Effect of Shear on Growth Rates During Polyethylene Melt Crystallization

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EFFECT OF SHEAR ON GROWTH RATES

DURING POLYETHYLENEMELT CRYSTALLIZATION

by

Orasa Tavichai

A Thesis Submitted to the Faculty ofGraduate Studies and Research

In Partial Fulfillment of the Requirements for the

Degree ofMaster ofEngineering

Department ofChemical Engineering

McGill University

Montreal, Canada

January 2002

© Orasa Tavichai 2002



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ABSTRACT

During processing, polymers are exposed to complex thermal and deformation fields.

Vnder these conditions, partially crystalline polymers undergo crystallization, which

contributes significantly to their ultimate properties. While the thermal effects on polymer

crystallization have been studied extensively, there is much less research carried out with

regard to the effects of deformation and stress on crystallization kinetics. This is in part due

to experimental difficulties in making appropriate measurements. In the present work, the

Linkam Shearing Cell, in conjunction with a polarized light microscope, was used to study

the effect of shear on the growth kinetics of various linear low-density polyethylene

(LLDPE) resins. Simultaneously, an effort was made to evaluate the effect of shear on

morphology. The experimental and analytical aspects of the work will be described, and

preliminary results will be reported.

The spherulitic growth rate increased under shear compared to that under quiescent

conditions. The circular shape morphology of spherulites was obtained under the shear rate

range of consideration (0-1 S·l). The effect ofmolecular structure in terms of co-monomer

and branching content on spherulitic growth rate under quiescent and shear condition wasobserved. Moreover, the effect oftemperature on growth rate under quiescent and shear (0.5

S·l) was studied. The modified Lauritzen-Hoffman equation was used to fit experimental

data. The diffusion energy barrier under shear condition (0.5 S·l) was estimated and was

found to be lower than the diffusion energy barrier under quiescent conditions.



RESUME

Pendant le traitement, des polymères sont exposés aux zones complexes d'courant

ascendant et de déformation. Dans ces conditions, les polymers partiellement cristallins

subissent la cristallisation, qui contribue de manière significative à leurs propriétés finales . .

Tandis que les effets thermiques sur la cristallisation de polymère ont été étudiés

intensivement, il y a beaucoup moins de recherche effectuée en ce qui concerne les effets de

la déformation et de l'effort sur la cinétique de cristallisation. C'est en partie dû aux

difficultés expérimentales en faisant des mesures appropriées dans actuel travail, Linkam

cisailler cellule, en même temps que un polariser photomicroscope, utiliser pour étudier effet

cisaillement sur croissance cinétique divers linéaire à basse densité polyéthylène (LLDPE)

résine. Simultanément, un effort a été fait d'évaluer l'effet du cisaillement sur la

morphologie. Les aspects expérimentaux et analytiques du travail seront décrits, et des

resultants préliminaires seront enregistrés.

La cadence de croissance spherulitic a augmenté sous le cisaillement comparé à celui

dans des conditions à l'état repos. La morphologie circulaire de forme des sphérolites a été

obtenue sous l'intervalle de cadence de cisaillement de la considération (0-1 S-I). On a

observé l'effet de la structure moléculaire en termes de comonomère et du contenu

s'embranchant sur la cadence de croissance spherulitic dans la condition à l'état repos et de

cisaillement. D'ailleurs, l'effet de la température sur la cadence de croissance sous à l'état

repos et le cisaillement (0.5 S-I) a été étudié. L'équation modifiée de Lauritzen-Hoffman a

été employée pour adapter des données expérimentales. On a estimé qu'et est avéré la

barrière d'énergie de diffusion dans la condition de cisaillement (0.5 S-I) inférieure à la

barrière d'énergie de diffusion dans des conditions à l'état repos.

i i



ACKNOWLEDEMENTS

l would like to express my gratitude to my supervisor Professor Musa R. Kamal, for

his valuable guidance and encouragement during this work.

l would also like to thank:

Mr. Lijun Feng for his useful suggestion on this work.

Nova Chemicals, Canada for material supplies.

National Metal and Materials Technology Center (MTEC), Thailand for financial

support.

Jonathan Webber for his encouragement and his help on English.

Finally, l would like to thank my family and friends for their love and continuous

mental support.

iii



TABLE OF CONTENTS

ABSTRACT 1

RESUME 11ACKNOWLEDEMENTS 111TABLE OF CONTENTS IV

LIST OF FIGURES VI

LIST OF TABLES X

NOMENCLATURE XI

1 INTRODUCTION 1

2 GENERAL BACKGROUND 4

2.1 Structure of crystalline polymers 5

2.1.1 Fringed micelle model 5

2.1.2 Single crystals 5

2.1.3 Folded chain model 7

2.2 Crystallization from polymer melts 8

2.2.1 Spherulites 9

2.2.2 Fibrils Il

2.3 Isothermal crystallization kinetics under quiescent state Il

2.3.1 General Avrami equation Il

2.3.2 Equilibrium melting temperature 142.3.3 Nucleation 15

2.3.4 Growth behavior 17

2.3.5 Lauritzen-Hoffman growth theory 17

2.4 Effect of shear on crystallization 19

3 LITERATURE REVIEW 21

3.1 Post-shearing crystallization 21

3.1.1 Structure and morphology 21

3.1.2 Effect ofshearing time 23

3.1.3 Crystallization kinetics 26

3.2 During shearing crystallization 27

3.2.1 Investigation ofshear-induced crystallization 273.2.2 Molecular structures andmorph%gy 31

3.2.3 Crystallization kinetics 33

4 SCOPE AND OBJECTIVES 39

5 MATERIALS AND METHODS 40

5.1 Linear low-density polyethylene resins 40

5.2 Instruments 40

IV



5.2.1 Olympus polarized light microscope 41

5.2.2 Linkam shearing cell 41

5.2.3 Linkam shearing cell setup 43

5.2.4 Zero point calibration 44

5.2.5 Lidposition 445.2.6 Referenceposition 44

5.2.7 Gap setting 44

5.2.8 Temperature calibration 45

5.3 Experimental procedures 47

5.3.1 Quiescent condition 47

5.3.2 Shear condition at different shear rates 48

5.3.3 Shear condition at different temperatures 49

6 DATA ANALYSES 50

6.1 Growth rate 50

6.2 Microsoft Power Point scale calibration 51

6.3 Experimental procedure verification 51

6.3.1 Thermal history 52

6.3.2 Temperature fluctuations during experiments 53

6.4 Estimation of factors affected by shear 54

7 RESULTS AND DISCUSSION 55

7.1 Morphological observation 55

7.1.1 Quiescent crystallization 55

7.1.2 Crystallization under shear 59

7.2 Growth behavior 62

7.3 Effects of shear rate on growth rate 64

7.4 Effect ofmolecular structure on growth rate 697.5 Effect oftemperature on growth rate 74

7.6 Fitting ofgrowth rate to Lauritzen-Hoffinan equation 78

7.6.1 Quiescent crystallization 78

7.6.2 Crystallization under shear 82

8 CONCLUSIONS 86

9 RECOMMENDATIONS FOR FUTURE WORK 88

10 REFERENCES 89

Il APPENDICES 94

Il.1 Appendix A 94Il.2 Appendix B 100Il.3 Appendix C 103

Il.4 Appendix D 108

Il.5 AppendixE 113

Il.6 Appendix F 114

Il.7 Appendix G 116

Il.8 Appendix H 121

v



LIST OF FIGURES

Figure 2.1 Schematic expression showing the three possible macro-conformations for the

molecules in polymerie solid (13) 4

Figure 2.2 Fringedmicelle structure for partially crystalline polymers (6) 5

Figure 2.3 Polyethylene single crystals (After A.l Pennings and A. M. Kiel) (16) 6

Figure 2.4 Schematic representation of a pyramidal polyethylene single crystal (After

Schultz) (17) 6

Figure 2.5 Schematic view of a polyethylene single crystal. (20) 7

Figure 2.6 Schematic illustrations of the different types offolding suggested for polymer

single crystals (21) 7

Figure 2.7 Super-fold model (7) 8

Figure 2.8 Schematic diagram represents the growth of a stack oflamellae in the me1t. The

growth fronts do not arrive simultaneously at the location of a single molecule (18).... 9

Figure 2.9 Schematic representation of a fully-deve1oped spherulite grown from melt. R is

the spherulite radius (25) 10Figure 2.10 Three growth regimes. (Each square represents the cross-section o f a stem)(7).

............................................ ............................................ ............................................. .. 18

Figure 2.11 Schematic curve of growth rate regime (7, 20,34) 19

Figure 3.1 A plot of the anisotropy which deve10ps as a function oftime following the

cessation o f shear flow and coincident temperature drop from 170 oC to 120 oC (t=O).

Prior shear rate is 0.08 S-1 . , 0.8 S - 1 0 , 8 S-1 22

Figure 3.2 Experimental protocol for shear-enhanced crystallization experiments (60,61).24

Figure 3.3 Effect of shearing time on the acceleration of crystallization kinetics of PP using

shear rate 5 S-1 (60,61) 25

Figure 3.4 Deve10pment o f storage modulus and tangent o f the loss angle for PP(Mw 500 kg,

Mn= 100 kg, MFh3ü = 4.0 dg/min) during a quench to 138°C after melting at 260°C

and subsequent shearing during the indicated times till Ys = tsy's =500 (62) 25

Figure 3.5 Onset time for crystallization tonset vs shearing time ts (62) 26

Figure 3.6 Pressure Vs temperature in the upstream reservoir with 1.5 mm capillary

diameter 29

Figure 3.7 (a) Apparent flow curves for the samples (b) Th e sample flow curve 30

Figure 3.8 The us e of incubation time as a measure of the nuc1eation rates (76) 31

Figure 3.9 Induction time to crystallization at 131.6 oC versus carrier phase birefringence for

severa1 indicated drop1et deformation rates (78) 33

Figure 3.10 Relative crystallinity at Tc=142.5 oC under various shear rates 34

Figure 3.11 ln NI Vs Tm/T (AT) for different shear rates (74) 35

Figure 3.12 Nuc1eation rate as a function of shear rate (74) 36

Figure 3.13 Th e evolution of the solid layer of PP (85) 37

Figure 3.14 Growth rate measurement as a function o f crystallization temperature and fiber

velocity (85) 37

Figure 3.15 Growth rate measurements o fGx, Gy and Gz as function of shear rate (82) 38

Figure 5.1 Experimental setup 41

Figure 5.2 Photographs of Linkam shearing cell 43

Figure 5.3 A sketch of the Linkam shearing cell 43

VI



Figure 5.4 The re1ationship between the reading scale and gap width. (*The difference

between reading scales of the microscope when focusing on the top and bottom

windows) 45

Figure 5.5 The re1ationship between measured temperature and reading temperature

obtained from Linkam shearing cell 46Figure 5.6 A typical set-point temperature profile during experiments 48

Figure 6.1 The diameter measurement of spherulites using PowerPoint program to obtain

growth rate 51

Figure 6.2 Diameter as a function oftime of four experiments (Resin J at Tc= 105.4 OC) with

different holding temperatures and times 52

Figure 6.3 Sample temperature profile during the experiment. 53

Figure 7.1 Photographs of resin G at two different crystallization temperatures at the

specified times under quiescent conditions 56

Figure 7.2 Photographs ofresin J at two different crystallization temperatures at the

specified times under quiescent conditions 57

Figure 7.3 The ring-typed spherulite of resin G at 116.3 oC 58Figure 7.4 Photographs of resins G at two different crystallization temperatures under shear

conditions 59

Figure 7.5 Photographs of resins J at two different crystallization temperatures under shear

conditions 60

Figure 7.6 The ring-type morphology found under shear conditions (Resin G, 116.3° C, ls-1)

....................................................................................................................................... 61

Figure 7.7 The impingement ofspherulites in the shear conditions. (Resin G, 116.3° C, ls-1)

....................................................................................................................................... 61

Figure 7.8 Stages in the deve10pment of a spherulite 62

Figure 7.9 The growth behavior ofspherulites. (ResinG at 116.3 oC, quiescent condition) 62

Figure 7.10 The growth behavior of spherulites. (ResinG at 116.3 oC, 0.5 s-l) 63

Figure 7.11 The diameter as a function oftime ofresin l at 95.4°C 63

Figure 7.12 The polymermelt at time to (resin L, 117.3 oC, quiescent condition) 64

Figure 7.13 Diameter as a function oftime under different shears (Resin H, 113.3°C) 65

Figure 7.14 Diameter as a function of time under different shears (Resin H, 116.3 OC) 65

Figure 7.15 The growth rate as a function of shear rate at two different temperatures

(a) resinC, (b) resin H, (c) resin G, (d) resin L, (e) resin land (t) resin J 68

Figure 7.16 Spherulite growth rate as a function ofprevious shear rate: 0 Tc= 133.9°C,

o Tc= 136.4°C, • Tc= 138.5°C (96) 69

Figure 7.17 Plot of growth rate as a function of shear rate for resinHat 116.3°C, resin C at

119.3°C and resin G at 119.3°C under growth regime II and supercooling 11°C.........70

Figure 7.18 Plot of growth rate as a function of shear rate for resin G at 116.3°C, resin C at

116.3°C, resin Hat 113.3°C under the same growth regime (regime III) and

supercooling (14 OC) 71

Figure 7.19 Plot of growth rate as a function of shear rate for (a) resin la t 99.4°C and resin J

at 109.4°C under the degree of supercooling of 14°C (growth regime II) (b) resin l at

95.4°C and res in J at 105.4°C under the degree of supercooling of 18°C (growth

regime III) 72

vu



Figure 7.20 Growth rate as a function of shear rate under the degree of supercooling of 14

oC for resin G and J 73

Figure 7.21 Plot of percent increase of growth rate with respect to quiescent condition as a

function of shear rate under the degree of supercooling of 14 oC for resin I and J 74

Figure 7.22 Diameter as a function of time under different crystallization temperature ofresin C, quiescent condition 75

Figure 7.23 Diameter as a function of time under different crystallization temperature of

resin C, shear rate = 0.5 S·l 76

Figure 7.24 Growth rate as a function of crystallization temperature under quiescent

condition 76

Figure 7.25 Growth rate as a function of crystallization temperature under shear (0.5 S·l) .. 77

Figure 7.26 Growth rate ofresin L under quiescent and shear condition (0.5 sol) 78

Figure 7.27 Statistical segment volume (v*) and ethyl branch relation (98) 79

Figure 7.28 Linear regression of the experimental data plot follows the modified LH

equation (resin I) 80

Figure 7.29 The relationship ofgrowth rate under shear rate of 0.5 S·l as a function ofsupercooling followed themodified LH equation compared to quiescent condition

(resin I) 83

Figure 7.30 The superposition of experimental data under shear condition onto the linear

regression of quiescent data after adjusting QD* (resin I) 84

Figure 7.31 Schematic illustration of the potentia1 barrier ( ~ G ) for flow in polymers (21). 85

Figure Il.1 Resin G at 116.3°C under the shear rate of 0.25 S·l 100

Figure 11.2 Resin G at 119.3°C under the shear rate of 0.5 S·l 100

Figure 11.3 Resin J at 105.4C under the quiescent condition 101

Figure Il.4 Resin J at 105.4C under the shear rate of 0.75 S·l 101

Figure II.5 Resin J at 109.4C under the shear rate of 0.5 S·l 102

Figure 11.6 Diameter as a function oftime under different shears (Resin C, 116.3 OC) 103

Figure 11.7 Diameter as a function oftime under different shears (Resin C, 119.3 OC) 103

Figure 11.8 Diameter as a function oftime under different shears (Resin G, 116.3 OC) 104

Figure 11.9 Diameter as a function oftime under different shears (Resin G, 119.3 OC) 104

Figure 11.10 Diameter as a function oftime under different shears (Resin L,I13.3 OC) 105

Figure Il.11 Diameter as a function of time under different shears (Resin L, 117.3 OC) 105

Figure 11.12 Diameter as a function of time under different shears (Resin I, 95.4 OC) 106

Figure 11.13 Diameter as a function oftime under different shears (Resin I, 99.4°C) 106

Figure 11.14 Diameter as a function oftime under different shears (Resin J, 105.4°C) 107

Figure 11.15 Diameter as a function oftime under different shears (Resin J, 109.4°C) 107

Figure 11.16 Diameter as a function of time for resin H under quiescent condition 108Figure 11.17 Diameter as a function oftime for resin H under shear rate of 0.5 s·l 108

Figure 11.18 Diameter as a function of time for resin Gunder quiescent condition 109

Figure 11.19 Diameter as a function oftime for resin Gunder shear rate of 0.5 S·l 109

Figure 11.20 Diameter as a function oftime for resin L under quiescent condition 110

Figure 11.21 Diameter as a function of t ime for resin L under shear rate of 0.5 S·l 110

Figure 11.22 Diameter as a function of time for resin I under quiescent condition 111

Figure 11.23 Diameter as a function of t ime for resin I under shear rate of 0.5 S·l 111

V111



Figure Il.24 Diameter as a function oftime for resin J under quiescent condition 112

Figure 11.25 Diameter as a function oftime for resin J under shear rate of 0.5 S-l 112

Figure 11.26 Growth rate as a function oftemperature for (a) resin H (b) resin C, (c) resin G,

(d) resin l and (e) resin J 114

Figure Il.27 Linear regression of the experimenta1 growth data under quiescent conditionsplot following the modified LH equation: (a) resin H, (b) resin C, and (c) resin G.... 114

Figure Il.28 Linear regression of the experimenta1 growth data under quiescent conditions

plot following the modified LH equation: (d) resin Land (e) resin J 115

Figure 11.29 Resin H before adjusting Qo* 116

Figure 11.30 Resin H after adjusting Qo* 116

Figure Il.31 Resin C before adjusting Qo* 117

Figure 11.32 Resin Cafter adjusting Qo* 117

Figure Il.33 Resin G before adjusting Qo* 118

Figure Il.34 Resin G after adjusting Qo* 118

Figure Il.35 Resin L before adjusting Qo* 119

Figure Il.36 Resin L after adjusting Qo* 119Figure 11.37 Resin J before adjusting Qo* 120

Figure Il.38 Resin J after adjusting Qo* 120

IX



LIST OF TABLES

Table 2.1 Avrami exponent (n) for different nuc1eation and growth mechanisms (7) 14

Table 5.1 Physical properties of resins used in the study 40

Table 5.2 Specification of Linkam shearing system 42

Table 5.3 Equilibrium me1ting temperatures and crystallization temperatures of the LLDPE

resins used in this study 48

Table 7.1 Growth rate obtained under different shear conditions 66

Table 7.2 Go and Kg in the growth regime II and III obtained from linéar regression 81

Table 7.3 The estimated values OfQD* under shear condition of 0.5 S-I 84

x



NOMENCLATURE

Symbols

bo

G

.MIu

Lilio

l

k

Kao

n*

N

R

r*

Trnc,n*

TOm

Greek letters

cr

Description

o

width of stem= 4.55 Agrowth rate

rate constant

free energy change required to form a nucleus of critical size

heat of fusion per unit

heat of fusion per unit volume

nucleation density (number ofnuclei per cubic meter per second)

Boltzmann constant

kinetic rate constant for secondary nucleation

maximum polymer chain length.

nucleation rate

energy of activation for the transport of chain units across the crystal-liquid

gas constant

radius of stable nucleicrystallization temperature

copolymer maximum melting temperature

limiting equilibrium melting temperature of infinite crystallites of the

copolymer

equilibrium melting temperature

the volume fraction of crystalline material.

surface energy of surface

folding surface energy

Xl



1 Introduction

The global thermoplastics market for polyethylene makes it the largest volume

thermoplastic resin in the world, followed by polypropylene and polyvinyl chloride

(PVC). According to the World Polyethylene study by The Freedonia Group (1), world

demand for polyethylene is expected to increase more than 5 percent per year, to nearly

54 million metric tons in 2003. The study showed that low density (LDPE), linear low

density (LLDPE) and high-density polyethylene (HDPE) have been used in many

different areas based on their characteristics and cost. LDPE and LLDPE are mainly used

for films and coatings and HDPE is predominantly used for blow molded and injection

molded containers. According to the study, PE is also gaining new uses at the expense of

polystyrene and PVC due to regulatory restrictions related to solid waste issues and

potential toxicity ofthese resins. New polymerization technologies are also enhancing the

performance characteristics, and cost structure ofPE, particularly LLDPE.

LLDPE is a partially crystalline polymer, consisting of copolymer of ethylene and .

a linear a-olefin co-monomer such as propylene, butene-l, pentene-l, hexene-l, and so

forth (2). Because the properties of LLDPE can be engineered to a great extent by the

incorporation of various co-monomers in the main chain (3), their advantageous

properties are high tensile strength, impact strength, toughness, stiffness, film gloss,

puncture resistance, tear strength, environmental stress cracking resistance, permeability

of water vapor and carbon dioxide (4). Therefore, LLDPE is suitable for making thin

films, sheets, lenses, storage tanks and packaging materials.

The physical properties of partially crystalline polymers, which inc1ude

mechanical and optical properties, permeability and chemical reactivity, are influencedby the crystalline characteristics, i.e. the size of the crystallites, the morphology of the

crystalline and amorphous regions, and the molecular orientation within the crystalline

and amorphous regions. These factors are related to crystallization kinetics, cooling rate,

and deformation history (5). Generally tensile modulus increases with increasing

1



crystallinity (6,7). The influence of molecular structure and crystallinity is manifested in

the differences between the tensile properties of the three types of polyethylene: HDPE,

LDPE and LLDPE. Properties up to and including yield are determined by the level of

crystallinity. Therefore, HDPE has a higher yield stress than both LDPE and LLDPE.

After yield, the strain depends on the amorphous region and the shape of the polymer

chain. In spite of higher crystallinity, the strain at failure of HDPE is higher than that of

LDPE, because of the absence of long chain branching in HDPE. The linearity and

greater amorphous content give LLDPE the very high elongation at break: (8).

Optical properties of polymers are important to evaluate their potential usefulness

in many applications such as films, lenses, coatings and packaging materials. In general,

transparency decreases radically when crystallization occurs, and light scattering results

from alteration in the refractive index by the crystalline order. It has been suggested that

light scattering relates to crystallite size. Consequently, sorne effort has been made

commercially to improve the transparency of film and molded articles by adding

nuc1eating agents to control spherulite size (6,8). However, the refractive index (n),

which is the ratio of the velocity oflight in vacuum to the velocity oflight in the material,

can be quantitatively estimated by the molar refraction (R), which represents the intrinsic

refractive power of the structural units constituting the materials. The refractive index can

be determined by the molar refraction RGD according to Gladstone and Dale (9) and

molar volume (V) as n =1+ RGD

• As a result, n generally decreases with increasingVtemperature and increases with increasing crystallinity (10).

Crystallinity and morphology have a profound effect on the impermeability of

polymers to gas and liquid. Irnpermeability is required in films and packaging materials.

Permeation normally depends on solubility and diffusion. The amorphous phase tends to

be more soluble than the crystalline phase. Thus, the presence of crystalline material in aproduct reduces its solubility. Moreover, the crystallites cause stiffening of the chain-

segments, and thus reduce the molecular motion responsible for diffusion (6,7,10).

The chemical degradation of PE is generally caused by thermal oxidation. The

oxidation of PE at high temperature occurs mainly in the amorphous regions. The attack

2



takes place between the spherulites and also between the fibrils in the spherulites.

Reducing spherulite size and increasing the fraction of tie-molecule between fibrils have

been found to be effective in reducing embrittlement caused by thermal oxidation (6).

Crystallization is dependent on processing conditions.In

a given crystallizablepolymer, the degree of crystallization depends on the thermal pretreatment.

Crystallization at high temperatures promotes high overall crystallinity due to the

formation of thick lamellae (7). The rate of cooling has a pronounced effect on

crystallinity. High cooling rates favor low crystallinity. They also cause less secondary

crystallization and insufficient annealing time for thickening of the lamellae (11). It was

found that spherulite size is affected only slightly by cooling rate (11). However, slow

cooling promotes high crystallinity and coarse texture (8), whereas rapid cooling

produces fine texture.

Crystallization of polymers is also influenced by mechanical history. Stress

applied during processing influences both crystallization kinetics and morphology.

Polymer molecules become oriented during deformation, thus the crystallization rate is

higher than in the quiescent state. The number, type and final crystalline structure of the

nuclei formed depends on the amount of stress applied during melt flow (12). Shish

kebabmorphology is normally found in flow-induced crystallization (5,6,7,12).

The present study attempts to evaluate the effect of shear on the crystallization

behavior and growth kinetics of polyethylene melts.

3



2 General Background

Polyethylene, a partially crystalline polymer, is composed ofboth crystalline and

amorphous phases. The crystalline region exhibits ordered regular chain structure and

preferred chain conformations. On the other hand, the presence of chain defects, for

example branches, leads to amorphous behavior. Some possible macro-conformations of

polymers in the solid state are shown in Figure 2.1 (13). The morphology of a partially

crystalline polymer usually exhibits all three types ofmacro-conformation.

Figure 2.1 Schematic expression showing the three possible macro-conformations for the

molecules in polymeric solid (13).

Crystalline structures of polymers differ in several important ways from those of

low molecular weight materials. Firstly, in low molecular weight materials, the growth

units are fully crystalline and continue to develop up to the point ofmutual impingement.

Then, grain boundaries separate the individual crystals. In polymers, sizeable fractions of

disordered structures are present in the growing structural units. Secondly, the melting of

crystalline structures of polymers occurs over a range of temperatures, because of the

varietyof

crystalline structural sizes, whereas the melting transition is quite sharp in lowmolecular weight materials. Thirdly, super-cooling can be eliminated in low molecular

weight materials, but hysteresis is always observed during successive melting and cooling

ofpolymers. Finally, crystalline polymers contain crystallites of differing sizes, as will be

shown be1ow, which small molecules tend to produce crystallites ofuniform size.

4



2.1 Structure of crystalline polymers

2.1.1 Fringed micelle model

The earliest model of the two-phase nature ofpolymers was introduced during the

1930s. It is known as the Fringed Micelle Model. This model was based on X-ray

diffraction experiments, which showed relatively sharp X-ray diffraction patterns similar

to the powder patterns of low molecular weight solids in microcrystalline form. The

dimensions revealed by the X-ray diffraction ring were in the range of 100-1000 A0 . This

observation led scientists to postulate the Fringed Micelle Model which depicted a

random arrangement of crystalline and amorphous regions. The crystalline regions are

formed by chain association. In the amorphous regions, single molecules meander from

one location to another, acting as a matrix in which the crystallites are embedded, as

shown in Figure 2.2.

1 .... i

7--1JL..•...·1 • •. •

1

1l'.••"'...J).1 ·•.. .11 1 ..

Figure 2.2 Fringed micelle structure for partially crystalline polymers (6).

2.1.2 Single crystals

Keller was the first to produce polymer single crystals in 1957 (13, 14, 15). A fiatlozenge of polyethylene single crystal was obtained by slow precipitation from

polyethylene-xylene dilute solution ( ~ 0 . 0 1 %), as shown in Figure 2.3. Polymer single

crystals are not always fiat. Many polymer crystals are in the form of hollow pyramids

since they collapse during solvent evaporation as shown in Figure 2.4.

5



Figure 2.3 Polyethylene single crystals (AfterAJ Pennings and A. M. Kiel) (16)

The thickness of the crystals is on the order of 100 A0, depending on

crystallization temperature and pressure. Lamellar size and shape also depend on cooling

rate, solution concentration and solvent type. Electron diffraction analysis showed that

the polymer chain axis in the crystal body was perpendicular to the large, fiat faces of the

crystal. Therefore, since polymer molecules have contour lengths reaching thousands of

angstrom, chain folding must take place. This conclusion was confirmed by Fischer and

Till (18, 19).

Figure 2.4 Schematic representation of a pyramidal polyethylene single crystal (After

Schultz) (17).

6



2.1.3 Folded chain model

A schematic illustrating the folded chain model of single crystals is shown in

Figure 2.5. Polyrner molecules fold back and along the thickness of crystal larnella with

adjacent re-entry.

Figure 2.5 Schematic view of a polyethylene single crystal. (20)

The way in which folding occurs is controversial. Several different models have

been proposed to explain the folding in polyrner crystals. The models range from a

random re-entry or a switch-board model, where molecules leave and re-enter a crystal

randomly, to adjacent re-entry models as shown in Figure 2.6. Two particular adjacent reentry models have been suggested, regular and tight folding and irregular with variable

length folding.

l1l i ~ D -

Figure 2.6 Schematic illustrations of the different types offolding suggested for polyrner

single crystals (21).

7



As mentioned earlier, considerable fractions of amorphous structures are present

in partially crystalline polyrners, as verified by density measurements of single crystals.

This indicates that the fold surfaces possess considerable disorder. Therefore, a

significant fraction of molecules do not bend back to enter the crystais at the adjacent

positions. The small-angle neutron scattering (SANS) study of deuterated and protonated

polyrner blends by Sadler and Keller (22, 23, 24) gave evidence of fold surface

structures. Taking into account data from SANS and wide-angle neutron scattering

(WANS), the super folding mode was proposed as shown in Figure 2.7. Spells, Keller

and Sadler (1984) (7) showed by infrared spectroscopy that 75% of the folds in solution

grown single crystals of polyethylene led to adjacent re-entry and that single molecules

were diluted by 50% along the (110) fold plane. Both observations are in agreement withthe super-foId model.

Figure 2.7 Super-foId model (7).

2.2 Crystallization from polymer melts

Crystallization from polyrner melts produces poly-crystalline structures, due to

the presence of a large number of growth-units, each of which nuc1eate separately. The

polyrner molecules add to a particular crystal surface simultaneously as they are highly

entangled.

The shapes of melt-grown crystals are the same as those of the solution-grown

crystals, in most respects. They have lamellar shape with a thickness-to-width ratio of

8



0.001-0.01. A typical characteristic of melt crystals is the formation of crystal stacks,

when many lamellae combine together with tie molecules. Neutron scattering

experiments by Fischer (18) confirmed that the well-defined c1usters of crystalline stems

in a single lamella belong to a single molecule. Such c1usters would not be formed if a

single molecule were responsible for a large number of tie-sequences between two

adjacent lamellae. Fischer explained the existence of weIl defined c1usters by suggesting

that the growth fronts within the lamellae of a stack did not arrive at the position of a

single macromolecule simultaneously. A schematic of growth of a stack of lamellae is

shown in Figure 2.8. The stepwise growth will result in approximately (n-l) tie

molecules if n is the average number of c1usters per molecule. The growth of the c1uster

within a single lamella is, according to Fischer's model, stopped by kinetic hindrance;

e.g. by entanglements and by a filling in of the growth front with parts of other

molecules.

Figure 2.8 Schematic diagram represents the growth of a stack of lamellae in the melt.

The growth fronts do not arrive simultaneously at the location of a single molecule (18).

2.2.1 Spheruli tes

A spherulite is a spherically symmetrical formation made of crystalline lamellar

stacks which grow radially from the center. Spherulites grow in crystallization under the

conditions ofhigh viscosity or super saturation of the medium, i.e. from polymer melts or

9



highly concentrated solution. The dimensions of spherulites range from fractions of a

millimeter to several microns, reaching values of a centimeter in sorne cases.

Polymer chains in a spherulite are arranged perpendicular to the radius of the

spherulite. The formation of spherulites occurs many stages. The first stage is the

formation of crystal nuclei, which are statistically scattered throughout the volume of the

sample. The second stage is the growth of independent crystalline lamellar structures,

called primary crystallization. This stage occurs at the same rate in all directions. After

the radial growth of spherulites is completed, the final stage of crystallization so-called

secondary crystallization starts. During this stage, the spherulites become more perfecto

Figure 2.9 shows a schematic representation of a spherulite.

Cryatalline po/ymer

Spherv!ite$unace

Figure 2.9 Schematic representation of a fully-developed spherulite grown from melt. R

is the spherulite radius (25).

Spherulites have anisotropie properties, because of the radial symmetry of their

structure. Consequent1y, they give different refractive indices in the radial and tangential

directions. The anisotropy leads to birefringence of spherulites when observed with a

polarized light microscope. Birefringence occurs because the orientation of the

crystallographic axes changes continuously in a spherulite along the angular coordinate.

A continuous change of the refractive indices occurs with respect to the plane of

10



polarization of incident light. As a result, various regions of the spherulite transmit

polarized light differently. This produces light-colored circular birefringence regions

intersected by dark regions in the form of a Maltese cross. The arms of the cross are

parallel to the directions of destruction of incident light.

2.2.2 Fibrils

Fibrils are fundamental units of spherulitic structures. In melt crystallization, a

condition occurs that favors fibril development, without subsequent organizatiQn into

spherulites. The condition is called trans-crystallization. This results from the occurrence

of an extended source of nuclei confined to a plane surface. Strain set up in the viscous

melt can induce this type of crystallization. Fibrils can radiate outwards from a central

nuc1eus and be organized into spherulites, if the nuc1eation density is sufficiently low to

enable growth units of one micron and larger to develop. PolYffier chains are generally

oriented at right angles to the long axis of the fibrils, indicating that growth occurs

through chain folding, by a mechanism resembling that found in solution-grown single

crystals.

2.3 Isothermal crystallization kinetics under quiescent state

2.3.1 General Avrami equation

The Avrami equation describes the time evolution of overall crystallinity. It has

been employed to describe the crystallization kinetics ofmany materials including metals

and polYffiers. The derivation of the Avrami equation for two crystallization cases,

athermal and thermal nucleation, is shown here.

The Avrami equation is derived by assuming that crystallization starts randomly

at different locations and propagates outwards from the nucleation sites. This can be

compared to raindrops falling randomly on a surface ofwater. Each raindrop creates one

expanding circular wave. The probability that the number of waves, which pass a

11



representative point P up to time t, is equal to c is givenby the Poisson distribution as

shown in equation 2-1.

()exp(-E)EC

pc =

clwhere E is the average value of the number of passing waves.

The probability that no fronts pass P is given by:

p(O) = exp(-E)

Equation 2-1

Equation 2-2

For athermal nuc1eation, aIl nuc1ei are formed and start to grow at time t=0. The.nuc1eation is foIlowed by a spherical free growth at constant growth rate ( r ) in three

•dimensions. The average number of crystal fronts (E) of aIl nuc1ei within radius r t from

point P is given by:

4 .E(t) = -T t (r t)3 g

3Equation 2-3

where g is the volume concentration of nuc1ei.

The probability p(O) is equivalent to the volume fraction (l-vc) of the polymer

which is still in the molten state.

p(O) =1 -vc

where Vc is the volume fraction of crystaIline material.

Combination of aIl equations gives:

Equation 2-4

Equation 2-5

In thermal nuc1eation, nuc1ei are formed at constant rates in both space and time,

as in the case of nonnal rain. For three-dimensional growth at a linear constant rate, the

number of waves (dE) which pass the arbitrary point (P) for nuc1ei within the spherical

sheIl confined between the radii r and r+dr is given by:

12



Equation 2-6

where r* is the nucleation density (number ofnuclei per cubic meter per second).

The total number of passing waves (E) is obtained by integration of dE between 0

and rt.

. ( .I ru* 3

E =J4rcr 2J* t - ~ J d r =__r_ t4

o r 3

Equation 2-7

After combining equations 2-4 and 2-7, the following equation is obtained (26).

( . ju* 3

1-vc=exp _+t 4

Equation 2-8

Therefore, equation 2-5 for athermal nucleation and equation 2-8 for thermal

nucleation can be written in the same general form as the Avrami equation:

Equation 2-9

Where, K and n are constants depending on nucleation and growth mechanisms,respectively. The values of the Avrami exponent (n) are shown in Table 2.1. It increases

with increasing dimensionality of the growth.

The basic Avrami equation was modified by taking into account non-isothermal

crystallization (27) and including the effect of secondary crystallization (28), to obtain

better improved representation of experimental data. Additionally, the Avrami rate

constant K may be related to a crystallization half time at different temperatures as

proposed by Hoffman (29,30,31,32)

13



Table 2.1 Avrami exponent (n) for different nuc1eation and growthmechanisms (7)

Growth geometry Athermala

Thermala

Thermala

Line 1 2 1

Two-dimensionalCircular 2 3 2

Three-dimensional

Spherical 3 4 5/2

Fibril1ar :::;1 :::;2

Circular lamel1ar :::;2 :::;3

Solid sheaf ~ ~ a Free growth; ; constant, b Diffusion control; ;u l

2.3.2 Equilibrium melting temperature

The equilibrium melting temperature ( T ~ ) is important in polymer crystallization,

because supercooling tJ.T is defined with reference to T according to the following

equation.

tJ.T = T ~ - ~ Equation 2-10

where, Tc is the crystallization temperature.

The equilibrium melting temperature is defined as the thermodynamic melting

temperature of homopolymers of infinite size (33). It can be obtained by extrapolating

experimental data according to existing relationship, such as the Hoffinan-Weeks (34)

and Gibbs-Thomson (21) equations. This melting parameter is a theoretical property

because the infinite molecular weight cannot be practically obtained. Additional1y, this

parameter is limited to homopolymers. Kamal et al. (35) proposed a new melting

parameter by taking into account chain length and copolymer effect. They defined the

copolymer maximum melting temperature (Trnc,n*), which is the melting temperature of

the copolymer with maximum achievable chain length. As a result, the derived equation

2-11, which is a modified form of the Gibbs-Thomson equation:

14



Equation 2-11

In this study, Tmc,n* is used in place of T ~ where Tmc,oo is the limiting equilibrium

melting temperature of infinite crystallites of the copolymer. ~ H is the heat of fusion per

unit. cre is the folding surface free energy, and n* is the maximum polymer chain length.

This equation can be used to calculate the maximum melting temperature only when the

co-unit volume effects can be neglected.

2.3.3 Nucleation

Nucleation is the process of forming stable nuclei, and may be explained by thefollowing treatment. The change in free energy during crystallization may be considered

as the sum of the negative value of the crystallization free energy and the positive value

of the surface energy, as shown in equation 2-12.

Equation 2-12

where ~ is the change in free energy on crystallization, ~ G is the specific change in

free energy, V is the volume of nuclei,cri

is the specifie surface energy of surface i, andAi is the area of surface i.

If the spherical crystal case is considered, ~ can be written as:

G4nr3 AG'+4 2=--0 nr cr3

Equation 2-13

where r is the radius of the spherical crystal and cr is the specifie free energy of the

surface.

The radius of sphere (r*) associated with free energy barrier ( ~ G * ) can be

presented as:

Equation 2-14

15



Setting the derivative of ~ G with r* equal to zero give the minimum radius of

stable nuclei as:

20-r*=-~ G

The temperature dependence of this equation lies in ~ G ' :

Equation 2-15

Equation 2-16

where ~ h is the heat of fusion per unit volume, T; is the equilibrium melting point,

T= T; -Tc is the degree of supercooling, and Tc is the crystallization temperature.

Therefore, the minimum stable radius of nuclei is given by:

Equation 2-17

Nuclei that are smaller than the critical size are unstable, and those larger than the

critical size can develop and grow into mature crystallites. The free energy barrier can be

represented as:

Equation 2-18

where is a geometrical constant.

As proposed by Hoffrnan et al. (20) based on Tumbull and Fisher's (36) theory,

the steady state nucleation rate can be expressed by the equation 2-19:

. ( Q* J ( ~ G * )=No exp - R ; exp RT Equation 2-19

where N = nucleation rate, No = a constant that is only slightly temperature dependent,

Q: = the energy of activation for the transport of chain units across the crysta1-liquid

interface, and ~ G = the free energy change required to forrn a nucleus of critical size.

16



Nucleation occurs more readily at lower crystallization temperatures because of

the lower critical nucleus size and the lower free energy barrier associated with the

process. Different types ofnucleation fonnation are possible. Primary nUcleation involves

the fonnation of six new surfaces, whereas the secondary and tertiary nucleation involvefewer, four and two, respectively. The free energy barrier is highest for tertiary

nucleation.

Nucleation can be divided into two principal types, homogeneous and

heterogeneous nucleation. Homogeneous nucleation consists of the spontaneous

aggregation of polymer chains at temperatures lower than the melting point. It occurs

very seldom. Both calculations and experimental data show that 50-100 K of

supercooling is needed to achieve true homogeneous nucleation. Instead, crystallization is

in aIl practical cases initiated at foreign particles, i.e. heterogeneous nucleation.

2.3.4 Growth behavior

Crystal growth occurs via secondary and tertiary nucleation. After the stable

nuclei have been fonned, they begin to grow by fonnation of a secondary nucleus, which

is followed by a series of tertiary nucleation events (6, 7). The growth of nuclei may be

one, two or three-dimensional, giving rods, dises, and spheres, respectively. At the end,

the growing elements collide, and the growth stops at the places of their contact. The

linear dimensions of growing crystal fonnation increase in time, t (37):

r =Gt

where, r = corresponding linear size, G = growth rate.

Equation 2-20

2.3.5 Lauritzen-Hoffman growth theoryThe Lauritzen-Hoffrnan (LH) growth theory (20) is based on a kinetic theory,

which acknowledges that the end state is not the state with the lowest possible free

energy. Kinetic factors control growth rate and morphology. The growth rate depends on

the crystal thickness. Crystals with a range of crystal thickness greater than a minimum

17



value (2a/ ~ G are formed. Growth mechanisms can be divided into three growth

regimes depending on crystallization temperature. The growth of Regimes l, II and III

occurs at high, moderate, and low temperatures, respectively. A schematic illustrating

these three regimes is shown in Figure 2.10.

, '

•

- Regime 1

Regime II

-Regime 111

Figure 2.10 Three growth regImes. (Each square represents the cross-section of a

stem)(7).

In regime l, the lateral growth rate is significantly greater than the growth rate in

the perpendicular direction, giving monolayer stems. This regime gives axialitic

morphology. The growth rate in the perpendicular direction is higher in regimes II and

III. Spherulitic morphology is obtained from both of these regimes.

The LH theory provides an expression for the linear growth rate as a function of

the degree ofsupercooling as shown in equation 2-21(38,39,40).

G = Go exp( - Q: Jexp( - Kg )RTe T e ~ T f

Equation 2-21

Where, Q* = 5736 Cal/mol for polyethylene (91). Go (mis) is the rate constant dependingD

on segmental flexibility and the regularity of polymers. Kg (K2) is the kinetic rate

constant for secondary nuc1eation and it can be divided into KgI,KgIJ,KgIII for regimes l,

18



II and III, respectively. K gI =K glII = 4boO"O" e T n ~ and K II = 2boO"O" e T n ~ ; bo is the widthkMl

mg kMl

m

o 2Tof stem= 4.55 A; k is Boltzmann constant; R is gas constant; and f = 0 c •

T", + 1;;

The three growth regimes can be manifested in the natural logarithmic plot of

equation 2-21, as shown in Figure 2.11.

T // T c ~ T fFigure 2.11 Schematic curve ofgrowth rate regime (7, 20,34).

2.4 Effeet of shear on erystallization

The effect of shear and applied flow field is of considerable importance in the

crystallization of polymer melts, because they generally undergo solidification under

stress and/or strain during polymer processing.

Shear has profound effects upon crystallizationof

polymers in many differentways. Crystallization could be induced by shear in polymers which were non

crystallizable under static conditions (41, 42, 43, 44). A competition exists between the

applied flow field and the Brownian motion of the molecules, which tends to cause

disorder and isotropicity occurred during shear flow.

19



For a crystallizable polymer such as polyethylene, shear influences nuc1eation,

growth behavior and the final morphology of the polymer. The induction time to

crystallization is reduced and the rate of crystallization is enhanced by shear. There are

various reports in the literature that have attempted to study the effect of shear on

crystallization kinetics under the processing condition (12, 45, 46, 47, 48, 49). The

present research attempts to obtain experimental data re1ating to the effect of shear on a

number of linear low-density polyethylene (LLDPE) resins.

20



3 Literature Review

The study of shear effects on the crystallization behavior of polymers can be

divided into two principle categories: the study of crystallization after cessation of flow is

categorized as "Post-shearing Crystallization", whereas, the real time observation of

crystallizationbehavior during shear flow is "During-shear Crystallization".

This literature review focuses on melt crystallization of polyethylene (PE) and

related materials such as polypropylene (PP).

3.1 Post-shearing crystallizationThe study of post-shearing crystallization originates from the attempt to

understand the influence of shear on crystallization in polymer processing. In most

polymer processing operations, molten polymers are exposed to shear stress. Because of

the short residence time, the effect of shear on the behavior of the material is not

spontaneouslyevident. However, shear stress affects material behaviors after the shearing

ends.

3.1.1 Structure andmorphology

It is weIl known that application of shear into a polymer melt can lead to the

development ofvarying degrees of orientation. Pople et al. (50) investigated the effect of

simple shear flow on molten polyethylene, using in situ time-resolving wide-angle x-ray

scattering (WAXS) in conjunction with a Linkam shearing cell. The shear rates of 0.08,

0.8, and 8 S-1 were applied to the 100J..lm thick samp1e at 170°C for 60 s. After shear was

stopped, the temperature was rapidly cooled to 120°C at the rate of20°C/min. The degree

of orientation <P 2> related to the crystalline structure in the samples was calculated from

the WAXS pattern. They conc1uded that considerably higher degrees of orientation were

achievable in the recrystallizedstate than induced in the melts. From the results shown in

Figure 3.1, they suggested that there was a critical shear rate of 1 S-1 over which the

21



higher level of orientation occurred. They explained that the increase in shear rate caused

an increase in the fraction of aligned molecules, but at the same time it increased the

number of shorter lengths that relaxed more rapidly when shear was stopped. Therefore,

to obtain a high degree of crystalline order, the applied shear rate had to exceed the

critical shear rate.

0.4 r - - - - - - - - - - - - - . . . ,

0.3 f t l ! ~ i i t t t t t I ± f t ' t i !t

t

0.1

oo

{

If! l ! ! / i l ~ \ \ ~ i i : !l(JO aoo 300 4tlO

Tfme (seconds)

Figure 3.1 A plot of the anisotropy which develops as a function of time following the

cessation of shear flow and coincident temperature drop from 170 oC to 120 oC (t=O).

Prior shear rate is 0.08 S- I . , 0.8 S-10, 8 S-1Â.

Using TEM analysis, Pople et al. (51) found that the critical shear rate of 1 S-1 did

not relate to shish-kebab morphology. The shish kebabs were obtained with shear rates up

to 40 S-I. The shish kebab morphology was also observed by Hsiao (52, 53), using wide

angle x-ray diffraction (WAXD) and small angle x-ray scattering (SAXS) during fiber

spinning and step-shearing ofPE and PP.

The morphology of PP after melt shearing, using a fiber-pullout technique, was

observed by Kamal and Lee (54) and Chen et al. (55, 56). Kamal (54) used a shearing

system consisting of the mechanical movement of a glass fiber in conjunction with a

polarized light microscope (PLM). The molten PP was exposed to shear rates up to 50 S-1

under isothermal conditions. Two different morphological characteristics were created

22



upon the fiber pullout. The bulk spherulites appeared far from the fiber and a shear

induced layer occurred near the fiber. Morphological differences between the bulk and

shear zones were reported by Chen et al. (55, 56). Shear force was introduced to the

molten pp sample under isothermal conditions by pulling a Kevlar fiber manually. The

micrographs from PLM, phase contrast optical microscopy (PCLM), scanning electron

microscopy (SEM), and atomic force microscopy (AFM) revealed a-cylindrites, ~ cylindrites and ~ - s p h e r u l i t e s near the sheared layer.

Highly oriented surface layers and fine grain layers were obtained from the

shearing experiment performed by Janeschitz-Kriegl et al. (57, 58). In this study, short

term shearing of molten pp was carried out in a small duct, and the subsequent

crystallization process was monitored at a low degreeof

supercooling. They found thatlong polymer molecules were predominantly responsible for the formation of highly

oriented surface layers under shear treatment.

Pogodina et al. (59) studied the effect of short-term shear (shearing time :$; 60 s)

with constant shear rate (10 S·l) on the crystallization of PP, using Linkam shearing stage

connected to a time-resolved small-angle light scattering (SALS). They found an

increase in nuc1eation rate together with a formation ofthread-like structure.

Komfield et al. (60, 61) observed the skin-core morphology in a horizontally

extruded sample, using a device with a maximum wall shear stress 0.1 MPa. This

morphology revealed highly oriented crystallites along the flow direction near the wall

and spherulites in the center of the sample.

3.1.2 Effect ofshearing time

Komfield et al. (60, 61) developed a new device to monitor crystallization and

morphology of pp after a brief shearing. This instrument consisted of a horizontaldisplacement piston extruding molten polymer through a small die (maximum wall shear

stress 0.1 MPa). A pressure transducer, visible and infrared polarimetry, and a light

scattering instrument were connected at the die zone. The design provided the retrievable

samples for ex situ optical and electron microscopy investigation. The experimental

23



protocol generated well-defined initial conditions for the polymer melt and a controlled

and simple deformation protocol as given by Komfield et al. (see Figure 3.2) "The

polymer melt is extruded from the reservoir using a low pressure drop across the flow

channel, PfilI, for a time tfill (top graph); then it is allowed to relax for time trelax at atemperature Tmelt that is above the equilibrium melting temperature TMû (middle graph).

When the polymer melt has relaxed, it is cooled to the crystallization temperature, Tcryst

and then subjected to shear as it is extruded at a high pressure, Ps, for a brief interval, ts.

The progress of crystallization with time, tcryst, is monitored using different probes,

induding turbidity (bottom graph)" (60,61)

1 1 l'pS1

11

11

11

1

PmI

1

1

1 1 I l1 1 I l

i ~ Mo

I lTcrysl

lI l

, 1,,I l

1 I l, I l1 , 11 I l

1 ,"1 II

1 1 I l1 1 I l1 1 , 1

1 1 , 1, ,

.. • • -tcrysl -Ifill lTeiax tcoo1 ts

Figure 3.2 Experimental protocol for shear-enhanced crystallization experiments (60,

61).

Turbidity and birefringence which indicated the development of crystallinity and

chain orientation were detected in-Hne by an optical instrument with visible laser (red

HeNe, Â,=632.8 nm). The effects of shearing on crystallization were examined using

shearing times ranging from 4 to 250s. The crystallization rate was tracked by monitoring

the intensity of light transmitted through the sample as shown in Figure 3.3. It was dearly

seen that shearing for short times (less than ls ) caused an acceleration of the

crystallization rate, and higher degrees of crystallinity were obtained with increasing

shearing time.

24



Stronger effect on crystallization during longer shearing times was reported by Meijer

(62). In the study, a cone-and-plate rheometer was used to apply shear to molten PP. The

development of the crystallization was investigated by dynamic oscillatory

measurements. Effects of shearing time on crystallization were studied by applying a

constant shear rate ofy's =5 S-1 for various times ts =25, 38, 50, 100 and 200 s at Tm. In

the experiments with the highest shearing times, ts , crystallization already set in before

completely isothermal conditions (t-500 s) were reached as shown in Figure 3.4.

-- 1.00 -"':::,W'_

PPI86/2.1,13;:a-'

" " ' = " ~o.=O.09MPa0.8 --

e;.....

d s=4s•••'r;; : .. .. I s=2 sc 0.6 . .

. t s= ls

•• .--

.5 · · "x" ."" · ---=:.. . x I s=0 .5 s

1~ •

0.4 .X • ...... • t s=O.25 s'§ 6 .)ncreasing ts '=:.... - QuiescentrJJ t • -"'=-.....c:: x

'".2 .... .....E JX..

\ . "0.0

0 2000 4000 6000 8000

tcrysl (s)

Figure 3.3 Effect of shearing time on the acceleration of crystallization kinetics of PP

using shearrate 5 S-1 (60,61).

1 00e!

. . n ~ . h e " ' l n g

10 ' ~ " " ' - - - - - - - - - - - - - - - - - ' 1 2t ahearlng l ime. ( .)

l::l,\ ·' ~ ; . ,

" { < ~ ..... -:,;,;,;,:,;:,.; : ' ~ ~ ~ ' " '

~ v ' ' ' : ,

.'c 200

25 .. t an a

10'

10. '-1-..J......L....l-J---,--,,-,--,-'J . . . . L - ' - " " - - ' - ~ - ' - " - - - ' - . . J . . . . . . L . . . . J - l - ' - : : '

0o 500 1000 1500 2000 2500

lime (s)

Figure 3.4 Development of storage modulus and tangent of the loss angle for PP(Mw 500

kg, Mn= 100 kg, MFh3û = 4.0 dg/min) during a quench to 138°e after melting at 2600e

and subsequent shearing during the indicated times till Ys = ts y's =500 (62).

25



The onset time for crystallization substantially decreased with increasing shearing time as

shown in Figure 3.5.

2000

...----------------------.

1500

......

;;

....

1000

1\\+1\1111\\\1\\1\1d

2500050000

500 l -> -- ' -........" " " ' " ' " _ l . - o . - - ' - - ' - - ' - - ~ - ' - - ' - " " " ' " ' " - ~ - - ' - ........-L.-.l ...-..l................. .......J

o

t. (s)

Figure 3.5 Onset time for crystallization tonset vs shearing time ts (62).

3.1.3 Crystallization kinetics

Kamal and Lee (54) monitored crystallization characteristics of pp after exposure

to high shear rates of la , 25, 50 S·I by using a fiber-pullout technique. The shear

apparatus, consisting of a single glass fiber sandwiched between two layers of pp films

mounted on a hot stage, was used in conjunction with a polarized light microscope. Shear

was introduced to the molten pp under isothermal condition for a specifie period of time,

and then the isothermal crystallization was observed after shear was stopped. On the basis

of the analysis of crystallization kinetics, they conc1uded that a higher nuc1eation rate

occurred in the shear zone compared to the bulk zone, but the spherulitic growth rate of

the two zones was the same. This observation was in agreement with results reprinted by

other researchers (63, 64, 65) that shear promoted nuc1eation. Kamal and Lee proposed

from this work that growth rate was independent of shear rate but strongly dependent on

the crystallization temperature. Yeh and Hong (66) estimated that the dramatic increase

26



of nuc1eation rates in sheared polyethylene melts could be several orders of magnitude

higher than that in the quiescent state if the nuc1eation was heterogeneous, with even

more enhancement if the nuc1eation was homogenous.

The effect of shear on nuc1eation kinetics without the disturbance from

subsequent crystal growth was monitored by Liedauer et al. (67). Short term shearing at

low degrees of supercooling was applied to a molten pp by flowing the polymer melt into

a small duct. They observed sporadic nucleation, and the nuclei grew out into thread-like

. .precursors. They defined the intensity of shear as y 4 t;, where y is shear rate and t is

shearing time.

An increase in the crystallization rate after melt shearing was reported by Somani

(68,69, 70) and Balta-Calleja et.al (71). By using SAXS and WAXD, they found that the

crystallization rate of PP, after a step shear at high shear strain of 1400% and a high shear

rate of 100 S-I under isothermal condition, increased by two orders of magnitude as

compared to quiescent crystallization. Other researchers reported that the crystallization

process, i.e. the nuc1eation and growth process, was affected by shearing time. If the

shearing time was not too long, the nucleation and growth processes of the shear-induced

layers could be were separated (72).

3.2 During shearing crystallization

3.2.1 Investigation ofshear-induced crystallization

The shear-induced crystallization of HDPE was investigated by Fortelny et. al

(73) using a capillary rheometer. AIso, the effect of molecular weight on flow-induced

crystallization was studied. HDPE samples with different molecular weight (MW) were

extruded at different temperatures and shear rates under isothermal conditions. Thepressure difference between the pressure applied to a piston and the pressure at ho1e, was

measured as a function of time. Flow-induced crystallization was indicated by a sharp

increase in the pressure difference. In this study, flow-induced crystallization took place.

at a wall whereas the molten HDPE was at the center of the capillary. The thermal

27



characteristics of extrudates were studied using Different Scanning Calorimetry (DSC) by

measuring the enthalpy of formation ( ~ H f ) at a scanning rate of 20°C/min and

temperature ranges of 30-200°C. It was found that the shear stress had pronounced effects

on Tfi and volume fraction of crystallization. The higher was the shear rate, the higher

was the Tfi and degree of crystallinity. It was also noted that the highest temperatures at

which crystallization could be induced by flow in the capillary increased with increasing

molecular weight ofHDPE.

Titomalio and Marrucci (74) studied flow-induced crystallization of HDPE using

a capillary apparatus equipped with a downstream reservoir ta develop higher pressure

drops at the exitof

the main capillary. The downstream reservoir was setat

a hightemperature to avoid crystallization at its hale, and it could be disconnected. Since the

flow in the capillary was mainly elongational at the capillary entrance and shear flow

along the capillary, the effects of different flows on crystallization temperature were

observed. Pressure applied ta the piston was monitored during extruding HDPE melts at

180°C out of a capillary. As a temperature decreased, flow-induced crystallization was

indicated by a sudden increase of pressure as shown in Figure 3.6. The temperature at

which the pressure abruptly increased was defined as the crystallization temperature (Tc).

The results in Figure 3.6 show the effect of shear rate on the temperature that crystals

appeared. High shear rates (high flow rate, Q) resulted in high Tc. The effect of die length

on Tc was studied. For higher length of the die, higher Tc was obtained. The thermal

study by means of DSC showed a single peak for a short die which related ta a highly

oriented material, whereas bimodal peaks were obtained for a long die. It was not clear

whether bimodal peaks were caused by different kinds of crystals or different positions at

which crystals appeared.

28



tD=1.5,"",

e_Q' C.U onf......

a:0.10'1

1 ~ O . 0 ~ 5

0.031

....

.....

L,"""00 0.0 .0

30 0

Polrm. . F

T:C

10

10

13 0 150 170

Figure 3.6 Pressure Vs temperature in the upstream reservoir with 1.5 mm capillary

diameter.

Ness and Liang (75) studied the influence of temperature and shear rate on the

flow behavior of high-density polyethylene (HDPE) melts using a constant shear rate

type capillary rheometer. Extrusion experiments were carried out in which the test

temperatures varied from 160-200°C and shear rates varied from 50-1000s-1• The

molecular chains of crystallizable polymer melt were extended along the flow direction

and aligned in the entrance-converging flow zone. This caused flow resistance, resultingin an increase in pressure losses and shearstress. They suggested that factors affecting

flow-induced crystallization are: temperature, temperature gradient, flow rate, and

channel geometry.

29



- ; l4

~ '12

....,.. :J lO

8

o A/:,. B

200 400

(a)

800 lOOO

5.4

5.2

......

5.0:J..

4.8.-1

4.6

4.4o

2.2 2.4 2.6 2.8 3.0 3.2

-1lo g y..,(s )

(b)

Figure 3.7 (a) Apparent flow curves for the samples (b) The sample flow curve

Tan et al. (76) investigated the phenomenon of flow-induced crystallization of a

linear polyethylene above its normal melting point, using a biconical rheometer. They

studied nucleation rate by monitoring the incubation time. The incubation time (ti) was

defined as the time obtained by extrapolating the initial slope of stress increment. Based

on the nucleation rate and degree of supercooling relation proposed by Hoffman and

Lauritzen (21), the nucleation rate was replaced by the reciprocal of incubation time.

Equation 3-1

where N' is a constant term which includes the entropy of activation for interfacial

transport divided by the weight of stable nuclei formed at the time tj.~ F W L F

is the heat of

activation for transport according to the WLF equation; ~ H is the heat of fusion per unit

volume; cr, cre are the lateral and end surface energies; and TID0 is the melting point of

100% extended chain crystals.

30



It was found that the nucleation rate increased with increasing shear rates, as

illustrated by fitting of experimental data using Tm0equal to 160°C, as shown in Figure

3.8.

134 1 3a 140 14a

2.4 67.575/SEC.

....Q3-030ISB:.

tl: D 1.!5t5/SEC.

2!le.l....

i i i.

.Ji 1.6u.<1

+1.2

;:::i5 08S

4 6 .8 lO 12

J!iLT'AT)'

Figure 3.8 The use of incubation time as a measure ofthe nuc1eation rates (76).

3.2.2 Molecular structures and morphology

The molecular conformation of PE melts during flow was observed directly by

Chai et al. (77). The PE resin was melted and sheared in a Linkam shearing ceIl, and the

molecular structure was monitor using a Raman microscope. A series of shear rates from

0-50 S-l were applied to the samples under isothermal conditions. The Raman spectra of

sheared PE melts showed all-trans Raman bands at 1065 and 1130 cm-l, as a result of

molecular orientation. These bands did not appear in PE melt under the quiescent state.

According to this study, the all-trans bands could be c1early observed at shear rate of 15

s-l and higher shear rates. The intensity of the all-trans bands increased with increasing

shear rates. They conc1uded that flow-induced crystallization occurred, and this

conc1usion was supported by the fact that the all-trans bands could linger for several

hours after the cessation of shear.

31



Molecular orientation in a continuous PE melt flow was observed by Bushman

and Mchugh (78). In this study, extensional flow was produced by a four-roll-mill flow

equipped with an optical window that allowed birefringence and scattering dichroism

measurement. High-density polyethylene (HDPE) was used as the dispersed phase and

linear-low density polyethylene (LLDPE) was used as the carrier phase. A low extension

rate of 0.01-0.05 S· l was continuously applied to the sample under the isothermal

condition. The crystallization was detected from an increase in birefringence intensity

and the rapid drop of dichroism intensity. The crystallization induction time and rate of

crystallization were determined. It was apparent that the induction time decreased as

extension rates increased.

X-ray patterns of sheared PE melts during shear strain rate of 43-1383 S· l in a

coaxial cylinder rheometer showed the orientation of crystallites reported by Nagasawa et

al. (79). The orientation of crystallites changed gradually from isotropic to a-axis

orientation and then to c-axis orientation (fiber structure) with increasing shear rates.

Additionally, electron micrographs revealed that the lamellar crystals grew perpendicular

to the direction of shear strain. This observation was in agreement with the morphology

of PE melts investigated by Krueger and Yeh (66) and Bassett et al. (80). Well-oriented

PE lamellae perpendicular to the flow direction were observed under shear rate of 10 S· l

(81). Shish kebabs with their linear cores and transverse planar lamellae were observed

between two parallel and coaxial circular glass plates under shear rates of 30 S·l.

Using two parallel plates with longitudinal movement, Monasse (82) observed an

elliptical, row morphology of PE aligned in the shear direction during sheared melt

experiments with the maximum shear rate of 4.2 S·l, compared to the ringed, isotropic

spherulites randomly spread in samples in the quiescent condition.

From the fiber-pullout technique, the morphology of pp melt during shear was

reported by Duplay et al. (83, 84), using a fiber velocity of 350 !-tm/s and Jay (85), using

fiber velocity of 78 and 350 !-tm/s. Both a-phase columnar and a-monoc1inic phase

spherulitic structures were found during shear, with a concentration of colurnnar

structures near the fiber, and with a-monoc1inic phase spherulites located far from the

fiber. Under static conditions only a-monoc1inic phase spherulites were found.

32



3.2.3 Crystallization kinetics

3.2.3.1 Induction time

The reductionof

the crystallization induction timeof

PE melts compared to thatunder quiescent conditions was reported by Bushman and Mchugh (78), Jay (8S) and

Masubuchi (86). Planer extensional force with extension rates of 0.01-0.0S S- l was

applied to PE melt by using four-roll mill flow cell equipped with an optical window

(78). The crystallization of the sample was followed by the change of birefringence (Ll').

It was found that shorter induction times were obtained with higher shear rates as shown

in Figure 3.9.

Jay (8S) investigated the effect of shear on induction time using a fiber-pullout

technique with fiber speeds of 78 and 3S0 /lm/s. The experiments were conducted for two

different molecular weights and at two different isothermal crystallization temperatures

(12S0C and 130°C). It was found that the higher shear rate gave the shorter induction

time at both crystallization temperatures, and the same trend was obtained for two PE

samples.

140

130

120

3110

Ql

S 100E:::t:: 900

uBO;:l

"1::l.s

70

60

qO

40 0

°

234 5 6 7 B 9

ô' ......... , x 10 '

Figure 3.9 Induction time to crystallization at 131.6 OC versus carrier phase birefringence

for several indicated droplet deformation rates (78).

33



Lagasse and Maxwell (87) evaluated the relation between induction time and

shear rate, as flow induced crystallization occurred. The results showed that the induction

time decreased rapidly with increasing shear rate when the shear rate was greater than

1 S·I, and the induction time remained high (10-100 s) when the shear rate was smaller

than 1 S·l.

The in situ thermal analysis during steady shear induced crystallization of pp was

studied by Masubuchi (86) by using the shear flow thermal rheometer. The evolution of

crystallinity was analyzed using the Avrami equation. A drastic decrease of induction

time with increasing shear rate was observed. Crystallization developed faster at high

shear rates as shown in Figure 3.10.

6000

0.0 ï -= . . . . . . - . .. . ; ; . . .. ; . . . - r - - - - :: ; ' """"- - - - - r - - - - - - r - - - - '

{} 20ŒJ 4000t (sec)

Figure 3.10 Relative crystallinity at Tc=l42.5 oC under various shear rates.

1.0 _---'7""-----:..------:-----:0.-------,

0.2

.-..0.6-'<..

0.4

0.8

3.2.3.2 Nuc1eation rate

Few in-situ measurements conceming the density of nuc1ei formed during shear

were reported (79, 85, 88). The nuc1eation density and rate were strongly enhanced by

shear. This can be explained by two thermodynamics aspects. Shear causes an increase in

the free energy of the melt (7) and a decrease in entropy (79).

Ulrich (88) observed the nuc1eation behavior of sheared Poly (ethylene oxide)

(PEO) using a paralle1-plate rotational rheometer under a polarizing microscope. During

34



the experiments carried out under different shear rates and temperatures, nuclei were

observed through a microscope and pictures were taken. The particles per unit volume

were counted as a function of time, and the plots of density (particles/cm3) versus time

were recorded at different temperatures. At the same temperature, fast nuc1eation rates

were obtained under high shear rates, as illustrated in Figure 3.11. It was found that the

experimental data under quiescent condition could be fit very weIl with a linear function

according to equation 3-2.

l nN'= InN _ M _ I:1UTm

c RT TI:1TEquation 3-2

where N' is the nucleation rate; Ne is a constant; I:1E is the activation energy ofmolecular

transport, and I:1U is a term containing lateral and end interfacial free energies of nuclei

10.0

9.0

•InN8.0

7.0 228-1

12 8-1

6 8-1

o8-1

0.07 0.08Trn/TÔT

6.0 '--------'------'----

0.05

Figure 3.11 ln N' Vs Tm/T (I:1T) for different shear rates (74).

35



Nonlinear best-fit curves were drawn for the data under shear conditions. The deviations

in the condition under shear were believed to result from the additional supercooling

from stress caused by elastic orientation. The nucleation rate was linear with shear rate at

constant temperature as shown in Figure 3.12. This relationship was deseribed by

equation 3-3.

N = a+by Equation 3-3

where a is the nucleation rate at zero shear.

16050.4 oC

120N( partides )x l0-2

sec.cm3

80

51.6 oC

53.8 oC' --- ' -- ' --- '--- . .L.. .- l--- ' ---l--l. .-J. .. . . . . .L--- ' ---l-

24

40

Figure 3.12 Nucleation rate as a funetion of shear rate (74).

By eonsidering the change of entropy in the oriented state (6.so) as a function of

the birefringence ( ~ n ) , the ratio of the rate of nucleation in an oriented melt to the rate in

isotropie melt was determined by Nagasawa (79).

36



3.2.3.3 Growth rate

Many researchers reported that shear contributed to higher growth rates (82, 83,

85). The fiber-pullout results of Jay et al. (85) showed a pronounced effect of shear on

growth rate for high molecular weight PP, whereas only a small effect was found for low

molecular weight PP. The evolution of the solid layer under different shear rates is

depicted in Figure 3.13. The growth rate under shear condition compared to that under

static condition was shown in Figure 3.14. The significant increase in growth rate only

occurred at high shear rate.

Tc= 12S·C: v f= 3SQ J,lm s·1

F-'' '---------Fibrc - - - -_ -1

20

radiusr------------------,(I-lm)

40

ZOO cime (s)50OOU

O'-----.L-__ . .I .--__ . . . l -__ .....I..-__-. J

{)

Figure 3.13 The evolution of the solid layer ofPP (85).

Growth r : : - r a : : . : t ; e ~ ...,

(j.1.m s-l)

.'-0.1

- - . ~ Veo: 350 IJ.m S"

-,.- . _ , . ~ V

f", 781J,m $-1

O.QI'--..L.-- '- - --- ' ....

125 130

Figure 3.14 Growth rate measurement as a function of crystallization temperature and

fiber velocity (85).

37



Using two parallel plates with longitudinal movement at 4.2 S-I, Monasse studied

growth rates in the direction of applied shear (82). The growth rate of a PE melt increased

significantly with increasing shear rate in all directions, as shown in Figure 3.15.

40& - . .- - - . . . . 1 . - - - - . - . -- - - - - ' -- - - - - 1 - - - - '

o

-Ill 1

E::L

Figure 3.15 Growth rate measurements of Gx, Gy and Gz as function of shear rate (82).

The influence of shear on growth rate was confirmed for pp melt using the fiber

pullout technique with a constant fiber velocity of 350 ~ l . I n / s (83). The growth rate under

shear was higher than that under static conditions by almost a factor of 7.

38



4 Scope and Ç)bjectives

In-line measurements of crystallization kinetics of PE resins under shear were

presented by many researchers (50, 51, 76, 79, 82). New systems, with automatic

sampling, to study crystallization kinetics under shear have been proposed (60,61). Sorne

effort was also made to link experimental data on shear-induced crystallization of melts

with real processing conditions by using a capillary rheometer (74, 75). However, flow in

capillaries involves a variable shear rate field. This could lead to complex crystallization

behavior. Thus, usually the data relate to overall crystallinity, and cannot provide

profound insight into the effect of shear crystallization kinetics.

The Linkam shearing system provides a simple constant steady shear flow, in

which factors affecting crystallization can be easily controlled. The following aspects of

the crystallization kinetics of various PE resins during shear were studied in the present

work.

1. Observation of the spherulitic morphology ofPE resins during shear

2. Study of the effect of shear on spherulitic growth rate of PE resms and

comparison to the quiescent condition

3. Study of the effect oftemperature on growth rate under shear condition

4. Application of the Lauritzen-Hoffinan equation to the experimental data

regarding the effect of shear on spherulitic growth.

39



5 Materials and Methods

The resins and instruments used in the present study are described in this chapter.

Linear low-density polyethylene (LLDPE) resins were used since they are important

product of Canadian polymer industry. Moreover, the growth of polyethylene spherulites

can be easily and accurately monitored under the polarized light microscope. A Linkam

shearing cell and a polarized light microscope were used in this study.

S.l Linear low-density polyethylene resins

Various linear low-density polyethylene (LLDPE) resms were used. The

experimental resins were supplied by NOVA Chemicals, Calgary, Canada. They were

obtained by either metallocene or Ziegler-Natta catalyst polymerizations. The resins

contained butene, hexene, and octene co-monomers. The characteristics of the resins, as

supplied by NOVA Chemicals, are shown in the Table 5.1.

Table S.l Physical properties of resins used in the study

Resin Co- method Co- Branches Mn*E-3 Mw*E-3 Meil MwlMn Density

monomer monomer PerKC (g/mol) (g/mol) (g/em3)

(%)

H Butene SoIn/ZN 3.80 18.90 24.9 120.0 54.7 4.8 0.9190

C Hexene SoIn/ZN 3.77 18.87 36.0 111.3 63.3 3.1 0.9234

G Oetene SoIn/ZN 3.20 15.80 17.0 106.0 42.4 6.2 0.9200

L Oetene SoIn/ZN 2.80 14 25.9 114.0 54.3 4.4 0.9222

l Oetene SolnIMet 5.00 24.80 22.0 53.0 34.1 2.4 0.9070

J Oetene SolnIMet 3.20 15.80 38.0 70.0 51.6 1.8 0.9180

Mn: Number average moleeular welght

Meff: Effective moleeular weight,Mer (MnMwO.5

ZN: Ziegler Natta eatalyst

S.2 Instruments

Mw: Welght average moleeular welght

SoIn: Solution polymerization

Met: Metalloeene eatalyst

The observation ofmorphology and the measurement of growth rate under steady

shear were performed through a polarized light microscope in conjunction with the

40



shearing cell. The shear effect was produced by a Linkam shearing cell. The schematic of

the experimental setup is shown in Figure 5.1.

Camera

DData Acquisition

Computer

Figure 5.1 Experimental setup

Camera Interphase

Temperature and motor

controller

1 1Polarized light

Microscope

Shearing Cell

5.2.1 Olympus polarized light microscope

The visualization was conducted with an upright polarized light microscope

(Olympus system microscope model BX50). Magnifications of 20x and SOx were used,

depending on the characteristics of the materials. For instance, resin G gave large

spherulites; therefore a magnification of 20x was used to follow the experiments. The

magnification of 50x was used in the study of resins C, H, J, L, and 1. During the

experiments, photographs were taken with a video camera (Sony Power HAD 3CCD

color), and the data were sent to a data acquisition computer through the camera adaptor

(Sony CMA-D2).

5.2.2 Linkam shearing cell

The shearing cell is mounted on the microscope. Resins are heated and sheared

simultaneously using the Linkam shearing cell (CSS450) (89). The specification of the

Linkam shearing cell is shown in Table 5.2. Figure 5.2 and Figure 5.3 give a photograph

and a sketch of the Linkam shearing cell, respectively (89,90,91). The main components

41



of the shearing cell are a top plate called "lid" and a bottom plate called "base". The

sample is loaded between the top and bottom highly polished quartz windows. The top

and bottom windows are parallel to within 2 f-lm. They were attached to the lid and base

respectively. The bottom window is attached to a metal dise, which rotates under thecontrol of a stepper motor. The top window is beveled to aid c1amping and to ensure it

does not move as the bottom window rotates against it.

Two motors are connected to the bottom of the base. One motor rotates the

bottom window, and the other moves the lid up and down. The silver block heaters are

located on both the lid and base, and are in thermal contact with the windows.

Thermocouples, attached to the interface between the heaters and windows, measure

temperatures, and the signal is sent to a temperature controller. The temperature

controller is connected to the shearing ceIl, and LinkSys 2.27 software was used to

operate the shearing cell and temperature program. The CUITent top or bottom temperature

of the shearing cell could be read from the LinkSys program.

The gap between the windows could be set to any value between 5 and 2500 f-lm.

The vertical movement of the lid could be controlled by the stepper motof. Reference

positions for the upper and lower limits were set by sensors in the body and lido

Table 5.2 Specification ofLinkam shearing system

Features Unit Ranges Resolution

Temperature oC Ambient-450 1

Heating rate OC/min 0.01-30 1

Holding times mm 1-9999 1

Gap setting f-lm 5-2500 1

Velocity Rad/sec 0.001-10 0.001

Shear rate S-l 0.003-7500 0.001

Sample field diameter mm. 30 -

Observation diameter mm. 7.5 -Viewing zone diameter mm 2.5 -Objective lens minimum working mm. 7.4 -distance

Condenser lens..

working 10mlmum mm. -distance

42



Figure 5.2 Photographs ofLinkam shearing ceIl

Lid

Observation diameter

7.5 m m ~ : : . - -

j Viewin

: ----jr-- 2.5mm

, Top window

Base

o

Rotating base Bottom window and sampIe loading

+ - ~ - - - , 4 - - G a p adjusting screws

Gap adjusting motor

Bottom window rotating motor

Figure 5.3 A sketch of the Linkam shearing ceIl

5.2.3 Linkam shearing cell setup

After mounting the shearing cel1 onto the microscope, the observation field had to

be aligned into the light path. The condenser concentration of the microscope was

adjusted to center the optical path by using a 10x objective lens, and the size of field

43



diaphragrn was detennined. The parameters discussed in section 5.2.4-5.2.8 had to be set,

in order to ensure that accurate data are obtained.

5.2.4 Zero point calibration

The zero point was the point at which the top window touched the bottom

window. This means that no gap existed between the two windows. PracticaIly, the zero

point setting was established by, first, drawing lines on the top and bottom windows, and

then winding the lid down until both lines were in the same focus. This zero position was

recorded by the sensor.

5.2.5 Lidposition

The position of the lid, e.g. open or c1osed, had to be adjusted to be in agreement

with the lid indicator in the LinkSys software. After the zero position had been obtained,

the shearing stage was connected to the controller and the software. The lid and base of

the shearing cell were connected together by a screw and the sensor recognized the c10sed

position of the lido This was important, because the speed motor would not operate if the

lid were indicated open.

5.2.6 Reference position

After the zero point and the lid position were set, the vertical motor moved the lid

up to 2500 ~ m which was a reference position specified by the LinkSys program. This

was also verified by using a micrometer to measure the gap. The reference position was

also recognized by the sensor.

5.2.7 Gap setting

The gaps of 0 and 2500 !lm were verified by focusing the microscope and using a

micrometer, respectively, as mentioned in section 5.2.4 and 5.2.6. Any gap set between 5

to 2500 ~ was obtained automatically by the LinkSys program. In order to verify the

44



gap setting, the difference of the reading scale when focused on the top and bottom

window was recorded. This difference reflected the actual gap size between the two

windows. Figure 5.4 shows the re1ationship of the difference of reading scales from the

microscope and the gap size adjusted by the program. A linear re1ationship with an R2

of

0.9999 was obtained. Therefore, the gap setting accuracy of the LinkSys program was

verified.

3000 , ,

-1<",2500

.;

~ 2 0 0 0...."Cl

..

'= 1500

=1000.......

"Cl

-=E-< 500

y = 0.9946x+ 6.4778

R2 = 0.9999

3000500000500gap (nm)

100000

O$'-----,-----,--------.-----.--------.------l

o

Figure 5.4 The relationship between the reading scale and gap width. (*The difference

between reading scales of the microscope when focusing on the top and bottom windows)

5.2.8 Temperature calibration

Temperature calibration was done to verify the accuracy of the temperatures

obtained by the temperature system of LinkSys program. Several temperatures were set

and the actual temperature of the shearing stage was measured using a thermocouple. The

actual temperature was then compared to the temperature obtained by the program as

shown in Figure 5.5. It is worth noting that the temperature calibration was done without

45



loading a sample. Therefore, the difference between the sample temperature and the

reading temperature would be smaller in the stagnant case, because the thermal

conductivity of the polymer is higher than that of air.

140

-120'- 'ri)

<li

; 100

t

S' 80

as 60;ri)

<li 40 M = 0.9952R -0.0993

R2= 1

20

160400 80 100 120

Reading temperatures ( C)

400

O+------,----,--------.----,------,---.,---.----i

o

Figure 5.5 The relationship between measured temperature and reading temperature

obtained from Linkam shearing cell.

Let R= reading temperature which is the display temperature from Link8ys Program.

M= measured temperature which is the temperature obtained by extemal

thermocouple.

The actual temperature can be calculated from the equation: M=O.9952R-O.0993

46



5.3 Experimental procedures

The isothennal crystallization of LLDPE resins was carried out under quiescent

and shear conditions. Three types of experiments, namely the static condition, shear

condition at various shear rates, and shear condition at various temperatures, were

perfonned.

5.3.1 Quiescent condition

LLDPE resins in pellet fonn were loaded on the shearing cell at room

temperature. The sample was heated to 180 oC and the temperature was held at 180 oC

for 10 minutes to erase any thennal history. During this time, the window gap was set to

30 !lm. The microscope was focused on the top and bottom windows. The difference of

the reading scale is as shown on the curve in Figure 5.4. The focus was changed to the

halfposition between top and bottom windows aiming at the middle layer of the sample.

The middle layer of the samples was chosen to minimize wall effects. Additionally, this

made it possible to make measurements of growth rates at the same plane in aIl

experiments. As a result of the geometry of the cell, the shear rate varied in the radial

direction. However, the observation field of this instrument was fixed at a constant radius

of 7.5 mm. Accordingly, the shear rate at the measurement point (window) was constant

during any given experiment. Subsequently, the temperature was lowered at the rate of 30

oC/min until it reached four degrees above the equilibrium melting temperature (Tfi c,n *).

Then the temperature was held for 5 minutes to ensure that no temperature lag between

the sample and recorded temperatures. The sample was cooled again at the same rate to

the desired crystallization temperature. The point at which the temperature reached the

crystallization temperature was considered the initial time (1:0). The evolution of crystals

was photographed from the initial time to the end of the experiment. A new sample was

used for each crystallization experiment. A schematic of a typical temperature profile isshown in Figure 5.6. The temperature lag between the set point and the measured plate

temperature during the final cooling appeared to be insignificant.

47



200

-160

U-; 120

•S' 80

40

10 min

isothermal c stallization

room temp

600000

0+-----.,-----,------,------,-----,........-----1

o 30

time (min)

Figure 5.6 A typica1 set-point temperature profile during experiments

The equilibrium melting temperatures and the crystallization temperatures of the

LLDPE resins used in this study are shown in the Table 5.3.

Table 5.3 Equilibrium melting temperatures and crystallization temperatures of the

LLDPE resins used in this study

Resin Trnc,n TCl TC2 ~ T ~ T (OC) ( OC) (OC) (OC) (OC)

H 128.3 113.3 116.3 14.9 12.0

C 130.6 116.3 119.3 14.3 11.3

G 131.1 116.3 119.3 14.8 11.8

L 131.8 113.3 117.3 18.5 14.5

l 113.6 95.4 99.4 18.2 14.2

J 123.6 105.4 109.4 18.2 14.2

5.3.2 Shear condition at different shear rates

The effect of shear on growth rates in isothermal crystallizations was studied.

Shear effects were produced by the steady rotation of the bottom window, which was

48



driven by a step motor. The experiments were performed using the same procedure as

under static conditions, but shear was introduced to the sample at initial time (1:0), as

described in Figure 5.6. The growth rate was investigated under constant temperature at

the following shear rates: 0.25, 0.5, 0.75 and 1 S·l. A new sample was used for each shear

rate.

5.3.3 Shear condition at different temperatures

The effect of temperature was studied under shear conditions. Experiments were

carried out at a constant shear rate of 0.5 S·l. Temperatures were varied in 1°C steps in the

temperature region corresponding to regime l and II growth mechanisms.

49



6 Data Analyses

In this chapter, the data analyses performed in this study are described. The

method of determination of growth rate is outlined in the next section. The following

sections deal with the thermal history of the samples, and the temperature fluctuations

during the experiments. The procedures to estimate factors affected by shear are

described in the last section.

6.1 Growth rate

The photographs taken by the digital camera using the LinkSys program were

transferred to Microsoft Power Point software. The photographs were amplified 2500

times, in order to obtain detailed information. The diameter of spherulites was measured

using the circular object as shown in Figure 6.1. The diameter of spherulites in llm was

recorded as a function of time.

Gnly the diameters of the clearly defined spherulites were measured, because only

the spherulites in the middle layer were of interest, as mentioned in section 5.3.1. The

focus was set for the middle layer of the sample to minimize wall effects on growth rate.

Additionally, observing only clearly defined spherulites minimized measurement erroI.

The growth rate (llm/S) was obtained by applying linear regression to the

relationship between diameter (llm) and time (s). Therefore, the growth rate in this

experiment was based on the increment of the diameter of the spherulite as a function of

time.

The growth of the same spherulite was observed throughout a given experiment in

the quiescent state. However, under shear, the positions of spherulites changed.

Therefore, the same spherulite could not be observed. A global growth rate was obtained

under shear conditions.

50



Figure 6.1 The diameter measurement of spherulites using PowerPoint program to obtain

growth rate

6.2 Microsoft Power Point scale calibration

The dimensions obtained with Microsoft Power Point were calibrated usmg

LinkSys. LinkSys provided a reliable dimension bar with micrometer units (!lm), based

on the objective lens used. To calibrate the dimensions obtained in Power Point, ten lines

with different lengths (in !lm) were drawn, and then the picture was transferred to Power

Point. The 2500 times amplification was performed in the same manner as in the

experiments, and the lengths of the resulting lines were measured using Power Point. The

average scale of 1 inch in Power Point is equal to 4.734 !lm for the 50x objective lens and

1.877 !lm for the 20x objective lens. The actual observation area was 93.87xI25.2 !lm.

6.3 Experimental procedure verification

Two potential issues: thermal history and temperature fluctuations, are discussed

in this section. Since the thermal history of the sample cau distort the experimental results

51



it is necessary to ensure that the previous thermal history of the sarnple is erased.

Additionally, the temperature fluctuations during each experiment should be taken into

account because they can lead to misinterpretation of the experimental results, especially

when shear is applied at different temperatures.

6.3.1 Thermal history

Ta verify that holding at 180aC for 10 minutes was sufficient ta erase the thermal

history of the sample, four experiments were carried out by changing the holding

temperature and holding time as follows: in experiment A the sarnple temperature was

held at 180aC for 10 minutes, in experiment B at 200aC for 10 minutes, in experiment C

at 180aC for 15 minutes, and in experiment D at 180aC for 5 minutes. The resulting

variation of spherulite diarneter as a function of time after cooling ta the desired

crystallization temperature is shawn in Figure 6.2.

o A(180C-1Omn)

1::. B(200C-10 rrin)

o C(180C-15mn)

x D(180C-5mn)

14

13

12

11

---e10=- "

l-o

lU 9....

lU

e 8...

Q7

6

S

4

SO 100 ISO 200

time(s)

2S0 300 3S0

Figure 6.2 Diameter as a function of time of four experiments (Resin J at Tc= 105.4 ac)

with different holding temperatures and times.

52



From Figure 6.2, it can be seen that experiments A, B and C gave similar results,

but a different result was obtained for experiment D. The growth rate determined by the

slope of the plot between diarneter and time is 0.0365 Ilm/s for experiment A, 0.0363

Ilm/s for experiment B and 0.0365 Ilm/s for experiment C, whereas the growth rate

obtained for experiment D is 0.0304 Ilm/s.

It can be concluded that holding the temperature at 180°C for 10 minutes is

sufficient to erase the previous thermal history of the sarnple. A higher temperature or

longer holding time is likely to cause thermal degradation in the sarnple, especially if the

sample is heat sensitive.

6.3.2 Temperature fluctuations during experiments

The variation of temperature profile during an isothermal experiment is recorded

by LinkSys prograrn. A typical sarnple temperature profile is shown in Figure 6.3.

117.1

'1'" .

·l·········· -.............. . >- - ,. 117.0

.. '" . f-116.9 T

12:22:092:16:52

Time (h:m:s)

em

. . . r . . .. . ..... 1 . .. .. of - 116. 8 p

........................................................ ; . j...... . ···················l················ f- 11 E;7 C

l ;

......................................................····t················································· + ···········f···············+ 115 5

f ---T---r-r--r-"" '-T""" '"1-+

i-r--r-"" '-T""" '"1---r-r-- i ' - --r-r--r-" '--T""" '"1r--T"-+' -r-.. . .- '- 116.5

12:11

1:362:06:07

Figure 6.3 Sample temperature profile during the experiment.

53



From the temperature profile recorded by LinkSys, the standard deviation of the

temperature is on the order of about 0.1 oc. Due to this temperature control limitation, the

experiments were performed at temperature intervals of 1°C.

6.4 Estimation of factors affected by shear

The modified Lauritzen-hoffrnan (LH) equation and the related theoretical

consideration were discussed in section 2.3.5. The natural logarithmic form was

employed and TmC,n* ( see section 2.3.2) was used in place ofTmo in the calculation of the

degree of supercooling. Thus, the growth rate dependence on temperature was described

by equation 6-1.

lnG+ Q; = lnG _ [ ~ ] [ T;'"* ]RT 0 TC.n* T t11'l'

c m c J

Equation 6-1

The naturallogarithm of the growth rate (G), obtained as described in section 6.1,

was plotted as a function of Tmc,n* / Tct1Tf. A value of the diffusion energy barrier

(QD*), equal to 5736 Cal/mol (92) for polyethylene, was used in the calculation. This

expression showed the effect of temperature on growth rate under quiescent conditions.

Under quiescent conditions, the plot fol1owed the LH theory. The results obtained for

shear conditions appeared to fol1ow the L-H theory, except that there was a simple shift

above the data obtained from quiescent conditions. Therefore, the value of the diffusion

energy barrier (QD*), which is affected by shear (88), was determined for the shear

experiment by a least square fit to shift the data under shear to superimpose on the lines

describing the quiescent data and shear data for the same temperature. Microsoft Excel

was used for this purpose.

54



7 Results and Discussion

7.1 Morphologica lobservat ion

7.1.1 Quiescent crystallization

Isothermal crystallizations were perforrned under quiescent conditions at various

crystall ization temperatures. The sample was photographed under polarized light at

predeterrnined time intervals from the initial time (10) to the time at which the boundary

of spherulites could not be observed in the field of view. Time intervals used for

experiments under low and high crystallization temperatures were 4 and 12 s,

respectively.Two isotherrnal crystallization temperatures (Tet, Te2) were chosen, as indicated

in Table 5.3. The two temperatures should lie in different growth regimes, according to

LH theory: Tcl represented the behavior in Regime III and Te2 in Regime II. The two

sketched temperatures also represented the same degrees of supercooling (about 14 and

11°C) for resins H, C and G. They also represented the same degrees of supercooling (lS

and 14°C) for resins L, l and J. The experiments could not be perforrned at the same

degrees of supercooling in aIl cases, because at low temperatures, resins H, C and G

crystallized too fast to observe under the microscope. Therefore, the high degree of

supercooling (lSOC) could not be set for these resins. However, the crystallization

temperatures, Tel and Te2 , for resins H, C and G are in the Regimes III and II,

respectively. Typical photos for resins Gand J at the two different crystallization

temperatures under quiescent condition are shown in Figure 7.1 and Figure 7.2. The

photos of resins H, C, L, and l are shown in Appendix A.

55



Resin G 116.3°C

3 min

Resin G 119.3°C

5 min 7 min

10min 18 min 28 min

Figure 7.1 Photographs of resin G at two different crystallization temperatures at the

specified times under quiescent conditions.

56



Resin J 105.4 oC

2 min

Resin J 109.4 oC

4 min 6 min

17 min 25 min 32 min

Figure 7.2 Photographs of resin J at two different crystall ization temperatures at the

specified times under quiescent conditions.

The photographs show that the spherulites were circular at aIl crystallization

temperatures. The spherulitic morphology obtained was in harmony with the assumptions

of the LH growth theory (20) as described in section 2.3.5. In growth regimes II and III,

spherulitic morphology is obtained.

Banded or ring-type spherulites were observed for resins H, C and G at the later

stages of growth, as shown in Figure 7.3. The ring-type spherulites were observed for

high molecular weight polyethylene (M> 20,000), as reported by Mandelkern (33).

GeneraIly, spherulitic structures were observed for copolymers and structurally irregular

polymers, but they were not ofthe banded type (93, 94). The results for resins H, C, and

57



G, appear to be in agreement with the observation ofMandelkem (33), who observed the

banded spherulitic structure in branched polyethylenes. The spacing of rings depends

upon the degree of branching as well as on the crystallization temperature (95).

Unfortunately, the ring spacing could not be distinguished c1early because of the

thickness of the samples.

Figure 7.3 The ring-typed spherulite ofresin G at 116.3 oC

The observed dimensions of the spherulites were different depending on

crystallization temperatures and the resins themse1ves. Spherulites grew slower at high

temperature. It could be seen that the spherulites obtained at high temperatures were

smaller than those obtained at lower temperatures. The resin characteristics influenced

the dimensions of the spherulites. Resins C, H, Gand L were in the group of large

spherulites, whereas resins 1 and J were in the group of small spherulites (Figure 7.1,

Figure 7.2 and AppendixA).

According to the material properties, resins C, H, Gand L were based on Ziegler

Natta catalysts, whereas resins 1 and J were based on metallocene catalysts. The Ziegler

Natta catalyst polymerization normally gives non-uniformbranch distribution, providing

long segments in the main chain. These long segments promote crystallization, giving

58



larger spherulites than those of the unifonn branch distribution samples obtained from

metallocene catalyst polYmerization.

7.1.2 Crystallization under shear

Photos of the samples were also taken at predetennined time intervals under

shear. The results are illustrated in Figure 7.4, Figure 7.5 and AppendixA.

Resin G 116.3°C, 1 S-l

3 min

Resin G 119.3°C, 1 S-l

4 min 5 min

12 min 14 min 16min

Figure 7.4 Photographs of resins G at two different crystallization temperatures under

shear conditions.

59



Resin J 105.4 oC, 1 s-1

3 min 4 min 5 min

Resin J 109.4 oC, 1 S-I

18 min 19 min 20min

Figure 7.5 Photographs of resins J at two different crystallization temperatures under

shear conditions.

Figure 7.4, Figure 7.5 and AppendixA show that the spherulites remained circular

and grew larger in the radial direction. Therefore, it appears that for shear rates employed

in the study (0.25-1s-1) , shear did not change the morphology of polyethylene spherulites.

Monasse (82) observed elliptical morphology of polyethylene melts at the shear rate of

4.2 S-I. In this work, we attempted to carry out experiments at higher shear rates, but the

morphological observations could not be performed due to the short residence t ime of

60



samp1es in the Vlewmg window. Additionally, the ring-type morpho1ogy was still

observed in resins H, C and Gunder shear as shown in Figure 7.6. Again, large spherulite

were observed with resins C, H, Gand Land small spherulites with resins land J.

Figure 7.6 The ring-type morpho1ogy found under shear conditions (Resin G, 116.3° C,

1S-I)

The samp1es were observed under the microscope until the samp1e solidified.

Impingement occurred at long times, as shown in Figure 7.7. Impingement was observed

with all po1ymer samples crystallized under shear.

Figure 7.7 The impingement ofspherulites in the shear conditions. (Resin G, 116.3° C,

ls-1)

61



7.2 Growth behavior

The growth of spherulites crystallized from polymer melts under quiescent

conditions consists of three stages, as proposed by Bernuer (6). Initially, spherulites

develop from a single crystal. Then, a sheaf-like polymer bundle is formed, and

eventually a polycrystalline state is obtained as radial growth occurs. The growth pattern

is shown in Figure 7.8.

Figure 7.8 Stages in the development of a spherulite.

Three-stage growth was observed for PE melts under quiescent conditions.

Spherulites developed from a sheaf-like bundle and became a polycrystalline state as

shown Figure 7.9. Similar growth features were observed for the crystallization under

shear conditions as shown in Figure 7.10.

Figure 7.9 The growth behavior of spherulites. (Resin G at 116.3 oC, quiescent

condition)

62



Figure 7.10 The growth behavior ofspherulites. (Resin G at 116.3 oC, 0.5 S-l)

After full development, the spherulites grew at a constant rate in the radial

direction. This could be verified by the measurement of the spherulitic diameter as a

function of time. It was found that the diameter of spherulites increased linearly with

time, as shown in Figure 7.11. This observation is in agreement with the growth theory

leading to Equation 2-20 (6, 7, 33, 37). The constant growth rate was observed for

crystallization under both quiescent and shear conditions.

10

9

8

Ê7

2- 6...

al 5-l

E 4Il

C3

2

1

0

0 100 200 300

time (5)

400 500

Figure 7.11 The diameter as a function oftime ofresin l at 95.4°C

In the plots of the linear increment of the diameter as a function of time (Figure

7.11), the crystals became c1early observable at about 100 s. The induction time could be

63



found by extrapolation of the plots to the abscissa. The induction time is defined as the

period of time required before the development of crystals. The x-intercept value

suggests that immediately after this point, the crystals developed. In this study,

extrapolation yielded negative induction times. This means that the crystals had already

developed at time to, because of the low cooling rate (30 oC/min) that was used. However,

there were no clear indications of crystals at time to, as shown in Figure 7.12, because of

the thickness of the samples. It was necessary to employa thickness of 30 /lm, in order to

allow the motor to operate under shear conditions.

Figure 7.12 The polymer melt at time ta (resin L, 117.3 oC, quiescent condition)

7.3 Effects of shear rate on growth rate

As reported by many researchers, shear causes an increase in spherulitic growth

rate during isothermal crystallization under shear (82, 83, 85). The evolution of the

diameters of the spherulites was plotted as a function of time, as shown in Figure 7.13

and Figure 7.14, for resin H under crystallization temperatures 113.3 oC and 116.3 oC,

respectively. The resu1ts for resins C, G, L, land J are shown in Appendix C. These

figures show that the growth of the diameters of the spherulites was linear with time, for

both quiescent and shear conditions. A constant growth rate with time was obtained (6, 7,

64



37, 82). The growth rates under the different conditions were obtained from the slope of

the linear fit of the data using linear regression. The results are summarized in Table 2.1.

35050 200 250 300time(s}

15 , ·····················································ô.: ,

14 ô x

13x A/;;/;;

Ô X d""x liÊ12 ÔÔ x è 0 0ô X /;;/i 000 0 0

-211 ô x è 00 0 0CI) ô X ./\li 00 0 0~ 1 ÔÔ x /;;/S" 000 0 0"" x/;;/;;!:S. 00 00

9 ÔÔ X /;;/i 00 000

ô XX o ~ 000

c 8 0 0ô ~ , A L ê J o 000

7 ô x 4tr-' 0

65+------,----..,------,----,-------,

100

100 5-1 00.255-1 /;; 0.55-1 x 0.75 5-1 ô 1 5-11

Figure 7.13 Diameter as a function oftime under different shears (Resin H, 113.3°C)

16 , . . . . __ _-....- .. . ..-

14

-12

-..oS 10CI)

Eca 8c

6

120000 600 800 1000time(s}

4+----,-----,-------r-----,------,

200

1005-1 00 .255-1 /;; 0.55-1 x 0.755-1 ô 1 5-11

Figure 7.14 Diameter as a function oftime under different shears (Resin H, 116.3 OC)

65



"Table 7.1 Growth rate obtained under different shear conditions

•Shear rate Growth rate (J.lm/s)

(s-') Hl13.3 H116.3 C116.3 C119.3 G116.3 G119.3 L113.3 L117.3 195.4 199.4 JI05.4 JI09.4

0 0.0276 0.0107 0.0406 0.0115 0.0561 0.0151 0.1706 0.0201 0.0119 0.0019 0.0295 0.0022

0.25 0.038 0.0136 0.0483 0.0128 0.0736 0.0171 0.1803 0.0303 0.0169 0.0026 0.0322 0.0032

0.5 0.0495 0.0156 0.0571 0.0141 0.0832 0.0201 0.1907 0.0312 0.0186 0.0037 0.0361 0.005

0.75 0.0578 0.0171 0.0617 0.0152 0.1004 0.0215 0.2152 0.033 0.0198 0.0038 0.0363 0.0063

1 0.0650 0.0182 0.0672 0.0169 0.1099 0.0251 0.238 0.036 0.0202 0.0041 0.0446 0.0084

66



The growth rate increased with increasing shear rate. In most cases, experiments with

1 S-I shear rate gave a two-fo1d increase in growth rate over the quiescent case. According to

the replicate experiments to eva1uate reproducibility of growth rates, as shown in Appendix

B, the average standard deviation was 0.00097 flm/S which was quite small in comparison

with the increase of growth rate due to the shear effect.

The effect of shear on the growth rate has been exp1ained by the higher mo1ecu1ar

a1ignment in the melt upon shearing, thus causing a decrease in the entropy (79).

Additionally, the shearing or e1ongationa1 flow of crystallizable polymer melts causes

orientation or alignment of the molecules and an increase in free energy of the melt (7).

These factors contribute to faster crystal formation. The plots of growth rate as a function of

shear rate are shown in Figure 7.15.

It can be seen from Figure 7.15 that growth rates increase linearly with increasing

shear rate for aIl resins, in the range of shear rate included in this study. A similar trend for

the effect of shear on growth rate was reported by Tribout et al. (96) in post shearing

experiments of PP, as shown in Figure 7.16.

Figure 7.15 (e) shows that the growth ofresin l seemed to slow down, when the shear

rate increased up to 0.75 S-I. This could arise from the combined effects of branching and

co-monomer content. Resin l contained high levels of co-monomer and the branching content

was almost twice that of the other resins. The effect of stereo-regularity on growth rate of pp

was reported by Duplay (83). High chain regularity contributes to high growth rates of

polymers, under both static and shear condition.

67



0.02

t.l

0.016 M<0......tG

0.012 'ûi'

E2-0.008

oC

l0.004 e

"

0.8

oX

0.4 0.6

5hear rate (5-1)

o

X

0.2

0.018 0.07

0.016UM t.l 0.06

0.014 en M... ..;... ;:: 0.05

0.012 ....III tG

0.01 0.04

E0.008 2- ::l

'; ' 0.03

0.006 ë.=:

lO.020.004

'3e e" " 0.010.002

0

0.8

oX

X

0.4 0.6

shear rate (s-1)

oX

0.2

o t - - - r - - - - - , - - - - r - - ~ ~ ~o

0.08

U 0.07M

0.06...

! 0.05

2- 0.04CI

'§ 0.03

.=:

'3 0.02e" 0.01

(a) resin C (b) resin H

0.Q35 t. l

..,0.03 ...0.025 !

.!!!E

0.02 2-

0.015oC

0.01 le

0.005 "

0.8

········._····__ ·_··· • •M. ·M• • • 0.04

0.4 0.65hear rate (5-1)

0.2

+----,----,...---r-----,---+O

0.03

uOOT0.025 g 0.2

en

i 0.15

......0.02 tG

.!!!

r0.015 2-

.s ë 0.1 lIII

0.01.. .=:oC ll e 0.05e

".005 "

00

00.8

X

o

0.4 0.6shear rate (s-1)

0.2

0+ - - - - , - - - - - , - - - - - , - - - - - , - - - -+

o

0.12

.!!!E2- 0.06

.sIII

;: 0.04

3oC, 0.02

g 0.1<0...i 0.08

(c) resin G (d) resin L

0.4 0.65hear rate (5-1)

0.008t.l

0.007 :X c...

X 0.006 tG

0'ûi'

0.005 E::l

0.004 '; '

0 tG0.003 ;:

l0.002 e

".001

0.2

0.005 0.05

0.045U t.l

0.004 : 0.04lti

a l Cl.... ... 0.035'" tG

0.003 'ûi' 0.03E E2- 2-0.025

0.002 '* .s 0.02.

.=:

'3 j 0.015

0.001 0.. e 0.01

" "0.005

00

.8.4 0.6

shear rate (s-1)

0.2

O+- - - , . . . - - - , . . . - - - r - - - - - - , - - _+_

o

0.025

u:; 0.02a l

1iî X0.015

§. 0

'* 0.01.

.=:

0.005

"

Figure 7.15 The growth rate as a function of shear rate at two different temperatures

(a) resinC, (b) resin H, (c) resin G, (d) resin L, (e) resin 1and (f) resin J.

(e) resin 1 (f) resin J

68



G (!lm/s)

0.2

0.1

oo 2 YS·l)

Figure 7.16 Spherulite growth rate as a function of previous shear rate: 0 Tc= 133.9°C,

o Tc= 136.4°C, • Tc= 138.5°C (96)

7.4 Effect of molecular structure on growth rate

The effect of molecular structure (co-monomer type, co-monomer and branching

content, and bàmch distribution) on growth rate was considered. Unfortunate1y, it was not

possible to obtain resin samples with a systematic variability of molecular weight or other

structural variables. Thus, the effects of molecular structure could not be evaluated in a

detailed systematic manner.

The effective molecular weights (M eff=(M wMn)O.5 ) of resins were found in the range

of 40,000-60,000 for most resins. It was found by Kamal et al. (35) that the effect of

molecular weight on crystallization is large when the effective molecular weight is less than

10,000. As the molecular weight increases, the effect becomes smaller and insignificant

when it is close to or higher than 100,000. This may be attributed to the role of self-diffusion

in crystallization. Self-diffusion becomes independent ofmolecular weight at high molecular

weights (97). Since the resins included in this study have approximately similar and

sufficiently high effective molecular weights, it is likely that the effect of molecular weight

on growth rate would be small in this study.

69



A comparison of growth rates was made between the various resins, based on the

growth regimes and degrees of supercooling (11 oC, 14°C and 18°C), as shawn in Table 5.3.

Resins H, C and G (different co-monomer types, and co-monomer and branching contents)

are compared. They were obtained by solution polymerization with Ziegler Natta catalyst,

which normally gives a non-uniform branching distribution. Resin H at 116.3°C, resin C at

119.3oC and resin G at 119.3oC were compared under the same supercooling (11°C), in

growth regime II as shown in Figure 7.17.

o.03 . . . . . - - - - - - - - - - - - . - - . ~ - - - - - ~ - - - - ------. -.----- .. ---.---- -.- ,

oXo

oo

oGo)-0.015

.c

0.01

' -

C) 0.005

_0.025en-E 0.02-

O-t-----.-----,-----,---------r-----;

o 0.2 0.4 0.6

shear rate (s-1)

0.8 1

Figure 7.17 Plot of growth rate as a function of shear rate for resin Hat 116.3°C, resin C at

119.3oC and resin G at 119.3oc under growth regime II and supercooling 11°C

Figure 7.17 shows that the growth rate of resin G is higher than those of resins C and

H under both quiescent and shear conditions. The resin with low co-monomer and branching

content (resin G) yie1ds higher growth rates, whereas higher co-monomer and branching

content samp1es (resins C and H) give lower growth rates. It can be seen that the growth rates

of resins C and H are approximate1y the same, since they have similar co-monomer and

branching content. This can be explained by the observation that molecular irregu1arity of the

polymer chains impedes crystal growth and crystallization (83, 98), and branches are mainly

70



rejected into the intercrystalline regions (33). These results are in agreement with the study

by Duplay et al. (83). They studied the effect of shear on growth rate of pp with different

stereo regularity. They found that high regularity samples gave relatively high growth rates.

The effect of molecular structure on growth rate can also be explained by using the

self-diffusion mechanism. Klein et al. (98, 99, 100, 101) studied the effect of molecular

structure (branching content) on the self-diffusion coefficient (D) of saturated polybutadiene

(PBD) melt in terms of an effective monomer mobility (Do). Do represents friction effects on

the chain segments as they move locally under Brownian motion. They found that Do

decreases exponentially with increasing number of branches (nb) as (lIDo) oc exp (Bnb) ,

where B is a constant. The increase in branching content decreases effective monomer

mobility resulting in lower self-diffusion of molecules to the crystal front. Therefore, the

growth rate is lower for high branching content samples. Similar results were obtained for

resins H, C, and Gunder growth regime III and a degree of supercooling of 14°C, as shown

in Figure 7.18. The effect of co-monomer type was not clearly identified in this study.

0.12

0.1

-J)

- 0.08E;:,-)

0.06-J :

0.040

(!)0.02

0

0

<>

<>

0

0 X

X

OC

xH

0.25 0.5 0.75 1shear rate{s-1)

Figure 7.18 Plot of growth rate as a function of shear rate for resin G at 116.3°C, resin C at

116.3°C, resin H at 113.3°C under the same growth regime (regime III) and supercooling

(14 OC).

71



The effect of co-monomer and branching content is confirmed by comparing resin I

and J, which have similar co-monomer type and polymerization method (solution

polymerization with metallocene catalyst), under a degree of supercooling of 14°C (growth

regime II) and 18°C (growth regime III). The higher co-monomer and branching content

(resin I) gave a lower growth rate than resin J in both growth regimes, as shown in Figure

7.19.

1

X X

o 0

0.5 0.75shear rate(s-1)

X

o

0.25

0.05 T-····················································........................................................•................................................................. ,

0.045

ûi' 0.04

E 0.0352. 0.03

0.025

0.020.015(!) 0.01

0.0050+ - - - - - - , - - - - - , . . . - - - - - - , - - - - - - - ,

o

fOJ1bJJ

ooX X

ox

0.25 0.5 0.75

shear rate(s-1)

0.009 , .._ .

0.008

ûi' 0.007

0.006

2 0.005Cll

0.004

0.003t5 0.002

0.001

0+----.,----,.--------,------;

o

(a) (b)

Figure 7.19 Plot of growth rate as a function of shear rate for (a) resin 1 at 99.4°C and resin J

at 109.4°C under the degree of supercooling of 14°C (growth regime II) (b) resin la t 95.4°Cand resin J at 1Ü5.4°C under the degree of supercooling of 18°C ( growth regime III).

The effect of branch distribution on growth rate was evaluated by comparing the

resms obtained from Ziegler Natta (resin G) and metallocene (resin J) catalyst

polymerization. Ziegler Natta catalyst polymerizat ion normally produces non-uniform

branch distribution, whereas metallocene catalyst polymerization yields uniform branch

distribution. Both resins G and J have similar co-monomer and branching content. Theresults are shown in Figure 7.20. It can be seen that the non-uniform branch distribution

obtained from Ziegler Natta catalyst polymerization (resin G) gives a higher growth rate. In

the non-uniform branch distribution, there is high probability to have long segments ofmain

chains, which contributes to the crystallization process.

72



0.12 ~ . ~ - _ . ~ ~ - - ~ - ~ , ~ - ~ ~ - - - - ~ - - - · - - - - - · - - " ~ - - 11

cb0.1 0

i

-i)

- 0.08 0:::J

0- iCD

0.06u

XJ.c

0.0410i

Co'0.02

1

X X )K

0

0 0.25 0.5 0.75 1shear rate(s-1)

Figure 7.20 Growth rate as a function of shear rate under the degree of supercooling of 14 oC

for resin G and J

To investigate the effect of shear on growth rate, the percent increase of growth rate

with respect to that of the quiescent state was calculated. The comparison was made between

the resins that had a similar co-monomer type and method of polymerization but different co

monomer and branching content. On this basis, resins land J were compared under the same

supercooling. The plots ofpercent increase of growth rate relative to the quiescent conditions

are shown in Figure 7.21.

The percent increase of growth rate relative to that of the quiescent state was higher

for resin J. This shows a stronger effect of shear on growth rate in the polymer with the lower

co-monomer and branching content. This is probably because shear enhances both the self

diffusion of molecules and the molecular alignment. However, the self-diffusion of highly

branched polymers would be less affected than lower branched ones.

73



300CD"Cc::JO 250S c a ~ I t - 200.s:::: 0

'i mo .5 150-mOIt - 0o

100D CDfi) Q.ca :J

fi) 500c:.-

0

0 0.2

oX

0.4 0.6shear rate (s-1)

o

X

0.8

....................cp

1

Figure 7.21 Plot ofpercent increase of growth rate with respect to quiescent condition as a

function of shear rate under the degree of supercooling of 14 oC for resin l and J.

7.5 Effect of temperature on growth rate

Temperature has a large effect on the growth rates of spherulites in isothermal

crystallization. At low and high temperatures, growth rates of polymerie spherulites are

small. Two competing mechanisms are active. Diffusion is important at low temperatures and

thermal energy is important at high temperatures (6, 7, 13, 15, 20, 25, 33). At high

temperatures, polymer molecules have such high thermal energy that the chain deposition

onto the crystal front is hindered. As the temperature is lowered, molecules become

sluggish, resulting in an increase in growth rate. At sorne point, a maximum growth rate is

obtained. If the temperature is still lowered further, the molecules cannot diffuse to the

crystal front easily, causing a decrease in growth rate. The growth rate becomes effectively

zero below the glass transition temperature.

The effect of temperature on growth rate was investigated by performing the

isothermal crystallization at seven different crystallization temperatures under both quiescent

and shear conditions. For the quiescent condition, a plot of diameter as a function of time is

74



shown in Figure 7.22 for resin C. The spherulitic growth as a function of temperature for

resins H, G, L,land J is shown inAppendix D. Figure 7.22 shows that the slope of diameter-

time relation, which represents growth rate, increases with decreasing temperature. The

growth is still linear with time for the different temperatures. It is also seen that longer time

was required to observe the initial spherulites at high temperature. This suggests that long

induction times are associated with higher temperatures.

To study the effect of temperature under shear conditions, the shear rate was fixed at

0.5 S-1 and the isothermal crystallization at this shear rate was followed at varying

crystallization temperatures. The plot of diameter as a function of time, for resin C, is shown

in Figure 7.23. The pattern of behavior is similar to observations made in the quiescent

experiments.

15 , ;

12

-2-9...CI)I)E 6ca.-C

3

oo 200 400 600 800 1000 1200

time (s)

10114.3 C x 115.3 C b,116.3 C 0117.3 C + 118.3 C <> 119.3 C -120.3 cl


resin C, quiescent condition

75



15 -y - - - - - - ~ - . - - - - - -- ..- - - - - - - - - . - ..- - --- --- --..--.- --.- - . . . . . -- ~ - - - - . - - - - .. --.- .. ------ -- ,

12

-2.9....!CI)

E 6ca

c3

0+- - - - , - - - - - - , - - - - , - - - - , - - - - - , - - - - - - - -1

o 200 400 600 800 1000 1200time (5)

I0114.3C x115.3C l',.116.3C o 117.3C +118.3C <>119.3C -120.3C!


resin C, shear rate = 0.5 S-I.

The growth rates of the different resins at different crystallization temperatures,

under quiescent shear conditions are shown in Figure 7.24 and Figure 7.25, respective1y.

Figure 7.24 Growth rate as a function of crystallization temperature under quiescent

condition.

124

XGii

OC:

DL!

6H :

- J :

<> l ,i

o

0.25

0.2

E2.

015

. œ0.1

6C) 0.05 6 0 X

o + - - - ' < > ~ ~ 9 _ _ _ , - ~ - - - " - - " " " " " " " r - - ~ 6 _ , ~ - = ~ = L = - , = ~ - - - - - i94 99 104 109 114 119

Crystallization temperature (C)

76



124

xG

oC

DLLH-J

<>1

0.4 -l ' -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i " " " " ~ ,o

0.35

99 104 109 114 119

Crystallization temperature (C)

Figure 7.25 Growth rate as a function of crystallization temperature under shear (0.5 S-I)

The growth rate decreased dramatically with increasing crystallization temperatures

in both quiescent and shear conditions. The growth rate-temperature relation can be

described by the phenomenologicallaws, which have led in many crystallization theories to

the relation: G oc exp ( - K g / T c ~ T ) (7, 20, 38, 39, 88). As shown below the growth rates in this

work follow the exponential relationship depicted in the Lauritzen-Hoffman equation, for

both quiescent and shear conditions, but higher growth rates were obtained under shear

conditions. The results for resin L are shown in Figure 7.26. The results for resins H, C, G, 1

and J are shown in Appendix E. The effect of shear seems to be higher at high degrees of

supercooling, which is in agreement with the results ofUlrich (88).

77



0.4/':-, 160.55-1

_0.35 005-1

0.3E2. 0.25Q)

- 0.2'lS 0 6-

i 0.150 /':-,e 0.1

C) 0.05 0 60 d ê 6

0

112 114 116 118 120temperature (C)

Figure 7.26 Growth rate ofresin L under quiescent and shear condition (0.5 S-l).

7.6 Fitting of growth rate to Lauritzen-Hoffman equation

7.6.1 Quiescent crystallization

The modified Lauritzen-Hoffinan equation (see section 2.3.5) was applied to the

experimental data. The final modified LH equation is shownbelow:

lnG+ (-Q_:_J - lnG - ( _ K _ g - J ( _ T - , , ~ , , - - - , _ n . _ JRTe - 0 T ~ , n . Te!1Tf

Equation 7-1

The value ofQD* used in this study was proposed by Hoffinan (92) for a linear polyethylene,

based on the self-diffusion mechanism investigated by Klien et al. (98, 99, 100, 101). At

temperatures far above the glass transition temperature, the diffusion coefficient of polymer

molecules can be described by Eyring's free volume model as Doc A exp (-QD*/kT) (98,

102). A is a constant containing the mo1ecu1ar jump frequency and jump distance. For the

molecular motion of a polymer melt, the diffusion occurs by segmental movement, which

provides the basic steps for the overall translation. Therefore, Qo*= Erotation + 4nr*2y,where y

is an effective surface energy. The term 4nr*2y relates to free volume. Klien et al. (99)

reported that the diffusion energy barrier (Qo*) is dependent on molecular weight at low

78



degrees of polymerization, but it is independent of molecular weight for high degrees of

polymerization (N 10,000). Moreover, QD* depends on the free volume (98) which is

affected by the number ofbranches as shown in Figure 7.27. However, this effect can be seen

mainly in samples with high branch density. Due to the high molecular weights and low

amounts of branches in our samples, we assume that QD* is constant for all resins and equal

to the value for linear polyethylene, as proposed by Hof:fi:nan.

170

160

'>

150

140

130

/20

o 10 20 30 40 50Ethyl bratlchesi100 backbonecarbon units

Figure 7.27 Statistical segment volume (v*) and ethyl branch relation (98)

After applying the modified LH equation to the experimental data, a typical plot is

shown in Figure 7.28 for resin 1. Similar plots for resins H, C, G, Land J are shown in

Appendix F. It can be seen from the plot that the experimental data fall in growth regime II

(

TC,no Jand III, for the high and low values of m , respectively.

Tc/)'Tf

79



_ -9

E-10-

--11

a -12+(!)

s::: -13

y =-174.67x + 0.3602

R2=0.9998

y =-64.526x - 7.2623

R2 =0.9841

0.085.080.075

(1/K)

0.065 0.070

Tm*/(TcdTf)0.060

-14 +-----,------,----,-------,-------,----------1

0.055

Figure 7.28 Linear regression of the experimental data plot follows the modified LH

equation (resin 1)

Linear regression was performed on the experimental data under the quiescent state as

shown in Figure 7.28. The least square error coefficient of approximate1y 0.9 was obtained

for all samples (see also Appendix F). The slope change in Figure 7.28 signifies the presence

of regime transition. The transition from regime II to regime III was normally found in

polyethylene melt crystallization as reported by Hoffinan and Miller (39). This transition

arises from the same basic nuc1eation mode1 giving the spherulitic morphology. It was found

that the slope of the Lauritzen-Hoffinan plot in growth regime III is approximately twice that

of growth regime II (39). Similar values of the sIope change as those reported by Hoffinan

and Miller were obtained in this study for all resins (Figure 7.28 and Appendix F). The values

of Go in the units of Ilm/s and Kg in the units of Kelvin2

in growth regimes II and III were

obtained from the y-intercepts and slopes of the plots according to the modified LH equation.

They are summarized in Table 7.2.

80



"Table 7.2 Go and Kg in the growth regime II and III obtained from Iinear regression.

•

T C,n* Growth regime II Growth regime IIIIn

Resin (K) InGo Go (Jlm/s) Kg/Tmc, n* 2InGo Go (Jllnls) C n* 2

Kgfl (K ) Kg/Tm' KgIlI (K )

H 401.5 -6.0679 2.32E-03 55.465 2.23E+04 -1.2242 2.94E-01 118.44 4.76E+04

C 403.8 -5.2764 5.11E-03 60.322 2.44E+04 -0.3692 6.91 E-01 121.68 4.91E+04

G 404.3 -5.7371 3.22E-03 55.255 2.23E+04 -1.134 3.22E-01 113.4 4.58E+04

L 405 -2.7746 6.24E-02 103.05 4.17E+04 1.9402 6.96E+00 176.61 7.15E+04

1 386.8 -7.2623 7.01E-04 64.526 2.50E+04 0.3602 1.43E+00 174.67 6.76E+04

J 396.8 -2.7419 6.44E-02 128.8 5.11E+04 2.7278 1.53E+Ol 210.31 8.35E+04

81



Kg is a kinetic constant for the secondary nucleation. It expresses the temperature

dependence of the secondary nuc1eation rate. As shown in Table 7.2, different values of

Kg were obtained in the different crystallization temperature regions (growth regimes II

and III). At low temperatures (growth regime III), the secondary nuc1eation rate is faster

than the rate at moderate temperatures (growth regime II). From the values of K gII and

d b L · d H ffm (K 2boC5C5 J n d K 4boC5C5 e T (K gIlI purpose y auntzen an 0 an gI/ = an glIl = see

kMIm kMIm

2.3.5)), KgIl I is twice the value of K gII for a given polyrner. This is in agreement with the

results obtained in this study as shown in Table 7.2. The experimental results of Kg II and

KgIlI obtained are of the same order ofmagnitude as those ca1culated by Hoffrnan (92).

The pre-exponential constant (Go) relates to the segmental flexibility and

regularity of polyrners. Go = 0 for an atactic polyrner, and it is low for very inflexible

polyrners. The effect of molecular structure on Go can be seen by comparing resins l and

J (sarne co-monomer type and polyrnerization method). Resin l (high irregularity because

ofhigh degree of co-monomer and branches) gives much lower Go than resin J.

7.6.2 Crystallization under shear

The modified LH equation was applied to the experimental data obtained under

0.5 S-1 shear rate, by using the same value of diffusion energy (Qo*) as in the case of

quiescent crysta11ization. It was found that the experimental data fo11owed the LH theory

and fe11 in the growth regimes II and III. However, the values of InG+Qo*IRTc were

higher under shear conditions. This resulted from the higher spherulitic growth rates

under shear. The plot for resin l is shown in Figure 7.29. The difference between the

InG+Qo*/RTc values was higher than the experimental error shown by error bars.

Calculation of experimental error is shown inAppendixH.

According to the LH theory (7, 20), the rate constant (Go) depends on the

segmental flexibility and the regularity of the polyrner. Therefore, it should be the sarne

for a given polyrner and is not changed by shear effects. The kinetic constant for

secondary nuc1eation (Kg) reflects the temperature dependence of crysta11ization rate.

Thus, it is also not affected by shear. The diffusion energy barrier (Qo*) depends on the

82



rate of short-range transport of the crystallizing segments according to William-Landel

Ferry (WLF) equation (7). This is the only one parameter which could be affected by

shear. Ulrich and Price (88) proposed that the transport energy decreases with increasing

shear. They explained that the higher spherulitic growth rate under shear compared to that

under quiescent conditions is caused by the lowering of the diffusion energy barrier.

-8 , ,

- -9en-2. -10

l -et: -11

C Q" -12C>

L::-13

/05-1

0.55-1

/D

0.085.080.075

(1/K)

0.065 0.070

Tm*/(TcdTf)

0.060

-14 +-----r----,----.,---r-------,----j

0.055

Figure 7.29 The relationshipof

growth rate under shear rateof

0.5 S-I as a functionof

supercooling followed the modified LH equation compared to quiescent condition (resin

1).

The value of (QO*)shear under shear was estimated by minimizing the sum of

squared difference between the linear regression of quiescent data using (QO*)quiescent and

shear data using (QO*)shear . The solver in Microsoft Excel was used for this purpose.

After the QD* parameter was adjusted, the experimental data under shear superimposed

perfectly on the linear regression for the quiescent condition, as shown in Figure 7.30 for

resin 1. The Qo* was estimated for an resins, and the results are shown in Appendix G.

83



-8 , ,

- -9lA-2,.-10

....

-11:j;"-e

Cl -12C)

.5 -13

0.085.080.075

(1/K)

0.065 0.010

Tm */(TcdTf)

0.060

-14 +-- - , - - - - - - -c , - - - - - - r - - - , - - - - , - - - - i

0.055

Figure 7.30 The superposition of experimental data under shear condition onto the linear

regression of quiescent data after adjusting Qo* (resin 1)

The estimated values of Qo* at 0.5 S-I shear rate are shown in Table 7.3. The

value ofQo* is lower than the corresponding value in the quiescent state as expected.

Table 7.3 The estimated values OfQD* under shear condition of 0.5 S-I

Resin Co-monomer Polyrn-method QD*(0.5 S-I) (cal/mol)

H Butene Solution/ZN 5365±15

C Hexene Solution/ZN 5525±15

G Octene Solution/ZN 5390±11

L Octene Solution/ZN 5294±5

l Octene SolutionIMet 5291±55

J Octene SolutionIMet 5237±61

84



The decrease in the value of QD* under shear is about one-tenth of the value of

QD*under quiescent conditions. (QD*)shear was expected to have a similar value for all

resins, if it does not depend on molecular structure. However, the (QD*)shear values

obtained are different for the various resins. No publications propose the estimation of

activation energy under shear. The existing explanation describes the decrease of

activation energy due to the high energy of oriented melt compared to the original state

(7).

According to Eyring theory for viscous flow (20, 102), the segments of the

polymer chains can be considered as being in a pseudo-lattice. Under flow, the segments

must move to adjacent sites. Moving to the adjacent sites in flow, the segments have to

overcome an energy barrier. At a given temperature, the energy barriers under unstressed

and stressed conditions are schematically shown in Figure 7.31. Shear-induced self

diffusion was also reported in polymer suspensions (103, 104) and polymer melts (105,

106).

1 (b) Stressed

i

---- itt.G1 1----- __ 1-: 1

!i

>..10"....V iCiw i

(al Unstressed

Position Position

Figure 7.31 Schematic illustration of the potential barrier ( ~ G ) for flow in polymers (21).

85



8 Conclusions

On-line monitoring of isothennal crystallization under shear was perfonned.

Infonnation was obtained regarding morphology, growth behavior and growth rate. The

following conclusions can be made:

1. Spheru1itic morphology was not changed by shearing in the shear rate range under

consideration (0-1 S-I). The spherulites developed from single crystals and became

polycrystalline. Ring-type morphology was observed in resins H, C and G.

2. Spherulites grew unifonnly in the radial direction. The growth rate, based on

diameter increase was obtained by perfonning a linear regression on the diameter versus

time data. The growth rates were constant with time, in both the quiescent and shear

conditions. The growth mechanisms followed regimes II and III crystallizations, yielding

the expected spherulitic morphology.

3. Higher spherulitic growth rates were obtained under shear compared to the quiescent

growth rates, probably because shear contributes to higher molecular alignment resulting

from a lower diffusion energy barrier. A linear relationship was obtained between growth

rate and shear rate, in the shear rate range under consideration (0-1 S-I).

4. Lower growth rates were observed for the polymers with high co-monomer and

branching content (H, C< G and I<J). This observation assumes that the effect of

molecular weight on growth rates is negligible, when molecular weight is sufficiently

high (Meff > 10,000). The effect of molecular structure (co-monomer and branching

content) on growth rate can be seen under both quiescent and shear conditions.

5. The effect of branching distribution was observed. A non-unifonn branching

distribution sample, obtained with Ziegler Natta catalyst polymerization (resin G) gave

86



higher growth rates than the unifonn branching distribution sample, obtained with

metallocene catalyst polymerization (resin J).

6. Spherulitic growth rates under quiescent and shear conditions decreased substantially

with increasing temperature. The trend followed the exponential re1ationship between

growth rate and the degree of supercooling, as indicated by Lauritzen-Hoffman equation.

7. Shear seems to have a stronger effect on growth rate at higher degrees of

supercooling.

8. The modified Lauritzen-Hoffman equation was applied to the experimental data

under quiescent conditions. Curve fitting was perfonned, and the values of Go and Kg

parameters were obtained in growth regimes II and III. It was found that the value ofKgIlI

was approximate1y twice that of Kg1b and Go, representing the segmental flexibility, was

lower for the high co-monomer and branching content sample (resin 1) than that of the

low co-monomer and branching content sample (resin J)

9. The diffusion energy barrier (Qo*), which is the most likely parameter to be affected

by shear, was estimated from the data on crystallization under shear. For aIl resins, Qo*was lower under shear than under quiescent conditions.

87



9 Recommendations for Future Work

The following works are suggested for further research. Instrument limitations prevented

the present undertaking of these works.

1) Study of effects of shear on growth rates and morpho10gy at higher shear

rates(>1s-\).

2) Thinner « 30llm) samples should be examined to obtain more information on

induction time and nucleation behavior. The present shearing stage could not provide

shear rates to such thin samples.3) Information regarding the evolution of crystallinity and morphology under shear

could be obtained by connecting the shearing stage to a Raman microscope and/or an x-

ray diffraction system.

4) It is highly desirable to measure shear stress during experiments. This might make

it easier to explain the results. Furthermore, such an arrangement would facilitate the

estimation ofviscosity.

88



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93



I l Appendices

11.1 Appendix A

Typical photos of resin H, C, Land 1 at two different

temperatures under quiescent and shcar conditions.

Resin Hat 113.3 oC

330 s

Resin H at 116.3 oC

380 s 500 s

760 s 1060 s 1360 s

94



Resin C at 116.3 oC

185 s 195 s 235 s

Resin C at 119.3 oC

Resin L 113.4 oC

1000 s 1120 s

20 s 40 s 60 s

95



Resin L 117.3 oC

2 min

Resin l 95.4 oC

4 min 6 min

5 min 6 min 7 min

Resin l 99.4 oC

24 min 28 min 32 min

96



Resin H at 113.3 oC, 1 S-I

Re8in Hat 116.3 oC, 1 8-1

6308 7308

13308 14508 1700

Re8in C at 116.3 oC, 1 8-1

1658 2158 2208

97



ResinCat 119.3 oC, 1 S-l

830 s 1180 s 1230 s

Resin L 113.4 oC, 1 S-l

Resin L 117.3 oC, 1 S-l

4 min

30 s

5 min

40 s

6 min

98



Resin l 95.4 oC, 1 S-l

3 min

Resin l 99.4 oC, 1 S-l

12 min

4 min

16 min

5 min

20 min

99



11.2 Appendix B

The reproducibility of growth rate measurements and calculation

of standard deviationThe reproducibility of growth rate measurements was evaluated by randomly

performing duplicate experiments. The replicates were performed at least twice. Some

replicates were shown below.

5000000

45

40

35

Ê 301: ' 25CIl-Ë201lIë 15

10

5 10 EX1!xEx2O-l-----,-------,,...-----,---====;

100 300time(s)

Figure 11.1 Resin Gat 116.3°C under the shear rate of 0.25S-1

105

40 .., ,

35

30

' [ 25-..20

CIl

15o

o Ex1

'" Ex2

x Ex3

O+-- - - - - , - - - - - , - - - - - , - - - - '=====i

o 500 1000 1500 2000time(s)

Figure 11.2 Resin G at 119.3°C under the shear rate of 0.5 S-1

100



9

8.5

8

-:::s 7.5-Q)7-)

E c;;#. 6.5c ~

xX

5.5XX

\0 EX1\XEx2

5

100 150 200 250 300time{s)

Figure 11.3 Resin J at 105.4C under the quiescent condition.

14 -- - -.-.-.- - - -.-- -- - - - -.- -.- --- ..--.- --.- - - -.----

12

300 35000 250time(s)

150

2 10 EX1!XEx2

0+----,--------,------,-------,-==:::::;

100

Figure 11.4 Resin J at 105.4C under the shear rate of 0.75 S-l.

101



2600

1

6EX1

1.Ex2:

2400800 2000 2200time(s)

1600

10 -............... . -- - --- - - - - .

[jj!J ocPJ

8

-6-

(1).-(1)

E 4co.-c

2

0

1400

Figure 11.5 Resin J at 109.4C under the shear rate of 0.5 S·I

The standard deviation of shear rate was found by using the following fonnu1a.

nl:>2 _(LX)2stdev =

n(n -1)

The average standard deviation was obtained by the summation of standard

deviation divided by the number of the populations.

102



Il.3 Appendix C

Diameter as a function of time under different shear rates

1700 90 110 130 150t ime (s)

12 , , ,

11

_10

E2-9...

.eSQ)

7

0 6

5

4+ - - - - - - - - - , - - -- - . , - - - . . ., - - - - - - - , - - - - -- . , - - - - - - - - - -,

50

10 0 5-1 0 0.25 5-1 60.5 5-1 X0.75 5-1 <> 1 5-11

Figure 11.6 Diameter as a function oftime under different shears (Resin C, 116.3 OC)

9000000time (s)

300

13 , _._. ..- -' - _............................................................................ .._ -.

12

11-~ 1 -.. 9.eQ) SEct! 7o

6 65 6 6

64+--------,------,------,----------,

100

1005-1 00.255-1 60.55-1 X 0.75 5-1 <> 1 5-1 [

Figure 11.7 Diameter as a function of time under different shears (Resin C, 119.3 OC)

103



40

35

-30::::s

-..!25Cl)

E· ~ 2 0c

15!:i.

10

100 200 .300( )tlme 5

400 500

1005-1 00.255-1 l:::. 0.55-1 X 0.755-1 <> 1 5-11

Figure 11.8 Diameter as a function oftime under different shears (Resin G, 116.3 OC)

100000tPOO

( )me 5400

5+------- , ------- , ------- , -------

200

100 5-1 00.255-1 l:::. 0.55-1 X 0.75 5-1 <> 1 5-11

Figure 11.9 Diameter as a function of time under different shears (Resin G, 119.3 OC)

104



60

1

10 20 t i ~ g ( s ) 40 50

100 s-1 00.25 8-1 [:, 0.5 8-1 X 0.75 8-1 <> 1 5-11

Figure 11.10 Diameter as a function oftime under different shears (Resin L, 113.3 OC)

14

12 -

-1 0 -E:::J- 8 -cu...cu 6 -E.-c 4 -

2 -

0

0

10

9

- 8 -:::J-CU 7....CU

Eca 6c

5

3005020Q )tlme(s

150

4 -+------..----I - - - - - - , - - - - - ~ - - - - - - - - - ;100

1008-1·00.258-1 [:, 0.58-1 X 0.758-101 8-11

Figure 11.11 Diameter as a function oftime under different shears (Resin L, 117.3 OC)

105



15 , _ ,

40050 200 t i ~ ~ ~ s ) 300 350

1005-1 00.255-1 t::. 0.55-1 X 0.755-1 <> 1 5-11

5 - + - - : > . . L - - - - , - - - ~ - - - , - - - - - - , - - - - - - - r - - - - - ,100

13

7

_.E~ 1 G)...,G)

E 9cu.-o

Figure 11.14 Diameter as a function of time under different shears (Resin J, 105.4OC)

1<>

<>

<>

10

9

8E72..6

.B 5G)

E 4CU

C 3

2

1

O+------- ,------ . , -------r-------- i

o 1000 2000 3000 4000time(s)

100 5-1 00.25 5-1 ,6, 0.5 5-1 X 0.75 5-1 <> 1 5-11

Figure 11.15 Diameter as a function oftime under different shears (Resin J, 109.4°C)

107



Il.4 Appendix D

Diameter as a function of time at various crystallization

temperatures.

18 . . . . ._-- __ ._ ,

16

_14E

-ê- 12Cl)....Cl)

E 10. c 8

6

2550050050. ()1550t lme s

50

4+------,-----.-----.------,-------.

50

10 111.3C x 112.3C !:>.113.3C 0 114.3C + 115.3C 0 116.3C -117.3CI

Figure 11.16 Diameter as a function oftime for resin H under quiescent condition.

10000000. ()600tlme s

00

20

18

16

ê 142.12...

.s 10G)

E 8.!!!c 6

4

2

0+----,.----,.----,.----.,-----,

o

!0111.3C x112.3C t:.113.3C 0114.3C +115.3C 0116.3C -117.3C!

Figure 11.17 Diameter as a function oftime for resin H under shear rate of 0.5 S-l.

108



35 , _ - - _ , _ ,

30

- 2 5

E::1-= 20Q)-

15n:s

C 10

5

0+-------.-----. ,------. . . . ,-------,

o 500 1000 1500 2000

time(s)I0114.3C x115.3 t>116.3C o117.3C + 118.3C 0119.3C -120.3C!

Figure 11.18 Diarneter as a function oftime for resin Gunder quiescent condition

60 .., _ _ __._,

50

Ê 40:::J1:'"$ 30Q)

En:s

C 20

10

1

0+------.------.,------....,--------1o 500 1000 1500 2000

time(s)

[0 114.3C x 115.3C t>116.3C 0 117.3C + 118.3C 0 119.3C -120.3CI

Figure 11.19 Diameter as a function oftime for resin Gunder shear rate of 0.5 S-I.

109



16

149:

112

§10 ++- /..

.s 81)

6-t

-t.- -tc -t4 +

2

0

o 200 400 600

time(s)800 1000 1200

I0112.3C x113.3C o 114.3C 1'.115.3C +116.3C <>117.3C -118.3C!

Figure 11.20 Diameter as a function oftime for resin L under quiescent condition

14 , ,

12

-10E:::l

::-8c»-Ë6co

°42

O-+ ------ .----- .---- ,------r-----,------ ,

o 100 200 .300{) 400tlme 5

500 600

I0112.3C x113.3C 1'.114.3C D115.3C +116.3C <>117.3C -118.3CI

Figure 11.21 Diameter as a function oftime for resin L under shear rate of 0.5 S·l.

110



10 . . . . , - - - - - - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - - ,

9

8

'E 7

2 .6...

.s 5Q)

E 4ta

C 3

2

1

0+ - - - - - , . . - - - - - - , - - - - - - - - , - - - - - . , . . . - - - - - - - - ,

o 500 1000 1500 2000 2500time (5)

10 94.4C x 95.4C D. 96.4C 097 .4C + 98.4C o 99.4C - 1OO.4C 1

Figure 11.22 Diameter as a function of time for resin 1under quiescent condition

9 - - - - - - - - - - - - - - - - - - - - - - ~

-§ 6..Cl)...

)

Eta 3c

---

O+-----,.--------,--------r----,-------t

o 500 1000. 500 2000 2500tlme 5

o 94.4C X 95.4C D. 96.4C 0 97.4C + 98.4C 0 99.4C - 100.4C

Figure 11.23 Diameter as a function oftime for resin 1under shear rate of 0.5 S-I.

111



11 .0 , ------.--..- -.- ..-.- ---.--..-.-- - - .- ..---.- - - - ..- ..- -.-- -.-- - - --..-.--.-- - .

10.0

E"9.0

1:" 8.0Q).-Q)

E 7.0co.-c 6.0

5.0

4.0 +---.. . . . , . .---. . . . . , . .---. . . . . , . .---. . . . . , . .-----,----,

o 500 1000 1500 2000 2500 3000time(s)

10 104.4C X 10S.4C t:c. 106.4C 0 107.4C + 10a.4C <> 109.4C 1

Figure 11.24 Diameter as a function oftime for resin J under quiescent condition

20 --..- - - --- - - - -- -

18

16

E"142.1210.

10Q)

E 8co

c 6

4

2

o -+------- , ------- , ------- , ------ , ------ ,

o 500 1000. (1) 500tlme s 2000 2500

1 0 104.4C x 10S.4C 6. 106.4C 0 107.4C + 10a.4C <> 109.4C 1

Figure 11.25 Diameter as a function oftime for resin J under shear rate of 0.5 S·I.

112



Il.5 Appendix E

Growth rate as a function of temperature for isothermal

122

102.0

120

(b) resin

118temperature (c)

98.0 100.0

temperature (C)

116

96.0

o

0.04 T · · · A ~ : · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · _ · · · · · · · · · · F = : " = " i :160.55-1

1005-1.035

0.14 6

~ 0 . 1 2 0E2. 0.1

.!~ 0 . 0 8~ 0 . 0 6 6

e<:)0.04 0 6

0.02 0 6 Go+ -_ _ -...- .,..-_ _ -,-0-=---_--;

114

0.03E2.0.025.!

0.02 0

l O ~ 1 5 0 6

0.01

0 ~ 0 5 0 g g 6o+--__ - . -__ -,--__ ---r--=6'--_---;

94.0

6 1 ~ 0 . 5 5-10.12 005-1

0.16:1

~ " o . o 8 0

os~ 0 . 0 60

6

eO.046:) 0

0.02 0 66 ê

0

110 112 114 116 118temperature (c)

(a) resin H

0.2

_0.16

]2.012 0 6. ! .

.s0.08 06

e 06

<:)0.040 6

0 ê G0

114 116 118 120 122temperature(C)

(c) resin G0.07 T···································· ;==: : : : ; ,

0.06 6 I ~ ~ ~ ~ t l(d) resin l

CilE 0.05::1

i 0.04 0

0.03

e 0.02<:)

0.01

0 6

06

0 6 6 A

106 108 110 112temperature(C)

(e) resin J

Figure 11.26 Growth rate as a function of temperature for (a) resin H (b) resin C, (c)

resin G, (d) resin l and (e) resin J.

113



11.6 Appendix F

Linear regression of the quiescent experimental growth data plot

for the modified LH equation

y =-55.465x - 6.0679R2 =0.968

-9.5

-8.0 ,---.-.-.-- --..- - - --.. - - ~ ~ - -..- - - - -.. - - -,

-8.5.- .

.!!! -9.0E.2.

0.100.070 0.080 0.090

Tm*/(TcdTf} (1/K)

(a) Resin H

y = -118,44x - 1.2242

R2:::: 0.9822

-11.5

-12.0 +------ ,----- , . --- ,------- ,

0.060

1--10.0

a -10.5+C) -11.0c

0.10.07 O.OS 0.09Tm*/(TcdTf) (1/K)

/ ~ : 5 ; ~ ~ 9 7 3 7 1y:::: -113,4x - 1.134

R2 = 0.9831

-11.0

-11.5 +---------,-----,------,------i

0.06

-7.0 T···· ·-· · · · · · · · · ····..· ..··••····· ..··..-············..- - - -- - •.. - ",

-7.5

-S.OE2. -S.5

... -9.0a::

-9.5

~ - 1 0 . 0.=-10.5

-8.0 - - - - - - - - - - - - - - ~

-12.0 +-----,,----,---,---,.--___,

0.060 0.070 O.OSO 0.090 0.100 0.110Tm*/(TcdTf) (1/K)

Cil -9.0 Y:::: -60.322x - 5.2764

E R2:::: 0.9974

2....

e: -10.0•cy:::: -121.68x - 0.3692

R2:::: 0.9957

.= -11.0

(b) Resin C (c) Resin G

Figure 11.27 Linear regression of the experimental growth data under quiescentconditions plot following the modified LH equation: (a) resin H, (b) resin C, and (c) resin

G.

114



11.7 Appendix G

Comparison of quiescent growth data with growth at 0.5 S·l.

The following figures provide a comparison of experimental data at 0.5 S·l shear

rate and quiescent conditions after applying the modified LH equation to superimpose the

experimental data under shear onto the linear regression of quiescent data by adjusting

Qo*.

0.100

0.58-11<D

0.070 0.080 0.090

Tm*/(TcdTf) (1/K)

/08-1

-11.5

-12.0 +-----,-----.. . . . . , .------r-----,

0.060

-8.0 ...,..__ - ---- ,

-8.5-/)E -9.0

:J

- -9.5

~ - 1 0 . 0Q

0-10.5+C>-11.0s::

Figure 11.29 Resin H before adjusting Qo*

0.100.070 0.080 0.090Tm*/(TcdTf)

-8.0r

-8.5 l

f -9.0 j- -9.5....

-10.0"'Q

-10.5

C>s:: -11.0

-11.5

-12.0 +----,-----r-----,-----,

0.060

Figure 11.30 Resin H after adjusting Qo*

116



-8.0 ..., ..

-!!! -9.0E:::s--~ - 1 0 . 0c

o+

"-11 .O

/os-1

0.5 s-1

/

0.110.070 0.080 0.090 0.100Tm*/(TcdTf) (1/K)

-12.0 + - - - - - , - - - - r - - - - - , - - - - - - - , - - - - - - ,

0.060

Figure 11.31 Resin C before adjusting QD*

-8.0 ........_.... . .........................-.... . .

-/)

E -9.0:::s-

~ - 1 0 . 0c

o+

"-11 .O

o

0.110.070 0.080 0.090 0.100

Tm*/(TcdTf) (1/K)

-12.0+-----,----,-----,-----...,-----,

0.060

Figure 11.32 Resin Cafter adjusting QD*

117



-7.0

-7.5

en -8.0 <D--8.5 <D

- 0.5 5-11- -9.0<D

/::

-9.50 05-1 <D+-10.0C)

<Dc:::-10.5

-11.0

-11.5

0.06 0.07 0.08 0.09 0.10Tm*/(TcdTf) (1/K)

Figure 11.33 Resin G before adjusting QD*

0.10.07 0.08 0.09Tm*/(TcdTf) (1/K)

-7.0 __ _._. -_ _ _ _- _ _-_ .._ _._ _._ _._ _._.-..-.--.

-7.5

-.!!! -8.0E

-8.5-1- -9.00::

-9.5

-10.0C)

c::: -10.5

-11.0

-11.5 + - - , - ----,- , - - 0-1

0.06

Figure 11.34 Resin G after adjusting QD*

118



-7(J)

en -8- 0.55-1(J) ( J ) ~

-91-e::: (J)-IC (J)

0 -10

+ (J)C)

.5 -11

-12

0.050 0.060 0.070 0.080

Tm*/(TcdTf) (1/K)

Figure 11.35 Resin L before adjusting Qo*

en -8

-- -91-e::::;--

~ 1 +C)

.5-11

o

0.080.060 0.070Tm*/(TcdTf) (1/K)

-12 -t------,-------,-----.,----'

0.050

Figure 11.36 Resin L after adjusting Qo*

119



-8

-9 <D-IJ <D- 0.55-1E -10::s

<D

/1- -11a::

<D<D- -12le

C

a 05-1+ -13 <DC)c:

-14

-15

0.055 0.065 0.075 0.085

Tm*/TcdTf (1/K)

Figure 11.37 Resin J before adjusting QD*

-8 -,------------------------------------

-9- 0E -10::s

-,) -11l -a::;- -12caC; -13c:

-14

o

o

0.095.065 0.075 0.085Tm*/TcdTf (1/K)

-15 +--------,------,-----,--------,

0.055

Figure 11.38 Resin J after adjusting QD*

120



11.8 Appendix H

Calculation of error bars

The modified Lauritzen-Hoffman equation was applied to the growth rate

obtained by

duplicate experiments. The different values of InG+QD*/RT were obtained for each

replicate condition. Error bars were found from the average of the difference between

maximum and minimum values, as shown in the equation below. The error bar of ±

0.0858 Ilm/s was obtained.

Max.-MinErrorbar(llm/ s) =- - - -n

Max =maximum value obtained after applying the modified LH equation

Min =minimum value obtained after applying the modified LH equation

n = number of experimenta1 sets.

Effect of Shear on Growth Rates During Polyethylene Melt Crystallization

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Transcript of Effect of Shear on Growth Rates During Polyethylene Melt Crystallization