closely fitting into the cylinder, is used both to pressurize the polymer and to measure volumetric changes. Dilatometers based on this principle will be referred to as PD-dilatometers (Piston-Die dilatometers) [9–15]. The advantage of this principle is the simplicity in design that can be achieved. A disadvantage is that frictional forces can arise between the polymer and cylinder wall leading to loss of hydrostatic pressure in the sample in its solid state [3, 16]. A point of concern is the reduction of frictional forces by applying an anti-friction coating or lubricant, which should be non-reactive with the polymer. Tables 2.1 and 2.2 list the characteristics of just a limited number of CF and PD type dilatometers reported in literature. The dilatometers listed here are referred to as ’conventional’ because specific volume is measured only as a function of pressure and temperature. Dependent on design, elevated pressures up to 870 MPa and temperatures up to 370 oC can be achieved. Relative errors in measured specific volume are reported ranging from 0.04 to 1.0 % with the lower values reported for CF-dilatometers. The study of Luyé et al. [12] listed in table 2.2 is an example of the dilatometer originally developed by Menges et al. [14] and until recently made commercially available by SWO Polymertechnik GmbH (Krefeld, Germany). In the original work of Menges et al. there is no mentioning of characteristics or accuracy of the method. Typically, both types of conventional dilatometers do not accommodate to 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 reported by Zuidema et al. [8] and Chakravorty [15], see table 2.3. Zuidema et al. used a CF-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 pressure of only 17.7 MPa could be reached. Chakravorty used a PD-dilatometer reaching a maximum cooling rate of 2.5 oC/s in combination with a maximum pressure of 40 MPa. 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 cooling rate but failed to mention any dilatometer characteristics. Dilatometers to study the influence of deformation, i.e. shear and shear rate, on specific volume are reported by Fritzsche and Price [13], Pixa et al. [6], Duran and McKenna [7], and Watanabe et al. [18] (see table 2.4). Fritzsche and Price developed a PD-dilatometer with an annular sample chamber. This mixture in design between a conventional PD-dilatometer and a Couette rheometer was used to study the influence of steady shear on the crystallization kinetics of several polyethylene oxides (PEO). Unfortunately, the specific volume data used to derive the evolution of crystallinity as a function of shear rate and shear are not reported. Pixa et al. and Duran and McKenna developed a so called torsional dilatometer to study the effect of step shear, and subsequent stress relaxation, on the specific volume of PVC and epoxy resins in the solid state. The design of these dilatometers is dedicated to the application of solid state samples and not suited for analyzing the influence of processing conditions on specific volume such as encountered in injection molding or extrusion. All these experiments were performed at ambient pressure and the influence of cooling rate was not studied. Only Watanabe et al. investigated the influence of shear flow on the evolution of crystallinity, derived from specific volume, at elevated pressures but isothermal conditions. They modified a standard PD-dilatometer (Toyo Seiki Seisaku-sho, Ltd.) such that samples could be subjected to steady shear flow using a plate-plate geometry. However, applied shear rates are relatively low to a maximum of 0.5 1/s and the plate-plate geometry is not very well suited to apply a homogenous 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 modeling used in simulation software, it is necessary to measure specific volume at conditions comparable to industrial processing conditions. Dilatometry is one of the main techniques available to achieve this. However, there is a general lack of suitable dilatometers able to measure specific volume as a function of both thermal and mechanical 12 2 CONCENTRICCYLINDERDILATOMETER

¦ 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 accuracy (ε) for dilatometers used to analyze the inﬂuence of cooling rate on speciﬁc 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 deformation on speciﬁc volume.

history. In this chapter, the design and performance of a dilatometer based on the principle of confined compression is presented with the ability to measure specific volume as a function of elevated pressure, temperature, cooling rate, and shear flow in the range of processing conditions as found in injection molding or extrusion. The main goal is not to reach the maximum accuracy possible but rather the ability to analyze 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 injection molding 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 or elongation rates of O(102 − 104) 1/s. Incorporating all these functional demands into one dilatometer is a challenging task. The principle of piston-die is chosen as a basis for the dilatometer because of the relative simplicity in design that can be reached. The design of piston and die is chosen such that an annular shaped sample spacing is created, similar to dilatometers developed by Fritzsche and Price [13] and Chakravorty [15]. This particular sample shape is preferred for two reasons. First, since polymers are bad heat conductors, one of the sample dimensions has to be sufﬁciently 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 be chosen small while independently the height of the sample can be chosen such to guarantee enough sample volume necessary for a good signal to noise ratio. Based on a heat conduction analysis, the maximum allowable sample thickness is determined to be of O(10−4) m in case a cooling rate of O(102) oC/s is applied and homogeneous cooling is enforced. Secondly, similar to a Couette rheometer, an annular sample can easily be subjected to drag flow by rotating the outer wall of the sample spacing with respect to the inner. The dimensions of the annulus and material properties of the sample determine the shear rate that can be reached dependent on speed of rotation [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 combination with a hydraulically operating tensile testing machine (MTS 858 Mini Bionix) to form the dilatometer. Figure 2.1 shows a schematic drawing of the pressure cell as mounted to the tensile testing machine. Figure 2.2 shows the individual components and the polymer sample used. Important features of the tensile testing machine are its ability to subject samples simultaneously to compressive force and angular rotation while measuring axial displacement, angular displacement, and axial force. The advantage of this combination is that only the fairly simple pressure cell is custom designed while the tensile testing machine incorporates already the necessary actu- ators, instrumentation, and provides a platform with a stiff frame for mounting the pressure cell. This last feature is not a trivial one. Since the axial displacement is a measure for the volume of the sample, deformation of the frame due to mechanical loading introduces errors and should be minimized. The axial displacement is measured 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 transformer (ADT). The pressure cell can also be mounted on a more conventional tensile testing machine without the ability of applying angular rotation. In that case, the rotation should be realized in a different way, e.g. manually or by using an external device. The pressure cell has a height of approximately 110 mm and outer diameter of 60 mm. The piston (A), see figure 2.1, is made from tungsten carbide for optimal thermal 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 the inside 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 outer diameter of the piston, 22.0 mm, respectively 21.0 mm. It is also made from the same tungsten carbide as the piston. This part of the die and the piston fit together closely with 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 from stainless steel and contain 22 cooling channels with a diameter of 2.0 mm. Because of differences in thermal expansion between the various parts of the die, the individual parts are held together between two plates using tensile rods (see figure 2.2b). 14 2 CONCENTRICCYLINDERDILATOMETER

Rotary actuator & ADT

Linear actuator & LVDT

ressure Cell Load Cell (0 - 15 kN) F

Ωω

F C D E

Load Cell

Figure 2.1: Schematic representation of the tensile testing machine with instrumentation (top) and a cross section of the pressure cell (bottom). A: piston, B: die, C: sample, D: thermocouple locations, E: PTFE seal, F: electrical heater, G: ceramic insulator, H: water cooled interface. Arrows indicate ﬂow of cooling medium. 2.2 DESIGN AND INSTRUMENTATION 15

( a) ( b)

( c) ( d)

Figure 2.2: (a) piston with interface, (b) die with thermocouples, (c) annular sample with PTFE sealing, (d) drawing of piston-die assembly. 16 2 CONCENTRICCYLINDERDILATOMETER

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 in the so called isobaric-cooling mode, see section 2.3, accuracy of temperature control is not critical. The temperature of the sample is sensed with custom made K-type thermocouples 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 correspond to top, middle, and bottom of the sample. The distance between temperature readings and actual sample surface is about 0.5 mm. Because the temperatures are not recorded inside the polymeric sample, a correction has to be applied. The temperature of the sample is calculated using the energy balance equation and the heat conductive properties of tungsten carbide. To prevent polymeric material from leaking during experiments at high pressure and temperature, the sample spacing is sealed with PTFE rings (E) with a height of 2.0 mm. The interfaces (H) between pressure cell and tensile testing machine are actively cooled to prevent the machine from warming during experiments at elevated temperature. Both interfaces are made of aluminium and 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-permanent construction 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 screwed to 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 independently to improve control over homogeneity of sample cooling. Variation in flow rate and type of cooling medium (i.e. water, pressurized air) determines the effective cooling rate of the sample. Flow controllers (Kytölä Oy, 10 l/ min) are used in case water is used as cooling medium. In case of pressurized air, the flow rate is adjusted 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 cell enable quick cooling response. The piston is cooled from the inside using a nozzle construction. The cooling medium enters through three inlets, located at an angle of 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. As depicted in figure 2.4 where only a few of the 22 channels are shown. The flow direction per cooling channel is chosen such to minimize cooling gradients in the axial direction. 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 made thermocouples are listed in table 2.5. Accuracy of instrumentation is given for typical experimental range, i.e. −2 ≤ X ≤ 2 mm, −135 ≤ α ≤ 135 deg, and 0 ≤ F ≤ −3300 N. Note: X is the absolute position of the LVDT’s core with respect to its coil, determining the accuracy of the measured relative displacement 4x. For data acquisition purposes a PC with I/O board (National Instruments, PCI-6031E, 32 channels, 16 bit) 2.2 DESIGN AND INSTRUMENTATION 17

( a) ( b)

( c)

Figure 2.3: (a) interface, (b) component X, (c) assembly. 18 2 CONCENTRICCYLINDERDILATOMETER

Cooling medium

Flowcontroller

Cooling medium

Drain

=ElectromagneticValve

Figure 2.4: Schematic representation of the cooling system and detail of ﬂow through the 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 = angle 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 compression taken in order of increasing temperature, isothermal compression taken in order of decreasing temperature, isobaric heating, and isobaric cooling [12]. For isobaric cooling, the polymeric sample is first heated above its melting temperature, next the sample is pressurized, and finally the volume of the sample is measured while cooling to ambient conditions during which the pressure is maintained constant. If specific volume data are to be used in the analysis of industrial processes such as injection molding, the isobaric cooling mode should be applied [12]. The main reason for this is that during injection molding, the material transitions observed are crystallization or vitrification. Contrary to for example isobaric heating where the transition observed is melting. Secondly, when heating the polymer above its melting point for a sufficiently long time, the thermomechanical history of the material is erased. This rules out any influence of the sample preparation procedure on the measured specific volume. Furthermore, in case of PD-dilatometers, melting of the sample prior to the 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 sample during isobaric heating experiments in a PD-dilatometer. They concluded that only cooling experiments are suited to get reliable results using a PD-dilatometer. The measured displacement, i.e. the relative displacement of the core with respect to the coil of the LVDT, is influenced by many factors other than the volume of the polymeric sample. All these factors are functions of temperature and mechanical loading, e.g. thermal expansion of the rod carrying the core of the LVDT, deformation of 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 influences by calculating appropriate correction functions. Instead, the measured displacement of an experimental run is corrected using the measured displacement of an experiment performed at identical conditions but in the absence of sample material. This 20 2 CONCENTRICCYLINDERDILATOMETER

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 the relative volume change of the sample during cooling instead of the absolute volume. The relative specific volume measurements have to be completed with absolute specific volume data measured using standard techniques. To be exact, the specific volume of the polymer melt at maximum temperature is set equal to a value measured with a conventional dilatometer operating in isobaric mode at an identical pressure level. It can be assumed that the specific volume of the polymer melt at temperatures sufficiently high above the melting temperature is only a function of pressure and temperature [3]. This procedure can be used independent of the conditions applied during cooling. Based on the instrument accuracies listed in table 2.5, the accuracy for specific volume can be determined using equation 2.1.

¡ ¢ 4X · A (4x − 4x ) · π d2 − d2 ν = + v = 1 2 4 o i + v (2.1) m melt_c f m melt_c f

where 4x1 is the displacement measured in the experimental run, 4x2 the displacement 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 the absolute speciﬁc volume for the melt phase measured with a CF-dilatometer. The absolute accuracy of speciﬁc volume, δν, is determined from the individual accuracies according to:

¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ ∂ν ¯ ¯ ∂ν ¯ ¯ ∂ν ¯ ¯ ∂ν ¯ ¯ ∂ν ¯ δ = ¯ ¯ δ + ¯ ¯ δ + ¯ ¯ δ + ¯ ¯ δ + ¯ ¯ δ +δ ν ¯ ¯ 4x1 ¯ ¯ 4x2 ¯ ¯ do ¯ ¯ di ¯ ¯ m vmelt_c f ∂ (4x1) ∂ (4x2) ∂do ∂di ∂m (2.2)

−3 Both the diameters do and di are shaped with a maximum tolerance of ±2.5 · 10 −7 mm, the sample mass is measured with an accuracy of δm = ±5.0 · 10 kg, and the −3 displacement is measured with an accuracy δ4x1 = δ4x2 = ±5.0 · 10 mm. The

accuracy of measuring speciﬁc volume with the CF-dilatometer δvmelt_c f is estimated 3 3 3 to be about 1.25 · 10 mm /kg. This results in an absolute accuracy δν = 7.04 · 10 mm3/kg for the speciﬁc volume.

Sample preparation

Samples are prepared from standard sized pellets using compression molding. If the glass transition temperature of the material to be investigated is below room temperature, 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) - 4600 Pressurized Air 2 / 2 [bar] 600 Water 4.0 / 2.0 [l/ min] 15

Table 2.6: Examples of applied cooling media and cooling times needed to reach ambient conditions. material is in its rubbery state at room temperature, the strips can be bend into rings when loaded into the dilatometer. If the glass transition temperature of the material to be investigated is above room temperature the material is molded into cylindri- cally shaped samples with dimensions ∅ 23 x 22 mm. After demolding, the samples are 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 first heated to a temperature above the melting point of the sample. This is done with an average 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 minimized rather than maximized in order to prevent thermal degradation of the material. 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 = 33.77 mm2, a compressive force of about 3300 N is sufficient to reach a sample pressure of 100 MPa. The compressive force applied is corrected for the weight that the die exerts on the sample. The temperature control unit is shut off after the sample is fully pressurized and with a 5 seconds delay the data acquisition is started. After another 10 seconds, the electromagnetic valves are opened to start cooling. During cooling of the sample to ambient conditions, the compressive force is maintained constant to 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 medium and cooling flux applied. Because the flux of the cooling medium is constant, the resulting cooling rate is time dependent (see figure 2.5). Table 2.6 shows examples of the cooling medium used and the resulting cooling time when cooling from 210 oC to ambient conditions. As mentioned before, the flux of cooling medium through piston and die are adjusted separately to optimize for thermal homogeneity of the sample during cooling. After the sample is completely cooled down, it is taken out 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 of the sample for external influences such as thermal expansion of the dilatometer, deformation of the dilatometer due to mechanical loading, etc. 22 2 CONCENTRICCYLINDERDILATOMETER

200

150

T [C] 100

0 2 4 6 8 10 12 14 16

0 −20 −40 −60 −80 Cooling Rate [C/s] −100 0 2 4 6 8 10 12 14 16 t [s]

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

2.4 Comparison with conﬁning ﬂuid based dilatometer

As a check on the general experimental procedure described above, specific volume measurements of an isotactic polypropylene, Mw = 365000 g/mol and Mw/Mn = 5.4 (grade K2xmod, Borealis), are compared with isobaric cooling experiments performed using a CF-dilatometer. Additionally, the comparison helps to quantify the influence of friction forces that arise between sample and PD-dilatometer walls during solidification of the sample [16]. Experiments with the CF-dilatometer are performed at Moldflow Plastics Labs (Ithaca, USA) using a commercial dilatometer (Gnomix). Here the experimental procedure applied is as follows: loading of the sample to the desired pressure level, heating of the polymer to a temperature of 210 oC, holding the material for 10 min at maximum temperature, cooling at a constant cooling rate. The pressure levels applied are 10, 40, 80 MPa and cooling rates are 1.0 and 4.0 oC/min. Although the material is already pressurized during melting, the crystalline 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 the most stable α−monoclinic crystalline phase in iPP to be approximately 198 oC at a pressure of 100 MPa. Results of the measurements performed with the CF-dilatometer are shown in figure 2.6. Although both cooling rates are relatively low, the transition where crystallization becomes effective clearly shifts towards lower temperatures with increasing cooling rate. This agrees with results found by Luyé et al. [12], measuring specific volume 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 on the entire thermal history (especially the cooling rate). The experiments performed with 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 the samples to reduce the friction between sample and dilatometer walls. DSC measurements performed after the experiment on samples treated with grease and untreated samples, show no effect of the silicon grease on the crystallization kinetics of the iPP. Prior to cooling, the polymer is kept for 10 min at a maximum temperature of 210 oC to assure fully melting of the crystalline morphology. Figure 2.7 shows the results 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. In the molten state the comparison is good, as expected. More interesting is the good comparison with respect to the temperature where the transition from the melt to the semi-crystalline state becomes effective. This indicates that the effective thermal- histories experienced are comparable, despite the different cooling rates applied. The good comparison during crystallization is explained because the experienced cooling rates are almost the same in this range of temperatures, i.e. the average cooling rate during crystallization in the measurements using the PD-dilatometer is about 5 − 6 oC/min. Because the effective thermal histories of both measurements before and during crystallization show such good comparison, differences in solid state specific volume are considered negligible. Closer comparison of the specific volume for melt and solid state are shown in figure 2.8. For comparison, data of the CF-dilatometer are interpolated to values corresponding to 60 MPa. The relative differences in specific volume are calculated using equation 2.3 and results are listed in table 2.7.

¯ ¯ ¯ ¯ ¯νPD − νCF ¯ ε = ¯ ¯ ∗ 100% (2.3) νCF where: νPD : speciﬁc volume measured with PD-dilatometer νCF : 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 0.16 40 0.12 0.08 60 0.23 0.19

Table 2.7: Average values of the relative difference in speciﬁc volume for melt (εmelt) and solid state (εsolid). 24 2 CONCENTRICCYLINDERDILATOMETER

6 x 10 1.35 CF−1 10 MPa CF−4

1.3 40 MPa

1.25 80 MPa /Kg] 3 1.2 [mm ν

1.15

1.1

1.05 80 100 120 140 160 180 200 220 240 260 T [C]

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

6 x 10 1.35 PD CF 10 MPa

1.3 40 MPa

1.25 /Kg] 3 1.2 [mm ν

1.15

1.1

1.05 80 100 120 140 160 180 200 220 240 260 T [C]

Figure 2.7: Comparison of speciﬁc volume of iPP (K2xmod, Borealis) measured in isobaric mode at 10, 40 MPa with a CF-dilatometer at a constant cooling rate of 4.0 oC/min (¤) and the custom designed PD-dilatometer cooling in still air (5). 2.4 COMPARISON WITH CONFINING FLUID BASED DILATOMETER 25

6 x 10 1.35 10 MPa 1.3 40 MPa /Kg] 3 1.25 60 MPa [mm

am 1.2 ν

1.15 140 150 160 170 180 190 200 210 220 230

6 x 10 1.16 10 MPa 1.14 40 MPa /Kg] 3 1.12 60 MPa

[mm 1.1 cr ν 1.08 1.06 90 100 110 120 130 140 150 160 T [C]

Figure 2.8: Comparison of specific volume of iPP (K2xmod, Borealis) for melt (top) and solid state (bottom). Measurements performed with CF-dilatometer at a cooling rate of 4.0 oC/min (2) and PD-dilatometer (5) cooling in still air. 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 specific volume measurements in melt state can be neglected. Remarkably, εsolid is generally less than εmelt. The opposite is expected because of an additional error arising from friction forces and the resulting loss of hydrostatic pressure inside the sample. Most probably this is the result of the fairly narrow temperature range of specific volume data measured in solid state. In conclusion, the relative differences between specific volume data measured with a CF-dilatometer (Gnomix) and the PD-dilatometer are in the range of 0.1 − 0.4% in melt state including the temperature range where transition to the semi-crystalline phase becomes effective. Generally, the relative differences decrease with increasing pressure level. Furthermore, identical relative differences are assumed for specific volume measured during the first part of crystallization, since the ratio of shear and bulk modulus is still small and the influence of friction forces and loss of hydrostatic pressure can be neglected [16]. Although the relative differences in specific volume for the solid state range from 0.1 − 0.2%, these results are regarded to be more of qualitative than quantitative value. That is why the relative differences in specific volume for the latter part of crystallization and for solid state specific volume are assumed to be larger than 0.4% and this part of the measured specific volume curve should be taken as qualitative rather than quantitative. Finally, in case the PD-dilatometer is subjected to higher cooling rates, the influence of friction forces on 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- 26 2 CONCENTRICCYLINDERDILATOMETER

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 shearing on the specific volume of a linear iPP (grade HD120MO, Borealis) characterized by Mw = 365000 g/mol, Mw/Mn = 5.2. For reasons of comparison, in the latter figure the normalized specific volume ν∗ is plotted, defined as: ν − ν ν∗ = s (2.4) νm − νs

Here νs represents the value of the specific volume at room temperature in the solid state, in case the sample is not subjected to flow. Identically, νm represents the value of the specific volume in the melt state at 210 oC. Samples are prepared by compression 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 3 minutes at 210 oC with a force of 50 kN. The samples are cooled in a water cooled press during 5 minutes from 210 to 25 oC again with a force of 50 kN.

6 x 10 1.3

1.25

1.2 /kg] 3

[mm 1.15 ν

1.1

1.05 0 50 100 150 200 250 T [C]

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

Cooling rate and melt shearing clearly have a pronounced effect on the evolution of speciﬁc volume as a function of temperature, with opposing inﬂuences on the temperature where the transition from the melt to the semi-crystalline state becomes effective. The dependence of this transition as a function of processing conditions 2.6 CONCLUSIONS 27

0.8

0.6 [ − ] *

ν 0.4

0.2

0 50 100 150 200 250 T [C]

Figure 2.10: Influence of shear flow on the normalized specific volume of iPP. Shear is applied as a step function at 139 oC, with a shear rate of 39.0 1/s to a total 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/s and a pressure of 40 MPa. is for example of importance for the choice of the ’No Flow’ temperature, as used in numerical simulation codes. Furthermore, the resulting specific volume in the solid state clearly increases with increasing cooling rate. This agrees with results of others [23–25]. The shear flow applied only marginally affects the resulting specific volume in the solid state.

2.6 Conclusions

This chapter described the construction and first testing of a new device to study the influence of pressure, cooling rate, shear rate, and total shear on the specific volume. Comparison of results, measured at low cooling rates without applying shear, shows very good agreement with results obtained using a commercial bellows type dilatometer. First experiments using an isotactic polypropylene show a profound influence of both cooling rate and shear flow on the evolution of specific volume. The specific volume in the solid state increases with increasing cooling rate but is only marginally affected by the shear flow applied. 28 2 CONCENTRICCYLINDERDILATOMETER

References

[1] Hellwege, K.H., Knappe, W., Lehmann, P. Die isotherme Kompressibilität einiger amorpher und teilkristalliner Hochpolymerer im Temperaturbereich von 20-250 [oC] und bei Drucken bis zu 2000 Kp/Cm2. Kolloid-Zeitschrift und Zeitschrift für Polymere, 183(2):110 - 120, (1961). [2] Quach, A., Simha, R. Pressure-Volume-Temperature properties and transitions of amorphous polymers; polystyrene and poly (orthomethylstyrenes). Journal of Applied 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 dilatometer 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 volume 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 measurements on deformed glasses: instrument description and measurement on equilibrated 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 behavior 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 der Viskoelastischen 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 measurement methodology for semicrystalline polymers to simulate injection-molding process. 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 loaded axially in a rigid die. Polymer, 29:1784-1788, (1988). [17] Bhatt, S.M., McCarthy, S.P. Pressure, Volume and Temperature (PVT) apparatus for computer simulations in injection molding. Annual Technical Conference Society 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 shear ﬂow. Polymer, 44:5843-5849, (2003). [19] Ding, Z., Spruiell, J.E. An experimental method for studying nonisothermal crystallization 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 polymers: 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 of isotactic polypropylene. Polymer, 22:1673-1676, (1981). [23] Piccarolo, S. Morphological changes in isotactic polypropylene as a function of cooling rate. Journal of Macromolecular Science - Phys., B31(4):501-511, (1992). [24] Brucato, V., Piccarolo, S., La Carrubba, V. An experimental methodology to study polymer crystallization under processing conditions. The inﬂuence of high cooling rates. Chemical Engineering Science, 57:4129-4143, (2002). [25] La Carrubba, V., Brucato, V., Piccarolo, S. Phenomenological approach to compare the crystallization kinetics of isotactic polypropylene and polyamide-6 under pressure. Journal of Polymer Science: Part B: Polymer Physics, 40:153-175, (2002). 30 2 CONCENTRICCYLINDERDILATOMETER: DESIGNANDTESTING

2.A Appendix: material properties

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

Property Symbol Value Dimension Youngs 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 piston and most inner part of the die. 2.A APPENDIX: MATERIAL PROPERTIES 31 ‘Design B’ CHAPTERTHREE

The inﬂuence of cooling rate on speciﬁc volume1

The influence of cooling rate on the evolution of specific volume is studied. Average cooling rates imposed during crystallization of the material vary from 0.1 to 35 ◦C/s while pressures range from 20 to 60 MPa. Results show the well known profound influence of pressure and cooling rate on specific volume. An increasing cooling rate shifts the transition temperature Tc towards lower temperatures, increases the final specific volume, and the transition due to crystallization is more gradual and widespread. Increasing pressure has an opposite effect on the shift in Tc, while the final specific volume after pressure release also increases. Finally, comparison of numerical predictions with experimental data show that the predicted transition temperature Tc is consistently too low and that predictions at high cooling rates are sensitive to (small) variations in model parameters.

3.1 Introduction

Experimental studies investigating the influence of cooling rate on the specific volume of polymers can roughly be divided into dilatometric studies investigating the evolution of the specific volume with temperature and studies investigating the final specific volume. Table 3.1 shows a (limited) overview of dilatometric studies performed on polypropylene at various cooling rates and elevated pressures. However, most cooling experiments listed in table 3.1 are performed at cooling rates far less than (locally) expected during processing. Only recent studies report on the influence 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 of cooling rate on the speciﬁc volume of isotactic polypropylene at elevated pressures. Macromolecular Materials 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 polypropylene obtained at various cooling or heating rates and elevated pressures. Data indicated by * are obtained by increasing temperature from ambient conditions. Polypropylene grades used are characterized by Mn and Mw/Mn. general, results of these studies show the transition due to crystallization to shift towards lower temperatures and the specific volume after complete cooling to increase with increasing cooling rate. Unfortunately, the data of Chakravorty [3] are most likely influenced by thermal gradients in the sample considering the sample dimensions and cooling rates employed. This means that their data do not represent intrinsic material behavior. Even at the relatively low cooling rates, up to 0.5 ◦C/s, employed in the study of Luyé et al. [1], thermal gradients between 5 - 15 ◦C where found resulting from the large sample dimensions, i.e. a cylindrical sample with 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 levels encountered during processing. Studies reporting on the influence of cooling rate on the final specific volume are mostly performed in the frame work of understanding the crystallization kinetics of polymers. The final density, i.e. reciprocal value of specific volume, is typically measured ex situ using the technique of density gradient column (DGC). Table 3.2 shows some studies performed in this field. All studies characterize the applied (time de- ◦ pendent) cooling rate by its value at 70 C, i.e. T˙ 70. In the studies of Piccarolo [12,13], Pantani et al. [14], and Brucato et al. [15] a specially designed setup is used to quench 100-150 µm thin samples at atmospheric pressure. Cooling rates achieved are of order O(102 − 103) ◦C/s. La Carrubba et al. [16] used a modified injection molding machine to investigate the combined influence of cooling rate and pressure on final specific volume. From the injection molded samples microtome slices were taken, representing material subjected to cooling rates of O(102) ◦C/s and elevated pressure 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 crystalline morphology of polypropylene resulting from processing conditions. in specific volume, with increasing cooling rate associated to a decrease in degree of crystallinity. Interesting are the results of La Carrubba et al. [16] showing that increased pressure and increased cooling rate have a qualitatively similar effect on the specific volume of polypropylene. The studies mentioned in tables 3.1 and 3.2 are representative for the work done regarding the influence of cooling rate on the specific volume of polymers but most are far outside the range of processing conditions. Dilatometric studies typically investigate 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 processes such as injection molding. Only Zuidema et al. [2] were able to impose high cooling rates but, unfortunately, at relatively low pressure. Except for the study of La Carrubba et al. [16], the final specific volume of polymers is generally investigated at high cooling rates but atmospheric pressure. We conclude that the combined influence of cooling rate and elevated pressure, as encountered during industrial processing operations, is insufficiently investigated. In this chapter, the influence of cooling rate on the specific volume of isotactic polypropylene is investigated at elevated pressures. Numerical predictions of the temperature dependent behavior of specific volume using the model of Zuidema et al. [2] are compared with experimental data. Also the resulting crystalline morphology is investigated by means of wide angle 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 dimensions 2.5 x 65 x 0.4 mm are prepared by compression molding. First, pellets are melted at atmospheric pressure. Next, the material is compressed for 3 minutes at 210 ◦C with a force of 50 kN. The samples are cooled in a water cooled press during 5 36 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

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

Dilatometer experiments

The combined influence of cooling rate and pressure on the specific volume of isotactic polypropylene (iPP) is investigated using the custom dilatometer presented in 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 procedure: a) the sample is heated with an average heating rate of 5 ◦C/min to a temperature of 210 ◦C, b) kept for 10 minutes at 210 ◦C to ensure fully melting of the crystalline microstructure, c) pressurized to the desired level, d) cooled to room temperature during which the pressure is maintained constant to within ±0.3 MPa. Prior to the experiment, a synthetic grease (Krytox GPL 207, Dupont) is put on the surface of the sample to reduce the friction between sample and dilatometer wall during the experiment. The basis of this grease is a perfluoropolyether (PFPE) synthetic oil thickened with polytetrafluoroethylene (PTFE) and is chosen for non-reactive behavior and thermal stability (-30 to 288 ◦C). DSC measurements performed on samples treated with grease and untreated samples, show no effect of the silicon grease on the crystallization kinetics of the iPP. The cooling rate is determined by the type and flux of the cooling medium. The piston and die of the dilatometer are cooled independently to optimize for thermal homogeneity of the sample during cooling. Since the dilatometer is cooled with a constant flux of cooling medium, the cooling rate is time dependent (see also figure 2.5).

X-ray analysis

Wide Angle X-ray Diffraction (WAXD) experiments are performed at the materials beam-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 of 0.4956 Å. The detector used is a Frelon CCD detector with 1024 x 1024 pixels. Both horizontal and vertical pixels are 164.4 µm in size. From calibration experiments using Lanthanum Hexaboride (LaB6) a sample-to-detector distance of 439.9 mm is determined. The exposure time for all images is 30 seconds. Finally, all images are corrected for spatial distortion using the ’Fit2d’ software [17] and background noise is subtracted. 3.3 RESULTS AND DISCUSSION 37

Ωω

Force / rotation controlled die Cooling die

Sample Temperature reading

Fixed piston

Cooling piston

Figure 3.1: Working principle of the custom designed dilatometer.

Density measurements

Density gradient column (DGC) experiments are performed to determine the density of samples subjected to dilatometer experiments. The column is prepared according to ASTM D1505 using water and isopropanol (IPA), establishing a linear density distribution ranging from 0.87-0.94 g/cc. Measurements are performed at a column temperature of 23 ◦C. Prior to submergence into the column, samples are subjected to an ultrasonic bath for 20 minutes, which consists of a representative mixture of water and 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 different cooling profiles. These profiles are achieved either by cooling the dilatometer pas- sively to the surrounding air (T˙ low), or actively using either pressurized air (T˙ medium) or water (T˙ high) as cooling medium. Temperatures are recorded at 6 positions outside the polymeric sample, corresponding to respectively top, middle, and bottom of the sample measured at both the inner and outer sample surface (see figure 3.1). The corresponding (surface) temperatures of the sample are determined via heat conduc- 38 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

tion analysis using the experimentally measured temperatures, the heat conducting properties of the set up material, and the known distance (0.5 mm) between the tip of the thermocouples and the sample surface. Based on these corrected temperatures, an averaged temperature profile in time is determined which represents the thermal history of the sample and which is used in further analysis of the data. As a characteristic value for the thermal history experienced by the material, the value ◦ of the cooling rate at 70 C, T˙ 70, is often used [12–15, 18]. Studies of the crystalline morphology of iPP resulting from quenching experiments [12, 13] have shown that ◦ the maximum of the crystallization rate for iPP is found at 70 C. This is why T˙ 70 is regarded as a characteristic processing parameter for iPP, used to indicate quench effectiveness and for comparing crystalline morphology and resulting material properties obtained at different processing conditions [11]. These studies have been performed at ambient pressure. However, it is known that with increasing pressure 0 the polymer’s equilibrium melting temperature Tm increases [19], leading to crystallization at higher temperatures. Consequently, as the cooling rate is highest at high temperature, the effective cooling rate experienced by the material will increase in case the polymer is subjected to a time-dependent cooling rate. Any changes in material properties resulting from a change in pressure at an identical time-dependent cooling rate, i.e. constant T˙ 70, could be explained from a ‘processing point of view’ as a pressure effect. However, from a ‘material point of view’ this is at most a combined effect of cooling rate and pressure, since we can not distinguish for the pressure effect 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 characteristic value for the experienced thermal history of the polymer, i.e. the average of the cooling rates present during the transition in the specific volume. Our experience shows that this approach is a useful one, see also chapter 2, figure 2.7. Characteristic values for cooling rate are listed in table 3.4. Additionally, values for T˙ 70 are given to enable comparison with other studies such as listed in table 3.2. As already outlined in chapter 2, the measured specific volume data are completed with conventional pVT- data of the amorphous phase. These data are measured with a conventional bellows type dilatometer at low cooling rates (see Appendix 3.A). Figure 3.2 shows specific volume as a function of pressure and temperature measured at different cooling profiles. Each curve depicts the mean of 3 measurements with standard deviation. In case of T˙ high, curves represent the mean of 5 measurements. Figure 3.2a shows the specific volume of iPP measured at T˙ low and isobars 20, 40, 60 MPa. Characteristic for these measurements performed at a cooling rate of 0.1 ◦C/s is the sharp transition in the specific volume associated to the crystallization of the polymer. The temperature marking the start of this transition, further referred to as the transition temperature Tc, is defined arbitrarily as the temperature where the change in specific volume due to crystallization has reached 5 % of the total change. With increasing cooling rate, the characteristic shift of Tc towards lower temperatures is observed and the transition itself is getting less distinct and more wide spread [1–3].

Both the shift in Tc and the less distinct and more wide spread transition are re- 3.3 RESULTS AND DISCUSSION 39

6 6 x 10 x 10 1.35 1.35

1.3 1.3

1.25 1.25 /kg] /kg] 3 3 1.2 1.2 [mm [mm ν 1.15 ν 1.15

1.1 20 [MPa] 1.1 20 [MPa] 40 [MPa] 40 [MPa] 60 [MPa] 60 [MPa] 1.05 1.05 0 50 100 150 200 250 0 50 100 150 200 250 T [C] T [C]

( a) ( b)

6 x 10 1.35

1.3

1.25 /kg] 3 1.2 [mm ν 1.15

1.1 20 [MPa] 40 [MPa] 60 [MPa] 1.05 0 50 100 150 200 250 T [C]

( c)

Figure 3.2: Inﬂuence of cooling rate on the speciﬁc volume of iPP measured at various pressure levels: (a) 0.1 ◦C/s, (b) 1.2 - 1.4 ◦C/s, (c) 30.0 - 34.8 ◦C/s. For exact cooling rates per pressure level see table 3.4. 40 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

6 x 10 1.3

1.25

1.2 /kg] 3

[mm 1.15 ν

1.1

1.05 0 50 100 150 200 250 T [C]

Figure 3.3: Influence of cooling rate on the specific volume of iPP at a pressure of 40 MPa. 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 the competition between the time of cooling and the time necessary to crystallize. With increasing cooling rate, the time for spherulites to grow and new nuclei to form at a certain undercooling is less. Figure 3.3 more clearly illustrates the suppression of the crystallization process with increased cooling rate. The specific volume is measured at a constant pressure of ◦ 40 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 0.1 to respectively 1.2 and 32.5 ◦C/s. The real driving force for crystallization is the 0 undercooling 4T = Tm − T, which scales with temperature when the pressure is constant. Since the start of the transition can be regarded as a measure for the onset of crystallization, the shift in Tc towards lower temperatures indicates a delay in the onset of crystallization, i.e. crystallization starts at higher undercooling. With increased pressure, Tc shifts towards higher temperatures due to the pressure de- 0 pendence of the equilibrium melting temperature Tm [19]. However, independent of pressure the onset of crystallization will occur at the same undercooling for identical characteristic cooling rate, i.e. identical thermal history. For the relatively small pressure range that was experimentally accessible, the influence of pressure on Tc is about linear with a pressure dependence of 0.2700 ◦C/MPa. This is very similar to the pressure dependence of PP found by other authors: 0.2287 oC/MPa obtained at a cooling rate of 0.042 ◦C/s [8], 0.2625 oC/MPa obtained at a cooling rate of 0.083 ◦C/s [1], and 0.2536 oC/MPa obtained at a cooling rate of 0.10 ◦C/s [20]. This last value is obtained from applying a linear fit to data of crystallization temperature Tc1, i.e. samples crystallized below a pressure of 340 MPa. 3.3 RESULTS AND DISCUSSION 41

160 20 [MPa] 40 [MPa] 150 60 [MPa] Luye − 40 [MPa] Luye − 80 [MPa] 140 Luye − 120 [MPa] [C]

1301/2 , T c

T 120

110

100 −2 −1 0 1 2 10 10 10 10 10 Cooling rate [C/s]

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 and pressure. Solid lines represent a linear ﬁt of the data according to equation (3.1) with coefﬁcients 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 rate dependence changes only little with pressure. The data obtained at 60 MPa show a somewhat different trend, which is mainly caused by determining Tc at the highest cooling rate. This is subject to small variations due to the less distinct transition in specific volume. Luyé et al. [1] analyzed the influence of pressure and cooling rate on the half-crystallization temperature T1/2. They performed measurements for a pressure 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 good agreement. Differences in temperature values could be resulting from the different material grades used and the different definitions used for Tc and T1/2. Finally, the specific volume at room temperature increases with increasing cooling rate. 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 is most likely the result of differences in material grade used. 42 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

0.92 20 [MPa] 40 [MPa] 0.915 60 [MPa] LaCarrubba 24 [MPa] LaCarrubba 40 [MPa] 0.91 LaCarrubba 60 [MPa] ] 3

0.905 [g/cm ρ 0.9

0.895

0.89 −2 −1 0 1 2 10 10 10 10 10 Cooling rate at 70 [C] [C/s]

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

P a0 a1 [MPa] [oC] [s] 20 125.8 -12.3226 40 129.2 -11.4890 60 135.6 -9.5691 40∗ 116.1 -13.0694 80∗ 127.8 -11.5269 120∗ 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 obtained from Luyé et al. [1]. 3.3 RESULTS AND DISCUSSION 43

X-ray (Scanning) T

X-ray (Single shot)

Figure 3.6: Schematic representation of an annular sample used in dilatometer experiments with indication of cooling direction. WAXD analysis is performed ex situ either in scanning mode (perpendicular to direction of cooling) or in single shot mode (parallel to direction of cooling).

Crystalline morphology

Wide angle X-ray diffraction (WAXD) experiments are performed to investigate the crystalline morphology depending on cooling rate and pressure. These experiments are performed in single shot mode, parallel to the direction of cooling. Additionally, the homogeneity of samples subjected to T˙ medium and T˙ high is analyzed by performing experiments 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 beam size to study possible heterogeneities at the edge of the sample. From the two dimensional WAXD images, one dimensional scattering (1D WAXD) profiles are obtained by integration of the Debye-Scherrer rings along the azimuthal angle. Furthermore, to correct for small variations in sample thickness and fluctuations of the beam, the intensity is normalized such that the area underneath the curve equals unity according to:

I (2θ) I∗ (2θ) = Z (3.2) I (2θ) d (2θ)

The degree of crystallinity is determined by subtracting the scattering pattern of a nearly 100% amorphous sample from the scattering patterns of semi-crystalline samples. To do this, the intensity is scaled such that the maximum of the amorphous 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 the crystalline phases in iPP (α-monoclinic, γ-orthorhombic crystalline phase) are determined from single shot experiments according to the method of Van der Burgt et o al. [24]. Changes in the (130)α scattering peak, which is located at 2θ = 5.94 for λ = 0.4956 Å, are taken as indicative for changes in α-monoclinic crystalline phase. o For the γ-orthorhombic crystalline phase the (117)γ peak at 2θ = 6.49 is used (see 44 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

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

Homogeneity of crystalline morphology

Figure 3.8 shows the running average of the degree of crystallinity χ as distribution across 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 subjected to T˙ high and 60 MPa. This is quite unexplained. A possible explanation could be the ∂T combined inﬂuence of spatial temperature gradients ∂x across the thickness of the sample, that increase with higher temperature values because of the time-dependent 0 nature of the cooling rate, and the shift of Tm towards higher temperatures with increasing pressure, i.e. with increasing pressure the polymer is subjected to higher cooling rates that could result in signiﬁcant spatial temperature gradients due to the relatively bad heat conductive properties of the polymeric sample. Samples subjected to T˙ medium show a very homogeneous morphology while samples subjected to T˙ high 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 experiments. When comparing the degree of crystallinity determined from single shot experiments (χ) with the averaged degree of crystallinity determined from scanning experiments (χµ), differences of ≤ 1.1% are observed except for 20 MPa and a cool- o ing rate 1.2 C/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 the degree of crystallinity. The standard deviation σ increases with cooling rate but is still 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 crystallinity 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, the degree of crystallinity decreases significantly with increasing cooling rate. The influence of pressure is however marginal for the pressure range employed, especially for T˙ medium and T˙ high. Furthermore, a combined influence of pressure and cooling rate is not observed. This agrees with results of La Carrubba et al. [25] who found the effect of pressure on (α-)crystallinity to be largest in the pressure range to about 10 MPa for cooling rates exceeding 1.5 ◦C/s. For pressures exceeding roughly 10 MPa at these cooling rates, the observed influence of pressure was negligible and no combined influence of cooling rate and pressure was detected. With respect to changes in the relative fractions of the α- and γ-crystalline phases we observe an increase in the relative amount of γ-crystalline phase with increasing pressure at low cooling rates [19, 20, 26, 27], and a rapid decrease in γ-crystalline 3.3 RESULTS AND DISCUSSION 45

( a)

( b)

Figure 3.7: 1D WAXD proﬁles showing the normalized intensity I∗ versus Bragg’s angle 2θ for samples crystallized at a pressure of 40 MPa and a characteristic cooling rate of (a) 0.1 ◦C/s and (b) 32.5 ◦C/s. The scaled amorphous halo is represented by the dashed line. 46 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

65 60 55 50

[%] 45 χ 40 35 30 25 −0.2 −0.1 0 0.1 0.2 X [mm]

Figure 3.8: The running average of the degree of crystallinity χ plotted against scanning 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, (•) 20 MPa - 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 43.7 20 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 0.9 20 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 relative crystalline fractions: χ = degree of crystallinity determined from single shot experiments, χµ = the average value of the degree of crystallinity determined from scanning experiments, σ = the standard deviation corresponding to values of χµ, f rac α = relative fraction of α-crystallinity, f rac γ = relative fraction of γ-crystallinity. 3.3 RESULTS AND DISCUSSION 47

Parameter Melt state (i=a) Solid state (i=sc) Dimension 6 6 3 νre f ,i 1.1379·10 1.0805·10 [mm /kg] ∂νi 2 2 3 ◦ ∂T 7.7028·10 4.3988·10 [mm /kg C] ∂νi −3 −2 3 ∂P -1.1232·10 -2.7242·10 [mm /kgPa] 2 ∂ νi −6 −6 3 ◦ ∂T∂P -1.3400·10 -3.0343·10 [mm /kg CPa] ∂2 νi 0 0 0 0 mm3 kg◦C2 ∂T2 · · [ / ] ∂2 νi 1.5443 10−11 2.6749 10−12 mm3 kgPa2 ∂P2 · · [ / ] ∂3 νi -5.3721 10−14 1.5359 10−14 mm3 kg◦CPa2 ∂T∂P2 · · [ / ]

Table 3.5: Partial derivatives for Taylor series description of the speciﬁc volume in melt and solid state. phase with increasing cooling rate [24,28]. The presence of a smectic or mesomorphic phase, was analyzed using a WAXD-deconvolution method similar to La Carrubba et al. [25]. However, because of the large number of ﬁtting parameters introduced by taking all crystalline phases (α−, γ−crystallinity), mesomorphic and amorphous phase into account, this method failed to produce reliable results with respect to quantifying the presence of the mesomorphic phase. Optimization of this method is subject of future research.

Modelling aspects

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

ν = ξgνsc + (1 − ξg)νa (3.3) where νsc is the specific volume of the solid (semi-crystalline) state, νa the specific volume of the amorphous phase assumed equal to the specific volume of the polymer melt, and ξg the degree of space filling of spherulites. Both νsc and νa are described as a Taylor series in pressure and temperature.

∂ν ∂ν ∂2ν ∂2ν ν = ν + i 4T + i 4P + i 4T4P + i 4T2 + i re f ,i ∂T ∂P ∂T∂P ∂T2 ∂2ν ∂3ν i 4P2 + i 4T4P2 i = a, sc (3.4) ∂P2 ∂T∂P2

4T = T − Tre f (3.5) 48 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

4P = P − Pre f (3.6)

◦ with Tre f =0 C and Pre f =20 MPa. Values for the partial derivatives are determined by fitting (3.4) to specific volume data obtained during slow cooling (T˙ low) and are listed in table 3.5. The degree of space filling ξg is calculated using the Schneider rate equations for the description of quiescent crystallization kinetics in non-isothermal conditions [22]:

· 0 0 φ3 = 8πα (φ3 = 8π N) rate (3.7) · 0 0 φ2 = Gφ3 (φ2 = 4πRtot) radius (3.8) · 0 0 φ1 = Gφ2 (φ1 = Stot) sur f ace (3.9) · 0 0 φ0 = Gφ1 (φ0 = Vtot) volume (3.10) ¡ ¢ 0 0 φ0 = − ln 1 − ξg space filling (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 differential equations. Auxiliary functions φi are introduced by the step wise differentiation with respect to time, each of which can be related to the crystalline morphology: φ0 is equal to the undisturbed total volume Vtot of the spherulites per unit volume, φ1 is the total surface Stot of the spherulites per unit volume, φ2 is 4π times the sum of the radii of the spherulites per unit volume, and φ3 is 8π times the number of spherulites N per unit volume. Impingement and swallowing of spherulites are dis- regarded, i.e. unbounded growth of spherulites, which also implies that the rate of nucleation α is independent of the volume fraction of already crystallized material. An Avrami model, equation (3.11), is used to correct for impingement and swallowing of spherulites. Important input data for these rate equations are the experimentally measured thermal history (see ﬁgure 2.5) and the, degree of undercooling dependent, spherulitic growth rate G(T) and the number of nuclei per unit volume N(T) determined from polarized optical microscopy experiments. To describe spe- ciﬁc volume at elevated pressure, both G(T) and N(T) are corrected for pressure dependence and modelled in the following way:

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

N(T, p) = 10[n0+n1(T− fn(p))] (3.13)

where

2 fi(P) = pi04P + pi14P i = g, n (3.14)

4P = P − Pre f (3.15) 3.3 RESULTS AND DISCUSSION 49

Parameter Fit1 Fit2 Fit3 Dimension −6 −6 −6 Gmax 2.9669·10 2.9669·10 2.9669·10 [m/s] b 1.3000·10−3 1.3000·10−3 1.3000·10−3 [1/oC] 1 1 1 o Tre f 9.00·10 9.00·10 9.00·10 [ C] −7 −7 −8 pg0 2.7000·10 2.7000·10 7.0333·10 [K/Pa] −15 2 pg1 0·0 0·0 -4.7000·10 [K/Pa ] −7 −7 −7 pn0 2.7000·10 -7.4287·10 2.7000·10 [K/Pa] −14 2 pn1 0·0 1.3870·10 0·0 [K/Pa ] 1 1 1 3 n0 1.9067·10 1.9067·10 1.9067·10 [1/m ] −2 −2 −2 3 n1 -4.9800·10 -4.9800·10 -4.9800·10 [1/m K] 5 5 5 Pre f 1.0000·10 1.0000·10 1.0000·10 [Pa]

Table 3.6: Model parameters for the spherulitic growth rate G(T,p) and effective number 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 crystallization temperature Tc. The reason for this is that the pressure dependence of Tc 0 is related to the pressure dependence of the (equilibrium) melting temperature Tm, which in its turn affects the undercooling 4T, 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 and are indicated with ‘Fit 1’.

The predicted specific volume for a pressure of 40 MPa and T˙ low is shown in figure 3.9a, and for T˙ medium and T˙ high in figures 3.10a and 3.10b, respectively. Except for T˙ high, the predicted specific volume agrees rather well with experimental data. For T˙ high a large mismatch in the predicted start and evolution of the transition with respect to the experimental data is observed. A second and third approach to model the pressure dependence of G(T, p) and N(T, p) is to: i) adjust N(T, p) such that the predicted specific volume fits to the experimental data obtained at T˙ low, while G(T, p) is based on the pressure dependence of Tc (=fit 2), ii) adjust G(T, p) such that the predicted specific volume fits to the experimental data obtained at T˙ low, while N(T, p) is based on the pressure dependence of Tc (=fit 3). Although both approaches show similar results as fit 1 for T˙ low and T˙ medium, only fit 3 shows improvement of the predicted specific volume for T˙ high. The predicted evolution of the transition is quite improved using fit 3, while the mismatch in predicted start of the transition stays rather unaffected for all three approaches. These deviations could be resulting from experimental inaccuracies determining G(T) and N(T). See for example the compilation of growth speeds for the α-crystallinity of iPP as reported by Eder and Janeshitz-Kriegl [30] Here differences of up to a factor 2 in the reported Gmax of the α-crystalline phase of iPP can be observed. 50 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

6 x 10 1.3

1.25 /kg] 3 1.2 [mm ν 1.15

1.1 Fit 1 Fit 2 Fit 3 1.05 0 50 100 T [C] 150 200

( a)

6 x 10 1.3 Fit 3 n1 −10% 1.25 n1 +10% Tref −5% /kg] 3 1.2 Tref +5% [mm 1.15ν

1.1

1.05 0 50 100 150 200 T [C]

( b)

Figure 3.9: (a) Measured (¤) and calculated specific volume for a pressure of 40 MPa and a cooling rate of 0.1 ◦C/s, (b) influence of small variations in model parameters 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 description for G(T) and N(T) in figure 3.11. 3.3 RESULTS AND DISCUSSION 51

6 x 10 1.3

1.25 /kg] 3 1.2 [mm 1.15ν

1.1 Fit 1 Fit 2 Fit 3 1.05 0 50 100 150 200 T [C]

( a)

6 x 10 1.3

1.25 /kg] 3 1.2 [mm ν 1.15

1.1 Fit 1 Fit 2 Fit 3 1.05 0 50 100 150 200 T [C]

( b)

Figure 3.10: Measured (¤) and calculated speciﬁc volume for a pressure of 40 MPa and a cooling rate of (a) 1.4 ◦C/s and (b) 32.5 ◦C/s. 52 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

Another reason for the observed mismatch between the experimentally measured and numerically predicted specific volume could be because of inaccuracies in determining numerical descriptions for G(T, p) and N(T, p). To study the influence of the latter on predictions of specific volume, small variations in the parameters describing G(T, p) and N(T, p) are introduced (see figure 3.11). With respect to the modelling of 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 the predicted specific volume are shown in figure 3.9b and figure 3.12. Again, the prediction of the specific volume at T˙ high shows the largest susceptibility to variations in the model. If we focus on predictions for T˙ high (figure 3.12b), variation of parameter n1 with -10% does not show any change in predictions with respect to fit 3 (curves on top of each other). Variation of n1 with +10% gives a slightly worse prediction of the evolution of the transition. Changes of ±5% in Tre f result in larger differences in predicted transition. Because these changes in Tre f mainly affect the description of G(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 these low temperatures is of importance for the correct prediction of specific volume at high cooling rates. The mismatch in predicted start of the transition is however almost unaffected by all variations. Only (unrealistically large) variations of N(T, p), such that a larger number of nuclei becomes available at high temperatures, is able to improve this mismatch. This can be accomplished for example by choosing a constant and relatively large value for N(T, p), in combination with a description of G(T, p) according to fit 15.25 3 3. Here a value of 10 1/m is chosen for parameter n0 (see figure 3.11b). These deviations in predicted specific volume compared to experimentally determined values are still not well understood and are subject of future investigations. 3.3 RESULTS AND DISCUSSION 53

−6 10 G [m/s] −7 10 Exp. data Best fit Tref −5% Tref +5% −8 10 0 50 T [C] 100 150

( a)

20 10 Exp. data

] Best fit 3 n1 +10% n1 −10% 15.25 N [1/m N = 10 15 10

10 10 0 50 T [C] 100 150

( b)

Figure 3.11: Spherulitic growth rate G(T) and effective number of nuclei N(T) determined from polarized optical microscopy measurements at atmospheric pressure (O) and various numerical descriptions characterized by small variations in model parameters. 54 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

6 x 10 1.3

1.25 /kg] 3 1.2 [mm ν 1.15 Fit 3 n1 −10% 1.1 n1 +10% Tref −5% Tref +5% 1.05 0 50 100 150 200 T [C]

( a)

6 x 10 1.3

1.25 /kg] 3 1.2 Fit 3 [mm 1.15ν n1 −10% n1 +10% Tref −5% 1.1 Tref +5% N = 1015.25 1.05 0 50 100 150 200 T [C]

( b)

Figure 3.12: Influence of small variations in model parameters on the predicted specific 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 for G(T) and N(T) in figure 3.11. 3.3 RESULTS AND DISCUSSION 55

3.4 Conclusions

The influence of cooling rate and pressure on the specific volume of isotactic polypropylene was investigated using a custom designed dilatometer. A profound influence of both cooling rate and pressure on the crystallization temperature Tc and the final specific volume after cooling was observed. Comparison of these results with different literature sources showed good agreement. The need for homogeneous cooling restricts the maximum cooling rate that can be used. The influence of possible thermal gradients in the sample on the resulting crystalline morphology is however dependent on the actual undercooling. Because of the time-dependent nature of the cooling rate and the pressure dependence of the melting temperature of the polymer, also the pressure puts indirect restrictions to the maximum cooling rate to be used. In our study using isotactic polypropylene, analysis of the crystalline morphology via WAXD showed good homogeneity of samples up to a cooling rate of 32.4 ◦C/s and a pressure of 40 MPa. Finally, comparison of model predictions with experimental data at medium and high cooling rate showed at first large deviations in the prediction of start and evolution of the transition, i.e. the predicted crystallization temperature Tc and rate of crystallization. Deviations in the rate of crystallization could partly be explained from small variations in model parameters. These variations were justified from possible 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) and N(T, p) should be characterized for a sufficiently large temperature range, including temperatures typically lower than the temperature where the maximum in G(T, p) occurs. Deviations in predicted crystallization temperature Tc are however quite unexplained and could only be improved by introducing an unrealistic larger number of nuclei than determined experimentally at relatively high temperatures. This is subject to future investigation. 56 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

References

[1] Luyé, J.F., Regnie, G., Le Bot, P.H., Delaunay, D., Fulchiron, R. PVT measurement methodology for semicrystalline polymers to simulate injection-molding process. Journal of Applied Polymer Science, 79:302-311, (2001). [2] 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). [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 of cooling 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 polymers: 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 der Viskoelastischen und Physikalisch-Chemischen Eigenschaften von Polymeren. Markomolecular Chemistry, 178:2037-2047, (1977). [8] He, J. Zoller, P. Crystallization of Polypropylene, Nylon-66 and Poly(ethylene terephtalate) 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 semicrystalline polymers. Thermochimica Acta, 238:397-415, (1994). [10] Ito, H., Tsustumi, Y., Minagawa, K., Takimoto, J., Koyama, K. Simulations of 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 of cooling rate. Journal of Macromolecular Science - Phys., B31(4):501-511, (1992). [13] Piccarolo, S., Saiu, M., Brucato, V., Titomanlio, G. Crystallization of polymer melts 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 industrial polypropylene-EPR copolymer in process conditions. Journal of Applied Polymer Science, 81:267-278, (2001). [15] Brucato, V., Piccarolo, S., La Carrubba, V. An experimental methodology to study polymer crystallization under processing conditions. the influence of high cooling rates. Chemical Engineering Science, 57:4129-4143, (2002). [16] La Carrubba, V., Brucato, V., Piccarolo, S. Phenomenological approach to compare 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 solidified 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 of isotactic 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 (γ phase). 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 thermal treatments on the polymorphism in stereoirregular isotactic polypropylene: effect of stereo-defect distribution. Journal of Macromolecular Science. Part B: Physics, B41:1091-1104, (2002). [25] La Carrubba, V., Brucato, V. , Piccarolo, S. Isotactic Polypropylene solidification under 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-molecular weight polypropylene: 1. morphological aspects. Polymer, 34(23):4809-4816, (1993). [27] Brückner, S., Philips, P.J., Mezghani, K., Meille, S.V. On the crystallization of γ-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 nucleation agents at different cooling rates. Polymer, 42:1167-1176, (2001). [29] Zuidema, H., Peters, G.W.M., Meijer, H.E.H. Development and validation of a recoverable strain based model for flow induced crystallization of polymers. Macromolecular Theory and Simulation, 10(5):447-460, (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). 58 3 THE INFLUENCE OF COOLING RATE ON SPECIFIC VOLUME

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 designed dilatometer. Figure 3.13 shows the data, which are measured in isobaric mode at a constant cooling rate of 1.0 ◦C/min. Experiments are performed at Moldflow Plastics 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 is very similar in molecular weight and molecular weight distribution compared to the investigated polypropylene grade HD120MO, except that the latter does not include nucleation agent. The specific volume of the melt is assumed identical. A polynomial fit is determined to describe the specific volume of the melt as function of pressure and temperature:

2 2 ν (T, p) = a0 + a1T + a2T4P + a3T4P + a44P + a54P (A.1) with

4P = P − Pre f (A.2)

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

Parameter Value Dimension 6 3 a0 1.1348·10 [mm /kg] 2 3 o a1 8.6387·10 [mm /kg C] −6 3 o a2 −7.3487·10 [mm /kg CPa] −14 3 o 2 a3 4.0480·10 [mm /kg CPa ] −4 3 a4 −1.4359·10 [mm /kgPa] −12 3 2 a5 −1.7185·10 [mm /kgPa ] 7 Pre f 1.0·10 [Pa]

Table 3.7: Parameters for the polynomial description of the speciﬁc volume in the melt. 3.A APPENDIX: SPECIFIC VOLUME OF THE MELT 59

6 x 10 1.35 p = 10 [MPa] p = 40 [MPa] 1.3 p = 80 [MPa] p = 100 [MPa] 1.25 Fit /kg] 3 1.2 [mm ν 1.15

1.1

1.05 50 100 150 200 T [C]

Figure 3.13: Specific volume data of iPP (grade K2xmod, Borealis) measured in isobaric mode at a constant cooling rate of 1.0 ◦C/min. Solid lines represent the fit for the specific volume of the melt. ‘Design C’ CHAPTERFOUR

The influence of shear flow on specific volume1

The influence of shear flow on the temperature evolution of the specific volume of two iPP’s, differing in weight averaged molar mass Mw, was investigated at non-isothermal conditions and elevated pressures, using a custom designed dilatometer. These conditions are typically in the range of conditions as experienced during polymer processing. A pronounced influence of flow on the temperature marking the transition in specific volume and the rate of transition could be observed. In general, this influence increased with increasing shear rate, decreasing temperature where flow was applied, increasing pressure, and increased weight averaged molar mass Mw of the polymer. Although the degree of orientation and the overall structure of the resulting crystalline morphology were greatly affected by the flow, the resulting specific volume was only little affected by the thermomechanical conditions presently investigated. Finally, when flow was applied at sufficiently high temperature, in some cases the polymer was able to fully erase the effect of flow. This is attributed to remelting of the flow-induced crystalline structures.

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 influence 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 volume and 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 follow the crystallization process of polyethylene oxide (PEO) grades as a function of undercooling, shear rate, and molecular weight. This was derived from specific volume data. Steady shear experiments, with shear rates applied up to 140 1/s, were performed at isothermal conditions and atmospheric pressure. Results showed the start in crystallization, i.e. the transition in the specific volume, to occur at smaller times with increasing shear rate, increasing molecular weight, and higher undercooling. Fleishmann and Koppelmann [16] performed injection molding experiments and compared measured cavity pressure levels with calculated pressures, to draw conclusions with respect to the dependence of specific volume on applied flow. The agreement of calculated and experimental pressure data showed large deviations if standard ’slow cooling PVT-data’ were used as input for the model. A better agreement was obtained by shifting the transition temperature of specific volume towards higher temperatures to correct for the influence of flow. Watanabe et al. [17] used a dilatometer consisting of a mixture of a conventional piston-die dilatometer and a plate-plate rheometer, to study the influence of (steady) shear rate and elevated pressure at isothermal conditions on the relative degree of crystallinity as derived from specific volume data. The start of the transition in the specific volume of iPP was found to occur at smaller times with increasing shear rate and with increasing pressure. The influence of pressure was explained by the shift in the experimental melting temperature Tm towards higher temperatures leading to increased undercooling at a constant temperature. Unfortunately, only shear rates up to 0.5 1/s were applied at a maximum pressure of 20 MPa. These conditions are not very representative for the processing conditions as encountered during, for instance, injection molding. Moreover, the plate-plate geometry is not very well suited to study the influence of shear rate on specific volume because of its dependence on the sample radius, i.e. inhomogeneous distribution across the sample. This chapter deals with the influence of shear flow on the specific volume of isotactic polypropylene measured at conditions close to industrial processing conditions. The combined influence of shear rate, pressure, cooling rate, and the polymer’s molecular weight distribution on the temperature-dependent development of the specific volume is studied, using the technique of dilatometry. The results are explained using the present knowledge of (flow induced) crystallization and are related to the crystalline morphology, as investigated ex situ using wide angle X-ray diffraction (WAXD) and visualized by scanning electron microscopy (ESEM).

4.2 Experimental part

Materials

The materials used are two commercial isotactic polypropylenes (iPP). The ﬁrst material (iPP-1) is supplied by Borealis (grade HD120MO), the second material (iPP-2) 4.2 EXPERIMENTAL PART 63

0.7 iPP−1 0.6 iPP−2

0.5

0.4

0.3 Amount [%]

0.2

0.1

0 3 4 5 6 7 8 log M [g/mol] w

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

Material Mw Mw/Mn Tm [g/mol] [−] [oC] iPP-1 365000 5.2 162.7 iPP-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 distribution of both materials determined via GPC, and table 4.1 lists some main properties of both materials. Note that although iPP-2 was also used by Swartjes et al. [14], results 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 3 minutes at 210 ◦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. 64 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

B T D [O C]

P C Tt [s] [Mpa]

T Gg E t [s] [1/s ]

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 investigated using the custom designed dilatometer as described in chapter 2. Dilatometer experiments are performed in the isobaric cooling mode according to the procedure schematically depicted in figure 4.2: A) the sample is heated with an average heating rate of 5 ◦C/min to a temperature of 210 ◦C, B) kept for 10 minutes at 210 ◦C to ensure fully melting of the crystalline microstructure, C) pressurized to the desired level, D) cooled to room temperature during which the pressure is maintained constant to within ±0.3 MPa, E) and during cooling subjected to shear flow for a certain time and constant shear rate. After the sample is completely cooled down, it is taken out 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 of the sample for external influences such as thermal expansion of the dilatometer, deformation of the dilatometer due to mechanical loading, etc. Within minutes after finishing the experiments, the samples are removed from the dilatometer and stored in a freezer at −5 ◦C for later analysis of the crystalline morphology and resulting density.

Density Gradient Column

Density gradient column (DGC) experiments were performed according to ASTM D1505, establishing a linear density distribution ranging from 0.87-0.94 g/cc using 4.3 RESULTS AND DISCUSSION 65

water and isopropanol (IPA). Measurements were performed at a column temperature of 23 ◦C. Prior to submergence into the column, samples were subjected to an ultrasonic bath, consisting of a representative mixture of water and isopropanol, for 20 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 materials beam-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 0.4956 Å. The detector used is a Frelon CCD detector with 1024 x 1024 pixels. Both horizontal and vertical pixels are 164 µm in size. From calibration experiments, using Lanthanum 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 were subsequently 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 a SE-detector and operated at 5 kV.

4.3 Results and discussion

Speciﬁc volume

Dilatometer experiments were performed to study the combined influence of shear flow, pressure, and molecular parameters on the specific volume of iPP. Parameters that were varied are: a) average temperature during flow, b) shear rate at constant total shear, c) the molecular weight distribution (MWD) of the polymer, d) pressure during flow. In the following analysis of the results, the specific volume is normalized to make comparison of results obtained at various processing conditions more easy. The normalized specific volume ν∗ is defined as: ν − ν ν∗ = s (4.1) νm − νs

where ν is the measured specific volume, νs is the value of the specific volume in the solid state at room temperature (in case the sample was not subjected to flow), and ◦ νm represents the value of the specific volume in the melt state at 210 C. 66 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

200 150

T [C] 100 50 0 100 200 300 400 500 600

−2

−4

Cooling Rate [C/s] 0 100 200 300 400 500 600 t [s]

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

iPP-1 iPP-2 Tγ 4Tγ Tγ 4Tγ [◦C] [◦C] [◦C] [◦C] 139 59.2 133 65.2 154 44.2 153 45.2 193 5.2 193 5.2

Table 4.2: Temperatures Tγ where shear ﬂow is applied and associated undercooling 4Tγ for both iPP’s.

Inﬂuence of temperature during ﬂow

The influence of thermomechanical history on the specific volume of iPP was investigated by subjecting the polymer to shear flow at various temperatures. The pressure during the experiments was kept constant at 40 MPa and cooling as depicted in figure 4.3 was applied. Shear flow was applied as a step-function during cooling, with a shear 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 = 1.5 s, i.e. the total shear is approximately constant. Flow was applied at various temperatures, i.e. different degrees of undercooling. Since shear flow was applied during cooling over a small temperature range, the average value of this range is taken as a characteristic value and further referred to as Tγ. Values for Tγ and the associated 0 undercooling, 4Tγ = Tm − Tγ, are listed in table 4.2. For the equilibrium melting 0 ◦ temperature Tm at a pressure of 40 MPa a value of 198.2 C is used [24]. 4.3 RESULTS AND DISCUSSION 67

1 1

0.8 0.8

0.6 0.6 [ − ] [ − ] * * ν 0.4 ν 0.4

0.2 0.2

0 0

0 50 100 150 200 250 0 50 100 150 200 250 T [C] T [C]

( a) ( b)

1 1

0.8 0.8

0.6 0.6 [ − ] [ − ] * * ν ν 0.4 0.4

0.2 0.2

0 0

0 50 100 150 200 250 0 50 100 150 200 250 T [C] T [C]

( c) ( 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 during 3.0 s (4) or a shear rate of 78.0 1/s during 1.5 s (¤) at various temperatures, indicated by the arrows: (a) no shear flow applied, (b) Tγ = 193 ◦ ◦ ◦ C, (c) Tγ = 154 C, (d) Tγ = 139 C. Measurements performed in absence of flow are represented by (O). All measurements are performed at a constant pressure of 40 MPa. WAXD images show the influence of shear flow on the orientation of the resulting crystalline morphology, using a shear rate of 39.0 1/s during 3.0 s. 68 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

Figures 4.4 and 4.5 show the influence of shear flow applied at various temperatures Tγ on the normalized specific volume of respectively iPP-1 and iPP-2. Arrows indicate the temperature Tγ where flow is applied. The WAXD patterns give an indication of the orientation of the resulting crystalline morphology (flow direction is vertical). Furthermore, in each sub-figure the specific volume measured in the absence 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 onset of the transition, whereas the specific volume of the solid state is hardly affected. If shear flow has an effect, then Tc shifts towards higher temperatures and associated to this WAXD analysis shows arcing of the Debye-Scherrer rings. This is an indication for orientation of the resulting crystalline morphology. From a thermodynamic point of view, the shift in Tc towards higher temperatures can be explained from the orientation 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 a given temperature the effective undercooling 4T is therefore higher. From a crystallization kinetics point of view, molecular orientation yields an enhanced formation of (flow induced) primary nuclei [2, 3, 6, 9, 11, 19]. The number of flow induced nuclei can be some orders of magnitude higher than the number of nuclei formed at quiescent conditions [13]. Both effects will enhance the crystallization kinetics, enabling the process of crystallization to start at higher temperatures. Furthermore, with increasing Tγ the resulting crystalline morphology shows less orientation and the temperature interval between Tγ and Tc increases. Note that if iPP-1 is subjected ◦ to a shear rate of 39.0 1/s at Tγ = 193 C, the effect of flow can be fully erased (figure 4.4b). This ability of the melt to erase the influence of flow on the process of crystallization was also observed by others [20–22], and is attributed to remelting of the flow induced crystalline structure and relaxation of oriented chains. However, if the ◦ polymer is subjected to a shear rate of 78.0 1/s at Tγ = 193 C, the influence of flow is 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 of flow induced structures can be ignored [20]. The evolution of the specific volume in ◦ case the polymer is subjected to a shear rate of 39.0 1/s applied either at Tγ = 154 C ◦ or Tγ = 139 C matches surprisingly well. The temperature marking the start of the transition and the evolution of the transition itself are almost identical. This is more coincidence than rule and is treated in more detail in chapter 5. If the temperature at which shear flow is applied is taken as a reference, the polymer needs an additional undercooling of about 17 ◦C for the transition to start in case shear flow is applied ◦ ◦ at Tγ = 154 C. If shear flow is applied at Tγ = 139 C, the transition starts almost immediately, i.e. the time needed to start crystallization after application of flow reduces. There are several reasons for that. First, viscoelastic stresses arising from shear flow at lower temperature are higher, therefore leading to a higher number of 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 link molecules into a physical network [23]. Shear flow applied will thus have a larger orienting effect throughout the melt, potentially forming more flow induced nuclei. 4.3 RESULTS AND DISCUSSION 69

1 1

0.8 0.8

0.6 0.6 [ − ] [ − ] * * ν ν 0.4 0.4

0.2 0.2

0 0

0 50 100 150 200 250 0 50 100 150 200 250 T [C] T [C]

( a) ( b)

1 1

0.8 0.8

0.6 0.6 [ − ] [ − ] * * ν ν 0.4 0.4

0.2 0.2

0 0

0 50 100 150 200 250 0 50 100 150 200 250 T [C] T [C]

( c) ( 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 during 3.0 s (4) at various temperatures, indicated by the arrows: (a) no shear ◦ ◦ ◦ flow 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 measurements are performed at a constant pressure of 40 MPa. WAXD images show the influence of shear flow on the orientation of the resulting crystalline morphology. 70 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

6 6 x 10 x 10 1.108 1.108 iPP−1 / 39.0 [1/s] iPP−1 / Quiescent iPP−2 / 39.0 [1/s] iPP−1 / 78.0 [1/s] 1.106 iPP−1 / Quiescent 1.106 iPP−2 / Quiescent 1.104 1.104 /kg] /kg] 3 1.102 3 1.102 [mm [mm ν 1.1 ν 1.1

1.098 1.098

1.096 1.096

130 140 150 160 170 180 190 200 10 20 30 40 50 60 70 Tγ [C] P [MPa]

( a) ( b)

Figure 4.6: (a) The influence of shear flow, applied with a shear rate of 39.0 1/s during 3.0 s at a pressure of 40 MPa for various Tγ on the specific volume after complete cooling, (b) the influence of pressure on the resulting specific volume of iPP-1 when shear flow is applied with a shear rate of 78.0 1/s ◦ during 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 effects explain the enhanced crystallization process from the moment flow is applied and the higher degree of orientation visualized by WAXD in figure 4.4d compared to figure 4.4c. This agrees qualitatively with the resulting crystalline morphology as visualized by ESEM (figure 4.7). Pictures (a-c) correspond to iPP-1, and show the influence of flow applied at various temperatures Tγ. All images are taken close to the core of the sample. When shear flow is applied at lower Tγ, smaller spherulites are formed and the orientation of the morphology increases (row nucleation). Figure 4.4d furthermore shows that by increasing the shear rate to 78.0 1/s, the crystallization kinetics are more enhanced, i.e. the whole transition process takes place much faster. Finally, figure 4.6a shows the influence of Tγ on the resulting specific volume measured via DGC. The specific volume resulting from quiescent conditions, i.e. no shear flow 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 neglected. This despite the observed differences in the evolution of specific volume and 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 resulting crystalline morphology of iPP-2. With respect to iPP-1, this material has a higher weight averaged molar mass Mw. Comparing figures 4.4a and 4.5a we conclude that the normalized specific volume of both (polydisperse) iPP’s at quiescent conditions is practically identical. As expected, the effect of shear flow on the specific volume 4.3 RESULTS AND DISCUSSION 71

and the resulting crystalline morphology is significantly enhanced by the increase in 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), or the 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 the 0 equilibrium melting temperature Tm, the specific volume and crystalline morphology are affected (figure 4.5b).

Figure 4.7 (d-f), confirms the large influence of Mw on the crystallization kinetics after flow. Contrary to iPP-1, significant orientation of the morphology is already ◦ seen when shearing at Tγ = 193 C (figure 4.7d), which was already observed in the WAXD patterns in figure 4.5. With decreasing temperature of flow, (bundles) of ◦ highly oriented structures can be observed at Tγ = 154 C, and finally a densely packed highly oriented structure results across the whole sample thickness in case of ◦ Tγ=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 play a minor role in this.

Inﬂuence of pressure during ﬂow

The influence of the pressure during flow is investigated either for a constant temperature Tγ and for a constant undercooling 4Tγ. In both cases polymer iPP-1 is subjected to a step shear with a shear rate of 78.0 1/s during 1.5 s at pressure levels 20, 40, and 60 MPa. Figure 4.8 shows the results if shear flow is applied at Tγ = 140 ◦ C. All pressure levels display the typical shift of Tc towards higher temperatures while 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 even further with increasing pressure and the transition in specific volume is getting more abrupt. These last observations point to enhancement of the crystallization process after and during flow with increased pressure level. If the specific volume is analyzed as a function of time (see figure 4.8d), an increase in the transition rate is observed with respect to the quiescent situation by a factor 1.4, 4.6, and 6.0 for pressure levels of 20, 40, and 60 MPa, respectively. Figure 4.6b shows the specific volume after complete cooling, measured with DGC. Lines are used to guide the eye. The decrease in specific volume with respect to quiescent conditions is the same for every pressure level applied, about 0.28-0.29 %. Figure 4.9 shows the influence of shear flow applied on the specific volume measured at pressure levels 20, 40, and 60 MPa and an almost identical undercooling. Because 0 of the pressure dependence of the equilibrium melting temperature Tm of iPP [24], the temperature at which the flow is applied increases with increasing pressure. For ◦ pressure 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 0 [24] for the pressure dependence of iPP’s Tm, this resulted in an undercooling during 72 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

( a) ( d)

( b) ( e)

( c) ( f)

Figure 4.7: Crystalline morphology close to the core of the samples visualized using ESEM. Pictures (a-c) correspond to iPP-1 subjected to a shear rate of 39.0 ◦ ◦ ◦ 1/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 is vertical. 4.3 RESULTS AND DISCUSSION 73

1 1

0.8 0.8

0.6 0.6 [ − ] [ − ] * * ν 0.4 ν 0.4

0.2 0.2

0 0

0 50 100 150 200 250 0 50 100 150 200 250 T [C] T [C]

( a) ( b)

Quiescent − 20MPa 1 1 Quiescent − 40MPa Quiescent − 60MPa 0.8 0.8 Flow − 20MPa Flow − 40MPa Flow − 60MPa 0.6 0.6 [ − ] [ − ] * * ν ν 0.4 0.4

0.2 0.2

0 0

0 50 100 150 200 250 0 20 40 60 80 100 T [C] t [s]

( c) ( d)

Figure 4.8: Influence of the pressure during shear flow on the normalized specific volume of iPP-1. Shear flow is applied as a step function with a shear rate of ◦ 78.0 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 time is shown in (d) and illustrates the effect of pressure on the rate of crystallization. 74 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

0.8

0.6 [ − ] *

ν 0.4

0.2

−50 0 50 100 150 200 ∆T [C]

Figure 4.9: The influence of pressure on the normalized specific volume when applying 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 conditions is represented by open symbols, while the filled symbols represent specific volume subjected to shear flow.

ﬂow of 41.9, 44.6, and 43.1 ◦C, respectively. For all pressure levels we see an identical shift of Tc with respect to quiescent conditions (open symbols). Also the transition itself 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 and 4.5, can be further quantified using the Herman orientation factor f. The orientation function is defined as: ® 3 cos2 φ − 1 f = (4.2) 2 4.3 RESULTS AND DISCUSSION 75

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 hcos2 φi is defined as:

π/2 R 2 D E I(φ) cos φ sin φdφ cos2 φ = 0 (4.3) πR/2 I(φ) sin φdφ 0 where I(φ) is the pole concentration representing the relative amount of crystalline material having plane normals in the direction of φ, ψ, such that:

Z2π I (φ) = I (φ, ψ) dψ (4.4) 0 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 with respect to the direction of flow (see also figure 4.10a). The α-crystalline phase of polypropylene does not have a hkl-reflective plane which directly reveals the c-axis orientation. Therefore, the method of Wilchinsky [25] is used to derive the c-axis orientation using the (110) and (040) reflections and the angle of 72.5◦ between the b-axis and the (110) plane. For the angle σ between the c-axis and the direction of flow, the corresponding hcos2 σi is now calculated according: D E D E D E 2 2 2 cos σ = 1 − 0.901 · cos φ040 − 1.099 · cos φ110 (4.5)

When the c-axis is perfectly aligned to the direction of flow, f = 1, if the c-axis is aligned perpendicular to the direction of flow f = −1/2, and for random orientation f = 0. For both iPP’s, the Herman orientation factor f is given in figure 4.11 in case shear flow is applied with a shear rate of 39.0 1/s. Furthermore, to differentiate between c-axis orientation and a∗-axis orientation, caused by lamellar branching, the relative 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 versus azimuthal angle, depicted in figure 4.10b, following:

A∗ [A∗] = (4.6) C + A∗ where C is taken as the area around an azimuthal angle of 0◦ and A∗ the area around an 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 temperature Tγ 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 flow applied at lower temperature leads to higher viscoelastic stresses enabling a higher degree of orientation of the molecules. As expected, the higher molecular weight 76 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

1 I(φ ) 110

0.8

0.6

0.4

Relative intensity [−] C 0.2 A* B 0 0 20 40 60 80 Azimuthal angle [ o]

( a) ( b)

Figure 4.10: (a) Lamellar branched shish-kebab structure [27], (b) Method to determine fraction [A∗] from the relative intensity of the (110) reflective plane according to Fujiyama [26]. iPP-2 consistently shows higher values for f. Because of the higher rheological relaxation 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, leaving less time for secondary crystallization processes such as lamellar branching. Note that 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 images shown in figures 4.4 and 4.5. These (300)β reflections show the same arcing pattern as the (040)α reflections. The orientation of the c-axis of the β-crystals can however not 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 = 3.0 s at a pressure of 40 MPa. The degree of crystallinity χ and the relative amounts of α- and γ-crystalline phases are determined in the same way as described in section 3.3, a method also used for instance by Somani et al. [28] to derive the degree of crystallinity of oriented samples. The relative amount of the β-crystalline phase is determined from the (300)β diffraction peak which can be discerned as a shoulder o to the (040)α / (008)γ diffraction peak at approximately 2θ = 5.14 for λ = 0.4956 Å. The relative fractions are determined from the area beneath the respective scattering peaks in the 1D-WAXD patterns. Figure 4.12 shows a detail of the 1D-WAXD scattering proﬁles with the relevant diffraction peaks depicted, and the degree of crystallinity with relative amount of crystalline phases. For both iPP’s, the degree 4.3 RESULTS AND DISCUSSION 77

0.8

0.6 ] [−] *

f , [A 0.4

0.2

0 130 140 150 160 170 180 190 200 Tγ [C]

Figure 4.11: The Herman orientation factor f (open symbols) and fraction [A∗] (ﬁlled symbols) as a function of temperature Tγ where ﬂow is applied, at a pressure 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). The relative amount of β- and γ-crystals, next to the more common α-crystals, is however subject 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 if iPP-1 is subjected to shear flow at lower temperatures. This relates to the increase in orientation of (α-)crystals, i.e. increase in the Herman orientation factor, which was also found by Somani et al. [28], as according to [29–32], the surface of these oriented α-crystals would provide nucleation sites for β-crystals to grow. The 2D-WAXD patterns in figure 4.4 show an identical arcing pattern for the (300)β and (040)α reflections. The relative amount of γ-crystals is also enhanced with respect to quiescent conditions (see table 3.4). For iPP-2, figures 4.12c and 4.12d, the relative amount of β-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 Herman ◦ orientation factor (figure 4.11). For Tγ = 193 C, the relative amount of β-crystals is comparable 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 and ◦ Tγ = 133 C could be that the generally weak (300)β reflections are over powered by the very strong (040)α reflections. Another reason could be that because of the faster crystallization kinetics, the time is too short for the β-crystals to grow on the already formed α-crystals. 78 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

0.8 100 Quiescent 0.7 Tγ=139 [C] Tγ=158 [C] 80 0.6 β (300) Tγ=193 [C] 0.5 α (130) 60 0.4 χ [ − ] * I frac α 0.3 40 γ (117) frac β 0.2 frac γ 20 0.1 crystallinity and fractions [ % ]

0 5 5.5 6 6.5 0 2θ [deg] 140 160 Tγ [C] 180 200

( a) ( b) 0.7 100 Quiescent T =133 [C] 0.6 γ Tγ=154 [C] 80 α 0.5 (130) Tγ=193 [C]

0.4 60

[ − ] χ * I 0.3 β (300) γ (117) 40 frac α 0.2 frac β 20 frac γ 0.1 crystallinity and fractions [ % ]

0 5 5.5 6 6.5 0 2θ [deg] 140 160 Tγ [C] 180 200

( c) ( d)

Figure 4.12: 1D-WAXD diffraction plots showing the normalized intensity I∗, crystallinity χ, and relative amounts of the α-, β-, and γ-crystalline phases dependent on temperature of applied ﬂow: (a,b) iPP-1, (c,d) iPP-2. 4.3 RESULTS AND DISCUSSION 79

4.4 Conclusions

The influence of shear flow on the evolution of specific volume of two iPP grades at non-isothermal conditions and elevated pressures was investigated, via the technique of dilatometry. In general, shear flow has a pronounced effect on the evolution of specific volume. Especially the temperature marking the transition in specific volume Tc and the rate of transition are affected. The effect of flow on the evolution of specific volume increases with increasing shear rate, increasing pressure, decreasing temperature at which flow is applied, and higher Mw. Although the degree of orientation and the overall structure of the resulting crystalline morphology were greatly affected by the flow, the resulting specific volume was not significantly affected by the processing conditions employed and shows a clear link to the degree of crystallinity which was also hardly affected by shear flow. It is clear that flow can strongly enhance the occurrence of the β-crystalline phase. Crystallization models consisting of one crystalline phase are therefore most probably not sufficient to describe the crystallization kinetics during flow. If shear flow is applied at a sufficiently high temperature, dependent on material and shear rate applied, remelting of flow induced crystalline structures and relaxation of oriented chains is able to fully erase the effect of flow. With increasing Mw, the effect of flow is prevailed longer. Although not investigated in this study, we think that an increased cooling rate (i.e. less time to remelt flow induced structures) will also enlarge the resulting effect of flow. 80 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

References

[1] Lee, O. and Kamal, M.R. Experimental study of post-shear crystallization of polypropylene melts. Polymer Engineering and Science, 39:236-248, (1999). [2] Jerschow, P. and Janeschitz-Kriegl, H. On the development of oblong particles as precursors for polymer crystallization from shear flow: origin of the so-called fine grained layers. Rheologica Acta, 35(2):127-133, (1996). [3] Tribout, C., Monasse, B., and Haudin, J.M. Experimental study of shear-induced crystallization 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 crystallization. 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 of polypropylenes: 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 shear flow-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 crystallization in isotactic polypropylene. Part 3. Evidence for a kinetic pathway to nucleation. Macromlecules, 35:1762-1769, (2002). [10] Seki, M., Thurman, D.W., Oberhauser, J.P., and Kornfield, J.A. Shear-mediated crystallization of isotactic polypropylene: the role of long chain - long chain overlap. Macromolecules, 35:2583-2594, (2002). [11] Koscher, E., and Fulchiron, R. Influence of shear on polypropylene crystallization: morphology development and kinetics. Polymer, 43:6931-6942, (2002). [12] Elmoumni, A., Winter, H.H., and Waddon, A.J. Correlation of material and processing time scales with structure development in isotactic polypropylene crystallization. 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 induced crystallization 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 induced crystallization on the Pressure-Volume-Temperature diagram of isotactic polypropylene. 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 shear flow. 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 and structure 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 quiescent and moving polymer melts under heat transfer conditions. Progress in Polymer Science, 15:629-714, (1990). [21] Jerschow, P. and Janeschitz-Kriegl, H. The role of long molecules and nucleating agents in shear induced crystallization of isotactic polypropylenes. International Polymer Processing, 12(1):72-77, (1997). [22] Janeschitz-Kriegl, H., Ratasjski, E., and Wippel, H. The physics of athermal nuclei in polymer crystallization. Colloid Polymer Science, 277:217-226, (1999). [23] 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). [24] 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). [25] Wilchinsky, Z.W. Measurement of orientation in polypropylene film. Journal of Applied Physics, 31:1969-1972, (1960). [26] Fujiyama, M. and Wakino, T. Structure of skin layer in injection-molded polypropylene. Journal of Applied Polymer Science, 35:29-49, (1988). [27] Fujiyama, M. and Wakino, T.J. Distribution of higher-order structures in injection-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 of isotactic Polypropylene by crystallization in a temperature gradient. Journal of Polymer 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). 82 4 THE INFLUENCE OF SHEAR FLOW ON SPECIFIC VOLUME

[32] Varga, J. and Karger-Kocsis, J. Rules of supermolecular structure formation in sheared isotactic polypropylene melts. Journal of Polymer Science: Part B, Polymer Physics, 34:657-670, (1996). REFERENCES 83 ‘Design D’ CHAPTER FIVE

Classification of the influence of flow on specific volume: The Deborah number1

The use of the Deborah number in classifying the effect of shear flow on the evolution of the specific volume and resulting crystalline morphology is investigated. If flow is applied at large undercooling, the Deborah number can provide a good classification of the influence of flow on the orientation and structural properties of the resulting crystalline morphology as well as for the influence of flow on the evolution of specific volume. For the latter, the Deborah 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 to classify the influence of flow on the evolution of specific volume, as characterized by the dimensionless transition temperature and dimensionless rate of transition. If flow is applied at relatively low undercooling, remelting of flow-induced crystalline structures and relaxation of molecular orientation can play a significant role after cessation of flow. Therefore, in these cases the use of the Deborah or Weissenberg number is regarded of little use in classifying the effect of flow.

5.1 Introduction

In chapter 4, shear flow was shown to have a significant influence on the evolution of specific volume. Characteristic features of this evolution, e.g. the transition temperature Tc, the time needed for the transition to start after flow is applied, and the rate of crystallization, 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 for the evolution of specific volume. This makes predictions regarding the evolution of specific volume as influenced by flow rather complicated. In recent studies concern- ing the influence of flow on the process of crystallization, the dimensionless Deborah and Weissenberg numbers have proven to be helpful in quantifying the strength of the flow applied at various processing conditions [1,2] and in classifying flow conditions with respect to their influence on the resulting crystalline morphology [3]. The dimensionless Weissenberg (We) and Deborah (De) number are respectively defined as: · We = γτ (5.1)

τ De = (5.2) t · 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 the characteristic time of the process t is chosen equal to the reciprocal value of the shear · rate γ. Acierno et al. [1] used We to study the influence of shear flow on the crystallization behavior of various grades of isotactic poly(1-butene) (iPB), differing in molecular weight distribution (MWD), using a rotational rheometer equipped with plate-plate geometry. They determined We by setting τ equal to the maximum relaxation time resulting from small angle oscillatory shear (SAOS) rheological characterization. During isothermal crystallization experiments at 103 ◦C, the time needed to start crystallization and the (dimensionless) half-time for crystallization decreased with increasing We. Furthermore, a transition from spherulitic to ‘rod-like’ crystal- lite growth was observed for roughly We > 150. Elmoumni et al. [2] performed isothermal flow-induced crystallization experiments on various grades of isotactic polypropylene (iPP) at a temperature of 145 ◦C, also using a rotational rheometer but with cone-plate geometry. Here We was based on the relaxation time associated to the cross over of G’ and G". They also found the induction time of crystallization 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 nucleation density increased with increasing We. For We < 1 the resulting morphology showed a 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 critical value could shift with as much as 1 order of magnitude (We > 10). Van Meerveld et al. [3] proposed a classification of flow-induced crystallization (FIC) experiments, regarding their effect on the resulting crystalline morphology, based on values for De associated to the process of reptation (Derep) and chain retraction (Des) of the molecules in the high molecular weight (HMW) tail, i.e. Derep and Des should correspond to the relaxation dynamics of the HMW-tail. Roughly, Derep can be regarded as 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 effect of 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 analyze and classify the influence of flow on the resulting crystalline morphology, when flow is applied during isothermal conditions and atmospheric pressure. Furthermore, classification of the influence of flow on the morphology of iPP [2, 3] typically is done for experiments performed at a fairly large undercooling 4T = 36 − 46 ◦C, 0 ◦ if an equilibrium melting temperature Tm at atmospheric pressure of 186 C is assumed [4]. However, the question arises if the Deborah and Weissenberg number can similarly be used to classify the influence of flow on the crystalline morphology when flow is applied during conditions relevant for industrial processing of polymers, i.e. elevated pressures and non-isothermal conditions. Moreover, can these dimensionless numbers be used to classify the influence of flow applied on the evolution of specific volume? In this chapter, the use of the Deborah number to analyze and classify the influence of shear flow on the resulting crystalline morphology and evolution 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 and temperatures, 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 reference · temperature 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 done according to a WLF-description [5, 6] and the pressure shift aP is defined according to [7]: κP a = exp( ) (5.4) P T where κ = 8.405 · 10−6 K/Pa and assumed a generic value for polypropylene, P the pressure, and T the absolute temperature. The shear flow experiments performed in this 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 88 5 CLASSIFICATION OF THE INFLUENCE OF FLOW

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

µ ¶2 3 1.51 τrep = 3τeZ 1 − √ (5.5) Z

2 τs = τeZ (5.6)

with τe the equilibrium time which is independent of the molecular weight of the chain [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 permeation chromatography (GPC), and Me the molar mass between entanglements.

Dimensionless transition temperature

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

Tcγ − Tγ θc = (5.8) TcQ − Tγ

where Tcγ is the transition temperature in case shear flow is applied, Tγ the average temperature during shear flow, and TcQ the transition temperature in case no shear flow 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 dimensionless rate of transition λ deﬁned as: µ ¶ µ ¶ ∂ν ∂ν λ = ∂ / ∂ (5.9) T γ T Q REFERENCES 89

0.8

0.6 [ − ] *

ν 0.4

0.2

0 12 3

0 50 100 150 200 250 T [C]

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

∂ν where ∂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 the suffix Q indicates the rate of transition resulting from quiescent conditions. Note that both θc and λ refer to a relative change in Tc and the rate of transition with respect to quiescent conditions, the latter being dependent on cooling rate and pressure.

5.3 Experimental part

Materials

Two commercial grades isotactic polypropylenes (iPP) with various molecular weights (Mw) are used. The ﬁrst material (iPP-1) is supplied by Borealis (grade HD120MO), and is characterized by Mw = 365000 g/mol, Mw/Mn = 5.2. The second material (iPP-2) is supplied by DSM (grade Stamylan P 13E10) and is characterized by Mw = 636000 g/mol, Mw/Mn = 6.9. Samples with dimensions 2.5 x 65 x 0.4 mm are prepared by compression molding: the materials are compressed for 3 minutes at 210 ◦C with a force of 50 kN, and subsequently cooled in a water cooled press 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 = −8 3.54 · 10 s is assumed and the molar mass between entanglements Me = 4400 g/mol for a reference temperature of 190 ◦C. Time-temperature shifting is performed using the temperature shift factor aT. Table 5.1 lists the values for relaxation times 90 5 CLASSIFICATION OF THE INFLUENCE OF FLOW

Material MHMW Z τe τrep τs [g/mol] [−] ·10−8[s] ·104[s] [s] iPP-1 107.38 5469 3.54 1.7 1.0 iPP-2 107.64 9891 3.54 10.0 3.5

Table 5.1: Equilibrium time τe, relaxation time τrep associated to the process of reptation, and relaxation time τs associated to the process of retraction of chains in the HMW-tail, at a reference temperature of 190 ◦C and reference pressure 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 using the dilatometer described in chapter 2, using the experimental procedure depicted in figure 4.2, and processing conditions as listed in table 5.2. Note: shear flow is applied over a range of temperatures because of non-isothermal conditions. Therefore Tγ refers to the average temperature during flow and the thermal shift factor aT is determined using Tγ. The final crystalline structure formed is evaluated ex situ with wide angle X-ray diffraction (WAXD). WAXD experiments were performed at the materials beam-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 0.4956 Å. The detector used is a Frelon CCD detector with 1024 x 1024 pixels. Both horizontal and vertical pixels are 164 µm in size. From calibration experiments, using Lanthanum Hexaboride, a sample-to-detector distance of 439.9 mm was determined. The exposure time for all images was 30 seconds. The final crystalline morphology is adi- tionally visualized via scanning electron microscopy (ESEM) performed on a Philips XL30 ESEM using a SE-detector and operated at 5 kV.

5.4 Results and discussion

Classiﬁcation of the resulting crystalline morphology

Classiﬁcation of the resulting crystalline morphology using Des and Derep is done for samples of both iPP’s subjected to a shear rate of 39 1/s, a pressure of 40 MPa, and a cooling rate of 1.4 ◦C/s. Variation in Deborah numbers is achieved by applying shear ﬂow at different temperatures (see table 5.2). Note that the values for Des and Derep 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 5.0 142.5 7.5 4.8 40S78 40 0.1 78 140.2 12.2 7.7 20M78 20 1.2 78 127.4 11.7 7.4 131.0 9.6 6.1 140.0 8.3 5.3 150.1 5.9 3.8 169.6 3.1 1.9 210.0 1.3 0.8 40M39 40 1.4 39 138.6 6.4 4.1 154.1 3.7 2.4 193.0 1.3 0.8 40M78 40 1.4 78 131.8 13.9 8.8 141.2 12.0 7.7 153.6 7.7 3.9 200.6 2.4 1.5 60M78 60 1.4 78 140.2 18.4 11.7 150.4 12.9 8.2 151.3 12.2 7.7 160.7 9.2 5.9 iPP-2 40M39 40 1.4 39 133.0 39.2 13.6 152.5 24.2 8.4 192.5 7.5 2.6

Table 5.2: Overview of applied processing conditions during ﬂow and resulting Deb- orah numbers Derep, Des. 92 5 CLASSIFICATION OF THE INFLUENCE OF FLOW iPP-1

(110) (040) (130)

1A: Des = 0 1B: Des = 80 1C: Des = 237 1D: Des = 412 6 6 6 Derep = 0 Derep = 1.3 · 10 Derep = 3.7 · 10 Derep = 6.5 · 10 iPP-2

2A: Des = 0 2B: Des = 260 2C: Des = 842 2D: Des = 1364 6 6 6 Derep = 0 Derep = 7.5 · 10 Derep = 24.2 · 10 Derep = 39.2 · 10

Figure 5.2: Orientation of the crystalline morphology of samples subjected to a shear rate 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 different temperatures, see also table 5.2. orientation of crystals as visualized by WAXD analysis. The main reflections of the crystallographic planes (110), (040), and (130) of the α-crystalline phase are indicated for reference. The direction of flow in all pictures is vertical. Sub-figures 1A and 2A show WAXD images of samples crystallized in quiescent conditions, i.e. Des = 0, Derep = 0. Generally, an increase in the orientation of crystals is observed with higher Des and Derep. When subjecting iPP-1 to a flow character- 6 ized by Des = 80 and Derep = 1.3 · 10 the influence of flow on the resulting orientation of crystals is negligible (sub-figure 1B). However, the presence of the (300)β reflection, located between the (110)α and (040)α reflections, is evidence of the flow applied. Compared to results of Van Meerveld et al., who observed shish-formation for 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

◦ ◦ 0 Tγ = 193 C an undercooling of 4Tγ = 5.2 C results when assuming Tm = 198.2 ◦C at a pressure of 40 MPa [4], remelting of flow induced crystalline structures and relaxation of molecules after cessation of flow are thought to play a significant role such that the influence of flow on the orientation of the crystalline morphology is completely 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 is explained by the higher Mw and associated larger relaxation times of iPP-2, resulting in a stronger flow and slower relaxation of molecular orientation after cessation of flow. The increased strength of flow will not only result in a higher orientation of chains, but also in a higher number of chains to be oriented [15], potentially leading to a higher number of flow-induced nuclei. Comparing the Deborah numbers of sub-figure 2B with sub-figures 1C and 1D, a somewhat higher degree of orientation is expected. This also points to a noticable influence of remelting and molecular relaxation, (partially) erasing the effect of flow. Flow applied at undercooling ranging from 44.2 ≤ 4Tγ ≤ 65.2 is depicted in sub-figures C and D (see also table 5.3). The influence of remelting and relaxation is expected to be negligible at these undercoolings [2]. Consistent with an increase in Des and Derep, an increase in orientation is observed. Important features that can be related to orientation of chains in the direction of flow are the equatorial reflections of the (110)α and (040)α crystallographic planes. These can already be observed for Des = 237 but are significantly present for Des ≥ 842. A more detailed classification of the orientation and structural properties of the crystalline morphology is possible by visualizing the morphology using ESEM, figure 5.3. The numbering of sub-figures corresponds to figure 5.2. As already discussed, for iPP-1 the influence of shear flow applied at small undercooling is negligible (sub-figure 1B). Large spherulites are visible of up to 50 µm in size across the sample. However, iPP-2 samples subjected to shear flow applied at identical conditions already show significant orientation of the morphology. The bright lines in figure 2B are thought to be short row nucleated structures, observed at the core of the sample. At the edges, a somewhat stronger row nucleated morphology is observed with row lengths exceeding 20 µm and width of about 500 nm. If shear ◦ flow is applied to iPP-1 at an undercooling 4Tγ = 44.2 C, figure 1C, a mixture of spherulites and row nucleated structures is observed. Spherulites are typically about 10 - 20 µm in size while rows are about 30 µm in length and 500 nm wide. Again, the ◦ morphology of iPP-2 is much more affected by the shear flow at 4Tγ = 44.2 C. Fig- ure 2C clearly shows an abundant presence of densely packed and highly oriented crystallites (‘shish-kebabs’). Finally, shearing iPP-1 at an even higher undercooling ◦ of 4Tγ = 59.2 C, figure 1D, results in a mixed morphology of row nucleated and spherulitic crystallites in the core while additionally sporadic shish-kebab formation ◦ is observed at the edge. The morphology of iPP-2 sheared at 4Tγ = 65.2 C consists 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 ranging from 200 - 450 nm. Table 5.3 summarizes the observed morphology as a a function of 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 94 5 CLASSIFICATION OF THE INFLUENCE OF FLOW iPP-1

1B : Des = 80 1C : Des = 237 1D : Des = 412 6 6 6 Derep = 1.3 · 10 Derep = 3.7 · 10 Derep = 6.5 · 10

iPP-2

2B : Des = 260 2C : Des = 842 2D : Des = 1364 6 6 6 Derep = 7.5 · 10 Derep = 24.2 · 10 Derep = 39.2 · 10

Figure 5.3: Crystalline morphology visualized by ESEM of samples subjected to a shear 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 different 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 occurs for 240 ≤ Des ≤ 410. Saturation of the morphology with shish-kebab structures happens for 842 ≤ Des ≤ 1364.

Classiﬁcation of the evolution of speciﬁc volume

Figure 5.4 shows the dimensionless transition temperature θc and dimensionless rate of transition λ as a function of Deborah number Des. The use of Derep gives qualitatively the same trend of θc and λ, since for the values of Z of the materials used the ratio of Derep and Des is approximately constant and equal to 3 times Z. Lines are drawn to guide the eye. If Des is lower than a minimum value of approximately Des = 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 S iPP-1 1C 44.2 2.4 3.7 R, S iPP-2 2B 5.2 2.6 7.5 R, S iPP-1 1D 59.2 4.1 6.4 K, R, S iPP-2 2C 45.2 8.4 24.2 K, R iPP-2 2D 65.2 13.6 39.2 K

Table 5.3: Summary of the morphology features observed in ﬁgure 5.3 as a function of 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 applied to iPP-1 at small undercooling. When this value is superseded, at first only a shift 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, this corresponds 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 the shift 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, the upswing of λ at about Des = 500 correlates rather well with the transition from spherulitic to shish-kebab morphology (240 ≤ Des ≤ 410). Finally, for approximately Des ≥ 800, the crystallization process is enhanced such that the transition from the melt to the semi-crystalline state starts almost instantaneously the moment flow is applied (θc = 0). Therefore, a significant part of the flow is applied during crystallization. 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 is hardly affected by differences in cooling rate. 96 5 CLASSIFICATION OF THE INFLUENCE OF FLOW

0.8

0.6 [ − ] c

θ iPP1 − 20S78 0.4 iPP1 − 40S78 iPP1 − 20M78 0.2 iPP1 − 40M78 iPP1 − 60M78 iPP1 − 40M39 0 iPP2 − 40M39 1 2 3 4 10 10 log De [ − ] 10 10 s

( a) 6 iPP1 − 20S78 iPP1 − 40S78 5 iPP1 − 20M78 iPP1 − 40M78 iPP1 − 60M78 4 iPP1 − 40M39 iPP2 − 40M39

[ − ] 3 λ

1 2 3 4 10 10 log De [ − ] 10 10 s

( b)

Figure 5.4: The dimensionless transition temperature θc and the dimensionless rate of transition λ as a function of Deborah number Des. Data are coded corresponding to table 5.2. REFERENCES 97

5.5 Conclusions

Classification of the influence of flow on the resulting crystalline morphology was performed for samples of two iPP grades, subjected to flow at constant elevated pressure and during non-isothermal conditions. Variation in the strength of the flow applied was reached by shearing at different degrees of undercooling. Classification of the influence of flow on the orientation of the resulting crystalline morphology as visualized by WAXD could be performed if flow was applied at relatively large undercooling. However, the influence of remelting and relaxation of molecular orientation yields the Deborah number of little use if flow is applied at high temperatures and relatively low undercooling. For large undercooling, remelting and relaxation has little effect on the development of the flow-induced crystalline morphology as was already observed in a previous study [2]. These conclusions also hold for the classification of flow on the evolution of specific volume. If flow is applied at large undercooling, Des and Derep can equally well be used to classify the influence of flow on the dimensionless transition temperature and dimensionless transition rate. Even relatively large differences in cooling rate have little effect on the classification of flow applied at large undercooling. 98 5 CLASSIFICATION OF THE INFLUENCE OF FLOW

References

[1] Acierno, S., Palomba, B., Winter, H.H., and Grizutti, N. effect of molecular weight on the flow-induced crystallization of isotactic Poly(1-butene). Rheologica Acta, 42:243-250, (2003). [2] Elmoumni, A., Winter, H.H., and Waddon, A.J. Correlation of material and processing time scales wth structure development in isotactic Polypropylene crystallization. Macromolecules, 36:6453-6461, (2003). [3] Van Meerveld, J., Peters, G.W.M., and Hütter, M. Towards a rheological classification of flow induced crystallization experiments of polymer melts. Rheologica Acta, 44:119-134, (2004). [4] 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). [5] Swartjes, F.H.M., Peters, G.W.M., Rastogi, S., and Meijer, H.E.H. Stress induced crystallization 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 crystallization. Rheologica Acta, 35:391-399, (1996). [9] Seki, M., Thurman, D.W., Oberhauser, J.P., and Kornfield, J.A. Shear-mediated crystallization of isotactic Polypropylene: the role of long chain - long chain overlap. 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 modeling 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 in Polymer 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 Shear Flow-Induced Crystallization of I-PP: In Situ Small Angle X-Ray Scattering Study. Macromolecules, 33:9385-9394, (2000). [16] Eder, G., Janeschitz-Kriegl, H., and Liedauer, S. Crystallization processes in quiescent and moving polymer melts under heat transfer conditions. Progress in Polymer Science, 15:629-714, (1990). REFERENCES 99

[17] Zuidema, H., Peters, G.W.M., Meijer, H.E.H. Development and validation of a recoverable strain based model for ﬂow induced crystallization of polymers. Macromolecular Theory and Simulation, 10(5):447-460, (2001). [18] Ziabicki, A. and Alfonso, G.C. A simple model of ﬂow-induced crystallization memory. Macromolecular Symposia, 185:211-231, (2002). ‘Final’ CHAPTERSIX

Conclusions and recommendations

6.1 Main conclusions

In this thesis, the dependence of the specific volume of crystallizing polymers on the thermomechanical history as experienced during processing is investigated. The technique 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 relevant for industrial processing operations such as injection molding and extrusion. To extent the interpretation of the results obtained on the development of specific volume, structure properties of the resulting crystalline morphology are investigated using wide angle X-ray diffraction (WAXD) in combination with scanning electron microscopy (ESEM). In chapter 2 a custom designed dilatometer is presented as a new experimental tool to quantitatively investigate the evolution of specific volume as a function of 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, and allows the use of annular shaped samples having a radial thickness of 0.5 mm. A possible source of error known to dilatometers based on this principle is the occurrence of friction forces arising between solidifying sample and dilatometer wall. To quantify this error, a comparison was made with measurements performed on a dilatometer based on the principle of confining fluid (Gnomix). The specific volume was measured in the absence of flow, at isobaric conditions, and at a relatively low cooling rate of about 4-5 oC/min. Both sets of data agreed quite well with respect to 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 analysis showed a relative difference in specific volume of the melt of 0.1 - 0.4 %. An identical relative difference was assumed for the specific volume measured during the first

101 102 6 CONCLUSIONSANDRECOMMENDATIONS

part of crystallization, since the ratio of shear and bulk modulus is still small and the influence of friction forces and loss of hydrostatic pressure can be neglected. The relative 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 curve measured should be taken as qualitative rather than quantitative. In chapter 3, the influence of thermal history, i.e. the influence of cooling rate, on the specific volume and the resulting crystalline morphology of an isotactic polypropylene is investigated. Measurements are performed at cooling rates ranging from 0.1 to 35 oC/s, and at elevated pressures ranging from 20 to 60 MPa. A profound influence of cooling rate on the temperature at which the transition from the melt to the semi-crystalline state starts is found. With increasing cooling rate and constant pressure, this transition temperature shifts towards lower temperatures. At constant 0 pressure, the transition temperature scales with the undercooling, i.e 4T = T − Tm. Since the transition temperature can be regarded as a measure for the onset of crystallization, an increased cooling rate causes the crystallization to start at a higher undercooling. This is explained as a ‘suppression’ of crystallization. Additionally, an increasing cooling rate causes the final specific volume to increase, which agrees with a decrease in the degree of crystallinity determined from WAXD analysis. In contrast to results of Zuidema et al. [1], for the relatively small pressure range that was experimentally accessible, a combined influence of pressure and cooling rate on the specific volume or crystalline morphology was not found. Finally, comparison of numerical predictions with experimental data of the evolution of specific volume were performed using a constitutive description for specific volume as proposed by Zuidema et al. [1]. Predictions showed at first large deviations in the calculated start and rate of the transition. These deviations increased with increasing cooling rate. Deviations in the rate of transition could partly be explained from small variations in model parameters, that were justified from possible inaccuracies in the experimental characterization of important input parameters, i.e. the spherulitic growth rate G(T, p) and the number of nuclei per unit volume N(T, p), or from determining model parameters to describe these quantities numerically. Especially in the prediction during fast cooling, G(T, p) and N(T, p) should be characterized for a sufficiently large temperature range, including temperatures typically lower than the temperature where the maximum in G(T, p) occurs. Deviations in predicted transition temperatures are however quite unexplained and could only be improved by introducing an unrealistic larger number of nuclei than determined experimentally at relatively high temperatures. This is subject to future investigation. Next, the influence of thermo-mechanical history on the evolution of the specific volume is investigated in chapter 4. The combined influence of shear rate, pressure and temperature during flow is studied at non-isothermal conditions using two grades of isotactic polypropylene with different weight averaged molar mass (Mw). In general, shear flow has a pronounced effect on the evolution of specific volume. Especially the temperature marking the transition in specific volume Tc and the rate of transition are affected. The effect of flow on the evolution of specific volume increases with increasing shear rate, increasing pressure, decreasing temperature at which flow is REFERENCES 103

applied, and higher Mw. Although the degree of orientation and the overall structure of the resulting crystalline morphology are greatly affected by the flow, interestingly and remarkably the resulting specific volume is not and shows a clear link to the degree of crystallinity which is also hardly affected by shear flow. Analysis of the crystalline morphology shows that flow can strongly enhance the occurrence of the β-crystalline phase. Crystallization models consisting of one crystalline morphology type 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 melting 0 temperature Tm [2], i.e. at low undercooling, dependent on material and applied shear rate remelting of flow induced crystalline structures and relaxation of molecular orientation was able to fully erase the effect of flow. With increasing Mw, the 0 effect of flow applied near Tm prevailed longer. Although not investigated in this study, we think that an increased cooling rate (i.e. less time to remelt flow induced structures) would also enlarge the resulting effect on the evolution of specific volume when applied at low undercooling. In chapter 5, the use of the dimensionless Deborah number is investigated to analyze and classify the influence of shear flow on the specific volume and resulting crystalline morphology, when flow is applied at different processing conditions. Clas- sification of the influence of flow on the orientation of the resulting crystalline morphology as visualized by WAXD could be performed if flow was applied at relatively large undercooling. However, the influence of remelting and relaxation of molecular orientation yields the Deborah number of little use if flow is applied at high temperatures and relatively low undercooling. Even when strong flows are applied, i.e. high Deborah numbers, the influence of flow can be erased totally. For large undercooling, remelting and relaxation has little effect on the development of the flow-induced crystalline morphology as was already observed in a previous study [3]. These conclusions 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 process of chain retraction or Derep based on the process of reptation can equally well be used to classify the influence of flow on the evolution of specific volume, e.g. characterized by the dimensionless transition temperature θc and dimensionless rate of transition λ. Even relatively large differences in cooling rate have little effect on the classification of flow applied at large undercooling. Furthermore, classification of the resulting crystalline morphology can be performed. With increasing Des, Derep the orientation 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 the influence of thermomechanical history on the evolution of specific volume as experienced during processing operations, i.e. non-isothermal conditions. This does not require extensive control of the procedure of cooling. However, improved and auto- 104 6 CONCLUSIONSANDRECOMMENDATIONS mated control of cooling would enable isothermal experiments after an initial period of 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 sample is in the order of 0.1 mm with a larger radius of the sample, would enable even better homogeneous cooling conditions at high cooling rates and the application of increased shear rates. Finally, an alternative way for the application of pressure and rotation has to be found such that the use of the tensile testing machine is no longer necessary. In chapter 3, experimental validation of numerical constitutive modelling of the specific volume still showed deviations in predicted temperature of transition, especially at high cooling rates. This mismatch between experimentally determined and predicted specific volume could only be improved by introducing an unrealistically large number of nuclei at higher temperatures. Experimental characterization of the spherulitic growth rate G(T, p) and the number of nuclei per unit volume N(T, p) as a function of temperature and pressure could improve these predictions and would provide better understanding of the modelling. This characterization was already initiated and a proof of principle provided by the author of this thesis using optical microscopy in combination with a high pressure cell. The experiments performed in chapter 4 can be regarded as simplified injection molding experiments, i.e. the polymer is melted to above its melting temperature, subjected to flow, and finally cooled with relatively high cooling rate. The experimentally determined evolution of specific volume provides a direct way of vali- dating constitutive modelling of specific volume or modelling of the evolution of crystallinity, based on a combination of the Schneider rate equations for quiescent crystallization 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 predicted crystalline morphology is possible. In chapter 4 it was shown that shear flow did not have a significant effect on the resulting specific volume, for the processing conditions applied and a cooling rate of 1.4 oC/s. This agreed with the degree of crystallinity which was about constant during all shear flow experiments. However, the enhancement of crystallization kinetics by flow could give a significant difference with crystallization in quiescent conditions if an increased cooling rate is applied, e.g. a cooling rate where in quiescent conditions a significant suppression of crystallization occurs. Additionally, variation in cooling rate while applying shear flow near the equilibrium melting temperature 0 Tm would provide better understanding of the remelting of flow-induced crystalline entities 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 in a homogeneous crystalline morphology, even when subjected to high cooling rates and shear flow. For instance, in chapter 4 visualization with ESEM showed that samples with a homogeneous shish-kebab morphology could be prepared. Samples REFERENCES 105

subjected to a well controlled thermomechanical history could serve as basis for experimental studies investigating the influence of crystalline structure properties on intrinsic 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 the Deborah number as proposed by Van Meerveld et al. [4] was applied on the evolution of specific volume. Shear induced crystallization experiments in isothermal conditions and elevated pressures would provide an additional way for experimental validation of this classification. 106 6 CONCLUSIONSANDRECOMMENDATIONS

References

[1] 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). [2] 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). [3] Elmoumni, A., Winter, H.H., and Waddon, A.J. Correlation of material and processing time scales wth structure development in isotactic Polypropylene crystallization. Macromolecules, 36:6453-6461, (2003). [4] Van Meerveld, J., Peters, G.W.M., and Hütter, M. Towards a rheological classification of flow induced crystallization experiments of polymer melts. Rheologica Acta, 44:119-134, (2004). Samenvatting

Semi-kristallijne polymeren worden veelvuldig gebruikt in produkten die een grote dimensie-nauwkeurigheid en -stabiliteit vereisen. Het verband tussen procescondities en de belangrijkste eigenschap die bepalend is bij de controle van dimensie- nauwkeurigheid, te weten het specifieke volume, is echter nog steeds onvoldoende begrepen. In dit proefschrift wordt het specifieke volume van kristalli- serende polymeren onderzocht als functie van de thermomechanische geschiedenis zoals onder- vonden tijdens verwerking. Hierbij wordt de nadruk gelegd op procescondities die relevant zijn voor industriële verwerkingsprocessen zoals spuit- gieten en extrusie. Dilatometrie wordt gebruikt om de gecombineerde invloed van temperatuur, afkoelsnelheid, druk, en afschuifstroming op het specifieke volume te onderzoeken. Tevens wordt het verband tussen het specifieke volume en de kristallijne microstructuur die resulteert uit deze procescondities onderzocht. De eigenschappen van de kristallijne 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 van het 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 dilatometer is gebaseerd op het principe van ‘confined compression’ en maakt gebruik van ringvormige proefstukken met een dikte van 0.5 mm. De fout in het gemeten specifieke volume, die onstaat ten gevolge van wrijvingskrachten tussen het proef- stuk en de wand van de dilatometer, wordt gekwantificeerd door een vergelijking te maken met metingen uitgevoerd op een dilatometer gebaseerd op het principe van ‘confining fluid’ (Gnomix). Het specifieke volume gemeten in de afwezigheid van stroming, bij constante druk en bij een relatief lage afkoelsnelheid van ongeveer 4-5 oC/min komt goed overeen in de smelt fase, de temperatuur waarbij de transitie 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 echter te verwachten dat voor hoge afkoelsnelheden de fout ten gevolge van wrijving zal toenemen, waardoor het specifieke volume in de vaste fase meer van kwalitatieve dan van kwantitatieve waarde is.

107 108 SAMENVATTING

In hoofdstuk 3 is de invloed van de afkoelsnelheid op het specifieke volume en de resulterende kristallijne microstructuur van een isotactisch polypropyleen (iPP) onderzocht. Experimenten uitgevoerd bij afkoelsnelheden variërend van 0.1 tot 35 oC/s en drukken variërend van 20 tot 60 MPa tonen een grote invloed op de temperatuur die de transitie van de smelt naar de semi-kristallijne fase markeert en op het verloop van het specifieke volume als functie van temperatuur tijdens de transitie. Met toenemende afkoelsnelheid en constante druk, verschuift deze transitietemperatuur naar lagere waardes en het verloop van de transitie zelf is minder opvallend en over een groter temperatuurtraject uitgestrekt. Daarnaast zorgt een hogere afkoelsnelheid voor een toename in het specifieke volume gemeten bij kamertemperatuur, hetgeen overeenstemt met een afname van de graad van kristalliniteit zoals bepaald uit WAXD metingen. Onder de gebruikte meetcondities werd er geen gecombineerde invloed van druk en afkoelsnelheid op het specifieke volume en op de kristallijne microstructuur gevonden. Experimentele validatie van numerieke voorspellingen van het specifieke volume tonen aanvankelijk grote afwijkingen in de berekende transitietemperatuur en het verloop tijdens de transitie. Deze afwijkingen nemen toe met toenemende afkoelsnelheid. De afwijkingen in het specifieke volume tijdens de transitie kunnen gedeeltelijk verklaard worden uit de gevoeligheid voor kleine variaties in modelparameters. Deze volgen uit mogelijke onnauwkeurigheden in de experimentele karakterisering van belangrijke input parameters, zoals de groeisnelheid van sferulieten G(T, p) en het aantal nuclei per volume eenheid N(T, p), of onnauwkeurigheden in het bepalen van een numerieke beschrijving van deze groothe- den. Met name wanneer het specifieke volume wordt voorspeld bij hoge afkoelsnelheden, moeten G(T, p) en N(T, p) gekarakteriseerd worden voor een voldoende groot temperatuurtraject, inclusief temperaturen die typisch lager zijn dan de temperatuur waar het maximum in de groeisnelheid van sferulieten G(T, p) optreedt. Afwijkingen in de voorspelde transitietemperatuur kunnen echter niet geheel worden verklaard en kunnen alleen worden verbeterd door een onrealistisch en groter dan experimenteel waargenomen aantal nuclei bij relatief hoge temperatuur voor te schrijven. Dit blijft een onderwerp voor toekomstig onderzoek. De invloed van stroming op het verloop van het specifieke volume is onderzocht in hoofdstuk 4. De gecombineerde invloed van afschuifsnelheid, druk en temperatuur tijdens stroming is gemeten onder niet-isotherme condities gebruik makend van twee typen isotactisch polypropyleen met verschillend gemiddeld moleculairgewicht (Mw). Afschuifstroming heeft een groot effect op het verloop van het specifieke volume. De temperatuur die de transitie markeert en het verloop tijdens de transitie worden beïnvloed. De invloed van stroming neemt toe met hogere afschuifsnelheid, hogere druk, lagere temperatuur tijdens stroming, of een hoger gemiddeld moleculairgewicht Mw. Hoewel de mate van oriëntatie en de algemene opbouw van de kristallijne microstructuur in grote mate beïnvloed wordt door stroming, worden het resulterende specifieke volume en de graad van kristalliniteit nauwelijks beïnvloed door de toegepaste procescondities. Als stroming wordt toegepast bij relatief hoge temperatuur of lage onderkoeling, dan smelten stromingsgeïnduceerde 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. Hoewel niet onderzocht in deze studie, denken we dat een grotere afkoelsnelheid, hetgeen overeenkomt met minder tijd voor het smelten van stromingsgeïnduceerde structuren, ook het effect van stroming toegepast bij hoge temperatuur op het specifieke volume doet toenemen. In hoofdstuk 5 is onderzocht of het dimensieloze Deborah getal kan worden gebruikt voor de klassificatie van de invloed van stroming op het specifieke volume en op de resulterende kristallijne morfologie. Alleen bij een relatief grote onderkoeling volgt een zinvolle klassificatie van de invloed van stroming op de oriëntatie van de morfologie, gemeten via röntgen-diffractie technieken (WAXD). Bij lage onderkoeling volgt smelten van stromingsgeïnduceerde kristallijne structuren en relaxatie van georiënteerde moleculen en beperkt het gebruik van het Deborah getal. Zelfs de invloed van sterke stroming, gekenmerkt door een hoog Deborah getal, kan bij lage onderkoeling volledig worden uitgewist. Deze conclusies gelden ook voor de klassificatie van stromingsinvloed op het verloop van het specifieke volume. Als stroming wordt toegepast bij grote onderkoeling, kunnen Deborah getallen Des (gebaseerd op het proces van relaxatie van moleculen na rek) en Derep (gebaseerd op het proces van reptatie van moleculen) gelijkelijk worden gebruikt. Zelfs relatief grote verschillen in afkoelsnelheid hebben dan slechts weinig invloed op de klassificatie wanneer stroming wordt aangebracht bij grote onderkoeling. Met toenemend Des, Derep neemt de oriëntatie van kristallen toe en is een differentiatie in sferulitische, rij-genucleëerde en shish-kebab structuren mogelijk.

Dankwoord

Graag wil ik hier iedereen bedanken die meegeholpen heeft aan het tot stand komen van dit proefschrift. Allereerst wil ik Gerrit Peters bedanken voor zijn begeleiding, enthousiasme en zijn altijd kritische houding. Dit is de kwaliteit van dit werk zeker ten 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 Meijer bedanken voor het vertrouwen dat hij gedurende al deze jaren in mij heeft gesteld en voor het mogelijk maken van dit promotie project. Het DPI en TNO Industrie en Techniek wil ik bedanken voor het ﬁnancieel mogelijk maken van dit project en het creëren van een goede onderzoeksomgeving. Dank ook aan allen die meegeholpen hebben bij de uitvoering van de vele experimenten, 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 realiseren van de dilatometer en Denka Hristova voor haar hulp bij het uitvoeren van WAXD en ESEM experimenten. Tevens dank aan Anne Spoelstra, Luigi Balzano, Jan-Willem Housmans, Guido Heunen, Reinhard Forstner, Leon Govaert, Dejan Mitrovic, Ursula Kroesen, Johan van der Velden, Meindert Janszen, Jos de Laat, Rob van de Berg en Toon van Gils voor hun bijdragen. Ook dank aan Leo Wouters en Patrick van Brakel voor de numerieke ondersteuning. Daarnaast bedank ik Sanjay Rastogi voor alle hulp en het beschikbaar stellen van tijd voor het uitvoeren van WAXD experimenten, Gaetano Lamberti voor de interessante discussies op het gebied van röntgen-diffractie technieken, Frank van der Burgt voor het ter beschikking stellen van WAXD metingen aan amorf iPP, Markus Gahleitner voor 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 ondersteuning. 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 Jan Bolt voor begeleiding en Ed Berben voor zijn tomeloze inzet toen ik zo nodig naar Grenoble moest. Dank aan mijn (ex)kamergenoten (Richard Schaake, Marco van den Bosch, Alexander Sarkessov, Alpay Aydemir, Marcel Meuwissen, Marlies Terlouw, Georgo

111 112 SAMENVATTING

Angelis) en andere MaTe collega’s (Vinny Khatavkar, Roel Janssen, Jesus Mediavilla, Alexander Zdravkov, Edwin Klompen, Christophe Pelletier, Frank Swartjes) voor de 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 lieve Angela bedanken voor haar vertrouwen, geduld en altijd volwaardige steun, ook in tijden dat het niet zo lekker liep. Jij bent mijn beste ’promotor’.

Maurice van der Beek Eindhoven, 21 april 2005 Curriculum Vitae

Maurice van der Beek (Roermond, november 7 1970) graduated from secondary school 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 masters degree in the group of prof.dr.ir. H.E.H. Meijer on the analysis of constitutive equations for the prediction of viscoelastic stresses in complex polymer melt ﬂow. After a two year working period at Raytheon Engineers and Constructors, he was employed at TNO Industrial Technology in 1998, working in the ﬁeld of polymer processing with main focus micro injection molding. In 2000 he was offered the opportunity to 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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