1 Specific volume of polymers Influence of the thermomechanical history
2 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, Proefschrift. ISBN 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.
3 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 uur door Maurice Hubertus Elisabeth van der Beek geboren te Roermond
4 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
5 Veur mien maedje
7 Contents 1 Introduction Context Background Scope Outline References Concentric cylinder dilatometer: design and testing Introduction Design and instrumentation Experimental Sample preparation Procedure Comparison with confining fluid based dilatometer Example: isotactic polypropylene Conclusions References A Appendix: material properties The influence of cooling rate on specific volume Introduction Experimental part Materials Dilatometer experiments X-ray analysis Density measurements Results and discussion Specific volume Crystalline morphology Modelling aspects Conclusions References vii
8 viii CONTENTS 3.A Appendix: specific volume of the melt The influence of shear flow on specific volume Introduction Experimental part Materials Dilatometry Density gradient column X-ray analysis Scanning electron microscopy Results and discussion Specific volume Crystalline morphology Conclusions References Classification of the influence of flow on specific volume: The Deborah number Introduction Methods Deborah number Dimensionless transition temperature Dimensionless transition rate Experimental part Materials Experimental techniques Results and discussion Crystalline morphology Specific volume Conclusions References Conclusions and recommendations Main conclusions Recommendations References Samenvatting 107 Dankwoord 111 Curriculum Vitae 113
9 Summary Nowadays, semi-crystalline polymers are widely used in many product applications that display high dimensional accuracy and stability. However, the relationship 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 o C/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 o C/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 %. 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 %. However, especially for higher cooling rates, this part of the measured specific volume curve should be taken as qualitative rather than quantitative. ix
10 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 o C/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. 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. 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 (M w ). 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 M w. 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 at a temperature near the material s equilibrium melting temperature T 0 m, 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 M w, 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
11 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 De s (based on the process of chain retraction) or De rep (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 θ c 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.
12 xii SUMMARY
13 CHAPTER ONE 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 semicrystalline 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 plasticized by being heated to elevated temperatures, and injected into a mold where the 1
14 2 1 INTRODUCTION ( b) ( a) Figure 1.1: (a) Micromechanical component (gearbox) made from Polyoxymethylene, (b) gearbox and individual components compared to a needle . 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 phenomena 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 m 3 /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  and shows this behavior for an amorphous and a semicrystalline 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-
15 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 . mer should be characterized at conditions as (locally) experienced during processing. This means that characterization should include elevated pressures of O ( 10 2) MPa in combination with cooling rates of O ( 10 2) C/s and shear or elongation rates of O ( ) 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  and Spencer and Gilmore , 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. Examples include the Scheider rate equations  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.
16 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 Diffraction (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. Innovations 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
17 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.
18 6 1 INTRODUCTION References  Homepage Institut für Mikrotechnik Mainz (IMM),  Zoller, P., Walsh, D.J. Standard Pressure-Volume-Temperature Data for Polymers. Technomic, (1995).  Piccarolo, S. Morphological changes in isotactic Polypropylene as a function of cooling rate. Journal of Macromolecular Science - Phys., B31(4): , (1992).  Zuidema, H., Peters, G.W.M., Meijer, H.E.H. Influence of cooling rate on PVTdata of semicrystalline polymers. Journal of Applied Polymer Science, 82(5): , (2001).  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: , (2002).  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: , (2002).  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: , (2003).  Alfonso, G.C., Verdona, M.P., Wasiak, A. Crystallization kinetics of oriented poly(ethylene terephthalate) from the glassy state. Polymer, 19: , (1978).  Vleeshouwers, S., Meijer, H.E.H. A rheological study of shear induced crystallization. Rheologica Acta, 35: , (1996).  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 , (1997).  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: , (2000).  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: , (2001).  Koscher, E., Fulchiron, R. Influence of shear on Polypropylene crystallization: morphology development and kinetics. Polymer, 43: , (2002).  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: , (2003).  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).
19 REFERENCES 7  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: , (2003).  Hieber, C.A. Modelling the PVT behavior of isotactic Polypropylene. International Polymer Processing, 12(3): , (1997).  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): , (2001).  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).  Tait, P.G. Physics and Chemistry of the Voyage of H.M.S. Challenger. University Press, Cambridge, (1888).  Spencer, R.S., Gilmore, G.D. Equation of state for high polymers. Journal of Applied Physics, 21: , (1950).  Schneider, W., Köppl, A., Berger, J. Non-isothermal crystallization. Crystallization of polymers. International Polymer Processing, 2(3): , (1988).  Eder, G., Janescitz-Kriegl, H., Liedauer, S. Crystallization processes in quiescent and moving polymer melts under heat transfer conditions. Progress in Polymer Science, 15: , (1990)  Zuidema, H. Flow Induced Crystallization, PhD thesis Eindhoven University of Technology (2000).
20 Design A
21 CHAPTER TWO Concentric cylinder dilatometer: design and testing 1 We developed a dilatometer to investigate the specific volume of polymers as a function of pressure (up to 100 MPa), temperature (up to 260 o C), cooling rate (up to 100 o C/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 capability. 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 %. 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 distinguished. 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- 1 Reproduced 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
22 10 2 CONCENTRIC CYLINDER DILATOMETER Reference P max T max Tmax ε ν min [MPa] [ o C] [ o C/s] [%] [cc/g]      Table 2.1: Characteristic processing conditions (P max, T max, cooling rate), accuracy (ε), and resolution ( ν min ) 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 o C 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.  listed in table 2.2 is an example of the dilatometer originally developed by Menges et al.  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.  and Chakravorty , see table 2.3. Zuidema et al. used a CF-dilatometer, analyzing the influence of cooling rate as high as 54.2 o C/s on the
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bernoulli_0 A person holds their hand out of a car window while driving through still air at a speed of V car. What is the maximum pressure on the person s hand? V car 0 max car p p p V C. Wassgren, Purdue
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