Structure development and mechanical performance of polypropylene

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Structure development and mechanical performance of

polypropylene

Citation for published version (APA):

Erp, van, T. B. (2012). Structure development and mechanical performance of polypropylene. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR733403

DOI:

10.6100/IR733403

Document status and date: Published: 01/01/2012 Document Version:

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Structure Development and Mechanical Performance

of Polypropylene

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Structure Development and Mechanical Performance of Polypropylene by Tim B. van Erp. Technische Universiteit Eindhoven, 2012.

A catalogue record is available from the Eindhoven University of Technology Library ISBN: 978-90-386-3164-6

Reproduction: University Press Facilities, Eindhoven, The Netherlands. Cover design: Paul Verspaget (Verspaget & Bruinink) and Tim van Erp

This research is part of the research programme of the Dutch Technology Foundation STW, ”Predicting Catastrophic Failure of Semi-Crystalline Polymer Products”.

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Structure Development and Mechanical Performance

of Polypropylene

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 donderdag 5 juli 2012 om 16.00 uur

door

Tim Bernardus van Erp

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Dit proefschrift is goedgekeurd door de promotoren: prof.dr.ir. G.W.M. Peters

en

prof.dr.ir. H.E.H. Meijer

Copromotor: dr.ir. L.E. Govaert

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6 Prediction of Yield and Long-Term Failure of Oriented Polypropylene 103 6.1 Introduction . . . 104 6.2 Experimental . . . 105 6.2.1 Material . . . 105 6.2.2 Mechanical Testing . . . 106 6.3 Experimental Results . . . 106 6.4 Constitutive Modeling . . . 108 6.4.1 Viscoplastic Model . . . 108 6.4.2 Equivalent Stress . . . 109 6.4.3 Flow Function . . . 110 6.4.4 Time-to-Failure. . . 110

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viii Contents 6.5 Model Application . . . 112 6.5.1 Characterization . . . 112 6.5.2 Validation . . . 113 6.6 Conclusions . . . 114 References . . . 116

7 Mechanical Performance of Injection Molded Polypropylene 117 7.1 Introduction . . . 118

7.2.1 Material . . . 119

7.2.2 Injection Molding . . . 120

7.2.3 Optical Microscopy . . . 120

7.2.4 Fourier Transform InfraRed (FTIR) Spectrometry . . . 120

7.2.5 X-Ray . . . 121

7.2.6 Mechanical Testing . . . 121

7.3.1 Microstructure . . . 121

7.3.2 Mechanical Properties . . . 124

7.3.3 Model Application . . . 126

References . . . 130

Conclusions and Recommendations 133 Conclusions . . . 133 Recommendations . . . 134 References . . . 137 Samenvatting 139 Dankwoord 141 Curriculum Vitae 143 List of Publications 145

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Summary

Polymers are known for their ease of processability via automated mass production technologies. The most important process is injection molding that, due to its freedom in material choice and product design, allows producing a wide variety of thermoplastic products. Mechanical failure of these products, either upon impact or after prolonged exposure to load, limits their ultimate useful lifetime. To predict and control lifetime, understanding of the route from production to failure, i.e. the processing-structure-property relation, is necessary. This is a complex issue; especially in the case of semi-crystalline polymers. These are heterogeneous systems comprised of amorphous and crystalline fractions, of which the latter can be highly anisotropic with size and orientation that are strongly dependent on the precise processing conditions. As a consequence, these structural features in the microstructure, and the associated mechanical properties, generally exhibit distributions containing different orientations throughout a single processed product.

Understanding polymer solidification under realistic processing conditions is a prerequisite to predict final polymer properties, since only a complete characterization of the morphology distri-bution within a product can lead to a meaningful and interpretable mechanical characterization. In this thesis we study the relation between processing conditions, morphology and mechanical performance of a semi-crystalline polymer, isotactic polypropylene. Key issue is the accurate control over all relevant processing parameters. Therefore, different experimental techniques are used to obtain samples at different high cooling rates, at elevated pressures, and high shear rates.

A custom designed dilatometer (PVT- ˙T - ˙γ-apparatus) proves to represent the most important and

useful technique.

First, a predictive, quantitative model is presented for the crystallization kinetics of the multiple crystal structures of polypropylene, under quiescent conditions. The approach is based on the

nucleation rate and the individual growth rate of spherulites of each type of polymorphism (α-, β-,

γ- and mesomorphic phase), during non-isothermal, isobaric solidification. Using Schneider’s rate

equations, the degree of crystallinity and distribution of crystal structures and lamellar thickness is predicted. Next, the effect of flow is introduced. Flow strongly influences the kinetics of

the crystallization process, especially that of nucleation. Three regimes are observed in the

experiments; quiescent crystallization, flow enhanced point nucleation and flow-induced creation of oriented structures. To assess the structure development under flow, a molecular-based rheology model is used. Combining the models derived for quiescent and for flow-induced crystallization, yields the tool that is capable of predicting the volume distributions of both isotropic and oriented structures, under realistic processing conditions.

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x Summary

The kinetics of mechanical deformations strongly depend on the anisotropy in the crystalline morphology, thus the local orientation. To study this, uniaxially oriented tapes with a well defined, and high, degree of anisotropy are used as well as injection molded rectangular plates. Yield and failure are described using an anisotropic viscoplastic model, applying a viscoplastic flow rule. It uses the equivalent stress in Hill’s anisotropic yield criterion, and combines the Eyring flow theory with a critical equivalent strain. Factorization is used and the model is capable to quantitatively predict the rate, the angle and the draw ratio dependence of the yield stress, as well as the time-to-failure in various off-axis tensile loading conditions. To use the model, also for other polymers, characterization of only the isotropic state is sufficient. Therefore, the influence of the cooling rate on the deformation kinetics is studied in-depth on isotropic systems. Different cooling rates

induce different crystal phases, both the stableα-phase and the mesomorphic phase, while also the

degree of crystallinity and lamellar thickness are influenced. The deformation kinetics prove to be the same for the different microstructures, which means that the activation volume and energy are

independent of the thermodynamic state. Differences in thermal history are, consequently, solely

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Introduction

Background

Nowadays, plastics are prominent in our society due to their very wide range of application in various products and sectors. From a historical perspective this is quite impressive. Compared to the more traditional bulk materials, the mass production of plastics actually just started, ca. 100 years. In contrast, wood and clay have been used since the existence of mankind, glass for 5500 years, iron for 3500 years, paper for 2000 years and cement for 200 years. Over the last decades,

the worldwide production of plastics has exploded from_{∼1 Billion liters in 1950 to ∼240 Billion}

liters in 2007. Already in the late 1980s the volume of plastics produced exceeded that of steel (see Figure 1). The share of plastics has been increasing at the expense of the other bulk materials and the drivers in this growing demand of plastics are manifold. Economic growth, the increasing wealth in newly industrialized and developing countries play an important role. This increase is also partly a result of new needs, which can best be fulfilled by plastics, e.g. safety devices such as airbags or certain medical devices and implants. Another important driver is material substitution, e.g. the replacement of glass by polymers in consumer goods such as computer screens and the replacement of the traditional packaging materials like paper or board. In general, the cost balance for production and processing of the competing materials is decisive.

Figure 1: Historical world production of plastics and steel [1].

The dynamic development in the demand of plastics is mostly covered by the ”commodity thermoplastics” PVC, PP, PE and PS [2]. While in the 70s and 80s it was assumed that ”high performance polymers” would gain an increasing share of the total polymer market, the dominant

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2 Introduction

market position of commodity thermoplastics has increasingly consolidated itself since then, see Figure 2. To a great extent this results from a continuous development and modification of these materials; modern industrial policies demand to achieve this goal without developing ”new” polymers but, instead, making use of ”old” polymers that are based on relatively cheap and readily available monomers [3]. In addition, another possible explanation is given by the so-called ”experience or learning curve” which predicts that by doubling cumulative production a cost reduction of 20-30% is achievable simply by becoming more experienced with the product.

reality 1998 prediction 1975 for 1996 reality 1975 27 Mio t 122 Mio t HDPE LDPE/LLDPE PP PS PVS PC PBT PET PA ABS POM PMMA

LCP PEEK PPS PAR PES 88% 12% <<1% commodity plastics; 86% engineering plastics; 14% high performance plastics; <<1%

Figure 2: Share of commodity-, engineering and high performance thermoplastics in the global

consumption [2].

Among the ”commodity thermoplastics” an important class of polymers are the polyolefins; mainly PE and PP. The basis of the dynamic development of polyolefins and their still tremendous potential lies in [4]:

• Their versatility with respect to physical and mechanical properties and applications. • Their nontoxicity and bioacceptability.

• The energy savings during their production and use, in comparison with other materials. • Their low cost and the easily available raw materials.

• Their economic, versatile, and nonpolluting production.

The influence of the oil price on the price of petrochemical polymers like polyolefins needs special attention. From the experience curve theory it is expected that production cost go down over time due to gained experience. However, this relation can be masked when the costs are mainly determined by feedstocks which fluctuate in price over time; for bulk polymers like PE and PP the main feedstock is crude oil. The price of oil is to a large extent correlated (up to 82% for PP) to the polymer prices showing the importance of the oil feedstock [5]. In view of the high and ever growing production of plastics, the substantial concomitant environmental impacts and, more recently, very high oil prices, the replacement of petrochemical plastics by bio-based plastics is receiving increasing attention [6].

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Processing-Structure-Properties Relation 3

The relative size of end-use applications remained fairly stable the last decade with packaging remaining the largest segment and representing 39% of the overall demand, see Figure 3. However, this share is lower than the year before (40.1%) due to a higher growth of technical applications in 2010 over 2009. The packaging sector is followed by building & construction (20.6%), automotive (7.5%) and electrical & electronic equipment (5.6%). ”Others” (27.3%) include various sectors such as sport, health and safety, leisure, agriculture, machinery engineering, household appliances and furniture.

PE-LD PE-LLD

PE-HD PP PS PS-E PVC ABS,

SAN

PMMA PA PET Other PUR

Packaging Building & Construction Automotive Electrical & Electronic equipment Other Total: 46.4 Mtonne 39.0% 20.6% 7.5% 5.6% 27.3%

Figure 3: Europe plastics demand in 2010 by segments [7].

Society has always quested for new materials that can fulfill new needs or replace existing materials with ones possessing superior performance and have worked diligently throughout history to create new materials. Currently, the quest is not just seeking for strong materials, the desired materials should possess the added value of light weight. Therefore, materials that possess great specific modulus and strength are nowadays required. This quest comes especially from fields like transportation, architecture, medical care and social welfare. An illustrative example is the social and technological requirements and purposes like the reduction of fuel consumption by automobiles for environmental protection and fuel cost reduction. In Figure 4 it is shown that bulk polymers have a rather poor position in the specific strength-modulus window compared to e.g. glass, metals and ceramics. However, from these bulk polymers, and in particular semi-crystalline polymers, materials can be produced like glass reinforced polymers, high-strength fibers and composites. As such, their increased specific strength and modulus is competitive with materials frequently used where high specific strength or modulus is required.

Processing-Structure-Properties Relation

As pointed out, polyolefins constitute an extremely interesting family of materials including large-volume materials such as polyethylene and polypropylene. For these semi-crystalline polymers injection molding is one of the most widely employed mass production methods for manufacturing products. The properties of injection molded products of semi-crystalline polymers strongly depend on the final morphology, which itself depends on the complete (processing) history of the

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4 Introduction 1 10 100 1,000 10,000 1 10 100 1,000 0.1 0.01 SPECIFICSTIFFNESS (MNm/kg) Goodstif fness-to-weightratio Poorstif fness-to-weightratio SPECIFIC STRENGTH (kNm/kg) Good strength-to-weight ratio Poor strength-to-weight ratio Rubbers Foams Polymers Nylon Composites Ceramics Metals and alloys Glasses UF PMMA Polypropylene Polyethylene

Figure 4: Specific modulus versus specific strength for different materials.

material, as illustrated in Figure 5. This includes the polymerization, determining the molecular characteristics, and the thermomechanical history experienced during processing. Understanding every step from synthesis via processing to the resulting product properties could lead, eventually, to materials with properties tailored to the application. This thesis studies part of this process, mainly using polypropylene-based materials, and focuses on the influence of processing on morphology and morphology on resulting properties.

chemical composition material formulation additives processing thermomechanical history

crystallization (mechanical)_properties

catalyst reactor chain structure molecular weigth (distribution) this thesis

Figure 5: Flow chart illustrating the processing-structure-properties relationship in semi-crystalline

polymeric materials.

Mechanical performance of polymers is known to be influenced by its molecular properties such as the molecular weight distribution and its underlying morphology as a result of macromolecular orientation and thermal history, i.e. factors that are directly connected to processing conditions. The latter is particularly true for semi-crystalline polymers in which structural features, such as the degree of crystallinity, crystal size and orientation, may drastically vary depending on the manner in which the polymer is shaped into the final product. A particularly illustrative example is given in Figure 6, which shows an injection molded plate of high-density polyethylene (HDPE), revealing the well-known oriented layers of different thickness at various locations along the flow path [8]. The observed differences in the microstructure have a dramatic influence on the macroscopic mechanical properties of samples cut at different loci from the object, which range

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Scope of the Thesis 5

from brittle fracture to necking and homogeneous deformation (sections A, B and C resp.). From this simple example the complexity of the processing-structure-property relation becomes clear, and it is, therefore, evident that the ability to predict the mechanical properties of polymer products is uniquely linked to the capability to assess the development of the various structures during processing within a product.

70 x 70 x 1 mm injection of polymer A B C A B C

Figure 6: Variation in microstructure over the thickness in a simple product, and the resulting different

mechanical responses of samples cut from different parts of a typical injection molded plaque of high-density polyethylene.

Scope of the Thesis

Catastrophic failure of polymer artifacts, either upon impact (e.g. of protective products such as airbags and helmets) or after prolonged exposure to load (for instance supporting structures, high-pressure pipes), limits their ultimate useful lifetime. Hence, understanding of that process, and, ideally, being able to accurately predict when and under which circumstances this phenomenon occurs, is of critical importance, not only for the selection of the materials employed in such objects, but also for their optimal design for safe use. This issue is especially complex in the case of semi-crystalline polymers, which are heterogeneous systems comprised of an amorphous matrix with highly anisotropic crystallites of a size and orientation that are dependent on the molecular weight distribution and the conditions under which the material is processed. As a consequence, these structural features, and the associated mechanical properties, generally exhibit strong variations throughout even a single processed object.

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6 Introduction

In this thesis, we aim to identify basic principles and tools for process-induced structure development, but also provide direct assessment of its influence on the resulting short and long-term mechanical performance of the final product. This thesis focusses on two aspects, both related to the processing-structure-property relationship of isotactic polypropylene; isotropic and anisotropic systems.

In Chapter 1 a method is presented to quantify the effect of thermal and pressure history on the isotropic and quiescent crystallization kinetics of four important crystalline structures of

isotactic polypropylene, i.e. theα-, β-, γ- and mesomorphic phase. Subsequently, the mechanical

performance of PP-based systems comprised of only α- and mesomorphic phase as a result of

systematic variations in thermal history is discussed in Chapter 2.

Oriented systems are obtained either by deformation of the polymer melt or in the solid state. Chapters 3, 4 and 5 focus on the flow-enhanced nucleation and crystallization kinetics during non-isothermal crystallization. Based on a unique set of experiments using extended dilatometry a rheological classification of flow-induced crystallization of iPP by incorporating in a controlled way the effect of pressure, undercooling and the effect of flow is presented. Special attention is given to the crystallization under moderate pressure in combination with strong shear flow creating

oriented specimens with high contents ofγ-phase (Chapter 4).

In Chapter 6 the mechanical performance of uniaxially oriented polypropylene tape is discussed. An anisotropic viscoplastic model is presented based on factorization of the rate and draw ratio dependence and is capable of quantitatively predicting the rate, angle and draw ratio dependence of the yield stress as well as time-to-failure in various off-axis tensile loading conditions characterized solely from the transverse direction. In Chapter 7 it is demonstrated that quantitative predictions of local mechanical properties in an injection molded polymer product can be made from using the orientation only in combination with the anisotropic viscoplastic model. Finally, the most important conclusions of this thesis are summarized and recommendations for future research are presented.

References

[1] www.plasticseurope.org .

[2] M Gahleitner and C. Paulik. Polyolefin basics. Technical report, Borealis GmbH, RPOD Linz (Austria), 2007. [3] V. Warzelhan and F. Brandstetter. Macromolecular Symposia 201:291–300, 2003.

[4] P. Galli and G. Vecellio. Journal of Polymer Science. Part A: Polymer Chemistry 42(3):396–415, 2004.

[5] T. Simon. Experience Curves in the World Polymer Industry: Quantifying Reductions in Production Cost. Master’s thesis, Utrecht University, 2009.

[6] M. K. Patel and M. Crank. Journal of Biobased Materials and Bioenergy 1(3):437–453, 2007.

[7] Plastics Europe. Plastics - the Facts 2011. An analysis of European plastics production, demand and recovery for 2010. Technical report, www.plasticseurope.org, 2007.

[8] B. A. G. Schrauwen. Deformation and Failure of Semicrystalline Polymer Systems: Influence of Micro and Molecular Structure. Ph.D. thesis, Eindhoven University of Technology, 2003.

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Quantification of Non-Isothermal, Multi-Phase

xxxxxxx

Crystallization: The Influence of Cooling

Rate and Pressure

Chapter 1

Abstract

The structure of semi-crystalline polymers is strongly influenced by the conditions applied during processing and is of major importance for the final properties of the product. A method is presented to quantify the effect of thermal and pressure history on the isotropic and quiescent crystallization kinetics of four important structures of polypropylene, i.e. the α-, β-, γ- and mesomorphic phase. The approach is based on nucleation and growth of spherulites during non-isothermal solidification, described by the Schneider rate equations combined with the Komogoroff-Avrami expression for space filling. Using an optimization routine to accurately describe the time-resolved multi-phase structure development, obtained from various experiments with and without in-situ or ex-situ WAXD, growth rates for the different phases and overall nucleation density are determined as

function of temperature and pressure. Addition of β-nucleating agent is interpreted as

a secondary nucleation density which is coupled to the growth rate of the β-phase. To

confirm the effect of pressure on the growth rate of theβ-phase additional measurements

are required. In spite of this, it is shown that the maximum growth rate of theα-, and

γ-phase increases with applied pressure, while it decreases for the mesomorphic γ-phase. In this way, the multi-phase structure development is accurately described for prescribed quiescent processing conditions.

Reproduced from: M. van Drongelen, T.B. van Erp, G.W.M. Peters. Quantification of Non-Isothermal, Multi-Phase Crystallization of Isotactic Polypropylene: The Influence of Cooling Rate and Pressure. submitted to Polymer.

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1

8 Quantification of Non-Isothermal, Multi-Phase Crystallization

1.1 Introduction

In commonly used production processes like injection molding, film blowing and fiber spinning, polymers are processed at elevated pressures and/or high deformation rates and simultaneously cooled from the melt within tenths of seconds. The crystallization process of semi-crystalline

polymers is strongly affected by these extreme processing conditions. Although flow has a

pronounced effect on the crystallization kinetics and resulting morphology, the focus of this study is on the quiescent non-isothermal and isobaric crystallization and structure development

of isotactic polypropylene (iPP) and β-nucleated isotactic polypropylene (β-iPP). The influence

of flow is ongoing work.

The most established physical picture of quiescent crystallization is nucleation and subsequent growth of spherulites; crystalline lamellae grow in three dimensions starting from point-like nuclei. The nucleation density and growth rates have been studied for a range of materials, including iPP [1]. The reported growth rates of iPP homopolymer are comparable for different grades, e.g. diverse molecular weights, while the nucleation density is always unique due to residuals and catalysts remaining from the industrial synthesis [2, 3]. The nucleation density and growth rate are usually measured by optical microscopy in conditions that typically promote the

formation ofα-crystals. However, it is well known that iPP is a polymorphic material with several

crystal modifications [4]. Most common is the monoclinic α-phase, a stable crystal form created

under moderate conditions. Flow or nucleating agents result in formation of the hexagonal

β-form [5–7]. Theα- and β-phase forms are a special combination; β-α recrystallization occurs

upon heating due to the thermodynamically instable nature of the β-phase [8]. Moreover, the

growth rate of theβ-phase prevails the growth rate of the α-phase in the temperature window of

105-140 ◦C [9, 10]. Available nucleating agents contrast in efficiency and selectivity; the

β-phase formation is dependent on the nucleating agent concentration and its ability to solely induce

growth of theβ-phase. Even with recently developed agents a pure β-phase structure could not

be obtained at high concentrations indicating thatα-phase nucleation from the β-phase promoter

is not negligible [11]. Another crystal modification is the orthorhombicγ-crystal that is formed at

elevated pressures or in copolymers [12–16]. Furthermore, the mesomorphic phase, with features intermediate to those of the crystalline and amorphous state, is obtained when a sample is cooled from the melt at high cooling rates [17, 18]. Quenching the melt at high rates significantly hinders the crystallization process; high cooling rates postpone crystallization to lower temperatures due to insufficient time for formation and growth of crystals. Moreover, the crystalline structure changes fromα- to mesomorphic phase. This transition is studied in detail using a cooling device, which

combines severe cooling rates with in-situ X-ray collection [17, 19].

The growth of the different crystalline phases is not well established as a function of both temperature and pressure. An increase in pressure results in an increase of the nucleation density

[20] and the equilibrium melting temperatureT0

m [13] and thus in a higher undercooling (∆T =

T0

m− T ), which is the driving force for crystallization. However, the exact effect of pressure on

the growth rate of a given crystal phase is not yet known. For example, it is only speculated that

the growth rate of the α-phase shifts towards higher temperatures with pressure accompanied

with a decrease in the maximum growth rate [21]. Many attempts were made to model the crystallization process in semi-crystalline polymers [22–26]. In the case of iPP, most models

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1

Theory 9

lack an incorporation of the polymorphism behavior in a clear way or do not account for relevant processing conditions (especially the effect of pressure is often discarded). A counter example is

a kinetic model [23, 24] that uses pressure dependent rate equations for theα- and mesomorphic

phase. Unfortunately, the nucleation density and growth rate are indistinguishable in these rate equations and hence, the kinetic parameters lose their physical meaning.

The aim of this study is to develop a model that includes the effects of cooling rate and pressure, comparable to those experienced in industrial processing, on the formation of different crystal

phases, i.e. the α-, β-, γ- and mesomorphic phase. Material functions for the quiescent

crystallization process are determined; both the nucleation density and individual crystal growth rates are temperature and pressure dependent. These relations are incorporated in the Schneider rate equations [27] and combined with the Kolmogoroff-Avrami expression for space filling [2, 28–30]. A number of experimental setups are used in combination with in-situ and ex-situ X-ray collection to study the (time-resolved) structure formation of PP-based materials.

1.2 Theory

Polymer crystallization from the melt is dominated by heterogeneous nucleation. The nuclei grow in time, depending on the temperature and pressure, forming spherulites that will impinge and stop growing when complete space filling is reached. Therefore, a model describing polymer crystallization should contain expressions for the nucleation density and the spherulitic growth rates. Herein, the effects of secondary crystallization are not considered and not included in

the model. The proposed non-isothermal multi-phase crystallization model is based on the

Kolmogoroff-Avrami expression [28–30]. Space filling is given by:

ξ(t) = χ(t)

χ_∞ = 1 − exp (−φ0(t)) , (1.1)

whereχ(t) and χ_∞are the crystallized volume fractions at timet and in equilibrium conditions,

respectively. φ0 is the sum of the expected crystallized volume of the different phases if no

impingement would occur in the case of 3D spherulitic growth; φ0(t) = P φ0_,i(t). Parameter

χ_∞is interpreted as the maximum value of total crystallinity allowed by the external conditions,

such as the thermal and mechanical histories experienced by the sample [31]. Considering multiple

crystalline phases,χ_∞is the sum of the maximum crystallinity of each crystal phase:

χ_∞=Xψiχi,max, (1.2)

in whichψiis the final crystal fraction acquired by X-ray analyses andχi,maxa maximum crystal

fraction, both per phase i. For non-isothermal conditions, the crystal volumes φ0,i(t) are given

by the Schneider rate equations, which provide structure information in terms of the number of

spherulites, radius, surface and volume [27] (for clarity the indexi in this set of equations is left

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1

˙ φ3 = 8π ˙N (φ3 = 8πN ), (1.3) ˙ φ2 = Gφ3 (φ2= 8πRtot), (1.4) ˙ φ1 = Gφ2 (φ1= S_tot), (1.5) ˙ φ0 = Gφ1 (φ0= V_tot), (1.6)

with nucleation rate ˙N and crystal growth rate G. The morphology is described per phase i ( per

unit volume) by the total volume of spherulitesVtot, their total surfaceStot, the sum of their radii

Rtotand the number of nucleiN . We assume that only one nuclei reservoir is available in the melt

while each crystal phase has an individual growth rate. The nucleation densityN and the growth

rate per phaseGiare functions of the temperature and pressure and given by:

N (T, p) = Nrefexp (−cn(T (t) − TN ref(p))) , (1.7)

Gi(T, p) = Gmax,i(p)exp

−cg,i(T (t) − TGref,i(p))

2

, (1.8)

whereNref andGmax,i, are values at the reference temperaturesTN ref andTGref,i, respectively,

while bothcnandcg,i are constants. During solidification in a multi-phase system, every crystal

formi will generate a crystal volume fraction φ0_,i, using a share of the available number of nuclei

and its own growth rate. The ratio in which the nuclei are divided between the crystal phases is experimentally not accessible. Therefore, the assumption is made that the allocation of nuclei to a given crystal form scales with the ratio of the individual crystal phase growth rates at the current temperature and pressure. For isobaric conditions, the nucleation rate for a given crystal form is given by:

˙ Ni = gi

dN

dT T ,˙ (1.9)

with the growth rate fraction,gi, given by:

gi=

Gi

P Gi

. (1.10)

This approach is only valid for the crystal structures that are formed during crystallization from

the melt in quiescent conditions; theα-, γ- and mesomorphic phase.

In order to capture all possible polymorphs in iPP,β-nucleating agent is added to the homopolymer

to enableβ-phase formation. The presence of the nucleating agent is considered as a secondary

source of nuclei,Nβ, coupled to the growth rate of theβ-phase, Gβ. A selectivity of the nucleating

agent,s, is introduced which assigns a share of Nβto either theα- or β-phase. It is stressed that Gβ

is excluded from Equation (1.10). For clarification, Figure 1.1 schematically shows the allocation

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1

Theory 11

N

β

G

β

G

α

G

γ

G

_m (1-s) gα gγ gm s

Figure 1.1: Schematic overview of the interplay between nucleation densities and growth rates for each

crystal phase.

To account for the selectivity, Equation (1.9) is extended; the nucleation rates for theα-phase and

β-phase in β-iPP become:

˙ Nα = gα dN dT + (1 − s) dNβ dT ˙ T , N˙β = s dNβ dT T .˙ (1.11)

The influence of pressure on the crystallization process is twofold; 1) a yet to be determined

influence on the growth rate parameter Gmax,i and 2) a shift of the reference temperatures in

Equations (1.7) and (1.8). This shift is given by:

Tk,ref,i= Tk,ref,i0 + ζ(p − p0), (1.12)

whereζ is a constant and T0

k,ref,iare reference temperatures at atmospheric conditionsp0fork =

N, G. For iPP, the effect of pressure on the glass transition temperature, Tg, is not well established,

but it is assumed thatTgshifts withζ similar to Tm[32, 33]. The bell-shaped growth rate function

(Equation (1.8)) is valid in between Tg and Tm and herein, TGref,i, is an intermediate value.

Therefore, it is valid to shift the reference temperatures of all individual crystal phase growth

rates according to Equation (1.12). SinceTg andTm equally shift with pressure, the width of the

growth rate function is maintained and thuscg,iis independent of pressure. Similar to the pressure

dependence of the growth rate, the effect of pressure on the nucleation density is implemented by

shifting the reference temperatureTN ref.

With the nucleation density and individual growth rates modified for non-isothermal and isobaric conditions, space filling in a multi-phase structure is calculated as a function of time using:

˙ξi = (1 − ξ) ˙φ0,i. (1.13)

For computational purposes, the set of rate equations in Equations (1.3)-(1.6) is numerically

integrated using an explicit Euler scheme to calculate φ0_,i. A single set of parameters for the

growth rate of each phase and the nucleation density are determined with an algorithm based on the interior-reflective Newton method [34, 35]. The input consists of the temperature and

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pressure history and the time resolved crystallinity fractions of the present crystal phases (both

per experimental data set), see Figure 1.2. The number of free parameters depends on the

corresponding crystal phases concerned.

G

max,i

T

Gref,i cg,i

N

ref TNref cn processing conditions input T(t), p optimized parameter set structure development input χ i(t) χ calc,i(t)

Figure 1.2: Schematic overview of the optimization approach to determine the parameter set to describe

the crystallization kinetics.

1.3 Experimental

1.3.1 Materials

Two isotactic polypropylene (iPP) homopolymer grades were used; iPP1 (Borealis HD234CF)

with a weight averaged Mw = 310 kg.mol−1 and polydispersity Mw/Mn = 3.4 [36] and iPP2

(Borealis HD601CF) withMw= 365 kg.mol−1andMw/Mn= 5.4 [37, 38]. These two grades are

selected due to their well known difference in crystallization kinetics [3]. To study the kinetics of theβ-phase, β-iPP is produced by adding 40 ppm pure γ-quinadricone β-nucleating agent (kindly

provided by Borealis) to iPP2 using an in-house mixer.

1.3.2 Fast Cooling Experiments

A quenching device (University of Genova (Italy), see Cavallo et al. for a complete description [17, 19]) is used to perform fast cooling experiments with and without in-situ X-ray collection. A 250-300 µm thick specimen is placed in a vertical holder, where it is heated to a controlled temperature by a heating gun which blows hot air tangential to the sample surface. Quenching is performed by blowing compressed air at both sides of the sample using two small hoses. When use is made of X-ray collection, the sample is placed perpendicular to the X-ray beam which is directed to a selected volume at 1 mm from an embedded thermocouple. Samples are melted and kept at

220◦C for 3 minutes before cooling at various cooling rates of ca. 10 to 260◦C.s−1. Cooling rates

in all experiments are defined by the slope between 195 and 130◦C in the time-temperature history.

In literature other definitions are found for determination of the cooling rate. When the cooling

rate is determined as the temperature gradient at 70◦C, around the temperature of the maximum

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Experimental 13

◦_C.s−1_{. Values are in the range of ca. 7 to 200}◦_C.s−1 _{when the cooling rate is determined by the}

slope between the equilibrium melting temperature at 195◦C and the crystallization temperature.

1.3.3 Differential Fast Scanning Calorimetry

Isothermal crystallization experiments are performed using a power compensation differential fast scanning chip calorimeter FLASH DSC 1 from Mettler Toledo (FDSC) in combination with a Huber intracooler TC100, for all details about this technique the reader is referred to various papers [39–41]. Specimens of a few nanograms (dimensions are ca. 10 x 10 x 10 µm) have been prepared from compression molded films. Dry nitrogen was used as a purge gas at a rate of 20

mL.min−1. Samples were heated to 220◦C at a rate of 100 ◦C.s−1, kept at this temperature for

0.1 s and cooled to the desired crystallization temperature at 2000 ◦C.s−1. Half crystallization

time is determined by calculating the time when 50% of the the area underneath the exothermal crystallization peak is reached. With the FDSC technique, the size and mass of the sample used are difficult to measure. However, both are irrelevant for the results concerned in this work and no further attention is paid to both specifications.

1.3.4 Multipass Rheometer (MPR)

A MultiPass Rheometer (Cambridge, UK) is used to perform pressurized cooling experiments in combination with in-situ X-ray collection (for a detailed description of the MPR the reader is referred to various papers [42, 43]). The MPR consists of two reservoir barrels equipped with a pressure transducer with integrated thermocouple, two servo hydraulically driven pistons and a slit flow geometry with diamond windows allowing X-ray experiments. The sample (dimensions are

120 x 6 x 1.5 mm) is placed in the flow cell and heated to a temperature of 220 ◦C and kept for

10 minutes to erase previous thermal history. Pressure is applied by moving both pistons towards each other and cooling occurs by pumping either a cooling medium through the flow cell (2.0

◦_C.s−1_{) or cooling the flow cell via natural convection (0.1}◦_C.s−1_{). Pressure is set to 50, 150 and}

250 bar (which is the maximum pressure).

1.3.5 Dilatometry

Dilatometry experiments were performed with the Pirouette PVT apparatus (IME technologies) [44–47]. It allows investigation of the evolution of (absolute) specific volume of polymers as a function of pressure, temperature, cooling rate and shear rate by measuring the volume change of the sample. The apparatus consists of a pressure cell that combines a traditional ”piston-die type” dilatomer with a Couette rheometer. The Pirouette requires ring-shaped samples with mass of_{∼75 mg, an inner diameter of 20 mm, thickness of 0.5 mm and height of 2.5 mm. Experiments} were performed in isobaric cooling mode and pressures are set to 300, 600, 900 and 1200 bar. The

sample is heated to 220◦C and kept at this temperature for 10 minutes to erase previous thermal

history in the material. The piston and die are cooled by natural convection or with a constant flux

of air or water, resulting in average cooling rates of 0.1, 1.5 and 90◦C.s−1, respectively. Ex-situ

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1.3.6 X-Ray

Wide-angle X-ray diffraction (WAXD) measurements were carried out at the Dutch-Belgian (DUBBLE) beamline BM26 of the European Synchrotron Radiation Facility in Grenoble (France) [48]. Two set-ups were used to collect both in- and ex-situ X-ray data. First, the in-situ fast cooling and ex-situ PVT measurements were collected using a Pilatus 300 K-W detector with 1475 x 195

pixels of 172 x 172 µm2 placed at 182 mm and using a wavelength of 1.24 ˚A. The exposure time

for the fast cooling and PVT experiments were 47 ms and 15 s, respectively. Secondly, for the

in-situ MPR experiments a Photonica CCD detector with 2048 x 2048 pixels of 48.8 x 48.8 µm2was

placed at 195 mm using a wavelength of 0.9538 ˚A with exposure time of 5 s. All WAXD data were

background subtracted and integrated with the software package FIT2D. The fraction of crystal phases is determined by a deconvolution procedure based on fitting Lorentzian functions to the WAXD experimental data, which is considered to be the superposition of independent diffractions associated with all types of structural order [49–51]. The deconvolution procedure discriminates

between different crystalline components; monoclinicα-phase, hexagonal β-phase, orthorhombic

γ-phase and mesomorphic phase. Five Lorentzian functions are used to describe the α-phase

(Bragg spacingd = 6.26, 5.24, 4.78, 4.17 and 4.05 ˚A), two for theβ-phase (d = 5.53 and 4.22 ˚A),

one for theγ-phase (d = 4.38 ˚A) and two for the mesomorphic phase (d = 5.98 and 4.07 ˚A). Good

fits were always achieved as illustrated by the examples in Figure 1.3. The amount of the different phases was calculated similar to Housmans et al. [52], but in this work as the ratio between the

area of the corresponding fitted peaks to the sum of these peaks. An uncertainty of±1.5% on the

absolute value of phase content is present, well in agreement with typical errors for this type of deconvolution.

(a) (b) (c)

Figure 1.3: Examples of WAXD pattern deconvolution of samples obtained by (a) fast cooling, (b) MPR

or (c) PVT experiments. Experimental data (grey dots) and fitted curve (thick black line) resulting from deconvolution of α-phase (black dashed-dotted line), γ-phase (thin black line), mesomorphic phase (thin grey line) and amorphous phase (grey dashed line).

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Results and Discussion 15

1.4 Results and Discussion

1.4.1 Experimental Approach

The crystallization processes for iPP1, iPP2 and β-iPP are studied using multiple experimental

setups allowing to probe the structure development in time for various cooling conditions at atmospheric and elevated pressures. The experimental data are used to determine the temperature and pressure dependent material functions; the nucleation densities of both grades, the secondary

nucleation density induced by the β-nucleating agent and the spherulitic growth rates of the

different polymorphs. In the following, the approach is elucidated in a prescribed order.

• Fast cooling experiments in combination with in-situ X-ray collection on iPP1 and iPP2 are

performed and give the time resolved structure formation of theα- and mesomorphic phase.

The experiments in which only α-phase develops are selected to optimize the nucleation

densities as function of temperature for both grades. The growth rate Gα is taken (and

fixed) from literature [20, 53]. Initial input values for the nucleation densities are taken from Housmans et al. [3].

• With N(T ) and Gα(T ) known, data from fast cooling and FDSC experiments are

used to determine the growth rate of the mesomorphic phase, Gm, as function of

temperature. Isothermal FDSC experiments are used to supply crystallization half-times

of the mesomorphic phase in the temperature range 0-50◦C which were not accessible in

the fast cooling experiments.

• Next, fast cooling experiments are performed for β-iPP. Since N(T ), Gα(T ) and Gm(T )

of the matrix material iPP2 are already determined, these experiments are used to obtain the

growth rate of theβ-phase, Gβ(T ), the secondary nucleation density Nβand the selectivity,

s, of the nucleating agent. Initial values for the growth rate are taken from Varga et al. [10]

and for the nucleation density from personal communication with the supplier [54].

• The effect of pressure on the crystallization kinetics of iPP2 is obtained using MPR

experiments. As a result of the applied cooling and pressure conditions only formation

of the α- and γ-phase is observed. This data is used for optimization of Gα, i.e. the

pressure dependence ofGmax,α. Furthermore, the growth rate of theγ-phase is determined

as function of the temperature and pressure.

• Dilatometry experiments are performed on iPP2 with a wide range of cooling rates and

pressures while structural data is collected ex-situ. This data is used to tune the pressure

dependencies of the maximum growth rates of theα-, γ- and mesomorphic phase.

Based on the results presented in this chapter, the values for χi,max (see Equation (1.2)) are set

to 0.6, 0.6, 0.75 and 0.5 for the α-, γ-, β- and mesomorphic phase, respectively. The value of

the constantζ (Equation (1.12)) is set to 27.5◦_C.kbar−1 _{based on the pressure dependence of the}

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1.4.2 Fast Cooling Experiments

A quenching device is used to perform multiple cooling experiments with iPP1 and iPP2 to

determine the crystallization temperature, Tc. In Figure 1.4, the crystallization temperature

for both materials is plotted against crystallization time in a so-called continuous cooling transformation (CCT) diagram. Two regions can be distinguished; a range of cooling rates where

iPP2 crystallizes at higher temperatures compared to iPP1 (50-100 ◦C) and a range where both

materials crystallize at similar temperatures (30-50◦C).

0 5 10 15 0 20 40 60 80 100 120 time [s] crystallization temperature [ ° C] iPP−1 iPP−2

Figure 1.4: Crystallization temperature Tc for iPP1 () and iPP2 (◦) as function of time obtained by

applying various cooling rates from the melt. Cooling starts from 220◦C at t = 0 s. Data is kindly provided by the group of Prof. Alfonso (University of Genova). Lines are a guide to the eye.

The first region is referred to as theα-region, where for both materials the applied cooling rates

(<100 ◦_C.s−1_{) result into formation of prevailing}_{α-phase. The transition to the second region}

marks formation of the mesomorphic phase. Here, high cooling rates (>200◦_C.s−1_{) are applied}

andTc is reached within a second. The growth rate for the α-phase (at atmospheric pressure) is

reported in literature and found to be similar for different iPP grades [2, 53]. Since non-isothermal crystallization is understood as nucleation and subsequent growth of spherulites, the difference in

Tc in theα-region is, most probably, caused by a difference in nucleation density, supported by

the literature values for nucleation density of these grades [3]. The transition temperature between

both regions is found to be_∼50◦C. Since, in time, this crystallization temperature is reached with

lower cooling rates for iPP1, it can be concluded that the mesomorphic phase is formed more easily for iPP1 compared to iPP2. However, it seems that for both grades the crystallization temperatures coincide on the same CCT curve in the mesomorphic phase region. For quenching from the melt at these high cooling rates, an extremely large number of nuclei are created and crystallization is completed within a second. Based on this kind of experiments it is impossible to differentiate the effect of nucleation density and/or growth rate on the resulting crystallization temperature. However, it is still assumed that the growth rate for the mesomorphic phase is identical for iPP1 and iPP2.

Fast cooling experiments with iPP1 and iPP2 are performed in combination with real-time WAXD collection. By means of deconvolution, the evolution of the different crystal fractions as a function

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mesomorphic phase for six cooling rates for iPP1 and iPP2, respectively. Crystallization is a

kinetic process and, therefore, the formation of α-phase is suppressed with increasing cooling

rate which leads to a decrease of Tc. The total crystallinity, which is divided between the

α-and mesomorphic phase α-and determined using Equation (1.2), is determined at ∼0.6 for the

experiments in which only the _{α-phase develops and at ∼0.55 for the experiments where both}

the α- and mesomorphic phase are present. As expected, the mesomorphic phase is formed at

high cooling rates and, compared to iPP2, at a lower critical cooling rate for iPP1.

The mesomorphic phase is formed at a lower temperature range in addition to theα-phase. When

complete space filling has occurred before this temperature range is reached, as in relatively

slow cooling experiments, the crystalized volume will purely consist of α-phase. Applying

high cooling rates, the crystallizing material will reach a lower temperature region in less time,

which gives a lowerTc and enables a competition between theα- and mesomorphic phase until

complete solidification is reached. The evolution of theα-phase is described with Gα taken from

literature [20, 53] and the parameters for the nucleation density,N , which are determined for both

grades using the cooling rate data where only the α-phase is formed. In this way, an accurate

description of the formation of theα-phase for both grades is obtained, see Figures 1.5 and 1.6.

The optimized parameters describing the nucleation density are different compared to the initial

values for both materials; mainlycn(describing the slope of the nucleation density) increases for

both iPP1 and iPP2, see Table 1.1. However, the parameters are still comparable to those reported in literature [20]. 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T_{= 30}◦_C/s α meso (a) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T_{= 43}◦_C/s α meso (b) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T_{= 91}◦_C/s α meso (c) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T_{= 121}◦_C/s α meso (d) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T_{= 149}◦_C/s α meso (e) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T_{= 234}◦_C/s α meso (f)

Figure 1.5: Experimental (symbols) and computed (lines) crystallinity evolution for α- () and

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25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T= 7◦_C/s α meso (a) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T= 17◦_C/s α meso (b) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T= 53◦_C/s α meso (c) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T= 103◦_C/s α meso (d) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T= 169◦_C/s α meso (e) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T= 178◦_C/s α meso (f)

Figure 1.6: Experimental (symbols) and computed (lines) crystallinity evolution for α- () and

mesomorphic phase (⋄) for iPP2 at atmospheric pressure. Cooling rate increases from (a)-(f).

Table 1.1: Nucleation density and growth rate parameters for iPP1 and iPP2 at atmospheric pressure.

Parameters indicated by (*) are taken from literature [20, 53]. The value marked by (†) is

determined at a pressure of 50 bar.

parameter iPP1 iPP2 unit

Nref 2.7·1014 1.2·1014 [m−3] TN ref 383 383 [K] cn 0.181 0.219 [K−1] Gmax,α 4.5·10−6* 4.5·10−6* [ms−1] TGref,α 363* 363* [K] cg,α 2.3·10−3* 2.3·10−3* [K−2] Gmax,m 7.4·10−7 7.4·10−7 [ms−1] TGref,m 308 308 [K] cg,m 2.7·10−3 2.7·10−3 [K−2] Gmax,γ 1.0·10−6 † [ms−1] TGref,γ 377 [K] cg,γ 3.5·10−3 [K−2]

A certain crystal fraction will only increase noticeably in time if nuclei are appointed to this crystal phase and the growth rate of that phase is significant. Since it is proposed that nuclei are

divided between the crystal phases according to their respective growth rate ratiogi(see Equation

(1.10)) it is concluded that the growth rate curve of the mesomorphic phase,Gm, must be located

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1.5 and 1.6 is insufficient to determine Gm in a substantial temperature range since data on the

mesomorphic structure formation is limited between 30 and 50◦C. Therefore, in order to increase

the crystallization temperature window, where Gm can be determined, FDSC experiments are

performed at temperatures down to 0◦C.

The overall crystallization rate can be expressed in terms of the crystallization half-time,t1/2and

is obtained with isothermal crystallization experiments, like those presented in Figure 1.7. Again,

two regions can be distinguished marked by a transition temperature at∼50◦_{C; a range at high}

temperatures where theα-phase prevails, followed by a range of mesomorphic phase formation at

low temperatures [56, 57]. The difference in crystallization half-time between the two grades is again caused by the difference in nucleation density.

0 25 50 75 100 10−2 10−1 100 101 temperature [°C] t 1/2 [s] iPP−1 iPP−2

Figure 1.7: Crystallization half-time t1/2as a function of temperature determined with FDSC for iPP1 ()

and iPP2 (◦) and corresponding model descriptions for iPP1 (dashed line) and iPP2 (solid line).

Although it has been proposed that the formation of the mesomorphic phase is governed by homogeneous nucleation [57, 58], in this work the mesomorphic structure is considered as the result of growth from heterogeneous nuclei (see Equation (1.7)). Our nucleation density in the low

temperature region of mesomorphic growth is very high (_∼1024m3at 0◦C for iPP2) translating in

a crystallite radius of_{∼6 nm, which is in accordance with experimental observations by Androsch}

et al. [59].

The mesomorphic growth rateGmis determined such that the calculatedt1_/2for the mesomorphic

region (0-50◦C) corresponds with the experimental values. It is found thatGm, which is assumed

equal for both grades, is located in a lower temperature region compared toGα, marked byTref,m

= 35◦C. Herein, quantitative agreement is found with values describing mesomorphic growth for

a kinetic model [24]. Moreover, the obtained Gm captures the formation of the mesomorphic

phase in non-isothermal conditions, see Figures 1.5 and 1.6. Also, the crystallization half-time in theα-region described by the model is in agreement with the FDSC experiments (Figure 1.7). A

complete overview of the optimized parameters is given in Table 1.1.

For the crystallinity development as displayed in Figure 1.5f, a discrepancy between the calculated

and experimental crystal fractions is found. It is stressed that when a mixture of α- and

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superposition of the independent diffractions peaks around the same diffraction angle. This leads to a slight mismatch in the described crystallinity levels for both phases present. Nonetheless, the total crystallinity level and onset of crystallization are in agreement with the experimental data.

In order to investigate the formation ofβ-phase in quiescent processing conditions, a β-nucleating

agent is added to the iPP2 grade. Fast cooling experiments in combination with WAXD collection

are performed for β-iPP and deconvolution of the acquired patterns shows a complex interplay

between the α-, β- and mesomorphic phases as function of temperature, see Figure 1.8. For

cooling rates lower than_∼250◦C.s−1 only_{β-phase is formed with a crystallinity level of ∼0.75,}

while for even higher cooling rates an increase inα-phase and additionally the mesomorphic phase

is observed. Notwithstanding the presence of a specificβ-nucleating agent, no β-phase is detected

for the higher cooling rates.

25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T_{= 42}◦_C/s α meso β (a) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T_{= 83}◦_C/s α meso β (b) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T_{= 152}◦_C/s α meso β (c) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T= 190◦_C/s α meso β (d) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T= 263◦_C/s α meso β (e) 25 50 75 100 125 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] ˙ T= 293◦_C/s α meso β (f)

Figure 1.8: Experimental (symbols) and computed (lines) crystallinity evolution for β- (◦), α- () and

mesomorphic phase (⋄) for β-iPP at atmospheric pressure. Cooling rate increases from (a)-(f).

The computed crystal fractions are displayed in Figure 1.8 using nucleation and growth data

presented in Table 1.1 and 1.2. The parameter set of iPP2 for the nucleation densityN and growth

ratesGαandGmare already determined for the homopolymer and as such used forβ-iPP. Initial

values forGβ are taken from literature [10], initial values for Nβ are based on data provided by

the supplier [54] and are linearly scaled to the concentration of the nucleating agent used here, resulting in initial values ofNref,β= 2.4·1014m−3andcn,β = 0.26 K−1.

The optimizedGβis characterized by a highGmax,βcompared to theα-phase, see Figure 1.9. The

interplay betweenNβ andGβ leads to the understanding of the suppression of theβ-phase with

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Table 1.2: Growth rate and nucleation density parameters for β-iPP at atmospheric pressure.

parameter β-iPP unit

Nref,β 1.1·1015 [m−3] TN ref,β 383 [K] cn,β 0.288 [K−1] Gmax,β 7.1·10−6 [ms−1] TGref,β 380 [K] cg,β 6.6·10−3 [K−2]

insufficient time is spend in this region and hereafter growth of the α-phase becomes dominant.

Two intersection points are observed forGαandGβwhich are 97.5 and 134.3◦C, see Figure 1.9.

These values are in agreement with the experimental results of Varga [10] and Lotz et al. [60].

The selectivity of theβ-nucleating agent, s, is determined at 0.975. For a modern nucleating agent,

such as theγ-quinacridone used, this is considered as an efficient and expected value [11]. Finally,

the crystallization kinetics of both theα- and β-phase in β-nucleated iPP are well captured (see

Figure 1.8) and thus the introduction of selectivity is justified, resulting in a proper description of the multi-phase structure.

25 50 75 100 125 150 175 10−9 10−8 10−7 10−6 10−5 temperature [°C] growth rate [m.s −1 ] Varga (1997) Lovinger (1977) Ratajski (1996)

Figure 1.9: Experimental (symbols) and computed (dotted line) growth rate of the β-phase, compared to

the growth rate of the α-phase (solid line). Data is taken from Varga [10], Lovinger et al. [61] and Ratajski and Janeschitz-Kriegl [62].

1.4.3 Pressurized Cooling Experiments

The effect of pressure on the crystallization process is studied for iPP2 for three different pressure levels and two cooling rates in combination with in-situ X-ray collection. Deconvolution of the

acquired WAXD patterns shows that, as a result of the applied pressure,γ-phase is always formed

in combination with theα-phase and the corresponding onset temperatures of the individual crystal

phases are similar. The observed crystallinity evolution of theα- and γ-phase for these conditions

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lowering the level ofα-phase. Furthermore, the final γ-fraction is higher for the lower cooling rate.

Comparable results considering the formation of theγ-phase are previously reported in literature;

γ-phase is obtained at elevated pressures with low cooling rates [63] or for isothermal conditions

at high pressures [14, 64]. 75 100 125 150 175 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] 50 bar− ˙T_{= 0.1}◦_C/s α γ (a) 75 100 125 150 175 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] 150 bar− ˙T_{= 0.1}◦_C/s α γ (b) 75 100 125 150 175 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] 250 bar− ˙T_{= 0.1}◦_C/s α γ (c) 75 100 125 150 175 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] 50 bar− ˙T_{= 2.0}◦_C/s α γ (d) 75 100 125 150 175 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] 150 bar− ˙T_{= 2.0}◦_C/s α γ (e) 75 100 125 150 175 0 0.2 0.4 0.6 0.8 1 temperature [°C] crystallinity [−] 250 bar− ˙T_{= 2.0}◦_C/s α γ (f)

Figure 1.10: Experimental (symbols) and computed (lines) crystallinity evolution for α- () and γ-phase

(△) for iPP2 at different constant pressures and two cooling histories. Pressure and cooling

rate are given in each figure.

The assignment of nuclei to a given crystal phase scales with the ratio of their respective growth

rates values, gi. For low cooling rates, such as 0.1 ◦C.s−1, the material will spend sufficient

time in a high temperature range wheregγ is large before complete space filling is reached. For

the 2.0◦C.s−1 cooling rate, the temperature range before complete solidification holds a larger

overallgαand thus more nuclei are appointed to theα-phase. From this it is concluded that Gγis

located in a higher temperature range thanGα. An increase of the finalγ-fraction with pressure is

also explained by means of the growth rate fractiongi; only when the applied pressure increases

Gmax,γ with respect toGmax,α more nuclei will be appointed to theγ-phase. In addition, on the

basis of experimental observations by Alamo et al. , it was concluded thatGmax,γ is lower than

Gmax,αdue to the unusual packing of theγ-form [65].

Above considerations enable the choice of an initialGγ relative toGα. The parameter TGref,γ

is chosen higher than TGref,α and Gmax,γ is set lower than Gmax,α. The parameter cg,γ is

independent of pressure and initially chosen to be equal to cg,α. Values for Gα and N at

atmospheric pressure are already previously determined, see also Table 1.1. The effect of pressure

is incorporated by shifting the reference temperatures in the expressions forN and Giaccording

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The resulting computed crystal fractions, presented in Figure 1.10, show that a correct description of the formation of both phases is obtained. It follows from the optimized set of parameters, that

Gmax,αis almost constant with the applied pressure, whileGmax,γ increases with pressure. The

optimalGγ gives a good description of the formation of theγ-fraction for all applied conditions.

At atmospheric pressure Gmax,γ is set to zero since no γ-phase is present in the fast cooling

experiment series in the previous section.

1.4.4 Dilatometry

Dilatometer experiments are performed at four different pressures and at three cooling rates for iPP2 and structural characterization is done by ex-situ X-ray analysis. The dilatometer supplies

structure information in terms of specific volume, ν, as function of temperature at different

pressures for three cooling rates, see Figure 1.11. It is found that a higher pressure results in a lower specific volume and that the transition region, representing crystallization, starts at a higher

temperature due to an increase in the equilibrium melting temperature T0

m [13]. With increasing

cooling rate, the transition region spreads out over a wider temperature range and Tc shifts to

lower temperatures, which is in agreement with the conclusions drawn from the CCT diagram (see Figure 1.4). 0 50 100 150 200 250 1.1 1.2 1.3 x 106 temperature [°C] specific volume [mm 3 .kg −1 ] 300 bar 600 bar 900 bar 1200 bar ˙ T_{= 0.1}◦_C/s (a) 0 50 100 150 200 250 1.1 1.2 1.3 x 106 temperature [°C] specific volume [mm 3.kg −1 ] 300 bar 600 bar 900 bar 1200 bar ˙ T_{= 1.0}◦_C/s (b) 0 50 100 150 200 250 1.1 1.2 1.3 x 106 temperature [°C] specific volume [mm 3.kg −1 ] 300 bar 600 bar 900 bar 1200 bar ˙ T_{= 90.0}◦_C/s (c)

Figure 1.11: Influence of pressure and cooling rate on the specific volume of iPP2 measured at 300 bar

(), 600 bar (◦), 900 bar (⋄) and 1200 bar (△). Cooling rates increase from (a) to (c).

A clear correlation between the phase contents and the pressure is observed, see Figure 1.12. With

increasing cooling rate, theα-phase increases at the cost of the γ-phase and for the highest cooling

rate a relatively low fraction of the mesomorphic phase is present while noγ-phase is formed. The

cooling rate of 90◦C.s−1results in a decrease of theα-phase content and a subsequent increase

of the mesomorphic fraction with pressure. Even at the highest pressure, this cooling rate is

sufficient to prevent any formation of the γ-phase. With an increase in pressure the fraction of

γ-phase increases at cost of the α-phase. The fact that the highest fraction of the γ-phase is found

for the lowest cooling rate is understood by the location ofGγat a higher temperature region than

Gα. With a large growth rate fractiongγat high temperatures, a considerable amount of nuclei will

grow into spherulites consisting ofγ-crystalline lamellae. In addition, the increase of the γ-phase

with pressure indicates an increase ofGmax,γ, while Gmax,α is found to be constant. Therefore