Tài liệu Structure Development and Mechanical Performance of Polypropylene docx

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, grow

Structure Development and Mechanical Performance

of Polypropylene

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 LibraryISBN: 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”

Structure Development and Mechanical Performance

of Polypropylene

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan deTechnische Universiteit Eindhoven, op gezag van derector magnificus, prof.dr.ir C.J van Duijn, voor eencommissie aangewezen door het College voorPromoties in het openbaar te verdedigen

op donderdag 5 juli 2012 om 16.00 uur

door

Tim Bernardus van Erp

geboren te Helmond

Dit proefschrift is goedgekeurd door de promotoren:

Background 1

Processing-Structure-Properties Relation 3

Scope of the Thesis 5

References 6

1 Quantification of Non-Isothermal, Multi-Phase Crystallization 7 1.1 Introduction 8

1.2 Theory 9

1.3 Experimental 12

1.3.1 Materials 12

1.3.2 Fast Cooling Experiments 12

1.3.3 Differential Fast Scanning Calorimetry 13

1.3.4 Multipass Rheometer (MPR) 13

1.3.5 Dilatometry 13

1.3.6 X-Ray 14

1.4 Results and Discussion 15

1.4.1 Experimental Approach 15

1.4.2 Fast Cooling Experiments 16

1.4.3 Pressurized Cooling Experiments 21

1.4.4 Dilatometry 23

1.5 Conclusions 27

References 27

v

vi Contents

2.1 Introduction 32

2.2 Experimental 33

2.2.1 Materials 33

2.2.2 Fast Cooling 34

2.2.3 X-Ray 34

2.2.4 Mechanical Testing 35

2.3 Results 35

2.3.1 Processing - Structure Relation 35

2.3.2 Yield Kinetics 38

2.3.3 Time-to-Failure 42

2.3.4 Structure - Properties Relation 43

2.3.5 Discussion 45

2.4 Conclusions 48

References 49

3 Structure Development during Cooling at Elevated Pressure and Shear Flow 53 3.1 Introduction 54

3.2 Experimental 55

3.2.1 Material 55

3.2.2 Dilatometry 55

3.2.3 X-Ray 57

3.2.4 Transmission Electron Microscopy (TEM) 58

3.3 Methods 58

3.3.1 Normalized Specific Volume 58

3.3.2 Weissenberg Number 59

3.3.3 Dimensionless Numbers 60

3.4 Results and Discussion 60

3.4.1 Dilatometry 60

3.4.2 Morphology 65

3.5 Conclusions 73

References 73

Contents vii

4.1 Introduction 78

4.2 Experimental 79

4.3 Results and Discussion 79

4.4 Conclusions 83

References 83

5 Flow-Enhanced Crystallization Kinetics during Cooling at Elevated Pressure 85 5.1 Introduction 86

5.2 Experimental 87

5.2.1 Material 87

5.2.2 Dilatometry 87

5.2.3 X-Ray 88

5.3 Methods 88

5.3.1 Normalized Specific Volume 88

5.3.2 Weissenberg Number 89

5.3.3 Dimensionless Numbers 90

5.4 Modeling 90

5.4.1 Quiescent Crystallization 90

5.4.2 Flow Effects on Crystallization 92

5.5 Results and Discussion 94

5.6 Conclusions 99

References 100

5.7 APPENDIX 102

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

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 Experimental 119

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 Results and Discussion 121

7.3.1 Microstructure 121

7.3.2 Mechanical Properties 124

7.3.3 Model Application 126

7.4 Conclusions 129

References 130

Conclusions and Recommendations 133 Conclusions 133

Recommendations 134

References 137

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 andproduct 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 ultimateuseful lifetime To predict and control lifetime, understanding of the route from production tofailure, 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 andorientation that are strongly dependent on the precise processing conditions As a consequence,these structural features in the microstructure, and the associated mechanical properties, generallyexhibit 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 bution within a product can lead to a meaningful and interpretable mechanical characterization

distri-In this thesis we study the relation between processing conditions, morphology and mechanicalperformance of a semi-crystalline polymer, isotactic polypropylene Key issue is the accuratecontrol over all relevant processing parameters Therefore, different experimental techniques areused 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 anduseful technique

First, a predictive, quantitative model is presented for the crystallization kinetics of the multiplecrystal structures of polypropylene, under quiescent conditions The approach is based on thenucleation 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 rateequations, 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 ofthe crystallization process, especially that of nucleation Three regimes are observed in theexperiments; quiescent crystallization, flow enhanced point nucleation and flow-induced creation

of oriented structures To assess the structure development under flow, a molecular-based rheologymodel 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 orientedstructures, under realistic processing conditions

ix

x Summary

The kinetics of mechanical deformations strongly depend on the anisotropy in the crystallinemorphology, 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 andfailure are described using an anisotropic viscoplastic model, applying a viscoplastic flow rule Ituses the equivalent stress in Hill’s anisotropic yield criterion, and combines the Eyring flow theorywith a critical equivalent strain Factorization is used and the model is capable to quantitativelypredict 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 coolingrate on the deformation kinetics is studied in-depth on isotropic systems Different cooling ratesinduce different crystal phases, both the stableα-phase and the mesomorphic phase, while also thedegree of crystallinity and lamellar thickness are influenced The deformation kinetics prove to bethe 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

captured by two rate constants which are a function of the microstructure

Background

Nowadays, plastics are prominent in our society due to their very wide range of application invarious products and sectors From a historical perspective this is quite impressive Compared tothe more traditional bulk materials, the mass production of plastics actually just started, ca 100years In contrast, wood and clay have been used since the existence of mankind, glass for 5500years, 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 Billionliters 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 materialsand the drivers in this growing demand of plastics are manifold Economic growth, the increasingwealth in newly industrialized and developing countries play an important role This increase isalso partly a result of new needs, which can best be fulfilled by plastics, e.g safety devices such asairbags 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 thereplacement of the traditional packaging materials like paper or board In general, the cost balancefor 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 ”commoditythermoplastics” PVC, PP, PE and PS [2] While in the 70s and 80s it was assumed that ”highperformance polymers” would gain an increasing share of the total polymer market, the dominant

1

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 cheapand 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 acost reduction of 20-30% is achievable simply by becoming more experienced with the product

reality 1998

prediction

1975 for 1996

reality 1975

HDPE LDPE/LLDPE PP PS PVS

PC PBT PET PA ABS POM PMMA

LCP PEEK PPS PAR PES

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 tremendouspotential 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 specialattention From the experience curve theory it is expected that production cost go down overtime due to gained experience However, this relation can be masked when the costs are mainlydetermined by feedstocks which fluctuate in price over time; for bulk polymers like PE and PPthe 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 andever growing production of plastics, the substantial concomitant environmental impacts and, morerecently, very high oil prices, the replacement of petrochemical plastics by bio-based plastics isreceiving increasing attention [6]

Processing-Structure-Properties Relation 3

The relative size of end-use applications remained fairly stable the last decade with packagingremaining 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 sectorssuch as sport, health and safety, leisure, agriculture, machinery engineering, household appliancesand furniture

PE-LD PE-LLD

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

Society has always quested for new materials that can fulfill new needs or replace existingmaterials with ones possessing superior performance and have worked diligently throughouthistory to create new materials Currently, the quest is not just seeking for strong materials, thedesired materials should possess the added value of light weight Therefore, materials that possessgreat specific modulus and strength are nowadays required This quest comes especially fromfields 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 thatbulk polymers have a rather poor position in the specific strength-modulus window compared toe.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-strengthfibers and composites As such, their increased specific strength and modulus is competitive withmaterials 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 volume materials such as polyethylene and polypropylene For these semi-crystalline polymersinjection molding is one of the most widely employed mass production methods for manufacturingproducts The properties of injection molded products of semi-crystalline polymers stronglydepend on the final morphology, which itself depends on the complete (processing) history of the

large-4 Introduction

1 10 100 1,000 10,000

1 10 100 1,000

Good to-weight ratio Poor strength-

strength-Rubbers

Foams

Polymers Nylon

Composites

Ceramics

Metals and alloys

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

material, as illustrated in Figure 5 This includes the polymerization, determining the molecularcharacteristics, and the thermomechanical history experienced during processing Understandingevery 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 onmorphology and morphology on resulting properties

chemical composition

material formulation

additives

processing

thermomechanical history

crystallization (mechanical)properties

catalyst

reactor

chain structure

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 macromolecularorientation 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 asthe degree of crystallinity, crystal size and orientation, may drastically vary depending on themanner 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 theflow path [8] The observed differences in the microstructure have a dramatic influence on themacroscopic mechanical properties of samples cut at different loci from the object, which range

Scope of the Thesis 5

from brittle fracture to necking and homogeneous deformation (sections A, B and C resp.) Fromthis 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 duringprocessing within a product

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 asairbags 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 phenomenonoccurs, is of critical importance, not only for the selection of the materials employed in suchobjects, but also for their optimal design for safe use This issue is especially complex in thecase of semi-crystalline polymers, which are heterogeneous systems comprised of an amorphousmatrix with highly anisotropic crystallites of a size and orientation that are dependent on themolecular weight distribution and the conditions under which the material is processed As aconsequence, these structural features, and the associated mechanical properties, generally exhibitstrong variations throughout even a single processed object

6 Introduction

In this thesis, we aim to identify basic principles and tools for process-induced structuredevelopment, 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, bothrelated to the processing-structure-property relationship of isotactic polypropylene; isotropic andanisotropic systems

In Chapter 1 a method is presented to quantify the effect of thermal and pressure history onthe isotropic and quiescent crystallization kinetics of four important crystalline structures ofisotactic polypropylene, i.e theα-, β-, γ- and mesomorphic phase Subsequently, the mechanicalperformance of PP-based systems comprised of only α- and mesomorphic phase as a result ofsystematic 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 arheological classification of flow-induced crystallization of iPP by incorporating in a controlledway the effect of pressure, undercooling and the effect of flow is presented Special attention isgiven to the crystallization under moderate pressure in combination with strong shear flow creatingoriented 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 ratiodependence 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 conditionscharacterized solely from the transverse direction In Chapter 7 it is demonstrated that quantitativepredictions of local mechanical properties in an injection molded polymer product can be madefrom using the orientation only in combination with the anisotropic viscoplastic model Finally,the most important conclusions of this thesis are summarized and recommendations for futureresearch 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.

Quantification of Non-Isothermal, Multi-Phase

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 the β-phase additional measurements are required In spite of this, it is shown that the maximum growth rate of the α-, and γ- phase increases with applied pressure, while it decreases for the mesomorphic 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.

7

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 subsequentgrowth of spherulites; crystalline lamellae grow in three dimensions starting from point-likenuclei 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 differentgrades, e.g diverse molecular weights, while the nucleation density is always unique due toresiduals and catalysts remaining from the industrial synthesis [2, 3] The nucleation density andgrowth rate are usually measured by optical microscopy in conditions that typically promote theformation ofα-crystals However, it is well known that iPP is a polymorphic material with severalcrystal modifications [4] Most common is the monoclinic α-phase, a stable crystal form createdunder 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 occursupon heating due to the thermodynamically instable nature of the β-phase [8] Moreover, thegrowth rate of theβ-phase prevails the growth rate of the α-phase in the temperature window of105-140 ◦C [9, 10] Available β-nucleating agents contrast in efficiency and selectivity; the β-phase formation is dependent on the nucleating agent concentration and its ability to solely inducegrowth 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 atelevated pressures or in copolymers [12–16] Furthermore, the mesomorphic phase, with featuresintermediate to those of the crystalline and amorphous state, is obtained when a sample is cooledfrom the melt at high cooling rates [17, 18] Quenching the melt at high rates significantly hindersthe crystallization process; high cooling rates postpone crystallization to lower temperatures due toinsufficient time for formation and growth of crystals Moreover, the crystalline structure changesfromα- to mesomorphic phase This transition is studied in detail using a cooling device, whichcombines 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 bothtemperature 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 onthe growth rate of a given crystal phase is not yet known For example, it is only speculated thatthe growth rate of the α-phase shifts towards higher temperatures with pressure accompaniedwith a decrease in the maximum growth rate [21] Many attempts were made to model thecrystallization process in semi-crystalline polymers [22–26] In the case of iPP, most models

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

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)

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

out):

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 crystalformi will generate a crystal volume fraction φ0 ,i, using a share of the available number of nucleiand its own growth rate The ratio in which the nuclei are divided between the crystal phases isexperimentally not accessible Therefore, the assumption is made that the allocation of nuclei to agiven crystal form scales with the ratio of the individual crystal phase growth rates at the currenttemperature and pressure For isobaric conditions, the nucleation rate for a given crystal form isgiven by:

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 secondarysource of nuclei,Nβ, coupled to the growth rate of theβ-phase, Gβ A selectivity of the nucleatingagent,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

of nuclei depending on the growth rate fractiongiand selectivitys

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

β-phase in β-iPP become:

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:

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

pressure history and the time resolved crystallinity fractions of the present crystal phases (bothper experimental data set), see Figure 1.2 The number of free parameters depends on thecorresponding crystal phases concerned

Gmax,i TGref,i cg,i

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.

1.3.1 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 areselected due to their well known difference in crystallization kinetics [3] To study the kinetics oftheβ-phase, β-iPP is produced by adding 40 ppm pure γ-quinadricone β-nucleating agent (kindlyprovided 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 controlledtemperature by a heating gun which blows hot air tangential to the sample surface Quenching isperformed 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 coolingrate is determined as the temperature gradient at 70◦C, around the temperature of the maximumgrowth rate of theα-phase at atmospheric pressure, the cooling rates correspond to ca 1 to 130

◦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

X-ray measurements are performed to determine the crystal fractions in each sample

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).

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

melting temperature,Tm[55]

1.4.2 Fast Cooling Experiments

A quenching device is used to perform multiple cooling experiments with iPP1 and iPP2 todetermine the crystallization temperature, Tc In Figure 1.4, the crystallization temperaturefor both materials is plotted against crystallization time in a so-called continuous coolingtransformation (CCT) diagram Two regions can be distinguished; a range of cooling rates whereiPP2 crystallizes at higher temperatures compared to iPP1 (50-100 ◦C) and a range where bothmaterials crystallize at similar temperatures (30-50◦C)

0 20 40 60 80 100 120

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 prevailingα-phase The transition to the second regionmarks formation of the mesomorphic phase Here, high cooling rates (>200◦C.s−1) are appliedandTc is reached within a second The growth rate for the α-phase (at atmospheric pressure) isreported in literature and found to be similar for different iPP grades [2, 53] Since non-isothermalcrystallization 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 bythe literature values for nucleation density of these grades [3] The transition temperature betweenboth regions is found to be∼50◦C Since, in time, this crystallization temperature is reached withlower cooling rates for iPP1, it can be concluded that the mesomorphic phase is formed more easilyfor iPP1 compared to iPP2 However, it seems that for both grades the crystallization temperaturescoincide 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 differentiatethe 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 iPP1and iPP2

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

of time and temperature is accessed Figures 1.5 and 1.6 show the evolution of the α- and

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

(b)

0 0.2 0.4 0.6 0.8 1

(e)

0 0.2 0.4 0.6 0.8 1

(f)

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

mesomorphic phase ( ⋄) for iPP1 at atmospheric pressure Cooling rate increases from (a)-(f).

0 0.2 0.4 0.6 0.8 1

(a)

0 0.2 0.4 0.6 0.8 1

(b)

0 0.2 0.4 0.6 0.8 1

(c)

0 0.2 0.4 0.6 0.8 1

(d)

0 0.2 0.4 0.6 0.8 1

(e)

0 0.2 0.4 0.6 0.8 1

(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.

at a lower temperature range than the growth rate of the α-phase However, the data in Figures

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

Figure 1.7: Crystallization half-time t1 /2 as 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 (∼1024

m3at 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

mesomorphic fractions is present, the deconvolution technique is difficult to apply because of the

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, thetotal 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-nucleatingagent is added to the iPP2 grade Fast cooling experiments in combination with WAXD collectionare performed for β-iPP and deconvolution of the acquired patterns shows a complex interplaybetween the α-, β- and mesomorphic phases as function of temperature, see Figure 1.8 Forcooling rates lower than∼250◦C.s−1 onlyβ-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 detectedfor the higher cooling rates

0 0.2 0.4 0.6 0.8 1

(a)

0 0.2 0.4 0.6 0.8 1

(b)

0 0.2 0.4 0.6 0.8 1

(c)

0 0.2 0.4 0.6 0.8 1

(d)

0 0.2 0.4 0.6 0.8 1

(e)

0 0.2 0.4 0.6 0.8 1

(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 datapresented in Table 1.1 and 1.2 The parameter set of iPP2 for the nucleation densityN and growthratesGαandGmare already determined for the homopolymer and as such used forβ-iPP Initialvalues forGβ are taken from literature [10], initial values for Nβ are based on data provided bythe supplier [54] and are linearly scaled to the concentration of the nucleating agent used here,resulting in initial values ofNref,β= 2.4·1014

m−3andcn,β = 0.26 K−1

The optimizedGβis characterized by a highGmax,βcompared to theα-phase, see Figure 1.9 Theinterplay betweenNβ andGβ leads to the understanding of the suppression of theβ-phase withcooling rate; the temperature region of (significant)β-growth is limited For high cooling rates,

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

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

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

is displayed in Figure 1.10 For higher pressures a larger amount of the γ-fraction is produced,

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]

0 0.2 0.4 0.6 0.8 1

temperature [°C]

50 bar− ˙ T = 0.1 ◦ C/s

α γ

(a)

0 0.2 0.4 0.6 0.8 1

temperature [°C]

150 bar− ˙ T = 0.1 ◦ C/s

α γ

(b)

0 0.2 0.4 0.6 0.8 1

temperature [°C]

250 bar− ˙ T = 0.1 ◦ C/s

α γ

(c)

0 0.2 0.4 0.6 0.8 1

temperature [°C]

50 bar− ˙ T = 2.0 ◦ C/s

α γ

(d)

0 0.2 0.4 0.6 0.8 1

temperature [°C]

150 bar− ˙ T = 2.0 ◦ C/s

α γ

(e)

0 0.2 0.4 0.6 0.8 1

temperature [°C]

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 growthrates values, gi For low cooling rates, such as 0.1 ◦C.s−1, the material will spend sufficienttime in a high temperature range wheregγ is large before complete space filling is reached Forthe 2.0◦C.s−1 cooling rate, the temperature range before complete solidification holds a largeroverallgαand thus more nuclei are appointed to theα-phase From this it is concluded that Gγislocated in a higher temperature range thanGα An increase of the finalγ-fraction with pressure isalso 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 thebasis 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 isindependent of pressure and initially chosen to be equal to cg,α Values for Gα and N atatmospheric 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

to Equation (1.12) and by determiningGmax,iper pressure

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 increasingcooling 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

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

gγincreases with temperature and enhancesγ-formation for lower cooling rates

The thermal and pressure history of the samples serves as input for the non-isothermal model

to describe the final multi-phase structure Values for N , Gα, Gγ and Gm are obtained fromthe previous experiments The only allowed free parameters are the maximum growth ratelevels Gmax,i for the different phases, which are determined per pressure using the completeset of available cooling rates This enables the complete multi-phase description of the PVTexperiments, resulting in an accurate description of the crystal fractions for prescribed processingconditions, see Figure 1.12

0 0.2 0.4 0.6 0.8

γ meso

γ meso

γ meso

Figure 1.12: Final crystallinity fractions for the α- () γ- (△) and mesomorphic phase (⋄) as function of

pressure and cooling rate Open symbols are experimental data determined by ex-situ X-ray deconvolution and closed symbols are model predictions.

A discrepancy between model and measurements is observed in Figure 1.12c; an underestimation

of the α-phase, followed by a overestimation of the mesomorphic fraction For high pressurescombined with a high cooling rate, such as 90◦C.s−1, the temperature history of the sample iscritical for the final crystal structure The temperature of the sample, Tmeas, in the dilatometer

is probed using six thermocouples placed in the metal housing close to the sample [45] andsubsequently Tmeas is calculated using a heat balance However, we are not sure of the exactsample temperature Therefore, we examine the sensitivity of the results by varying the measuredtemperature according to:

Tcorr(t) = Tmeas(t) + a ·tt

r

whereTcorris the corrected temperature, Tmeas the measured temperature of the sample (using

a heat balance) and tr the time needed to reach room temperature With a = 6 the differencebetween the measured and corrected temperature is∼2.5◦C (Note, this problem does not occurfor the fast cooling experiments; here the thermocouple is embedded within the sample.) Usingthis correction, the model predictions of the final crystallinity fractions are in better agreementwith the experimental data, see Figure 1.13

Figure 1.14 shows the optimized values for Gmax,i; the maximum growth rate of theα-phaseslightly increases (consistent with pressurized cooling experiments results), increases for the γ-phase and decreases for the mesomorphic phase with pressure In this figure, Gmax,m is notincluded for 300 and 600 bar, for these conditions no mesomorphic content is observed and thus

0 0.2 0.4 0.6 0.8

1

α γ meso

˙

T = 90.0 ◦ C/s

pressure [bar]

Figure 1.13: Final crystallinity fractions for the α- () γ- (△) and mesomorphic phase (⋄) determined by

ex-situ X-ray deconvolution (open symbols) and as predicted by the non-isothermal model (closed symbols) accounting for the uncertainty ( ∼2.5 ◦

C) in the time-temperature history of the dilatometer.

Gmax,m could not be determined AlsoGβ is not included since no effect of pressure on the

crystallization kinetics of theβ-phase is observed in our experiments Ex-situ X-ray diffraction

patterns of theβ-iPP samples show no β-phase content for samples crystallized at pressures above

300 bar Although these observations are insufficient for quantification of Gmax,β, they suggest

that the formation of theβ-phase is suppressed with pressure

Figure 1.14: (a) Individual growth rate functions for the α- (solid line), γ- (dashed line) and mesomorphic

phase (dashed-dotted line) as a function of temperature at atmospheric pressure Arrows indicate the effective shift of G i with pressure (b) Effect of pressure on the individual maximum growth rate levels G max,i for the α- () γ- ( △) and mesomorphic phase (⋄) Lines

give the evolution of G max,i as a function of pressure using Equation (1.15).

In the model, the effect of pressure on the growth rate of a given crystal phase is introduced

by a shift of the reference temperature and via the pressure dependent maximum growth rate

Previously, Pantani et al proposed an exponential relationship between pressure and their

maximum kinetic parameter [25] Hence, we propose that the maximum growth rate depends

on pressure according to:

Gmax,i= G0max,iexp(ai(p − p0) + bi(p − p0)2), (1.15)

whereaiandbi are constants andG0max,iis the reference growth rate at atmospheric pressurep0.The constants in Equation (1.15) for each crystal phase are determined with the data presented inFigure 1.14b and are given in Table 1.3 Regarding the mesomorphic phase,amis determined at-4.9·10−8 Pa−1, which is in quantitative agreement with Pantani et al [25]

Table 1.3: Constants for each crystal phase for the maximum growth rate as a function of pressure for iPP2

using Equation (1.15).

G0 max,α 4.8·10−6 [ms−1]

aα 1.6·10−9 [Pa−1]

G0 max,m 7.4·10−7 [ms−1]

am -4.9·10−8 [Pa−1]

bm 1.7·10−16 [Pa−2]

G0 max,γ 1.1·10−6 [ms−1]

aγ 7.7·10−9 [Pa−1]

Finally, predictions of the crystallinity evolution as a result of various applied processingconditions are made with the complete set of optimized parameters As illustrated in Figure 1.15,the multi-phase structure development of iPP2 is satisfactory predicted using an approach in whichthe nucleation density and growth rate are functions of temperature and pressure

0 0.2 0.4 0.6 0.8 1

(a)

0 0.2 0.4 0.6 0.8 1

temperature [°C]

150 bar− ˙ T = 0.1 ◦ C/s

α γ

(b)

0 0.2 0.4 0.6 0.8

γ meso

Figure 1.15: Experimental (open symbols) and computed (lines in (a) and (b), closed symbols in (c))

crystallinity for the α- () γ- ( △) and mesomorphic phase (⋄) (a) fast cooling at 178

◦

C.s−1and at atmospheric pressure, (b) pressurized cooling at 150 bar and 0.1◦C.s−1and (c) dilatometer experiments at 300, 600, 900 and 1200 bar and 90◦C.s−1.

The influence of pressure and cooling rate has been studied on the multi-phase structure

development for two grades of iPP and one β-iPP by using various experimental setups in

combination with in-situ and ex-situ WAXD collection It is demonstrated that the proposed

non-isothermal crystallization model accurately describes multi-phase crystalline evolution for theα-,

β-, γ- and mesomorphic phase Temperature and pressure dependent nucleation densities and

growth rate functions for theα-, γ- and mesomorphic phase have been determined by using an

optimization routine Quantification of theγ-phase growth rate as a function of temperature and

pressure is done for the first time For theβ-phase, the addition of nucleating agent is considered

as a selective secondary nucleation density coupled to the growth rate of the β-phase, which

are both determined as a function of temperature The multi-phase crystal structure of isotactic

polypropylene, crystallized at multiple isobaric pressures and cooling rates, has been accurately

predicted with the model It is found that the nucleation density and individual growth rate shift

linearly with pressure Additionally, with increasing pressure the maximum growth rate increases

for theα- and γ-phase and decreases for the mesomorphic phase

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